global weak solution to the inhomogeneous navier stokes vlasov equations abstract the inhomogeneous navier stokes vlasov equations for fluid particle flows are considered in the three dimensional space the coupling in the fluid particle system arises from the drag force in the fluid equations and the acceleration in the vlasov equation an initial boundary value problem is studied in a bounded domain with large initial data the existence of global weak solution is established through an approximation scheme a fixed point argument energy estimates and a weak convergence method

quantum macrostates equivalence of ensembles and an h theorem before the thermodynamic limit macroscopic averages need not commute for a quantum system as a consequence aspects of macroscopic fluctuations or of constrained equilibrium require a careful analysis when dealing with several observables we propose an implementation of ideas that go back to john von neumann s writing about the macroscopic measurement we apply our scheme to the relation between macroscopic autonomy and an h theorem and to the problem of equivalence of ensembles in particular we show how the latter is related to the asymptotic equipartition theorem the main point of departure is an expression of a law of large numbers for a sequence of states that start to concentrate as the size of the system gets larger on the macroscopic values for the different macroscopic observables deviations from that law are governed by the entropy

robust estimation of egomotion from normal flow this paper investigates the robustness of an algorithm due to horn and weldon 1988 for recovery of egomotion from optic flow assuming only normal components of flow vectors are availableand that 3d angular velocity is known tight constraints can be constructed on the direction of translational motion or equivalently on the focus of expansion in practice however this is unacceptably restrictive some allowance must be made for uncertainty in angular velocity we show that the algorithm can indeed be extended to cope with such uncertainty with graceful degradation in accuracy of estimated position of the focus of expansion the shape of the error distribution depends on whether the focus of expansion is inside or outside the field of view if it is inside the error distribution is isotropic as it moves outside the distribution becomes increasingly anisotropic results from an implementation of the algorithm confirm the validity of the error bounds

efficient computation of gabor filter based multiresolution responses abstract multiresolution representation in machine vision systems provides a means to detect analyze and interpret the information content of an image at multiple resolutions the pyramidal representation of images suggested by burt and crowley and the hierarchical construction of orientation and velocity tuned filters developed by fleet and jepson are some of the examples for multiresolution representation of image details in recent years gabor filter based methods have been suggested by several researchers for machine vision applications such as edge detection texture classification and optical flow estimation these applications require generating a family of gabor filters tuned to several resolutions and orientations and computing their responses the computation of gabor filter responses at multiple resolutions and orientations is a very computationally intensive task two efficient schemes for computing gabor filter based multiresolution responses are proposed the first scheme namely recursive filtering method generates a family of gabor filters and their responses starting from a high resolution and proceeding towards the lowest resolution in steps of an octave the second approach namely successive sampling method generates the same responses in the reverse order in both these methods the symmetric asymmetric and wavelet nature of gabor filters are exploited in order to speed up the computation the applicability and usefulness of the schemes are established through experimental results special purpose architectures are proposed to implement the proposed techniques in hardware in order to further speed up the computation

dynamic theory of suspensions with brownian effects we consider a suspension of particles in a fluid settling under the influence of gravity and dispersing by brownian motion a mathematical description is provided by the stokes equations and a fokker planck equation for the one particle phase space density this is a nonlinear system that depends on a number of parametric functions of the spatial concentration of the particles these functions are known only empirically or for dilute suspensions we analyze the system its stability its asymptotic behavior under different scalings and its validity from more microscopic description we summarize our conclusions at the end

local random quantum circuits are approximate polynomial designs we prove that local random quantum circuits acting on n qubits composed of o t10n2 many nearest neighbor two qubit gates form an approximate unitary t design previously it was unknown whether random quantum circuits were a t design for any t 3 the proof is based on an interplay of techniques from quantum many body theory representation theory and the theory of markov chains in particular we employ a result of nachtergaele for lower bounding the spectral gap of frustration free quantum local hamiltonians a quasi orthogonality property of permutation matrices a result of oliveira which extends to the unitary group the path coupling method for bounding the mixing time of random walks and a result of bourgain and gamburd showing that dense subgroups of the special unitary group composed of elements with algebraic entries are copy tensor product expanders we also consider pseudo randomness properties of local random quantum circuits of small depth and prove that circuits of depth o t10n constitute a quantum t copy tensor product expander the proof also rests on techniques from quantum many body theory in particular on the detectability lemma of aharonov arad landau and vazirani we give applications of the results to cryptography equilibration of closed quantum dynamics and the generation of topological order in particular we show the following pseudo randomness property of generic quantum circuits almost every circuit u of size o nk on n qubits cannot be distinguished from a haar uniform unitary by circuits of size o n k 9 11 that are given oracle access to u

