towards a theory of bv functions in abstract wiener spaces functions of bounded variation in an abstract wiener space i e an infinite dimensional banach space endowed with a gaussian measure and a related differentiable structure have been introduced by m fukushima and m hino using dirichlet forms and their properties have been studied with tools from stochastics in this paper we reformulate with purely analytical tools the definition and the main properties of bv functions and start investigating further properties

galerkin projected residual method applied to diffusion reaction problems a stabilized finite element method is presented for scalar and linear second order boundary value problems the method is obtained by adding to the galerkin formulation multiple projections of the residual of the differential equation at element level these multiple projections allow the generation of appropriate number of free stabilization parameters in the element matrix depending on the local space of approximation and on the differential operator the free parameters can be determined imposing some convergence and or stability criteria or by postulating the element matrix with the desired stability properties the element matrix of most stabilized methods such as gls and ggls methods can be obtained using this new method with appropriate choices of the stabilization parameters we applied this formulation to diffusion reaction problems optimal rates of convergency are numerically observed for regular solutions

applications and generalizations of fisher hartwig asymptotics fisher hartwig asymptotics refers to the large n form of a class of toeplitz determinants with singular generating functions this class of toeplitz determinants occurs in the study of the spin spin correlations for the two dimensional ising model and the ground state density matrix of the impenetrable bose gas amongst other problems in mathematical physics we give a new application of the original fisher hartwig formula to the asymptotic decay of the ising correlations above tc while the study of the bose gas density matrix leads us to generalize the fisher hartwig formula to the asymptotic form of random matrix averages over the classical groups and the gaussian and laguerre unitary matrix ensembles another viewpoint of our generalizations is that they extend to hankel determinants the fisher hartwig asymptotic form known for toeplitz determinants

cyclic states berry phases and the schrodinger operator the evolution of a quantum mechanical system under a nonadiabatic external perturbation at a time interval 0 t is considered it is shown that all the cyclic states of the system mod psi t ei phi mod psi 0 are determined by the eigenvalues in quasi energies and associated eigenvectors mod phi in t of the schrodinger operator sq t h t i delta delta t acting on some hilbert space the set of linearly independent cyclic quasi energy states possess some properties similar to the properties of the stationary states of a closed system the berry phases of the states associated with eigenvectors of the discrete spectrum of sq t which are single valued functions of omega 2 pi t are supplied by the partial derivatives of the corresponding eigenvalues quasi energies with respect to omega the approach developed is illustrated by several applications to time dependent systems the system under an adiabatic perturbation the forced harmonic oscillator and the two level system even in the case of a system with a time independent hamiltonian there exist nonstationary quasi energy states that have nontrivial berry phases beta 2 pi not an integer the criterion of existence of such states is formulated in terms of the energies of the system and the corresponding expression for the berry phases is obtained some examples of nonstationary cyclic states of closed systems including the coherent states of a force free oscillator and the wannier states of electrons in the parabolic band are considered

bv functions in hilbert spaces we study the basic theory of bv functions in a hilbert space x endowed with a not necessarily gaussian probability measure nu we present necessary and sufficient conditions in order that a function u in l p x nu is of bounded variation we also discuss the de giorgi approach to bv functions through the behavior as t rightarrow 0 of int x vert nabla t t u vert d nu for a smoothing semigroup t t particular attention is devoted to the case where u is the indicator function of a sublevel set x g x r of a real borel function g we give several examples for different measures nu such as weighted gaussian measures infinite products of non gaussian measures and invariant measures of some stochastic pdes such as reaction diffusion equations and burgers equation

an exact riemann solver for wave propagation in arbitrary anisotropic elastic media with fluid coupling abstract we present a nonconformal mesh discontinuous galerkin pseudospectral time domain algorithm for arbitrary anisotropic elastic acoustic wave propagation problems an exact riemann solver is compactly derived to resolve the accurate coupling of multiple domains in the discontinuous galerkin framework including heterogeneous anisotropic solid solid acoustic acoustic and anisotropic solid fluid interactions we simplify the eigenvalue problem in the riemann solution from the rank of 9 to 3 and introduce the generalized wave impedance with more physical insight validations and verifications with independent codes and analytical solutions illustrate the accuracy flexibility and stability of our algorithm

