nonabelian bundle gerbes their differential geometry and gauge theory bundle gerbes are a higher version of line bundles we present nonabelian bundle gerbes as a higher version of principal bundles connection curving curvature and gauge transformations are studied both in a global coordinate independent formalism and in local coordinates these are the gauge fields needed for the construction of yang mills theories with 2 form gauge potential

reduced dynamics for entangled initial state of the full density operator starting from the schrodinger equation for a system and a reservoir we construct a quantum dynamical map that describes reduced dynamics we work with an arbitrary initial state for the system and reservoir and thus refrain from performing any factorizations the map is found to be nonlinear not completely positive and not unique to investigate the physical implications the bloch equations are constructed if the freedom the new map offers us is fully exploited then the classic inequality 2 for the damping coefficients must be replaced by a weaker condition

the unstable spectrum of oscillating shear flows a complete description is given for the unstable spectrum of the euler equation linearized about shear flows with sinusoidal profiles the spectral problem is treated analytically and numerically the spectral asymptotics are determined using the method of averaging for general rapidly oscillating profiles such flows are always unstable

higher gauge theory differential versus integral formulation the term higher gauge theory refers to the generalization of gauge theory to a theory of connections at two levels essentially given by 1 and 2 forms so far there have been two approaches to this subject the differential picture uses non abelian 1 and 2 forms in order to generalize the connection 1 form of a conventional gauge theory to the next level the integral picture makes use of curves and surfaces labeled with elements of non abelian groups and generalizes the formulation of gauge theory in terms of parallel transports we recall how to circumvent the classic no go theorems in order to define non abelian surface ordered products in the integral picture we then derive the differential picture from the integral formulation under the assumption that the curve and surface labels depend smoothly on the position of the curves and surfaces we show that some aspects of the no go theorems are still present in the differential but not in the integral picture this implies a substantial structural

quantum fluctuation relations for the lindblad master equation an open quantum system interacting with its environment can be modeled under suitable assumptions as a markov process described by a lindblad master equation in this work we derive a general set of fluctuation relations for systems governed by a lindblad equation these identities provide quantum versions of jarzynski hatano sasa and crooks relations in the linear response regime these fluctuation relations yield a fluctuation dissipation theorem fdt valid for a stationary state arbitrarily far from equilibrium for a closed system this fdt reduces to the celebrated callen welton kubo formula

qp structures of degree 3 and 4d topological field theory a bv algebra and a qp structure of the degree 3 is formulated a qp structure of degree 3 gives rise to lie algebroids up to homotopy and its algebraic and geometric structure is analyzed a new algebroid is constructed which derives a new topological field theory in 4 dimensions by the aksz construction

volumes of conditioned bipartite state spaces we analyze the metric properties of conditioned quantum state spaces these spaces are the convex sets of density matrices that when partially traced over m degrees of freedom respectively yield the given n n density matrix for the case n 2 the volume of equipped with the hilbert schmidt measure can be conjectured to be a simple polynomial of the radius of in the bloch ball remarkably for we find numerically that the probability to find a separable state in is independent of except for pure for the same holds for the probability to find a state with a positive partial transpose in these results are proven analytically for the case of the family of 4 4 x states and thoroughly numerically investigated for the general case the important implications of these findings for the clarification of open problems in quantum theory are pointed out and discussed

on the existence of quantum subdynamics it is shown using only elementary operator algebra that an open quantum system coupled to its environment will have a subdynamics reduced dynamics as an exact consequence of the reversible dynamics of the composite system only when the states of system and environment are uncorrelated furthermore it is proved that for a finite temperature the kms condition for the lowest order correlation function cannot be reproduced by any type of linear subdynamics except the reversible hamiltonian one of a closed system the first statement can be seen as a particular case of a more general theorem of takesaki on the properties of conditional expectations in von neumann algebras the concept of subdynamics used here allows for memory effects no assumption is made of a markov property for dynamical systems based on commutative algebras of observables the subdynamics always exists as a stochastic process in the random variable defining the open subsystem

