fractals in surface growth with power law noise the authors present a microscopic description of interface growth with power law noise distribution in the form p eta eta 1 approximately 1 mu which exhibits non universal roughening for the mu d 1 case in d 1 dimensions the existence of a fractal pattern in the bulk of the aggregate is explained leading trivially to the proof of the identity alpha z 2 for the roughening and the dynamical scaling exponents alpha and z respectively investigations on the distribution of step sizes of the discretized interface and the saturated growth speed further support the arguments

acoustic eigenvalues of rectangular rooms with arbitrary wall impedances using the interval newton generalized bisection method modal analysis of a rectangular room requires evaluation of the eigenvalues of the helmholtz operator while taking into account the boundary conditions imposed on the walls of the room when the walls have finite impedances the acoustic eigenvalue equation becomes complicated and a numerical method that can find all roots within a given interval is required to solve it in this study the interval newton generalized bisection in gb method is adopted for solving this problem for an efficient implementation of this method bounds are derived for the acoustic eigenvalues and their asymptotic behavior explored the accuracy of the in gb method is verified for a canonical problem by comparing the modal solution with the corresponding finite element solution furthermore reverberation times estimated using the in gb method are compared to those calculated using the finite difference method through these examples it is demonstrated that the in gb method provides a useful and efficient approach for estimat

quantum stochastic integrals under standing hypotheses abstract we study the meaning of stochastic integrals when the integrator is a quantum stochastic process which is not quite a martingale in that it obeys estimates of the type advocated by mcshane in the classical case we define the integral and solve stochastic differential equations when the von neumann algebra is finite and when it has a cyclic and separating state or weight when conditional expectations exist a quantum martingale continuity theorem is proved

scaling of surface fluctuations and dynamics of surface growth models with power law noise the authors report the results of extensive simulations of three surface growth models in the kpz universality class with a power law noise distribution of the form p eta approximately eta mu 1 in d 2 for all three models the width and height fluctuation distributions obey a scaling relation and exhibit power law tails this has implications for directly observing the presence of power law noise in experiments in addition they present extensive results for both scaling exponents alpha and beta as a function of mu for mu 2 8 although there is some variation in the results for different models for all three models they find anomalous exponents for 2 or mu or 7 while the scaling relation alpha z 2 holds for all mu for a linear model without sideways growth they verify that the presence of power law noise does not lead to anomalous exponents for mu 2

the ito clifford integral abstract we present a theory of non commutative stochastic integration analogous to the ito theory it is shown that wick products of fermi fields define martingales and that stochastic integrals with respect to these are defined for adapted operatorvalued square integrable integrands for square integrable martingales associated with an arbitrary probability gage space a stochastic integral is defined and a doob meyer decomposition for supermartingales obtained

effective edwards wilkinson equation for single file diffusion in this work we present an effective discrete edwards wilkinson equation aimed to describe the single file diffusion process the key physical properties of the system are captured defining an effective elasticity which is proportional to the single particle diffusion coefficient and to the inverse squared mean separation between particles the effective equation gives a description of single file diffusion using the global roughness of the system of particles which presents three characteristic regimes namely normal diffusion subdiffusion and saturation separated by two crossover times we show how these regimes scale with the parameters of the original system additional repulsive interaction terms are also considered and we analyze how the crossover times depend on the intensity of the additional terms finally we show that the roughness distribution can be well characterized by the edwards wilkinson universal form for the different single file diffusion processes studied here

a non commutative random stopping theorem abstract a theory of non commutative stopping time is presented in the case where the underlying von neumann algebra possesses only a faithful normal state in particular we prove an analogue of doob s optional stopping theorem and in the special case of the quasi free representation of the car we are also able to prove the random stopping theorem these results thus extend those established by c barnett and t j lyons 1985 math proc cambridge philos soc to include certain type iii factors

shift invariance and surface growth the invariance of equations for self affine surface growth to reparametrization under the abelian group of shift transformations h x t to h x t l is used to bound the form of nonlinear terms and related kinetic coefficients in relaxational surface growth equations for conserved growth small but relevant diffusive terms second order in the driving can always be expected it is also shown that the asymptotic growth distributions in d 2 can be expected to be skew and are not derivable from a hamiltonian description

a feynman kac formula for anticommuting brownian motion motivated by application to quantum physics anticommuting analogues of wiener measure and brownian motion are constructed the corresponding ito integrals are defined and the existence and uniqueness of solutions to a class of stochastic differential equations is established this machinery is used to provide a feynman kac formula for a class of hamiltonians several specific examples are considered

dynamic scaling of the interface in two phase viscous flows in porous media the time evolution and geometry of rough interfaces observed in experiments on immiscible displacement of viscous fluids in porous media are analysed using the concepts of dynamic scaling and self affine fractal geometry the authors find that the development of the interface is governed by dynamic scaling and they have determined the corresponding surface exponents alpha and beta the values of the exponents calculated for the experimental patterns are different from those obtained for a variety of two dimensional models of marginally stable interfaces

on non fock boson stochastic integrals abstract we show that certain non fock quantum boson stochastic integrals are canonically defined as closed operators we also present an alternative formulation of the martingale representation theorem of hudson and lindsay j funct anal 61 1985 202 221