traces of sobolev functions on regular surfaces in infinite dimensions abstract in a banach space x endowed with a nondegenerate gaussian measure we consider sobolev spaces of real functions defined in a sublevel set o x x g x 0 of a sobolev nondegenerate function g x r we define the traces at g 1 0 of the elements of w 1 p o for p 1 as elements of l 1 g 1 0 where is the surface measure of feyel and de la pradelle the range of the trace operator is contained in l q g 1 0 for 1 q p and even in l p g 1 0 under further assumptions if o is a suitable halfspace the range is characterized as a sort of fractional sobolev space at the boundary an important consequence of the general theory is an integration by parts formula for sobolev functions which involves their traces at g 1 0

on the space of bv functions and a related stochastic calculus in infinite dimensions functions of bounded variation bv functions are defined on an abstract wiener space e h in a way similar to that in finite dimensions some characterizations are given which justify describing a bv function as a function in l log l 1 2 with the first order derivative being an h valued measure it is also shown that the space of bv functions is obtained by a natural extension of the sobolev space d1 1 moreover some stochastic formulae related to bv functions are investigated

can chaotic quantum energy levels statistics be characterized using information geometry and inference methods abstract in this paper we review our novel information geometrodynamical approach to chaos igac on curved statistical manifolds and we emphasize the usefulness of our information geometrodynamical entropy ige as an indicator of chaoticity in a simple application furthermore knowing that integrable and chaotic quantum antiferromagnetic ising chains are characterized by asymptotic logarithmic and linear growths of their operator space entanglement entropies respectively we apply our igac to present an alternative characterization of such systems remarkably we show that in the former case the ige exhibits asymptotic logarithmic growth while in the latter case the ige exhibits asymptotic linear growth at this stage of its development igac remains an ambitious unifying information geometric theoretical construct for the study of chaotic dynamics with several unsolved problems however based on our recent findings we believe that it could provide an interesting innovative and potentially powerful way to study and understand the very important and challenging problems of classical and quantum chaos

absolutely continuous flows generated by sobolev class vector fields in finite and infinite dimensions abstract we prove the existence of the global flow ut generated by a vector field a from a sobolev class w1 1 on a finite or infinite dimensional space x with a measure provided is sufficiently smooth and that a a and a where a is the divergence with respect to are exponentially integrable in addition the measure is shown to be quasi invariant under ut in the case x r n and p dx where p w1 1loc r n is a locally uniformly positive probability density a sufficient condition is exp c a exp c a p p l1 for all c in the infinite dimensional case we get analogous results for measures differentiable along sufficiently many directions examples of measures which fit our framework important for applications are symmetric invariant measures of infinite dimensional diffusions and gibbs measures typically in both cases such measures are essentially non gaussian our result in infinite dimensions significantly extends previously studied cases where was a gaussian measure finally we study flows generated by vector fields whose values are not necessarily in the cameron martin space

random matrix theory and entanglement in quantum spin chains we compute the entropy of entanglement in the ground states of a general class of quantum spin chain hamiltonians those that are related to quadratic forms of fermi operators between the first n spins and the rest of the system in the limit of infinite total chain length we show that the entropy can be expressed in terms of averages over the classical compact groups and establish an explicit correspondence between the symmetries of a given hamiltonian and those characterizing the haar measure of the associated group these averages are either toeplitz determinants or determinants of combinations of toeplitz and hankel matrices recent generalizations of the fisher hartwig conjecture are used to compute the leading order asymptotics of the entropy as n this is shown to grow logarithmically with n the constant of proportionality is determined explicitly as is the next constant term in the asymptotic expansion the logarithmic growth of the entropy was previously predicted on the basis of numerical computations and conformal field theoretic calculations in these calculations the constant of proportionality was determined in terms of the central charge of the virasoro algebra our results therefore lead to an explicit formula for this charge we also show that the entropy is related to solutions of ordinary differential equations of painleve type in some cases these solutions can be evaluated to all orders using recurrence relations