multiaccess quantum channels shared communication channels are subject to multiple access interference transmitter and receiver design techniques that explicitly deal with this interference have been shown to improve substantially the performance of communication systems over radio frequency and other classical channels quantum multiple access communication channels on the other hand have received comparatively little attention in this paper an input output model for multiple access quantum channels relevant to optical communications is proposed the model accounts for multiaccess interference signal attenuation and random noise and can be used in the analysis and design of communication systems using a result from optimization a perturbation method is developed to find the minimum achievable error probability in small interference channels it is shown that the quantum measurement that minimizes the error probability in a no interference channel is robust in the presence of small multiaccess interference the results are illustrated with numerical examples which show that optimal quantum detectors can significantly outperform conventional detectors even for moderate levels of crosstalk

singularities of euler flow not out of the blue does three dimensional incompressible euler flow with smooth initial conditions develop a singularity with infinite vorticity after a finite time this blowup problem is still open after briefly reviewing what is known and pointing out some of the difficulties we propose to tackle this issue for the class of flows having analytic initial data for which hypothetical real singularities are preceded by singularities at complex locations we present some results concerning the nature of complex space singularities in two dimensions and propose a new strategy for the numerical investigation of blowup

control landscapes for two level open quantum systems a quantum control landscape is defined as the physical objective as a function of the control variables in this paper the control landscapes for two level open quantum systems whose evolution is described by general completely positive trace preserving maps i e kraus maps are investigated in detail the objective function which is the expectation value of a target system operator is defined on the stiefel manifold representing the space of kraus maps three practically important properties of the objective function are found a the absence of local maxima or minima i e false traps b the existence of multi dimensional sub manifolds of optimal solutions corresponding to the global maximum and minimum and c the connectivity of each level set all of the critical values and their associated critical sub manifolds are explicitly found for any initial system state away from the absolute extrema there are no local maxima or minima and only saddles may exist whose number and the explicit structure of the corresponding critical sub manifolds are determined by the initial system state there are no saddles for pure initial states one saddle for a completely mixed initial state and two saddles for partially mixed initial states in general the landscape analysis of critical points and optimal manifolds is relevant to explain the relative ease of obtaining good optimal control outcomes in the laboratory even in the presence of the environment

explicit small scale velocity simulation for high re turbulent flows a new approach two level simulation tls is developed based on the explicit reconstruction of the small scale velocity by solving the small scale governing equations on the domain with reduced dimension representing a collection of one dimensional lines embedded in the three dimensional flow domain a coupled system of equations that is not based on an eddy viscosity hypothesis is derived based on the decomposition of flow variables into the large scale and the small scale components without introducing the concept of filtering simplified treatment of the small scale equations is proposed based on neglecting the small scale advective and dissipative terms in the line orthogonal directions fully coupled simulation of the forced isotropic turbulence at re l 65 114 demonstrates potential benefits and challenges of the tls approach for high re turbulent flows using coarse grids

asymptotic solution for first and second order linear volterra integro differential equations with convolution kernels this paper addresses the problem of finding an asymptotic solution for first and second order integro differential equations containing an arbitrary kernel by evaluating the corresponding inverse laplace and fourier transforms the aim of the paper is to go beyond the tauberian theorem in the case of integral differential equations which are widely used by the scientific community the results are applied to the convolute form of the lindblad equation setting generic conditions on the kernel in such a way as to generate a positive definite density matrix and show that the structure of the eigenvalues of the correspondent liouvillian operator plays a crucial role in determining the positivity of the density matrix

the thermostatistical aspect of werner type states and quantum entanglement a general werner type state is studied from two viewpoints i an application of the dynamical interaction of the objective system with its environment represented by a unital positive operator valued measure povm which ensures an increase of entropy making the system evolve from an initial pure state to a mixed state of the werner type and ii the space of the objective system is constrained to have a given value of the fidelity then the maximum entropy principle is shown to yield the werner type state as a canonical ensemble with a projector hamiltonian this novel observation is illustrated by examples of bipartite systems the separability criteria of which are given in terms of the values of temperature the present viewpoint may cast light on the relevance of thermostatistics to the physics of quantum entanglement in addition the povm scheme presented here offers a way of experimentally generating the werner type thermal states