numerical solutions of the acoustic eigenvalue equation in the rectangular room with arbitrary uniform wall impedances two numerical procedures for finding the acoustic eigenvalues in the rectangular room with arbitrary uniform wall impedances are developed one numerical procedure applies newton s method here starting with soft walls the eigenvalues are found by increasing the impedances of each wall pair in small increments up to the terminal impedances another procedure poses the eigenvalue problem as one of homotopic continuation from a non physical reference configuration in which all eigenvalues are known and obvious the continuation is performed by the numerical integration of two differential equations the latter procedure was found to be faster and finds all possible solutions the set of eigenvalues allowed the room modal natural frequencies and damping constants to be obtained from sound decays measured in a hard walled rectangular room and from the collective modal decay curve the impedances of the hard walls are estimated these are then used to find the reverberation times of the modes in the room with the floor lined with sound absorbing material of known acoustic impedance it was found that a single reverberation time for all modes is only supported in the rectangular room with hard walls and at the higher frequency bands consistent with sabine s theory which assumes a diffuse sound field in the rectangular room with hard walls and at the lower frequency bands and in the rectangular room with the floor lined with sound absorbing material and for all frequency bands modes with rather distinctive reverberation times may produce sound decays not always consistent with sabine s prediction

stochastic integration on the cuntz algebra o abstract we develop a theory of non commutative stochastic integration with respect to the creation and annihilation process on the full fock space over l2 r our theory largely parallels the theories of non commutative stochastic ito integration on boson and fermion fock space as developed by r hudson and k r parthasarathy it provides the first example of a non commutative stochastic calculus which does not depend on the quantum mechanical commutation or anticommutation relations but it is based on the theory of reduced free products of c algebras by d voiculescu this theory shows that the creation and annihilation processes on the full fock space over l2 r which generate the cuntz algebra o can be interpreted as a generalized brownian motion we should stress the fact that in contrast to the other theories of stochastic integration our integrals converge in the c norm on o i e uniformly rather than in some state dependent strong operator topology or non commutative l2 norm

non commutative probability and non commutative processes beyond the heisenberg algebra a probability space is a pair a where a is an algebra and is a state on the algebra in classical probability a is the algebra of linear combinations of indicator functions on the sample space and in quantum probability a is the heisenberg or clifford algebra however other algebras are of interest in noncommutative probability after a short review of the framework of classical and quantum probability other noncommutative probability spaces are discussed in particular those associated with noncommutative space time a probability space is a pair a where a is an algebra and is a state on the algebra in classical probability a is the algebra of linear combinations of indicator functions on the sample space and in quantum probability a is the heisenberg or clifford algebra however other algebras are of interest in noncommutative probability after a short review of the framework of classical and quantum probability other noncommutative probability spaces are discussed in particular those associated with noncommutative space time

conserved noise restricted solid on solid model on fractal substrates a conserved noise restricted solid on solid model on both a sierpinski gasket substrate and a checkerboard fractal substrate is studied the interface width w grows as t at early time t and becomes saturated at l for t l z where l is the system size we obtain 0 0788 0 377 for a sierpinski gasket and 0 100 0 516 for a checkerboard fractal the dynamic exponent z 4 79 for a sierpinski gasket and z 5 16 for a checkerboard fractal are obtained by the relation z they satisfy the scaling relations 4 2 d f z and z 2 z rw where z rw is the random walk exponent of the fractal substrate a fractional langevin equation is introduced to describe the model

dynamic scaling behaviors of linear fractal langevin type equation driven by nonconserved and conserved noise abstract in order to study the effects of the microscopic details of fractal substrates on the scaling behavior of the growth model a generalized linear fractal langevin type equation h t 1 m 1 m z r w h z r w is the dynamic exponent of random walk on substrates driven by nonconserved and conserved noise is proposed and investigated theoretically employing scaling analysis corresponding dynamic scaling exponents are obtained

a non commutative martingale representation theorem for non fock quantum brownian motion abstract a non commutative theory of stochastic integration is constructed in which the integrators are the components of the quantum brownian motion with non unit variance unlike the unit variance fock case there is a kunita watanabe type representation theorem for processes which are martingales with respect to the generated filtration

the crossover phenomena in surface growth models with height dependent noise abstract in this paper we consider several known growth processes with height dependent noise this type of noise is interesting from a theoretical standpoint for example it paves the way to the derivation of the exact height distribution of the kpz equation through the hopf cole transformation in addition it may have implications for experimental growth processes using numerical methods we observe that adding such a noise to different growth processes can change their universality class or ruin the scaling laws in the case of mullins herring equation a two fold cross over is observed

static fluctuations of a thick one dimensional interface in the 1 1 directed polymer formulation numerical study we study numerically the geometrical and free energy fluctuations of a static one dimensional 1d interface with a short range elasticity submitted to a quenched random bond gaussian disorder of finite correlation length ensuremath xi g0 and at finite temperature t using the exact mapping from the static 1d interface to the 1 1 directed polymer dp growing in a continuous space we focus our analysis on the disorder free energy of the dp end point a quantity which is strictly zero in the absence of disorder and whose sample to sample fluctuations at a fixed growing time t inherit the statistical translation invariance of the microscopic disorder explored by the dp constructing a new numerical scheme for the integration of the kardar parisi zhang evolution equation obeyed by the free energy we address numerically the time and temperature dependence of the disorder free energy fluctuations at fixed finite ensuremath xi we examine on one hand the amplitude stackrel ifmmode tilde else fi d t and effective correlation length stackrel ifmmode tilde else fi ensuremath xi t of the free energy fluctuations and on the other hand the imprint of the specific microscopic disorder correlator on the large time shape of the free energy two point correlator we observe numerically the crossover to a low temperature regime below a finite characteristic temperature t c ensuremath xi as previously predicted by gaussian variational method computations and scaling arguments and extensively investigated analytically in phys rev e 87 042406 2013 finally we address numerically the time and temperature dependence of the roughness b t which quantifies the dp end point transverse fluctuations and we show how the amplitude stackrel ifmmode tilde else fi d ensuremath infty t ensuremath xi controls the different regimes experienced by b t in agreement with the analytical predictions of a dp toy model approach