explicit constructions of unitary transformations between equivalent irreducible representations irreducible representations irreps of a finite group g are equivalent if there exists a similarity transformation between them in this paper we describe an explicit algorithm for constructing this transformation between a pair of equivalent irreps assuming that we are given an algorithm for computing the matrix elements of these irreps along the way we derive a generalization of the classical orthogonality relations for matrix elements of irreps of finite groups we give an explicit form of such unitary matrices for the important case of conjugated young yamanouchi representations when our group g is the symmetric group s n

bootstrap resampling for image registration uncertainty estimation without ground truth we address the problem of estimating the uncertainty of pixel based image registration algorithms given just the two images to be registered for cases when no ground truth data is available our novel method uses bootstrap resampling it is very general applicable to almost any registration method based on minimizing a pixel based similarity criterion we demonstrate it using the ssd sad correlation and mutual information criteria we show experimentally that the bootstrap method provides better estimates of the registration accuracy than the state of the art cramer rao bound method additionally we evaluate also a fast registration accuracy estimation frae method which is based on quadratic sensitivity analysis ideas and has a negligible computational overhead frae mostly works better than the cramer rao bound method but is outperformed by the bootstrap method

hydrodynamic limit for the inhomogeneous incompressible navier stokes vlasov fokker planck equations abstract in this paper we study the hydrodynamic limit for the inhomogeneous incompressible navier stokes vlasov fokker planck equations in a two or three dimensional bounded domain when the initial density is bounded away from zero the proof relies on the relative entropy argument to obtain the strong convergence of macroscopic density of the particles n in l 0 t l 1 which extends the works of goudon jabin vasseur 15 and mellt vasseur 26 to inhomogeneous incompressible navier stokes vlasov fokker planck equations precisely the relative entropy estimates in 15 and 26 give the strong convergence of u and n and n respectively however we only obtain the strong convergence of n and u from the relative entropy estimate and we use another way to obtain the strong convergence of via the convergence of u furthermore when the initial density may vanish taking advantage of compactness result l m h 1 of orlicz spaces in 2d we obtain the convergence of n in l 0 t h 1 which is used to obtain the relative entropy estimate thus we also show the hydrodynamic limit for 2d inhomogeneous incompressible navier stokes vlasov fokker planck equations when there is initial vacuum

comutations underlying the measuremnt of visual motion abstract the organization of movement in a changing image provides a valuable source of information for analyzing the environment in terms of objects their motion in space and their three dimensional structure a description of this movement is not provided to our visual system directly however it must be inferred from the pattern of changing intensity that reaches the eye this paper examines the problem of motion measurement which we formulate as the computation of an instantaneous two dimensional velocity field initial motion measurements occur at the location of significant intensity changes as suggested by marr and ullman 1 these measurements provide only one component of velocity and must be integrated to compute the two dimensional velocity field a fundamental problem for this integration is that motion is not determined uniquely from the changing image an additional constraint of smoothness of the velocity field is formulated based on the physical assumption that surfaces are generally smooth allowing the computation of a unique solution a theoretical analysis of the conditions under which this computation yields the correct velocity field suggests that the solution is physically plausible empirical studies show the results to be consistent with human motion perception

subsystem eth motivated by the qualitative picture of canonical typicality we propose a refined formulation of the eigenstate thermalization hypothesis eth for chaotic quantum systems the new formulation which we refer to as subsystem eth is in terms of the reduced density matrix of subsystems this strong form of eth outlines the set of observables defined within the subsystem for which it guarantees eigenstate thermalization we discuss the limits when the size of the subsystem is small or comparable to its complement in the latter case we outline the way to calculate the leading volume proportional contribution to the von neumann and renyi entanglment entropies finally we provide numerical evidence for the proposal in the case of a one dimensional ising spin chain

a morphological affine and galilean invariant scale space for movies we study a model of multiscale analysis or scale space applied to movies this model comes from a thorough formalization that has been done in the theory of scale space of static image this formulation has led one to associate with each multiscale analysis a partial differential equation pde we examine the case of movies and insist on the motion aspects more precisely it has been proved by alvarez guichard lions and morel 1993 that there exists a unique affine and morphological and galilean invariant scale space for movies the amg model this model is described by a partial differential equation we focus on terms appearing in that equation we show that this model provides a reliable definition of an optical multiscale acceleration at the practical level scale is interpreted as a way of characterizing reliable trajectories as we prove by experiments the amg model is a riddle for decimating spurious trajectories due to any kinds of nonadditive impurities and noise simple discrete formulae are given to implement the model

concentration of haar measures with an application to random matrices abstract we show that the mixing times of random walks on compact groups can be used to obtain concentration inequalities for the respective haar measures as an application we derive a concentration inequality for the empirical distribution of eigenvalues of sums of random hermitian matrices with possible applications in free probability the advantage over existing techniques is that the new method can deal with functions that are non lipschitz or even discontinuous with respect to the usual metrics