geometric phases and critical phenomena in a chain of interacting spins the geometric phase can act as a signature for critical regions of interacting spin chains in the limit where the corresponding circuit in parameter space is shrunk to a point and the number of spins is extended to infinity for finite circuit radii or finite spin chain lengths the geometric phase is always trivial a multiple of 2p in this work two related signatures of criticality are proposed which obey finite size scaling and which circumvent the need for assuming any unphysical limits they are based on the notion of the bargmann invariant whose phase may be regarded as a discretized version of the berry phase as circuits are considered which are composed of a discrete finite set of vertices in parameter space they are able to pass directly through a critical point rather than having to circumnavigate it the proposed mechanism is shown to provide a diagnostic tool for criticality in the case of a given non solvable one dimensional spin chain with nearest neighbour interactions in the presence of an external magnetic field

entanglement entropy and conformal field theory we review the conformal field theory approach to entanglement entropy in 1 1 dimensions we show how to apply these methods to the calculation of the entanglement entropy of a single interval and the generalization to different situations such as finite size systems with boundaries and the case of several disjoint intervals we discuss the behaviour away from the critical point and the spectrum of the reduced density matrix quantum quenches as paradigms of non equilibrium situations are also considered

the stochastic reflection problem with multiplicative noise abstract this paper addresses the existence and uniqueness of strong solutions to the stochastic variational inequality d x x d t f t x d t x d t k 1 m x k d k t f t d t in a bounded domain o r d with dirichlet homogeneous conditions here r 0 for r 0 0 0 r 0 for r 0 an application to the one phase stefan problem with a stochastic heat source is given one studies also the corresponding stochastic parabolic equation with signorini boundary conditions x x 0 on o

asymptotics of toeplitz hankel and toeplitz hankel determinants with fisher hartwig singularities we study the asymptotics in n for n dimensional toeplitz determinants whose symbols possess fisher hartwig singularities on a smooth background we prove the general nondegenerate asymptotic behavior as conjectured by basor and tracy we also obtain asymptotics of hankel determinants on a nite interval as well as determinants of toeplitz hankel type our analysis is based on a study of the related system of orthogonal polynomials on the unit circle using the riemann hilbert approach

bv functions and distorted ornstein uhlenbeck processes over the abstract wiener space let e h be an abstract wiener space and h be the class of functions l1 e satisfying the ray hamza condition in every direction l e for h the closure e f of the symmetric form e u v e u z v z h z dz u v fc1b is a quasi regular dirichlet form on l2 f d f supp yielding an associated diffusion m xt pz on f called a distorted ornstein uhlenbeck process a function on e is called a bv function bv e in notation if p 1 lp e and v supg fc1b e g h z 1 e g z z dz is finite for h bv e there exist a positive finite measure d on f and a weakly measurable function f h such that z h 1 d a e and f g z z dz f g z z h d dz g fc1b e further the sample path of m admits an expression as a sum of e valued cafs xt x0 wt 12 t0 xs ds 12 t0 xs dl d s where wt is an e valued brownian motion and l d t is a pcaf of m with revuz measure d a measurable set e is called caccioppoli if i bv e in this case the support of the measure di is concentrated in and the above equations reduce to the gauss formula and the skorohod equation for the modified reflecting ornstein uhlenbeck process respectively a related coarea formula is also presented

the fisher hartwig conjecture and toeplitz eigenvalues abstract the conjecture of fisher and hartwig published in 1968 describes the asymptotic expansion of toeplitz determinants with singular generating functions for more than twenty years progress was made in extending the validity of the conjecture but recent computer experiments led to counterexamples that show the limits of the original conjecture and pointed the way to a revised conjecture this paper describes the history of the problem several numerical examples and the revised conjecture

bv functions in abstract wiener spaces abstract functions of bounded variation in an abstract wiener space i e an infinite dimensional banach space endowed with a gaussian measure and a related differential structure have been introduced by m fukushima and m hino using dirichlet forms and their properties have been studied with tools from analysis and stochastics in this paper we reformulate in an integral geometric vein and with purely analytical tools the definition and the main properties of bv functions and investigate further properties