kinetic roughening with power law waiting time distribution we introduce a surface growth model where the elementary events are characterized by a waiting time distribution p t exact relations to directed polymer statistics and to continuous time random walk problems are established for p t i the behaviour is similar to that of the zhang model where rare event dominated kinetic roughening occurs due to a power law noise in the surface increments a careful correction to scaling analysis of our numerical results in 1 1 dimensions indicates universality with the zhang model for fixed values of p

the optional stopping theorem for quantum martingales in classical probability theory a random time t is a stopping time in a filtration ft t 0 if and only if the optional sampling holds at t for all bounded martingales furthermore if a process xt t 0 is progressively measurable with respect to ft t 0 then xt is ft measurable unfortunately this is not the case in noncommutative probability with the definition of stopped process used until now it is shown in this article that we can define the stopping of noncommutative processes in fock space in such a way that all the bounded martingales can be stopped at any stopping time t are adapted to the filtration of the past before t and satisfy the optional stopping theorem

synchronization in weighted uncorrelated complex networks in a noisy environment optimization and connections with transport efficiency motivated by synchronization problems in noisy environments we study the edwards wilkinson process on weighted uncorrelated scale free networks we consider a specific form of the weights where the strength and the associated cost of a link is proportional to kikj beta with ki and kj being the degrees of the nodes connected by the link subject to the constraint that the total edge cost is fixed we find that in the mean field approximation on uncorrelated scale free graphs synchronization is optimal at beta 1 numerical results based on exact numerical diagonalization of the corresponding network laplacian confirm the mean field results with small corrections to the optimal value of beta employing our recent connections between the edwards wilkinson process and resistor networks and some well known connections between random walks and resistor networks we also pursue a naturally related problem of optimizing performance in queue limited communication networks utilizing local weighted routing schemes

interface depinning in a disordered medium numerical results abstract we propose a lattice model to study the dynamics of a driven interface in a medium with random pinning forces the critical exponents characterizing the depinning transition are determined numerically in 1 1 and 2 1 dimensions our findings are compared with recent numerical and analytical results for a langevin equation with quenched noise which is expected to be in the same universality class

symmetry based determination of space time functions in nonequilibrium growth processes we study the space time correlation and response functions in nonequilibrium growth processes described by linear stochastic langevin equations exploiting exclusively the existence of space and time dependent symmetries of the noiseless part of these equations we derive expressions for the universal scaling functions of two time quantities which are found to agree with the exact expressions obtained from the stochastic equations of motion the usefulness of the space time functions is illustrated through the investigation of two atomistic growth models the family model and the restricted family model which are shown to belong to a unique universality class in 1 1 and 2 1 space dimensions this corrects earlier studies which claimed that in 2 1 dimensions the two models belong to different universality classes

the ito clifford integral iii the markov property of solutions to stochastic differential equations it is shown that the solution to the ito clifford stochastic differential equationdx t f x t t d t d t g x t t h x t t dt wheref g h are suitable lipschitz functions and t is the fermion martingale satisfies a markov property

fermionic path integration and grassmann brownian motion a grassmann probability theory with anticommuting random variables and stochastic processes is developed using an extension of berezin integration to infinite dimensional spaces a kolmogorov type consistency condition allows integration on spaces of paths in anticommuting space one particular stochastic process grassmann brownian motion is described and the associated measure used to give a path integral formula for the kernel of the evolution operator in fermionic quantum mechanics the fourier mode expansion of grassmann brownian motion is derived

the ito algebra of quantum gaussian fields abstract the notion of mutual quadratic variation square bracket is extended to a quantum probabilistic framework the mutual quadratic variations of the annihilation creation and number fields in a gaussian representation are calculated in both the boson and the fermion case in the strong topology on a common invariant domain it is proved that the corresponding ito table closes at the second order the fock representation is characterized among the gaussian ones by the property that its ito table closes at the first order

kinetic roughening global quantities and fluctuation dissipation relations abstract growth processes and interface fluctuations can be studied through the properties of global quantities we here discuss a global quantity that not only captures better the roughness of an interface than the widely studied surface width but that is also directly conjugate to an experimentally accessible parameter thereby allowing us to study in a consistent way the global response of the system to a global change of external conditions exploiting the full analyticity of the linear edwards wilkinson and mullins herring equations we study in detail various two time functions related to that quantity this quantity fulfills the fluctuation dissipation theorem when considering steady state equilibrium fluctuations

persistence in nonequilibrium surface growth persistence probabilities of the interface height in 1 1 and 2 1 dimensional atomistic solid on solid stochastic models of surface growth are studied using kinetic monte carlo simulations with emphasis on models that belong to the molecular beam epitaxy mbe universality class both the initial transient and the long time steady state regimes are investigated we show that for growth models in the mbe universality class the nonlinearity of the underlying dynamical equation is clearly reflected in the difference between the measured values of the positive and negative persistence exponents in both transient and steady state regimes for the mbe universality class the positive and negative persistence exponents in the steady state are found to be 0 66 0 02 and 0 78 0 02 respectively in 1 1 dimensions and 0 76 0 02 and 0 85 0 02 respectively in 2 1 dimensions the noise reduction technique is applied on some of the 1 1 dimensional models in order to obtain accurate values of the persistence exponents we show analytically that a relation between the steady state persistence exponent and the dynamic growth exponent found earlier to be valid for linear models should be satisfied by the smaller of the two steady state persistence exponents in the nonlinear models our numerical results for the persistence exponents are consistent with this prediction we also find that the steady state persistence exponents can be obtained from simulations over times that are much shorter than that required for the interface to reach the steady state the dependence of the persistence probability on the system size and the sampling time is shown to be described by a simple scaling form