motion parameter estimation from global flow field data presented are two methods for the determination of the parameters of motion of a sensor given the vector flow field induced by an imaging system governed by a perspective transformation of a rigid scene both algorithms integrate global data to determine motion parameters the first the flow circulation algorithm determines the rotational parameters the second the foe search algorithm determines the translational parameters of the motion independently of the first algorithm several methods for determining when the function has the appropriate form are suggested one method involves filtering the function by a collection of circular surround zero mean receptive fields the other methods project the function onto a linear space of quadratic polynomials and measures the distance between the two functions the error function for the first two methods is a quadratic polynomial of the candidate position yielding a very rapid search strategy

ranging through gabor logons a consistent hierarchical approach in this work the correspondence problem in stereo vision is handled by matching two sets of dense feature vectors inspired by biological evidence these feature vectors are generated by a correlation between a bank of gabor sensors and the intensity image the sensors consist of two dimensional gabor filters at various scales spatial frequencies and orientations which bear close resemblance to the receptive field profiles of simple v1 cells in visual cortex a hierarchical stochastic relaxation method is then used to obtain the dense stereo disparities unlike traditional hierarchical methods for stereo feature based hierarchical processing yields consistent disparities to avoid false matchings due to static occlusion a dual matching based on the imaging geometry is used

approach to thermal equilibrium of macroscopic quantum systems we consider an isolated macroscopic quantum system let mathcal h be a microcanonical energy shell i e a subspace of the system s hilbert space spanned by the finitely many energy eigenstates with energies between e and e ensuremath delta e the thermal equilibrium macrostate at energy e corresponds to a subspace mathcal h eq of mathcal h such that text dim text mathcal h eq text dim text mathcal h is close to 1 we say that a system with state vector ensuremath psi mathcal h is in thermal equilibrium if ensuremath psi is close to mathcal h eq we show that for typical hamiltonians with given eigenvalues all initial state vectors ensuremath psi 0 evolve in such a way that ensuremath psi t is in thermal equilibrium for most times t this result is closely related to von neumann s quantum ergodic theorem of 1929

the design and use of steerable filters the authors present an efficient architecture to synthesize filters of arbitrary orientations from linear combinations of basis filters allowing one to adaptively steer a filter to any orientation and to determine analytically the filter output as a function of orientation steerable filters may be designed in quadrature pairs to allow adaptive control over phase as well as orientation the authors show how to design and steer the filters and present examples of their use in the analysis of orientation and phase angularly adaptive filtering edge detection and shape from shading one can also build a self similar steerable pyramid representation the same concepts can be generalized to the design of 3 d steerable filters

irreversibility and entropy production in transport phenomena ii statistical mechanical theory on steady states including thermal disturbance and energy supply abstract some general aspects of nonlinear transport phenomena are discussed on the basis of two kinds of formulations obtained by extending kubo s perturbational scheme of the density matrix and zubarev s non equilibrium statistical operator formulation both formulations are extended up to infinite order of an external force in compact forms and their relationship is clarified through a direct transformation in order to make it possible to apply these formulations straightforwardly to thermal disturbance its mechanical formulation is given in a more convenient form than luttinger s formulation by introducing the concept of a thermal field e t which corresponds to the temperature gradient and by defining its conjugate heat operator a h j h j r j for a local internal energy h j of the thermal particle j this yields a transparent derivation of the thermal conductivity of the kubo form and the entropy production d s d t irr e t 2 t mathematical aspects of the non equilibrium density matrix will also be discussed in paper i m suzuki physica a 390 2011 1904 the symmetry separated von neumann equation with relaxation terms extracting generated heat outside the system was introduced to describe the steady state of the system in this formulation of the steady state the internal energy h 0 t is time independent but the field energy h 1 t a t f decreases as time t increases to overcome this problem such a statistical mechanical formulation is proposed here as includes energy supply to the system from outside by extending the symmetry separated von neumann equation given in paper i this yields a general theory based on the density matrix formulation on a steady state with energy supply inside and heat extraction outside and consequently with both h 0 t and h 1 t constant furthermore this steady state gives a positive entropy production the present general formulation of the current yields a compact expression of the time derivative of entropy production which yields the plausible justification of the principle of minimum entropy production in the steady state even for nonlinear responses

asymptotic preserving schemes for kinetic fluid modeling of disperse two phase flows abstract we consider a system coupling the incompressible navier stokes equations to the vlasov fokker planck equation such a problem arises in the description of particulate flows we design a numerical scheme to simulate the behavior of the system this scheme is asymptotic preserving thus efficient in both the kinetic and hydrodynamic regimes it has a numerical stability condition controlled by the non stiff convection operator with an implicit treatment of the stiff drag term and the fokker planck operator yet consistent to a standard asymptotic preserving fokker planck solver or an incompressible navier stokes solver only the conjugate gradient method and fast poisson and helmholtz solvers are needed numerical experiments are presented to demonstrate the accuracy and asymptotic behavior of the scheme with several interesting applications