asymptotic stability of solitary waves we show that the family of solitary waves 1 solitons of the korteweg de vries equation partial t u u partial x u partial x 3 u 0 is asymptotically stable our methods also apply for the solitary waves of a class of generalized korteweg de vries equations partial t u partial x f u partial x 3 u 0 in particular we study the case wheref u up 1 p 1 p 1 2 3 and 3 0 withf c4 the same asymptotic stability result for kdv is also proved for the casep 2 the modified korteweg de vries equation we also prove asymptotic stability for the family of solitary waves for all but a finite number of values ofp between 3 and 4 the solitary waves are known to undergo a transition from stability to instability as the parameterp increases beyond the critical valuep 4 the solution is decomposed into a modulating solitary wave with time varying speedc t and phase t bound state part and an infinite dimensional perturbation radiating part the perturbation is shown to decay exponentially in time in a local sense relative to a frame moving with the solitary wave asp 4 the local decay or radiation rate decreases due to the presence of aresonance pole associated with the linearized evolution equation for solitary wave perturbations

complete positivity and thermodynamics in a driven open quantum system while it is well known that complete positivity guarantees the fulfilment of the second law of thermodynamics its possible violations have never been proposed as a check of the complete positivity of a given open quantum dynamics we hereby consider an open quantum micro circuit effectively describable as a two level open quantum system whose asymptotic current might be experimentally accessible this latter could indeed be used to discriminate between its possible non completely positive redfield dynamics and a completely positive one obtained by standard weak coupling limit techniques at the same time verifying the fate of the second law of thermodynamics in such a context

ab initio construction of an analytically tractable kraus map for non markovian quantum dissipation starting from a prescribed hamiltonian we construct a non markovian evolution equation for a non relativistic quantum system that exchanges energy with a large reservoir in order to create sufficient mathematical freedom the density operator is replaced by a more flexible entity that depends on two times if these times are chosen equal the density operator is recovered in deriving a non markovian integral equation for our bitemporal operator it is assumed that initially system and reservoir are completely uncorrelated furthermore in employing wick s theorem for factorization of reservoir correlation functions only those wick contractions between reservoir potentials are retained that belong to a generalized nearest neighbour class the latter is established by subjecting the set of plain nearest neighbour contractions to any cyclic permutation of reservoir potentials through generalizing the notion of nearest neighbour contraction it is ensured that the trace of the density operator is conserved by construction our bitemporal evolution equation agrees with the kraus map for quantum dissipation moreover a sound markovian limit exists that reproduces the complete van hove davies theory by making use of a rotating wave approximation and laplace transformation the density operator of a damped n level atom can be computed for large times and moderate coupling to the reservoir the atom ends up near the state of thermal equilibrium at zero temperature our non markovian integral equation gives an exact solution for the atomic density operator

von karman howarth equation for magnetohydrodynamics and its consequences on third order longitudinal structure and correlation functions a derivation in variable dimension of the scaling laws for mixed third order longitudinal structure and correlation functions for incompressible magnetized flows is given for arbitrary correlation between the velocity and magnetic field with full isotropy homogeneity and incompressibility assumed when close to equipartition between kinetic and magnetic energy the scaling relations involve only structure functions in a manner similar to the frac 4 5 law of kolmogorov

a square root method for the density matrix and its applications to lindblad operators abstract the evolution of open systems subject to both hamiltonian and dissipative forces is studied by writing the nm element of the time t dependent density matrix in the form nm t 1 a 1 a n t m t the so called square root factors the t s are non square matrices and are averaged over a systems of the ensemble this square root description is exact evolution equations are then postulated for the t factors such as to reduce to the lindblad type evolution equations for the diagonal terms in the density matrix for the off diagonal terms they differ from the lindblad equations the square root factors t are not unique and the equations for the t s depend on the specific representation chosen two criteria can be suggested for fixing the choice of t s one is simplicity of the resulting equations and the other has to do with the reduction of the difference between the t formalism and the lindblad equations when the method is tested on cases which have been previously treated by other methods our results agree with them examples chosen are i molecular systems such that are either periodically driven near level degeneracies for which we calculate the decoherence occurring in multiple landau zener transitions or else when undergoing descent around conical intersections in the potential surfaces ii formal dissipative systems with lindblad type operators representing either a non markovian process or a two state system coupled to bosons attractive features of the present factorization method are complete positivity the no higher than linear increase of the implementation effort with the number of states involved and the introduction of randomness only at the start of the process