on martingale inequalities in non commutative stochastic analysis we develop a non commutativelpstochastic calculus for the clifford stochastic integral anl2theory of which has been developed by barnett streater and wilde the main results are certain non commutativelpinequalities relating clifford integrals and their integrands these results are applied to extend the domain of the clifford integral froml2tol1integrands and we give applications to optional stopping of clifford martingales proving an analog of a theorem of burkholder the stopped clifford processfthas zero expectation providedet in proving these results we establish a number of results relating the clifford integral to the differential calculus in the clifford algebra in particular we show that the clifford integral is given by the divergence operator and we prove an explicit martingale representation theorem both of these results correspond closely to basic results for stochastic analysis on wiener space thus furthering the analogy between the clifford process and brownian motion

stochastic integral representation theorem for quantum semimartingales abstract the quantum stochastic integral of ito type formulated by hudson and parthasarathy is extended to a wider class of adapted quantum stochastic processes on boson fock space an ito formula is established and a quantum stochastic integral representation theorem is proved for a class of unbounded semimartingales which includes polynomials and wick exponentials of the basic martingales in quantum stochastic calculus

dynamical surface structures in multiparticle correlated surface growths we investigate the scaling properties of the interface fluctuation width for the q mer and q particle correlated deposition evaporation models these models are constrained with a global conservation law that the particle number at each height is conserved modulo q in equilibrium the stationary roughness is anomalous but universal with the roughness exponent alpha 1 3 while the early time evolution shows nonuniversal behavior with the growth exponent beta varying with models and q nonequilibrium surfaces display diverse growing and stationary behaviors the q mer model shows a faceted structure while the q particle correlated model shows a macroscopically grooved structure

scaling properties of the surface of the eden model in d 2 3 4 the surface of the eden model is investigated numerically by finite size scaling using a strip geometry three different versions are studied and it shows that the one mostly used previously exhibits strong finite size corrections in two dimensions it is found that the surface thickness simply grows as the square root of the width of the strip for infinitely long strips this result as well as the results in d 3 and d 4 suggest that the surface of the eden shares some properties with the equilibrium models used to describe the roughening transition moreover it is found that the surface thickness scales differently with the height of the cluster for infinitely large strips

quasifree stochastic cocycles and quantum random walks the theory of quasifree quantum stochastic calculus for infinite dimensional noise is developed within the framework of hudson parthasarathy quantum stochastic calculus the question of uniqueness for the covariance amplitude with respect to which a given unitary quantum stochastic cocycle is quasifree is addressed and related to the minimality of the corresponding stochastic dilation the theory is applied to the identification of a wide class of quantum random walks whose limit processes are driven by quasifree noises

a system of quantum stochastic differential equations in terms of non equilibrium thermo field dynamics within the framework of non equilibrium thermo field dynamics netfd quantum wiener processes at finite temperatures are constructed and its representation space is shown to be the thermal space after the introduction of the stochastic shrodinger equation a unified system of quantum stochastic differential equations including the quantum stochastic liouville equation and the quantum langevin equation is established within the quantum stochastic calculus

on the correlation measure of a family of commuting hermitian operators with applications to particle densities of the quasi free representations of the car and ccr let x be a locally compact second countable hausdorff topological space we consider a family of commuting hermitian operators a indexed by all measurable relatively compact sets in x a quantum stochastic process over x for such a family we introduce the notion of a correlation measure we prove that if the family of operators possesses a correlation measure which satisfies some condition of growth then there exists a point process over x having the same correlation measure furthermore the operators a can be realized as multiplication operators in the l2 space with respect to this point process in the proof we utilize the notion of positive definiteness proposed in y g kondratiev t kuna harmonic analysis on the configuration space i general theory infin dimens anal quantum probab relat top 5 2002 201 233 in particular our result extends the criterion of existence of a point process from that paper to the case of the topological space x which is a standard underlying space in the theory of point processes as applications we discuss particle densities of the quasi free representations of the car and ccr which lead to fermion boson fermion like and boson like e g para fermions and para bosons of order 2 point processes in particular we prove that any fermion point process corresponding to a hermitian kernel may be derived in this way

acoustic analysis of a rectangular cavity with general impedance boundary conditions a fourier series method is proposed for the acoustic analysis of a rectangular cavity with impedance boundary conditions arbitrarily specified on any of the walls the sound pressure is expressed as the combination of a three dimensional fourier cosine series and six supplementary two dimensional expansions introduced to ensure accelerate the uniform and absolute convergence rate of the series representation in the cavity including the boundary surfaces the expansion coefficients are determined using the rayleigh ritz method since the pressure field is constructed adequately smooth throughout the entire solution domain the rayleigh ritz solution is mathematically equivalent to what is obtained from a strong formulation based on directly solving the governing equations and the boundary conditions to unify the treatments of arbitrary nonuniform impedance boundary conditions the impedance distribution function on each specified surface is invariantly expressed as a double fourier series expansion so that all the relevant integrals can be calculated analytically the modal parameters for the acoustic cavity can be simultaneously obtained from solving a standard matrix eigenvalue problem instead of iteratively solving a nonlinear transcendental equation as in the existing methods several numerical examples are presented to demonstrate the effectiveness and reliability of the current method for various impedance boundary conditions including nonuniform impedance distributions