the feasibility of motion and structure from noisy time varying image velocity information this research addresses the problem of noise sensitivity inherent in motion and structure algorithms the motion and structure paradigm is a two step process first we measure image velocities and perhaps their spatial and temporal derivatives are obtained from time varying image intensity data and second we use these data to compute the motion of a moving monocular observer in a stationary environment under perspective projection relative to a single 3 d planar surface the first contribution of this article is an algorithm that uses time varying image velocity information to compute the observer s translation and rotation and the normalized surface gradient of the 3 d planar surface the use of time varying image velocity information is an important tool in obtaining a more robust motion and structure calculation the second contribution of this article is an extensive error analysis of the motion and structure problem any motion and structure algorithm that uses image velocity information as its input should exhibit error sensitivity behavior compatible with the results reported here we perform an average and worst case error analysis for four types of image velocity information full and normal image velocities and full and normal sets of image velocity and its derivatives these derivatives are simply the coefficients of a truncated taylor series expansion about some point in space and time the main issues we address here are just how sensitive is a motion and structure computation in the presence of noisy input or alternately how accurate must our image velocity information be how much and what type of input data is needed and under what circumstances is motion and structure feasible that is when can we be sure that a motion and structure computation will produce usable results we base our answers on a numerical error analysis we conduct for a large number of motions

matching two perspective views a computational approach to image matching is described it uses multiple attributes associated with each image point to yield a generally overdetermined system of constraints taking into account possible structural discontinuities and occlusions in the algorithm implemented intensity edgeness and cornerness attributes are used in conjunction with the constraints arising from intraregional smoothness field continuity and discontinuity and occlusions to compute dense displacement fields and occlusion maps along the pixel grids the intensity edgeness and cornerness are invariant under rigid motion in the image plane in order to cope with large disparities a multiresolution multigrid structure is employed coarser level edgeness and cornerness measures are obtained by blurring the finer level measures the algorithm has been tested on real world scenes with depth discontinuities and occlusions a special case of two view matching is stereo matching where the motion between two images is known the algorithm can be easily specialized to perform stereo matching using the epipolar constraint

estimation of motion from sequential images using integral constraints abstract a novel method for estimating nonuniform motion from sequential images is presented which is based on integral brightness constancy constraints the equations which transform arbitrary integrals between sequential images are expressed as a function of the displacement field and intensity changes the apparent displacement field is then computed by iterative projections onto the solution space of each linearized transformation equation some properties of this technique are demonstrated on a synthetic image pair realistic motion estimation is also demonstrated using sequential tagged cine magnetic resonance images

hierarchical construction of orientation and velocity selective filters as a step towards the early measurement of visual primitives the authors outline design criteria for the extraction of orientation and velocity information and present a variety of tools useful in the construction of simple linear filters a hierarchical parallel processing scheme is used in which nodes compute a weighted sum of inputs from within a small spatio temporal neighborhood the resulting scheme is easily analyzed and provides mechanisms sensitive to narrow ranges of both image velocity and orientation the hierarchical approach in combination with separability in the first levels yields an efficient implementation

optical flow using spatiotemporal filters a model is presented consonant with current views regarding the neurophysiology and psychophysics of motion perception that combines the outputs of a set of spatiotemporal motion energy filters to estimate image velocity a parallel implementation computes a distributed representation of image velocity a measure of image flow uncertainty is formulated preliminary results indicate that this uncertainty measure may be used to recognize ambiguity due to the aperture problem the model appears to deal with the aperture problem as well as the human visual system since it extracts the correct velocity for some patterns that have large differences in contrast at different spatial orientations

a new motion parameter estimation algorithm based on the continuous wavelet transform this paper presents a novel motion parameter estimation me algorithm based on the spatio temporal continuous wavelet transform cwt the multidimensional nature of the cwt allows for the definition of a multitude of energy densities by integrating over a subset of the cwt parameter space three energy densities are used to estimate motion parameters by sequentially optimizing a state vector composed of velocity position and size parameters this optimization is performed on a frame by frame basis allowing the algorithm to track moving objects the me algorithm is designed to address real world challenges encountered in the defense industry and traffic monitoring scenarios such as attaining robust performance in noise and handling obscuration and crossing object trajectories

a frequency domain algorithm for multiframe detection and estimation of dim targets an algorithm for detecting moving targets by imaging sensors and estimating their trajectories is proposed the algorithm is based on directional filtering in the frequency domain using a bank of filters for all possible target directions the directional filtering effectively integrates the target signal resulting in an improved signal to noise ratio working in the frequency domain facilitates a considerable reduction in computational requirements compared to time domain algorithms the algorithm is described in detail and its false alarm and detection probabilities are analyzed