spatial properties of velocity structure functions in turbulent wake flows in this paper we present experimental evidence that the scaling laws for the velocity structure functions s n r v x r ensuremath v x n n 2 4 6 8 hold in various parts of the flow domain the exponents that characterize the scaling are however a function of the position in the wake that is the local strength and ubiquity of coherent structures this variation is shown to be systematic and considerably exceeds the inaccuracy involved in the determination of the exponents this is an objective indication of the influence that the organized flow structures and inhomogeneity may have on intermittency in the analysis we invoke the concept of the extended self similarity ess

completely positive quantum operations generating thermostatistical states a comparative study abstract nonunitary quantum operations generating thermostatistical states and forming positive operator valued measures povms are of current interest as a useful tool for operational approach to quantum thermodynamics here two different operations generating the same thermostatistical state are studied one is related to thermofield dynamics and the other is the one proposed in a recent work abe et al 2010 a comparable study on them shows different behaviors of the von neumann entropy under repeated applications of these two operations it is shown that the entropy does not behave monotonically in general and can even decrease under the thermofield dynamical one in contrast to monotonic increase under the other

manin triples for lie bialgebroids in his study of dirac structures a notion which includes both poisson structures and closed 2 forms t courant introduced a bracket on the direct sum of vector fields and 1 forms this bracket does not satisfy the jacobi identity except on certain subspaces in this paper we systematize the properties of this bracket in the definition of a courant algebroid this structure on a vector bundle e rightarrow m consists of an antisymmetric bracket on the sections of e whose jacobi anomaly has an explicit expression in terms of a bundle map e rightarrow tm and a field of symmetric bilinear forms on e when m is a point the definition reduces to that of a lie algebra carrying an invariant nondegenerate symmetric bilinear form for any lie bialgebroid a a over m a notion defined by mackenzie and xu there is a natural courant algebroid structure on a oplus a which is the drinfel d double of a lie bialgebra when m is a point conversely if a and a are complementary isotropic subbundles of a courant algebroid e closed under the bracket such a bundle with dimension half that of e is called a dirac structure there is a natural lie bialgebroid structure on a a whose double is isomorphic to e the theory of manin triples is thereby extended from lie algebras to lie algebroids our work gives a new approach to bihamiltonian structures and a new way of combining two poisson structures to obtain a third one we also take some tentative steps toward generalizing drinfel d s theory of poisson homogeneous spaces from groups to groupoids

non markovian quantum trajectories instruments and time continuous measurements the linear and nonlinear non markovian quantum state diffusion nmqsd equations are well known tools for the description of certain non markovian open quantum systems in this work we systematically investigate whether the normalized linear nmqsd or the nonlinear nmqsd solutions can be generated by means of a time continuous measurement by considering any conceivable measurement scheme we derive a necessary criterion for the measurement interpretation of both equations concrete examples show that the normalized linear nmqsd solutions are realizable only in the markovian limit in general the application of the presented criterion to the nonlinear nmqsd remains an open issue furthermore this criterion is a necessary one not only in the context of the nmqsds but also for a much broader class of stochastic schrodinger equations

hyperviscosity for compressible flows using spectral methods abstract we describe a method for direct numerical simulations of highly turbulent compressible flows which permits an enhancement of the reynolds number a modification of the dissipative terms of the hydrodynamical equations is introduced in a way that preserves by construction the thermodynamic laws of the dissipation functions at constant cost the simulated reynolds numbers can be two orders of magnitude larger than with the standard navier stokes equation we also compare our method with the artifical viscosity scheme customary to spectral methods namely using high powers of the laplacian and show that results are improved in our case leaving out spurious oscillations near the shock in particular