interface growth with competing surface currents the authors examine the dynamics of interface growth under the combined influence of a stabilizing and a destabilizing surface current in 1 1 dimensions it has been shown that the surface is weakly stabilized if a newly deposited particle can move locally to maximize the total number of nearest neighbour contacts with the surface curvature driven current the introduction of a weak destabilizing surface tension term results in an almost periodic grooved surface the width of the surface grows linearly in time and does not reach a steady state it appears that such a formation cannot be described by a continuous langevin equation

classical and quantum probability we follow the development of probability theory from the beginning of the last century emphasizing that quantum theory is really a generalization of this theory the great achievements of probability theory such as the theory of processes generalized random fields estimation theory and information geometry are reviewed their quantum versions are then described

a model for temporal fluctuations of the surface width a stochastic one dimensional map a stochastic one dimensional map is introduced to model the steady state fluctuations of the surface width in far from equilibrium surface roughening the dynamics of the map and the correlations in the time sequence are investigated in particular for power law distributed noise a non trivial multi affine behaviour is observed

numerical study of a non equilibrium interface model we have carried out extensive computer simulations of one dimensional models related to the low noise solid on solid non equilibrium interface of a two dimensional anchored toom model with unbiased and biased noise for the unbiased case the computed fluctuations of the interface in this limit provide new numerical evidence for the logarithmic correction to the subnormal l frac 1 2 variance which was predicted by the dynamic renormalization group calculations on the modified edwards wilkinson equation in the biased case the simulations are in close quantitative agreement with the predictions of the collective variable approximation cva which gives the same l frac 2 3 behavior of the variance as the kpz equation

surface growth on percolation networks by a conserved noise restricted solid on solid growth model surface growth by the conserved noise restricted solid on solid model is investigated on diluted lattices i e on percolation networks that are embedded in two spatial dimensions the growth exponent and the roughness exponent are defined respectively by the mean square surface width via w 2 t t 2 and the mean square saturated width via w sat 2 l l 2 where l is the system size these are measured on both an infinite network and a backbone network and the results are compared with power counting predictions obtained using the fractional langevin equation while the monte carlo results on deterministic fractal substrates show excellent agreement with the predictions d h kim and j m kim phys rev e 84 011105 2011 the results on critical percolation networks deviate by 8 12 from these predictions

noise reduction in eden models ii surface structure and intrinsic width for pt i see ibid vol 20 p 257 1987 the authors suggest a picture of the intrinsic surface width in eden models and show that it is a major source of corrections to scaling of the surface roughness using the multiple hit noise reduction method they can control the intrinsic width and thereby improve the scaling behaviour systematically as is demonstrated in detailed calculations on the square lattice they calculate the number of excess perimeter sites as a function of time and find that its asymptotic value decays with a power law as a function of increasing hitting number substrate effects and anisotropy become more apparent if noise reduction is applied

renormalization of stochastic lattice models basic formulation we describe a general method for the multiscale analysis of stochastic lattice models beginning with a lattice langevin formulation of site fluctuations we derive stochastic partial differential equations by regularizing the transition rules of the model subsequent coarse graining is accomplished by calculating renormalization group rg trajectories from initial conditions determined by the regularized atomistic models the rg trajectories correspond to hierarchies of continuum equations describing lattice models over expanding length and time scales these continuum equations retain a quantitative connection over different scales as well as to the underlying atomistic dynamics this provides a systematic method for the derivation of continuum equations from the transition rules of lattice models for any length and time scales as an illustration we consider the one dimensional 1d wolf villain wv model europhys lett 13 389 1990 the rg analysis of this model which we develop in detail is generic and can be applied to a wide range of conservative lattice models the rg trajectory of the 1d wv model shows a complex crossover sequence of linear and nonlinear stochastic differential equations which is in excellent agreement with kinetic monte carlo simulations of this model we conclude by discussing possible applications of the multiscale method described here to other nonequilibrium systems

kinetic roughening with multiplicative noise in this letter a new approach to the investigation of the effects of quenched randomness in the experiments on kinetic roughening is introduced by considering a stochastic differential equation for the surface development with a multiplicative noise the authors argue that this type of noise corresponds to the experimental situation in cases when the development of the interface is dominated by pinning forces by numerically integrating the proposed equation they have obtained i surfaces remarkably similar to those observed in the experiments and ii a scaling of the surface width as a function of time with an exponent being in an excellent agreement with the measured value variations of the model crossovers and questions concerning the applicability of additive noise to wetting experiments are also discussed

a representation free quantum stochastic calculus abstract we develop a representation free stochastic calculus based on three inequalities semimartingale inequality scalar forward derivative inequality scalar conditional variance inequality we prove that our scheme includes all the previously developed stochastic calculi and some new examples the abstract theory is applied to prove a boson levy martingale representation theorem in bounded form and a general existence uniqueness and unitarity theorem for quantum stochastic differential equations

natural processes and doob meyer decompositions over a probability gage space wilde department of mathematics bedford college london nw1 4ns england communicated by l gross received february 21 1984 the notion of naturalness for l processes over a probability gage space is defined and the uniqueness of doob decompositions of supermartingales is discussed in particular it is shown that if a is an itbclifford stochastic integral martingale then x x has a unique decomposition into the sum of an l martingale and an increasing lx process null at

relaxation function and dynamic exponent for discrete growth models abstract we develop a new method of measuring the dynamic exponent z for discrete growth models starting from a sinusoidal initial surface of a selected wavelength l we consider a relaxation function r t l which is a quantity similar to the autocorrelation function of the surface height typically the relaxation function decays exponentially following e g t l where l is the relaxation time and it depends on the wavelength l the dynamic exponent z is measured by the relation l l z we find that g x scales as x 1 0 for the family model and as x 1 5 for the restricted solid on solid model the advantages of the method are also discussed