kolmogorov equation associated to the stochastic reflection problem on a smooth convex set of a hilbert space we consider the stochastic reflection problem associated with a selfadjoint operator a and a cylindrical wiener process on a convex set k with nonempty interior and regular boundary e in a hilbert space h we prove the existence and uniqueness of a smooth solution for the corresponding elliptic infinite dimensional kolmogorov equation with neumann boundary condition on e

on the quantization of the modified poschl teller potential it is shown that the connection one form on the prequantization line bundle that generates the correct energy spectrum for the modified poschl teller potential consists of the canonical one form on the corresponding cotangent bundle together with an adjustment term that arises from the berry s connection

the fisher hartwig formula and entanglement entropy toeplitz matrices have applications to different problems of statistical mechanics recently it was used for calculation of entanglement entropy in spin chains in the paper we review these recent developments we use the fisher hartwig formula as well as the recent results concerning the asymptotics of the block toeplitz determinants to calculate entanglement entropy of large block of spins in the ground state of xy spin chain

quantum spin chain toeplitz determinants and the fisher hartwig conjecture we consider the one dimensional quantum spin chain which is called the xx model xx0 model or isotropic xy model in a transverse magnetic field we are mainly interested in the entropy of a block of lneighboring spins at zero temperature and of an infinite system we represent the entropy in terms of a toeplitz determinant and calculate the asymptotic analytically we derive the first two terms of the asymptotic decomposition interestingly these two terms of decomposition clearly show a length scale related to the field h

sobolev functions on infinite dimensional domains abstract we study extensions of sobolev and bv functions on infinite dimensional domains along with some positive results we present a negative solution of the long standing problem of existence of sobolev extensions of functions in gaussian sobolev spaces from a convex domain to the whole space

maximal l 2 regularity for ornstein uhlenbeck equation in convex sets of banach spaces abstract we study the elliptic equation u l u f in an open convex subset of an infinite dimensional separable banach space x endowed with a centered non degenerate gaussian measure where l is the ornstein uhlenbeck operator we prove that for 0 and f l 2 the weak solution u belongs to the sobolev space w 2 2 moreover we prove that u satisfies the neumann boundary condition in the sense of traces at the boundary of this is done by finite dimensional approximation

an h1 ph coercive discontinuous galerkin formulation for the poisson problem 1 d analysis coercivity of the bilinear form in a continuum variational problem is a fundamental property for finite element discretizations by the classical lax milgram theorem any conforming discretization of a coercive variational problem is stable i e discrete approximations are well posed and possess unique solutions irrespective of the specifics of the underlying approximation space based on the prototypical one dimensional poisson problem we establish in this work that most concurrent discontinuous galerkin formulations for second order elliptic problems represent instances of a generic conventional formulation and that this generic formulation is noncoercive consequently all conventional discontinuous galerkin formulations are a fortiori noncoercive and typically their well posedness is contingent on approximation space dependent stabilization parameters moreover we present a new symmetric nonconventional discontinuous galerkin formulation based on element green s functions and the data local to the edges we show that the new discontinuous galerkin formulation is coercive on the broken sobolev space h1 ph viz the space of functions that are elementwise in the h1 sobolev space the coercivity of the new formulation is supported by calculations of discrete inf sup constants and numerical results are presented to illustrate the optimal convergence behavior in the energy norm and in the l2 norm

unfolding a diabolic point a generalized crossing scenario the typical avoided crossings for hermitian quantum systems depending on parameters the diabolic crossing scenario are generalized to the non hermitian case e g for resonances two types of crossings appear for type i the real parts show an avoided and the imaginary parts a true crossing of the eigenenergies and for type ii the opposite is found a simple symmetric non hermitian two state matrix hamiltonian is analysed in detail the diabolic point bifurcates into two exceptional ones on exceptional lines where the matrices are defective the adiabatic transport of eigenvectors and eigenstates in parameter space is discussed in this generalized diabolic crossing scenario in particular the geometric berry phases for a cyclic variation of system parameters depending on the topology of the closed curves with respect to the exceptional lines