symmetry of bilinear master equations for a quantum oscillator abstract we study the most general continuous transformation on the generators of bilinear master equations of a quantum oscillator we find that transformation operators that preserve the hermiticity of density operators and conserve the probability of reduced dynamics should be adjoint symmetric and they are not limited to the pure product of unitary operators in the bra and ket space but could be a mixture of them we need to include the more general transformation operators to explore the full symmetry of generic reduced dynamics we discuss how the operators are related to those considered in previous works and illustrate how they leave the reduced dynamics form invariant or map one into the other the positive semidefinite requirement on the density operator can be imposed to give a valid range of transformation parameters

a level set approach to simulate magnetohydrodynamic instabilities in aluminum reduction cells magnetohydrodynamic instabilities at the metal bath interface in aluminum reduction cells is an important and not fully understood topic to simulate the two fluid three dimensional unstationary flow subject to a background magnetic field a level set approach is proposed it features a formulation in terms of the magnetic vector potential to avoid a numerical growth of the divergence of the magnetic field the same exact projection scheme with staggered grids is used for both the velocity field and the magnetic vector potential test simulations show that the overall method behaves well in purely hydrodynamic as well as in fully magnetohydrodynamic regimes in both cases with a single fluid and with two fluids we also simulate with our technique the metal pad roll instability and trace the behavior of coupled interracial modes

impact of positivity and complete positivity on accessibility of markovian dynamics we consider a two dimensional quantum control system evolving under an entropy increasing irreversible dynamics in the semigroup form considering a phenomenological approach to the dynamics we show that the accessibility property of the system depends on whether its evolution is assumed to be positive or completely positive in particular we characterize the family of maps having different accessibilities and show the impact of that property on observable quantities by means of a simple physical model

completely positive maps and classical correlations we expand the set of initial states of a system and its environment that are known to guarantee completely positive reduced dynamics for the system when the combined state evolves unitarily we characterize the correlations in the initial state in terms of its quantum discord 1 we prove that initial states that have only classical correlations lead to completely positive reduced dynamics the induced maps can be not completely positive when quantum correlations including but not limited to entanglement are present

the wigner representation of classical mechanics quantization and classical limit abstract starting from the liouvillian formulation of classical physics it is possible by means of a fourier transform to introduce the wigner representation and to derive an operator structure to classical mechanics the importance of this new representation lies in the fact that it turns out to be the suitable route to establish a general method of quantization directly from the equations of motion without alluding to the existence of hamiltonian and lagrangian functions following this approach we quantize only the motion of a brownian particle with non linear friction in the markovian approximation the thermal bath may be quantum or classical thus when the bath is classically described we obtain a master equation which reduces to the caldeira leggett equation vide a o caldeira and a j leggett physica a 121 1983 587 for the linear friction case and when the reservoir is quantum we get an equation reducing to the one found by caldeira et al phys rev a 40 1989 3438 by neglecting the environmental influence we show that the system can be approximately described by equations of motion in terms of wave function such as the schrodinger langevin equation and equations of the caldirola kanai type finally to make the present study self consistent we evaluate the classical limit of these dynamical equations employing a new classical limiting method 0

phenomenological criteria for the validity of quantum markovian equations we revisit the constraints on the coefficients of a quantum markovian equation recently obtained by dekker and valsakumar we extend these criteria for time dependent coefficients and establish further criteria where appropriate phenomenological behaviour is required such as dissipation and a boltzmann asymptotic equilibrium state

notes on the riccati operator equation in open quantum systems a recent problem b gardas j math phys 52 042104 2011 concerning an antilinear solution of the riccati equation is solved we also exemplify that a simplification of the riccati equation even under reasonable assumptions can lead to a not equivalent equation

solutions of generic bilinear master equations for a quantum oscillator positive and factorized conditions on stationary states abstract we obtain the solutions of the generic bilinear master equation for a quantum oscillator with constant coefficients in the gaussian form the well behavedness and positive semidefiniteness of the stationary states could be characterized by a three dimensional minkowski vector by requiring the stationary states to satisfy a factorized condition we obtain a generic class of master equations that includes the well known ones and their generalizations some of which are completely positive a further subset of the master equations with the gibbs states as stationary states is also obtained for master equations with not completely positive generators an analysis on the stationary states for a given initial state suggests conditions on the coefficients of the master equations that generate positive evolution