spatiotemporal wavelets a group theoretic construction for motion estimation and tracking this paper presents a new group theoretic perspective for signal and image analysis it addresses the problem of motion analysis and trajectory determination the construction exploits the properties of motion parameters to be structured in lie algebras and lie groups the motion models are provided by the group structure which carries an entire theoretical build up this theoretical construction is based on a natural association of lie group representations minimum mean squared error estimations and variational principles of optimality these concepts naturally provide a corresponding association of tools based on continuous wavelet transforms kalman filters and lagrangians these tools result in highly parallelizable algorithms based on ffts gradients and dynamic programming the core of the construction is made of spatiotemporal continuous wavelets that are tuned to the motion parameters to perform motion estimation the motion parameters consist of scale orientation location velocity acceler

typicality of pure states randomly sampled according to the gaussian adjusted projected measure consider a mixed quantum mechanical state describing a statistical ensemble in terms of an arbitrary density operator of low purity tr 2 1 and yielding the ensemble averaged expectation value tr a for any observable a assuming that the given statistical ensemble is generated by randomly sampling pure states according to the corresponding so called gaussian adjusted projected measure goldstein et al in j stat phys 125 1197 2006 the expectation value a is shown to be extremely close to the ensemble average tr a for the overwhelming majority of pure states and any experimentally realistic observable a in particular such a typicality property holds whenever the hilbert space of the system contains a high dimensional subspace with the property that all are realized with equal probability and all other are excluded

regularization of inverse visual problems involving discontinuities inverse problems such as the reconstruction problems that arise in early vision tend to be mathematically ill posed through regularization they may be reformulated as well posed variational principles whose solutions are computable standard regularization theory employs quadratic stabilizing functionals that impose global smoothness constraints on possible solutions discontinuities present serious difficulties to standard regularization however since their reconstruction requires a precise spatial control over the smoothing properties of stabilizers this paper proposes a general class of controlled continuity stabilizers which provide the necessary control over smoothness these nonquadratic stabilizing functionals comprise multiple generalized spline kernels combined with noncontinuous continuity control functions in the context of computational vision they may be thought of as controlled continuity constraints these generic constraints are applicable to visual reconstruction problems that involve both continuous regions and discontinuities for which global smoothness constraints fail

deformations of polyhedra and polygons by the unitary group we introduce the set of framed convex polyhedra with n faces as the symplectic quotient c2n su 2 a framed polyhedron is then parametrized by n spinors living in c2 satisfying suitable closure constraints and defines a usual convex polyhedron plus extra u 1 phases attached to each face we show that there is a natural action of the unitary group u n on this phase space which changes the shape of faces and allows to map any framed polyhedron onto any other with the same total boundary area this identifies the space of framed polyhedra to the grassmannian space u n su 2 u n 2 we show how to write averages of geometrical observables polynomials in the faces area and the angles between them over the ensemble of polyhedra distributed uniformly with respect to the haar measure on u n as polynomial integrals over the unitary group and we provide a few methods to compute these integrals systematically we also use the itzykson zuber formula from matrix models as the generating function

smoothness of wave functions in thermal equilibrium we consider the thermal equilibrium distribution at inverse temperature or canonical ensemble of the wave function of a quantum system since l2 spaces contain more nondifferentiable than differentiable functions and since the thermal equilibrium distribution is very spread out one might expect that has probability zero to be differentiable however we show that for relevant hamiltonians the contrary is the case with probability 1 is infinitely often differentiable and even analytic we also show that with probability 1 lies in the domain of the hamiltonian

quantum analysis non commutative differential and integral calculi a new scheme of quantum analysis namely a non commutative calculus of operator derivatives and integrals is introduced this treats differentiation of an operator valued function with respect to the relevant operator in a banach space in this new scheme operator derivatives are expressed in terms of the relevant operator and its inner derivation explicitly derivatives of hyperoperators are also defined some possible applications of the present calculus to quantum statistical physics are briefly discussed

a voting based computational framework for visual motion analysis and interpretation most approaches for motion analysis and interpretation rely on restrictive parametric models and involve iterative methods which depend heavily on initial conditions and are subject to instability further difficulties are encountered in image regions where motion is not smooth typically around motion boundaries this work addresses the problem of visual motion analysis and interpretation by formulating it as an inference of motion layers from a noisy and possibly sparse point set in a 4d space the core of the method is based on a layered 4d representation of data and a voting scheme for affinity propagation the inherent problem caused by the ambiguity of 2d to 3d interpretation is usually handled by adding additional constraints such as rigidity however enforcing such a global constraint has been problematic in the combined presence of noise and multiple independent motions by decoupling the processes of matching outlier rejection segmentation and interpretation we extract accurate motion layers based on the smoothness of image motion and then locally enforce rigidity for each layer in order to infer its 3d structure and motion the proposed framework is noniterative and consistently handles both smooth moving regions and motion discontinuities without using any prior knowledge of the motion model