eigenpairs of toeplitz and disordered toeplitz matrices with a fisher hartwig symbol toeplitz matrices have entries that are constant along diagonals they model directed transport are at the heart of correlation function calculations of the two dimensional ising model and have applications in quantum information science we derive their eigenvalues and eigenvectors when the symbol is singular fisher hartwig we then add diagonal disorder and study the resulting eigenpairs we find that there is a bulk behavior that is well captured by second order perturbation theory of non hermitian matrices the non perturbative behavior is classified into two classes runaways type i leave the complex valued spectrum and become completely real because of eigenvalue attraction runaways type ii leave the bulk and move very rapidly in response to perturbations these have high condition numbers and can be predicted localization of the eigenvectors are then quantified using entropies and inverse participation ratios eigenvectors corresponding to runaways type ii are most localized i e super exponential whereas runaways type i are less localized than the unperturbed counterparts and have most of their probability mass in the interior with algebraic decays the results are corroborated by applying free probability theory and various other supporting numerical studies

diabolical points in the spectra of triangles accidental degeneracies between energy levels e j and e j 1 of a real hamiltonian can occur generically in a family of hamiltonians labelled by at least two parameters x y energy level surfaces in e x y space have locally a double cone diabolo connection and we refer to the degeneracies themselves as diabolical points we studied the family of systems in which a particle moves freely within hard walled triangles vibrations of triangular membranes with x and y labelling two of the angles using an efficient green function technique to compute the levels we found several diabolical points for low lying levels as well as some symmetry degeneracies the lowest diabolical point occurred for levels 5 and 6 of the triangle 130 57 30 73 18 70 the conical structure was confirmed by noting that the normal derivative u of the wavefunction at a boundary point changed sign during a small circuit of the diabolical point the form of the variation of u around a circuit and the changing pattern of nodal lines of agreed with theoretical expectations an estimate of the total number of degeneracies n d j involving levels 1 through j based on the energy scaling of cone angles and the level spacing distribution gave n d j j 2 5 and our limited data support this prediction analytical theory confirmed that for thin triangles where our computational method is slow there are no degeneracies in the energy range studied

a discontinuoushpfinite element method for diffusion problems we present an extension of the discontinuous galerkin method which is applicable to the numerical solution of diffusion problems the method involves a weak imposition of continuity conditions on the solution values and on fluxes across interelement boundaries within each element arbitrary spectral approximations can be constructed with different orderspin each element we demonstrate that the method is elementwise conservative a property uncharacteristic of high order finite elements for clarity we focus on a model class of linear second order boundary value problems and we developpriorierror estimates convergence proofs and stability estimates the results of numerical experiments onh andp convergence rates for representative two dimensional problems suggest that the method is robust and capable of delivering exponential rates of convergence

lagrangian flows driven by bv fields in wiener spaces we establish the renormalization property for essentially bounded solutions of the continuity equation associated to bounded variation bv fields in wiener spaces with values in the associated cameron martin space thus obtaining by standard arguments new uniqueness and stability results for correspondent lagrangian flows

feynman graphs and the large dimensional limit of multipartite entanglement in this paper we extend the analysis of multipartite entanglement based on techniques from classical statistical mechanics to a system composed of n d level parties qudits we introduce a suitable partition function at a fictitious temperature with the average local purity of the system as hamiltonian in particular we analyze the high temperature expansion of this partition function prove the convergence of the series and study its asymptotic behavior as d we make use of a diagrammatic technique classify the graphs and study their degeneracy we are thus able to evaluate their contributions and estimate the moments of the distribution of the local purity

continuous discontinuous finite element approximations of fourth order elliptic problems in structural and continuum mechanics with applications to thin beams and plates and strain gradient elasticity abstract a new finite element method for fourth order elliptic partial differential equations is presented and applied to thin bending theory problems in structural mechanics and to a strain gradient theory problem the method combines concepts from the continuous galerkin cg method the discontinuous galerkin dg method and stabilization techniques a brief review of the cg method the dg method and stabilization techniques highlights the advantages and disadvantages of these methods and suggests a new approach for the solution of fourth order elliptic problems a continuous discontinuous galerkin c dg method is proposed which uses c 0 continuous interpolation functions and is formulated in the primary variable only the advantage of this formulation over a more traditional mixed approach is that the introduction of additional unknowns and related difficulties can be avoided in the context of thin bending theory the c dg method leads to a formulation where displacements are the only degrees of freedom and no rotational degrees of freedom need to be considered the main feature of the c dg method is the weak enforcement of continuity of first and higher order derivatives through stabilizing terms on interior boundaries consistency stability and convergence of the method are shown analytically numerical experiments verify the theoretical results and applications are presented for bernoulli euler beam bending poisson kirchhoff plate bending and a shear layer problem using toupin mindlin strain gradient theory