fast numerical simulations of 2d turbulence using a dynamic model for subfilter motions we present numerical simulations of 2d turbulent flow using a new model for the subfilter scales which are computed using a dynamic equation linking the subfilter scales with the resolved velocity this equation is not postulated but derived from the constitutive equations under the assumption that the non linear interactions of subfilter scales between themselves are small compared to their distortions by the resolved scales such an assumption results in a linear stochastic equation for the subfilter scales which can be numerically solved by a decomposition of the subfilter scales into localized wave packets the wave packets are randomly produced by the smallest of the resolved scales they are further transported by the resolved scale velocity and they have wavenumbers and amplitudes which evolve according to the resolved strain performance of our model is compared with direct numerical simulations of decaying and forced turbulence for the same resolution numerical simulations using our model allow for a significant reduction of the computational time of the order of 100 in the case we consider and allow to achieve of significantly larger reynolds number than the direct method

decoherence from internal degrees of freedom for clusters of mesoparticles a hierarchy of master equations a mesoscopic evolution equation for an ensemble of mesoparticles follows from the elimination of internal degrees of freedom if the system is composed of a hierarchy of scales then the reduction procedure could be worked repeatedly and the characterization of this iterating method is carried out namely a prescription describing a discrete hierarchy of master equations for the density operator is obtained decoherence follows from the irreversible coupling between the system defined by mesoscopic variables and internal degrees of freedom we briefly discuss the existence of systems with the same dynamics laws at different scales we made an explicit calculation for an ensemble of particles with internal harmonic interaction in an external anharmonic field new conditions related to the semiclassical limit for mesoscopic systems wigner function are conjectured

a sparse mode spectral method for the simulation of turbulent flows we propose a new algorithm belonging to the family of the sparse mode spectral method to simulate turbulent flows in this method the number of fourier modeskincreases withkmore slowly thankd 1in dimensiond while retaining the advantage of the fast fourier transform examples of applications of the algorithm are given for the one dimensional burgers equation and two dimensional incompressible mhd flows

the first pontryagin class of a quadratic lie 2 algebroid in this paper we first give a detailed study on the structure of a transitive lie 2 algebroid and describe a transitive lie 2 algebroid using a morphism from the tangent lie algebroid t m to a strict lie 3 algebroid constructed from derivations then we introduce the notion of a quadratic lie 2 algebroid and define its first pontryagin class which is a cohomology class in h5 m associated to a clwx 2 algebroid there is a quadratic lie 2 algebroid naturally conversely we show that the first pontryagin class of a quadratic lie 2 algebroid is the obstruction class of the existence of a clwx extension finally we construct a quadratic lie 2 algebroid from a trivial principle 2 bundle with a gamma connection and show that its first pontryagin class is trivial

reference state for arbitrary u consistent subspace the reduced dynamics of the system s interacting with the environment e is not given by a linear map in general however if it is given by a linear map then this map is also hermitian in order that the reduced dynamics of the system is given by a linear hermitian map there must be some restrictions on the set of possible initial states of the system environment or on the possible unitary evolutions of the whole se in this paper adding an ancillary reference space r we assign to each convex set of possible initial states of the system environment for which the reduced dynamics is hermitian a tripartite state which we call the reference state such that the set is given as the steered states from the reference state the set of possible initial states of the system is also given as the steered set from a bipartite reference state the relation between these two reference states is as where is the identity map on r and is a hermitian assignment map from s to se as an important consequence of introducing the reference state we generalize the result of buscemi 2014 phys rev lett 113 140502 we show that for a u consistent subspace the reduced dynamics of the system is completely positive for arbitrary unitary evolution of the whole system environment u if and only if the reference state is a markov state in addition we show that the evolution of the set of system environment system states is determined by the evolution of the reference state

virtues and limitations of markovian master equations with a time dependent generator a markovian master equation with time dependent generator is constructed that respects basic constraints of quantum mechanics in particular the von neumann conditions for the case of a two level system bloch equations with time dependent parameters are obtained necessary conditions on the latter are formulated by employing a time local counterpart of the nakajima zwanzig equation we establish a relation with unitary dynamics we also discuss the relation with the weak coupling limit on the basis of a uniqueness theorem a standard form for the generator of time local master equations is proposed the jaynes cummings model with atomic damping is solved the solution explicitly demonstrates that reduced dynamics can be described by time local master equations only on a finite time interval this limitation is caused by divergencies in the generator a limit of maximum entropy is presented that corroborates the foregoing statements a second limiting case demonstrates that divergencies may even occur for small perturbations of the weak coupling regime