probability distribution of the interface width in surface roughening analogy with a levy flight the authors present a closed form expression for the probability distribution of the height fluctuations in the zhang model of anomalous surface roughening the result which includes both the steady state behavior and the time evolution to the steady state is based on an analogy between the d 1 1 dimensional surface problem and a d 1 levy flight in the limit case of conventional ballistic deposition they obtain a gaussian distribution for the height fluctuations their results are corroborated by detailed numerical simulations

numerical analysis of eigenproblem for cavities by a particular integral method with a low frequency approximation of surface admittance in this paper a three dimensional boundary element method for the eigenanalysis of complex shaped cavity is presented a particular integral method is proposed with general absorbing boundary conditions well suited for determination of the lower modes in this approach a polynomial approximation of surface admittance is used with a recent class of compactly supported radial basis function two common absorbent models are employed in order to demonstrate the relevance of high order approximation of the admittance resulting eigenproblems of several orders linear to cubic are thus performed on basic geometries and a car interior results show significant improvements for the computed damped eigenfrequencies and the associated modal reverberation time while using an approximation polynomial matching the surface admittance variation order

generalized survival in equilibrium step fluctuations we investigate the dynamics of a generalized survival probability s t r defined with respect to an arbitrary reference level r rather than the average in equilibrium step fluctuations the exponential decay at large time scales of the generalized survival probability is numerically analyzed s t r is shown to exhibit simple scaling behavior as a function of system size l sampling time ensuremath delta t and the reference level r the generalized survival time scale ensuremath tau s r associated with s t r is shown to decay exponentially as a function of r

the surface statistics of a granular aggregate the problem of the surface fluctuations in a settled granular material is posed a simple model is given which describes the process by which a particle settles and comes to rest on the existing surface of the packing and from this a set of langevin equations for the fourier modes of the surface are derived these equations imply that the fourier amplitudes behave like the velocities of a set of independent brownian particles we show that this results in logarithmically divergent surface fluctuations if the flux of particles onto the surface is random the divergence being removed by a more accurate description of the settling material for example by having the granules fall through a sieve

extreme fluctuations in stochastic network coordination with time delays we study the effects of uniform time delays on the extreme fluctuations in stochastic synchronization and coordination problems with linear couplings in complex networks we obtain the average size of the fluctuations at the nodes from the behavior of the underlying modes of the network we then obtain the scaling behavior of the extreme fluctuations with system size as well as the distribution of the extremes on complex networks and compare them to those on regular one dimensional lattices for large complex networks when the delay is not too close to the critical one fluctuations at the nodes effectively decouple and the limit distributions converge to the fisher tippett gumbel density in contrast fluctuations in low dimensional spatial graphs are strongly correlated and the limit distribution of the extremes is the airy density finally we also explore the effects of nonlinear couplings on the stability and on the extremes of the synchronization landscapes

a central limit theorem for the kpz equation we consider the kpz equation in one space dimension driven by a stationary centred space time random field which is sufficiently integrable and mixing but not necessarily gaussian we show that in the weakly asymmetric regime the solution to this equation considered at a suitable large scale and in a suitable reference frame converges to the hopf cole solution to the kpz equation driven by space time gaussian white noise while the limiting process depends only on the integrated variance of the driving field the diverging constants appearing in the definition of the reference frame also depend on higher order moments

superroughening by linear growth equations with spatiotemporally correlated noise we give an extensive study on a class of interfacial superroughening processes with finite lateral system size in 1 1 dimensions described by linear growth equations with spatiotemporally power law decaying correlated noise since some of these processes have an extremely long relaxation time we first develop a very efficient method capable of simulating the interface morphology of these growth processes even in very late time we numerically observe that this class of superrough growth processes indeed gradually develops macroscopic structures with the lateral size comparable to the lateral system size through the rigorous analytical study of the equal time height difference correlation function the different time height difference correlation function and the local width we explicitly evaluate not only the leading anomalous dynamic scaling term but also all the subleading anomalous dynamic scaling terms which dominate over the ordinary dynamic scaling term moreover the relation between the macroscopic structure formation and anomalous interfacial roughening of the superrough growth processes is analytically investigated in detail

joint distributions of partial and global maxima of a brownian bridge we analyze the joint distributions and temporal correlations between the partial maximum m and the global maximum m achieved by a brownian bridge on the subinterval and on the entire interval respectively we determine three probability distribution functions the joint distribution of both maxima the distribution p m of the partial maximum and the distribution of the gap between the maxima we present exact results for the moments of these distributions and quantify the temporal correlations between m and m by calculating the pearson correlation coefficient

acoustic modeling of a three dimensional rectangular opened enclosure coupled with a semi infinite exterior field at the baffled opening a modeling method is proposed for the acoustic analysis of a three dimensional 3d rectangular opened enclosure coupled with a semi infinite exterior field by a rectangular opening of arbitrary size and with general wall impedance in contrast to existing modeling methods that solve the differential equations the energy principle in combination with a 3d modified fourier cosine series is employed in the present method for the modeling of this system under this theoretical framework the effect of an opening in the wall of a rectangular enclosure is taken into account via the work done by the sound pressure acting on the opening between the finite enclosure and exterior domain the sound pressure inside the opened enclosure is expressed as the combination of a 3d trigonometric cosine series and one supplementary 2d expansion introduced to ensure uniform convergence of the solution over the entire solution domain including opening boundary the acoustic responses of the opened enclosure are obtained bas