on the foundations of relaxation labeling processes a large class of problems can be formulated in terms of the assignment of labels to objects frequently processes are needed which reduce ambiguity and noise and select the best label among several possible choices relaxation labeling processes are just such a class of algorithms they are based on the parallel use of local constraints between labels this paper develops a theory to characterize the goal of relaxation labeling the theory is founded on a definition of con sistency in labelings extending the notion of constraint satisfaction in certain restricted circumstances an explicit functional exists that can be maximized to guide the search for consistent labelings this functional is used to derive a new relaxation labeling operator when the restrictions are not satisfied the theory relies on variational cal culus it is shown that the problem of finding consistent labelings is equivalent to solving a variational inequality a procedure nearly identical to the relaxation operator derived under restricted circum stances serves in the more general setting further a local convergence result is established for this operator the standard relaxation labeling formulas are shown to approximate our new operator which leads us to conjecture that successful applications of the standard methods are explainable by the theory developed here observations about con vergence and generalizations to higher order compatibility relations are described

approach to typicality in many body quantum systems the recent discovery that for large hilbert spaces almost all that is typical hamiltonians have eigenstates that place small subsystems in thermal equilibrium has shed much light on the origins of irreversibility and thermalization here we give numerical evidence that many body lattice systems generically approach typicality as the number of subsystems is increased and thus provide further support for the eigenstate thermalization hypothesis our results indicate that the deviation of many body systems from typicality decreases exponentially with the number of systems further by averaging over a number of randomly selected nearest neighbor interactions we obtain a powerlaw for the atypicality as a function of the hilbert space dimension distinct from the power law possessed by random hamiltonians

local ergodicity in coupled harmonic vibrators classical and quantal treatments ensemble time ergodicity is proven under some restrictive assumptions for a classical system comprising interacting harmonic oscillators an atom in a monatomic chain or lattice is shown to behave ergodically in the sense that the time average behavior of a lattice point is identical to the ensemble average of the behavior of a lattice point at any long time in large excess of the inverse vibrational frequencies this equivalence for local observables differs from the fermi pasta ulam result for mode energies which are non local then the analogous quantal result is derived with extensions to wider instances relationships to canonical typicality and to the eigenstate thermalization hypothesis are discussed and possibilities of experimental verifications of the results are indicated

global existence and large time behavior of classical solutions to the euler maxwell vlasov fokker planck system abstract we consider global classical solutions to the cauchy problem for an euler maxwell vlasov fokker planck system which is a fluid particle model describe the evolutions of disperse two phase flows in these two phase flows the compressible euler maxwell equations modeling a dense phase fluid and the vlasov fokker planck equation for the dispersed phase particles which is usually considered from the statistical view of point they are coupled through the friction force global existence of classical solutions to the cauchy problem in r 3 is established when initial data is a small perturbation of some given equilibrium the algebraic rate of convergence of solution toward the equilibrium state is also obtained under additional conditions on initial data the proof is based on the classical energy estimates and fourier multiplier technique which are considerably complicated and some new ideas and techniques are thus required

local random quantum circuits are approximate polynomial designs numerical results we numerically investigate the statement that local random quantum circuits acting on n qubits composed of polynomially many nearest neighbor two qubit gates form an approximate unitary poly n design brandao et al 2012 arxiv 1208 0692 using a group theory formalism spectral gaps that give a ratio of convergence to a given t design are evaluated for a different number of qubits n up to 20 and degrees t t 2 3 4 and 5 improving previously known results for n 2 in the case of t 2 and 3 their values lead to the conclusion that the previously used lower bound that bounds spectral gaps values may give very little information about the real situation and in most cases only tells us that a gap is closed we compare our results to another lower bounding technique again showing that its results may not be tight

numerical evidence for approximate consistency and markovianity of some quantum histories in a class of finite closed spin systems closed quantum systems obey the schrodinger equation whereas nonequilibrium behavior of many systems is routinely described in terms of classical markovian stochastic processes evidently there are fundamental differences between those two types of behavior we discuss the conditions under which the unitary dynamics may be mapped onto pertinent classical stochastic processes this is first principally addressed based on the notions of consistency and markovianity numerical data are presented that show that the above conditions are to good approximation fulfilled for heisenberg type spin models comprising 12 20 spins the accuracy to which these conditions are met increases with system size