large time behavior and asymptotic stability of the 2d euler and linearized euler equations abstract we study the asymptotic behavior and the asymptotic stability of the 2d euler equations and of the 2d linearized euler equations close to parallel flows we focus on flows with spectrally stable profiles u y and with stationary streamlines y y 0 such that u y 0 0 a case that has not been studied previously we describe a new dynamical phenomenon the depletion of the vorticity at the stationary streamlines an unexpected consequence is that the velocity decays for large times with power laws similarly to what happens in the case of the orr mechanism for base flows without stationary streamlines the asymptotic behaviors of velocity and the asymptotic profiles of vorticity are theoretically predicted and compared with direct numerical simulations we argue on the asymptotic stability of this ensemble of flow profiles even in the absence of any dissipative mechanisms

a note on exponential families of distributions we show that an arbitrary probability distribution can be represented in an exponential form in physical contexts this implies that the equilibrium distribution of any classical or quantum dynamical system is expressible in a grand canonical form

positive maps positive polynomials and entanglement witnesses we link the study of positive quantum maps block positive operators and entanglement witnesses with problems related to multivariate polynomials for instance we show how indecomposable block positive operators relate to biquadratic forms that are not sums of squares although the general problem of describing the set of positive maps remains open in some particular cases we solve the corresponding polynomial inequalities and obtain explicit conditions for positivity

dynamics in spectral solutions of burgers equation for low values of the viscosity coefficient burgers equation can develop sharp discontinuities which are difficult to simulate in a computer oscillations can occur by discretization through spectral collocation methods due to gibbs phenomena under a dynamic point of view these instabilities are related to bifurcations arising to the discretized equation for different values of discretized points herein a study is performed of the dynamics and bifurcations occurring in the spectral solutions of burgers equation with symmetry several phenomena are observed from limit cycles strange attractors to the presence of bistability with two periodic attractors with a periodic attractor and a strange attractor and with two strange attractors also other stable equilibrium points can occur diverse from the ones corresponding to the solution of burgers equation

reduced dynamics need not be completely positive the reduced dynamics of a quantum system in contact with a reservoir is generally thought to be completely positive this is certainly true if product initial conditions are used to define the dynamics we show that with correlated initial conditions it need not be so in this case the dynamics can properly be defined only on a subset of initial system states extension by linearity to all possible initial states is trivially possible but the extension may not be physically realizable and may not even be positive let alone completely positive

structure function scaling of bounded two dimensional turbulence statistical properties of forced two dimensional turbulence generated in two different flow domains are investigated by numerical simulations the considered geometries are the square domain and the periodic channel domain both bounded by lateral no slip sidewalls the focus is on the direct enstrophy cascade range and how the statistical properties change in the presence of no slip boundaries the scaling exponents of the velocity and the vorticity structure functions are compared to the classical kraichnan batchelor leith kbl theory which assumes isotropy homogeneity and self similarity for turbulence scales between the forcing and dissipation scale our investigation reveals that in the interior of the flow domain turbulence can be considered statistically isotropic and locally homogeneous for the enstrophy cascade range but it is weakly intermittent however the scaling of the vorticity structure function indicates a steeper slope for the energy spectrum than the kbl theory predicts near the walls the turbulence is strongly anisotropic at all flow scales

differential geometry of gerbes abstract we define in a global manner the notion of a connective structure for a gerbe on a space x when the gerbe is endowed with trivializing data with respect to an open cover of x we describe this connective structure in two separate ways which extend from abelian to general gerbes the corresponding descriptions due to j l brylinski and n hitchin we give a global definition of the 3 curvature of this connective structure as a 3 form on x with values in the lie stack of the gauge stack of the gerbe we also study this notion locally in terms of more traditional lie algebra valued 3 forms the bianchi identity which the curvature of a connection on a principal bundle satisfies is replaced here by a more elaborate equation