mathematics of random growing interfaces we establish a thermodynamic limit and gaussian fluctuations for the height and surface width of the random interface formed by the deposition of particles on surfaces the results hold for the standard ballistic deposition model as well as the surface relaxation model in the off lattice setting the results are proved with the aid of general limit theorems for stabilizing functionals of marked poisson point processes

quantum ito s formula and stochastic evolutions using only the boson canonical commutation relations and the riemann lebesgue integral we construct a simple theory of stochastic integrals and differentials with respect to the basic field operator processes this leads to a noncommutative ito product formula a realisation of the classical poisson process in fock space which gives a noncommutative central limit theorem the construction of solutions of certain noncommutative stochastic differential equations and finally to the integration of certain irreversible equations of motion governed by semigroups of completely positive maps the classical ito product formula for stochastic differentials with respect to brownian motion and the poisson process is a special case

roughening of the interfaces in 1 1 dimensional two component surface growth with an admixture of random deposition we simulate competitive two component growth on a one dimensional substrate of l sites one component is a poisson type deposition that generates kardar parisi zhang kpz correlations the other is random deposition rd we derive the universal scaling function of the interface width for this model and show that the rd admixture acts as a dilatation mechanism to the fundamental time and height scales but leaves the kpz correlations intact this observation is generalized to other growth models it is shown that the flat substrate initial condition is responsible for the existence of an early nonscaling phase in the interface evolution the length of this initial phase is a nonuniversal parameter but its presence is universal we introduce a method to measure the length of this initial nonscaling phase in application to parallel and distributed computations the important consequence of the derived scaling is the existence of the upper bound for the desynchronization in a conservative update algorithm for parallel discrete event simulations it is shown that such algorithms are generally scalable in a ring communication topology

a modal spectral model for flanking transmissions abstract a model for the prediction of direct and indirect flanking sound transmissions is presented it can be applied to geometries with extrusion symmetry the structures are modelled with spectral finite elements the acoustic domains are described by means of a modal expansion of the pressure field and must be cuboid shaped these reasonable simplifications in the geometry allow the use of more efficient numerical methods consequently the coupled vibroacoustic problem in structures such as junctions is efficiently solved the vibration reduction index of t junctions with acoustic excitation and with point force excitation is compared the differences due to the excitation type obey quite general trends that could be taken into account by prediction formulas however they are smaller than other uncertainties not considered in practice the model is also used to check if the sound transmissions of a fully vibroacoustic problem involving several flanking paths can be reproduced by superposition of independent paths there exist some differences caused by the interaction between paths which are more important at low frequencies

correlations in a generalized elastic model fractional langevin equation approach the generalized elastic model gem provides the evolution equation which governs the stochastic motion of several many body systems in nature such as polymers membranes and growing interfaces on the other hand a probe tracer particle in these systems performs a fractional brownian motion due to the spatial interactions with the other system s components the tracer s anomalous dynamics can be described by a fractional langevin equation fle with a space time correlated noise we demonstrate that the description given in terms of gem coincides with that furnished by the relative fle by showing that the correlation functions of the stochastic field obtained within the fle framework agree with the corresponding quantities calculated from the gem furthermore we show that the fox h function formalism appears to be very convenient to describe the correlation properties within the fle approach

minimal path on the hierarchical diamond lattice we consider the minimal paths on a hierarchical diamond lattice where bonds are assigned a random weight depending on the initial distribution of weights we find all possible asymptotic scaling properties the different cases found are the small disorder case the analog of levy s distributions with a power law decay at and finally a limit of large disorder which can be identified as a percolation problem the asymptotic shape of the stable distributions of weights of the minimal path are obtained as well as their scaling properties as a side result we obtain the asymptotic form of the distribution of effective percolation thresholds for finite size hierarchical lattices

dynamic scaling and phase transitions in interface growth abstract the dynamic scaling approach is an effective tool for understanding the temporal evolution of fluctuating interfaces the surface width w obeys the scaling form w l t l t l where and are exponents which characterize how the surface width grows with the length scale l and the time t applications of dynamic scaling to a number of surface growth models are discussed the results of a large scale simulation of the ballistic deposition model in three dimensions are presented and compared with recent conjectures the question of universality in interface growth is addressed and a finite temperature generalization of the restricted solid on solid model is studied this model appears to undergo a phase transition from the usual rough phase at high temperatures to a new phase at low temperatures numerical solutions of the generalized langevin equation indicate that there is no phase transition in 2 1 dimensions thus the relation between the continuum equation and the discrete models is still an open question

an introduction to quantum filtering this paper provides an introduction to quantum filtering theory an introduction to quantum probability theory is given focusing on the spectral theorem and the conditional expectation as a least squares estimate and culminating in the construction of wiener and poisson processes on the fock space we describe the quantum ito calculus and its use in the modeling of physical systems we use both reference probability and innovations methods to obtain quantum filtering equations for system probe models from quantum optics

towards a satisfactory formulation of the quantum langevin equation the quantum mechanical langevin equation for a damped harmonic oscillator with operator valued noise dat dt i omega gamma at lambda w t is reinvestigated by assuming the canonical commutation relation at initial time a0 a0 1 and a hermitian operator for the gaussian quantum noise w t it is shown that streater s procedure to satisfy at at 1 for all later time yields an improved result the noise operator w t can be determined universally and normalised such that by choosing lambda 2 2 gamma beta h cross omega 1 the symmetrised power spectrum of w t is equal to the physically significant form 1 2 beta h cross omega coth 1 2 beta h cross omega where beta is the inverse temperature of the heat bath thus ensuring the beta kms correlation functions for any pair of operators