quantal phase factors accompanying adiabatic changes a quantal system in an eigenstate slowly transported round a circuit c by varying parameters r in its hamiltonian r will acquire a geometrical phase factor exp i c in addition to the familiar dynamical phase factor an explicit general formula for c is derived in terms of the spectrum and eigenstates of r over a surface spanning c if c lies near a degeneracy of c takes a simple form which includes as a special case the sign change of eigenfunctions of real symmetric matrices round a degeneracy as an illustration c is calculated for spinning particles in slowly changing magnetic fields although the sign reversal of spinors on rotation is a special case the effect is predicted to occur for bosons as well as fermions and a method for observing it is proposed it is shown that the aharonov bohm effect can be interpreted as a geometrical phase factor

fluctuation path integrals in the generalized coherent states representation fluctuations around classical solutions are evaluated by the path integral method based on the generalized coherent states a simple expression for the semiclassical propagator is derived and applied to the su 2 character formula it is also pointed out that several versions of the coherent states path integral can be considered owing to the nonorthogonal character of the coherent states and they are compared by applying them to the su 2 character formula

berry s phase hannay s angle and coherent states through the use of coherent states describing the action angle variables the authors establish a strict parallelism between berry s phase and hannay s angle in particular they define a geometrical transport for classical tori which leads to hannay s angle as in the case of berry s phase the transport can be associated with the minimization of a distance

a new correlator in quantum spin chains we propose a new correlator in one dimensional quantum spin chains the s emptiness formation probability s efp this is a generalization of the emptiness formation probability efp which is the probability that the first n spins of the chain are all aligned downwards in the s efp we let the spins in question be separated by s sites the usual efp corresponds to the special case when s 1 taking s 1 allows us to quantify non local correlations we express the s efp for the anisotropic xy model in a transverse magnetic field a system with both critical and non critical regimes in terms of a toeplitz determinant for the isotropic xy model we find that the magnetic field induces an interesting length scale

difference system for selberg correlation integrals the selberg correlation integrals are averages of the products with respect to the selberg density our interest is in the case m 1 1 when this corresponds to the th moment of the corresponding characteristic polynomial we give the explicit form of an n 1 n 1 matrix linear difference system in the variable which determines the average and we give the gauss decomposition of the corresponding n 1 n 1 matrix for a positive integer the difference system can be used to efficiently compute the power series defined by this average

on the dirichlet semigroup for ornstein uhlenbeck operators in subsets of hilbert spaces we consider a family of self adjoint ornstein uhlenbeck operators l in an infinite dimensional hilbert space h having the same gaussian invariant measure for all 0 2 0 1 we study the dirichlet problem for the equation l f in a closed set k with f 2 l 2 k we first prove that the variational solution trivially provided by the lax milgram theorem can be rep resented as expected by means of the transition semigroup stopped to k then we address two problems 1 the regularity of the solution which is by definition in a sobolev space w 1 2 k of the dirichlet problem 2 the meaning of the dirichlet boundary condition concerning regularity we are able to prove interior w 2 2 regularity results concerning the boundary condition we consider both irreg ular and regular boundaries in the first case we content to have a solution whose null extension outside k belongs to w 1 2 h in the second case we exploit the malliavin s theory of surface integrals which is recalled in the appendix of the pa per then we are able to give a meaning to the trace of at k and to show that it vanishes as it is natural