weakly non ergodic statistical physics for weakly non ergodic systems the probability density function of a time average observable overline mathcal o is f alpha overline mathcal o 1 over pi lim epsilon to 0 mbox im sum j 1 l p mathrm eq j overline mathcal o mathcal o j i epsilon alpha 1 over sum j 1 l p mathrm eq j overline mathcal o mathcal o j i epsilon alpha where mathcal o j is the value of the observable when the system is in state j 1 l pjeq is the probability that a member of an ensemble of systems occupies state j in equilibrium for a particle undergoing a fractional diffusion process in a binding force field with thermal detailed balance conditions pjeq is boltzmann s canonical probability within the unbiased sub diffusive continuous time random walk model the exponent 0 1 is the anomalous diffusion exponent x2 t found for free boundary conditions when 1 ergodic statistical mechanics is recovered lim alpha to 1 f alpha overline mathcal o delta overline mathcal o langle mathcal o rangle we briefly discuss possible physical applications in single particle experiments

about the role of chaos and coarse graining in statistical mechanics abstract we discuss the role of ergodicity and chaos for the validity of statistical laws in particular we explore the basic aspects of chaotic systems with emphasis on the finite resolution on systems composed of a huge number of particles

quantum equilibrium and the origin of absolute uncertainty what is randomness probability certainty knowledge these are old and difficult questions and we shall not focus on them here nonetheless we shall obtain sharp striking conclusions concerning the relationship between these concepts

on the distribution of the wave function for systems in thermal equilibrium for a quantum system a density matrix that is not pure can arise via averaging from a distribution of its wave function a normalized vector belonging to its hilbert space while itself does not determine a unique additional facts such as that the system has come to thermal equilibrium might it is thus not unreasonable to ask which if any corresponds to a given thermodynamic ensemble to answer this question we construct for any given density matrix a natural measure on the unit sphere in denoted gap we do this using a suitable projection of the gaussian measure on with covariance we establish some nice properties of gap and show that this measure arises naturally when considering macroscopic systems in particular we argue that it is the most appropriate choice for systems in thermal equilibrium described by the canonical ensemble density matrix 1 z exp h gap may also be relevant to quantum chaos and to the stochastic evolution of open quantum systems where distributions on are often used

the quantum canonical ensemble the phase space of quantum mechanics can be viewed as the complex projective space cpn endowed with a kahlerian structure given by the fubini study metric and an associated symplectic form we can then interpret the schrodinger equation as generating a hamiltonian dynamics on based upon the geometric structure of the quantum phase space we introduce the corresponding natural microcanonical and canonical ensembles the resulting density matrix for the canonical ensemble differs from the density matrix of the conventional approach as an illustration the results are applied to the case of a spin one half particle in a heat bath with an applied magnetic field

minimal geodesics on groups of volume preserving maps and generalized solutions of the euler equations the three dimensional motion of an incompressible inviscid fluid is classically described by the euler equations but can also be seen following arnold 1 as a geodesic on a group of volume preserving maps local existence and uniqueness of minimal geodesics have been established by ebin and marsden 16 in the large for a large class of data the existence of minimal geodesics may fail as shown by shnirelman 26 for such data we show that the limits of approximate solutions are solutions of a suitable extension of the euler equations or equivalently are sharp measure valued solutions to the euler equations in the sense of diperna and majda 14 1999 john wiley sons inc

from quantum dynamics to the canonical distribution general picture and a rigorous example derivation of the canonical or boltzmann distribution based only on quantum dynamics is discussed consider a closed system which consists of a mutually interacting subsystem and a heat bath and assume that the whole system is initially in a pure state which can be far from equilibrium with small energy fluctuation under the hypothesis of equal weights for eigenstates we derive the canonical distribution in the sense that at sufficiently large and typical time the instantaneous quantum mechanical expectation value of an arbitrary operator of the subsystem is almost equal to the desired canonical expectation value we present a class of examples in which the above derivation can be rigorously established without any unproven hypotheses

on the explicit constructions of certain unitary t designs unitary t designs are good finite subsets of the unitary group ug d that approximate the whole unitary group ug d well unitary t designs have been applied in randomized benchmarking tomography quantum cryptography and many other areas of quantum information science if a unitary t design itself is a group then it is called a unitary t group although it is known that unitary t designs in ug d exist for any t and d the unitary t groups do not exist for t geq 4 if d geq 3 as it is shown by guralnick tiep 2005 and bannai navarro rizo tiep bnrt 2018 explicit constructions of exact unitary t designs in ug d are not easy in general in particular explicit constructions of unitary 4 designs in ug 4 have been an open problem in quantum information theory we prove that some exact unitary t 1 designs in the unitary group ug d are constructed from unitary t groups in ug d that satisfy certain specific conditions based on this result we specifically construct exact unitary 3 designs in ug 3 from the unitary 2 group sl 3 2 in ug 3 and also unitary 4 designs in ug 4 from the unitary 3 group sp 4 3 in ug 4 numerically we also discuss some related problems and a few applications to physics problems