stochastic integral representation of bounded quantum martingales in fock space it is a classical theorem of kunita and watanabe 6 that every square integrable martingale adapted to the standard brownian motion can be uniquely expressed as the stochastic integral of a nonanticipating square integrable brownian functional with respect to the same brownian motion the central aim of this paper is to establish a similar integral represen tation of a quantum martingale with respect to the annihilation creation and gauge processes in the context of quantum stochastic calculus in fock space as developed in 11 in the case of non fock quantum brownian motion such an integral representation was achieved by hudson and lindsay 2 33 with much less difficulty owing to the non existence of the so called gauge processes as special cases of our main result we obtain the differentials of hilbert schmidt and unitary martingales 4 as an application the uniqueness of fermion martingales in boson fock space is established the first author wishes to thank hudson and lindsay for several useful conversations on this subject 2

schramm loewner evolution theory of the asymptotic behaviors of 2 1 dimensional wolf villain model abstract although extensive analytical and numerical work has focus on investigating the 2 1 dimensional wolf villain wv model some problems concerning its asymptotical behaviors such as the universality class to which it belongs remain controversial the schramm loewner evolution sle theory is an attractive approach to describe the fluctuation phenomena and random processes and has also been applied to the analysis of the stochastic growth of surfaces in this work we applied sle theory to the analysis of the saturated surface to conduct in depth research with a new perspective on the asymptotical behaviors of the 2 1 dimensional wv model on the basis of the analysis of the saturated surface contour lines we determine that the diffusion coefficient calculated for 2 1 dimensional wv model is 2 91 0 01 and that for family model is 2 88 0 01 accordingly we can conclude from the view of sle theory that the 2 1 dimensional wv model similar to the family model also belongs to the edwards wilkinson universality class

anomalous fluctuations in surface growth we have studied fluctuations in the steady state ofa modified ballistic deposition model the ensemble fluctuations of the surface width averaged over a time sequence which involves temporal correlations exhibit a peak around the previously proposed phase transition point in bath 2 1 and 3 i dimensions we show that the time series of a finite system is self averaging and the anomaly is in the fluctuations of the temporal correlations we discuss the implications of our results in 2 1 dimensions for the structure of the renormalization group rows non equilibrium surface interface growth problems have attracted great interest recently in particular much attention has been focused on a roughening phase transition between two phases with different scaling l 61 these problems are associ ated with models which are described in the continuum limit by a nonlinear stochastic equation

quantum and non causal stochastic calculus the quantum stochastic calculus initiated by hudson and parthasarathy and the non causal stochastic calculus originating with the papers of hitsuda and skorohod are two potent extensions of the ito calculus currently enjoying intensive development the former provides a quantum probabilistic extension of schrodinger s equation enabling the construction of a markov process for a quantum dynamical semigroup the latter allows the treatment of stochastic differential equations which involve terms which anticipate the future in this paper the close relationship between these theories is displayed and a noncausal quantum stochastic calculus already in demand from physics is described

mapping spatial persistent large deviations of nonequilibrium surface growth processes onto the temporal persistent large deviations of stochastic random walk processes spatial persistent large deviations probability of surface growth processes governed by the edwards wilkinson dynamics px x s with 1 or s or 1 is mapped isomorphically onto the temporal persistent large deviations probability pt t s associated with the stochastic markovian random walk problem we show using numerical simulations that the infinite family of spatial persistent large deviations exponents thetax s characterizing the power law decay of px x s agrees as predicted on theoretical grounds by phys rev lett 86 3700 2001 with the numerical measurements of thetat s the continuous family of exponents characterizing the long time power law behavior of pt t s we also discuss the simulations of the spatial persistence probability corresponding to a discrete model in the mullins herring universality class where our discrete simulations do not agree well with the theoretical predictions perhaps because of the severe finite size corrections which are known to strongly inhibit the manifestation of the asymptotic continuum behavior in discrete models involving large values of the dynamical exponent and the associated extremely slow convergence to the asymptotic regime

on the distribution of surface extrema in several one and two dimensional random landscapes we study here a standard next nearest neighbor nnn model of ballistic growth on one and two dimensional substrates focusing our analysis on the probability distribution function p m l of the number m of maximal points i e local peaks of growing surfaces our analysis is based on two central results i the proof presented here of the fact that uniform one dimensional ballistic growth process in the steady state can be mapped onto rise and descent sequences in the ensemble of random permutation matrices and ii the fact established in ref g oshanin and r voituriez j phys a math gen 37 6221 2004 that different characteristics of rise and descent patterns in random permutations can be interpreted in terms of a certain continuous space hammersley type process for one dimensional system we compute p m l exactly and also present explicit results for the correlation function characterizing the enveloping surface for surfaces grown on 2d substrates we pursue similar approach considering the ensemble of permutation matrices with long ranged correlations determining exactly the first three cumulants of the corresponding distribution function we define it in the scaling limit using an expansion in the edgeworth series and show that it converges to a gaussian function as l

quasi free quantum stochastic integrals for the car and ccr abstract a theory of quantum martingales and quantum stochastic integrals in quasi free representations of the car and ccr is presented for the car the results generalize some of those developed in barnett streater and wilde j funct anal 48 1982 172 212 j london math soc 27 1983 373 384 and for the ccr the results contain the standard ito theory of stochastic integration with respect to brownian motion as a special case

a new example of independence and white noise we examine the notion of free independence according to voiculescu this form of independence is used for defining free white noise or process with stationary and freely independent increments we prove a general limit theorem giving the combinatorics of infinitely freely divisible states and thus of free white noises with the help of admissible partitions we realize the free analogues of the wiener process and of the poisson process as processes on the full fock space ofl2