the emergence of typical entanglement in two party random processes we investigate the entanglement within a system undergoing a random local process we find that there is initially a phase of very fast generation and spread of entanglement at the end of this phase the entanglement is typically maximal in oliveira et al 2007 phys rev lett 98 130502 we proved that the maximal entanglement is reached to a fixed arbitrary accuracy within o n3 steps where n is the total number of qubits here we provide a detailed and more pedagogical proof we demonstrate that one can use the so called stabilizer gates to simulate this process efficiently on a classical computer furthermore we discuss three ways of identifying the transition from the phase of rapid spread of entanglement to the stationary phase i the time when saturation of the maximal entanglement is achieved ii the cutoff moment when the entanglement probability distribution is practically stationary and iii the moment block entanglement exhibits volume scaling we furthermore investigate the mixed state and multipartite setting numerically we find that the mutual information appears to behave similarly to the quantum correlations and that there is a well behaved phase space flow of entanglement properties towards an equilibrium we describe how the emergence of typical entanglement can be used to create a much simpler tripartite entanglement description the results form a bridge between certain abstract results concerning typical also known as generic entanglement relative to an unbiased distribution on pure states and the more physical picture of distributions emerging from random local interactions

density and spacings for the energy levels of quadratic fermi operators the work presents a proof of convergence of the density of energy levels to a gaussian distribution for a wide class of quadratic forms of fermi operators this general result applies also to quadratic operators with disorder e g containing random coefficients the spacing distribution of the unfolded spectrum is investigated numerically for generic systems the level spacings behave as the spacings in a poisson process level clustering persists in the presence of disorder

the notion of convexity and concavity on wiener space abstract we define in the frame of an abstract wiener space the notions of convexity and of concavity for the equivalence classes of random variables as application we show that some important inequalities of the finite dimensional case have their natural counterparts in this setting

sets of finite perimeter and the hausdorff gauss measure on the wiener space abstract in euclidean space the integration by parts formula for a set of finite perimeter is expressed by the integration with respect to a type of surface measure according to geometric measure theory this surface measure is realized by the one codimensional hausdorff measure restricted on the reduced boundary and or the measure theoretic boundary which may be strictly smaller than the topological boundary in this paper we discuss the counterpart of this measure in the abstract wiener space which is a typical infinite dimensional space we introduce the concept of the measure theoretic boundary in the wiener space and provide the integration by parts formula for sets of finite perimeter the formula is presented in terms of the integration with respect to the one codimensional hausdorff gauss measure restricted on the measure theoretic boundary

convergence analysis of a discontinuous finite element formulation based on second order derivatives a new discontinuous galerkin formulation is introduced for the elliptic reaction diffusion problem that incorporates local second order distributional derivatives the corresponding bilinear form satisfies both coercivity and continuity properties on the broken hilbert space of h 2 functions for piecewise polynomial approximations of degree p p 2 optimal uniform h and p convergence rates are obtained in the broken h 1 and h 2 norms convergence in l 2 is optimal for p p 3 if the computational mesh is strictly rectangular if the mesh consists of skewed elements then optimal convergence is only obtained if the corner angles satisfy a given regularity condition for p 2 only suboptimal h convergence rates in l 2 are obtained and for linear polynomial approximations the method does not converge 2005 elsevier b v all rights reserved

asymptotics of toeplitz determinants and the emptiness formation probability for the xy spin chain we study an asymptotic behaviour of a special correlator known as the emptiness formation probability efp for the one dimensional anisotropic xy spin 1 2 chain in a transverse magnetic field this correlator is essentially the probability of formation of a ferromagnetic string of length n in the antiferromagnetic ground state of the chain and plays an important role in the theory of integrable models for the xy spin chain the correlator can be expressed as the determinant of a toeplitz matrix and its asymptotical behaviours for n throughout the phase diagram are obtained using known theorems and conjectures on toeplitz determinants we find that the decay is exponential everywhere in the phase diagram of the xy model except on the critical lines i e where the spectrum is gapless in these cases a power law prefactor with a universal exponent arises in addition to an exponential or gaussian decay the latter gaussian behaviour holds on the critical line corresponding to the isotropic xy model while at the critical value of the magnetic field the efp decays exponentially at small anisotropy one has a crossover from the gaussian to the exponential behaviour we study this crossover using the bosonization approach