a computational framework and an algorithm for the measurement of visual the robust measurement of visual motion from digitized image sequences has been an important but difficult problem in computer vision this paper describes a hierarchical computational framework for the determination of dense displacement fields from a pair of images and an algorithm consist ent with that framework our framework is based on the separation of the image intensity information as well as the process of measuring motion according to scale the large scale intensity information is first used to obtain rough estimates of image motion which are then refined by using intensity information at smaller scales the estimates are in the form of displacement or velocity vectors for pixels and are accompanied by a direction dependent confidence measure a smoothness constraint is employed to propagate the measurements with high confidence to their neigboring areas where the confidences are low at all levels the computations are pixel parallel uniform across the image and based on information from a small neighborhood of a pixel for our algorithm the local displacement vectors are determind by mini mizing the sum of squared differences ssd of intensities the confidence measures are derived from the shape of the ssd surface and the smoothness constraint is cast in the form of energy minimization results of applying our algorithm to pairs of real images are included in addition to our own

normal typicality and von neumann s quantum ergodic theorem we discuss the content and significance of john von neumann s quantum ergodic theorem qet of 1929 a strong result arising from the mere mathematical structure of quantum mechanics the qet is a precise formulation of what we call normal typicality i e the statement that for typical large systems every initial wave function 0 from an energy shell is normal it evolves in such a way that t t is for most t macroscopically equivalent to the micro canonical density matrix the qet has been mostly forgotten after it was criticized as a dynamically vacuous statement in several papers in the 1950s however we point out that this criticism does not apply to the actual qet a correct statement of which does not appear in these papers but to a different indeed weaker statement furthermore we formulate a stronger statement of normal typicality based on the observation that the bound on the deviations from the average specified by von neumann is unnecessarily coarse and a much tighter and more relevant bound actually follows from his proof

a unified approach to boundary perception edges textures and illusory contours a model consisting of a multistage system which extracts and groups salient features in the image at different spatial scales or frequencies is used in the first stage a gabor wavelet decomposition provides a representation of the image which is orientation selective and has optimal localization properties in space and frequency this decomposition is useful in detecting significant features such as step and line edges at different scales and orientations in the image following the wavelet transformation local competitive interactions are introduced to reduce the effects of noise and changes in illumination interscale interactions help in localizing the line ends and corners and play a crucial role in boundary perception the final stage groups similar features aiding in boundary completion the different stages can be identified with processing by simple complex and hypercomplex cells in the visual cortex of mammals experimental results demonstrate the performance of this model in detecting boundaries both real and illusory in real and synthetic images

computation and analysis of image motion a synopsis of current problems and methods the goal of this paper is to offer a structured synopsis of the problems in image motion computation and analysis and of the methods proposed exposing the underlying models and supporting assumptions a sufficient number of pointers to the literature will be given concentrating mostly on recent contributions emphasis will be on the detection measurement and segmentation of image motion tracking and deformable motion issues will be also addressed finally a number of related questions which could require more investigations will be presented

force estimation and prediction from time varying density images we present methods for estimating forces which drive motion observed in density image sequences using these forces we also present methods for predicting velocity and density evolution to do this we formulate and apply a minimum energy flow mef method which is capable of estimating both incompressible and compressible flows from time varying density images both the mef and force estimation techniques are applied to experimentally obtained density images spanning spatial scales from micrometers to several kilometers using density image sequences describing cell splitting for example we show that cell division is driven by gradients in apparent pressure within a cell using density image sequences of fish shoals we also quantify 1 intershoal dynamics such as coalescence of fish groups over tens of kilometers 2 fish mass flow between different parts of a large shoal and 3 the stresses acting on large fish shoals

convergence to equilibrium under a random hamiltonian we analyze equilibration times of subsystems of a larger system under a random total hamiltonian in which the basis of the hamiltonian is drawn from the haar measure we obtain that the time of equilibration is of the order of the inverse of the arithmetic average of the bohr frequencies to compute the average over a random basis we compute the inverse of a matrix of overlaps of operators which permute four systems we first obtain results on such a matrix for a representation of an arbitrary finite group and then apply it to the particular representation of the permutation group under consideration

microscopic origins of irreversible macroscopic behavior time asymmetric behavior as embodied in the second law of thermodynamics is observed in individual macroscopic systems it can be understood as arising naturally from time symmetric microscopic laws in accord with the ideas of thompson maxwell and boltzmann alternative explanations based on equating irreversible macroscopic behavior with the mixing type of behavior already present in the time evolution of ensembles probability distributions of certain systems having only a few degrees of freedom are in my opinion unnecessary misguided and misleading

analysis of multichannel narrow band filters for image texture segmentation a model for texture analysis and segmentation using multiple oriented channel filters is analyzed in the general framework several different arguments are applied leading to the conclusion that the two dimensional gabor filters possess strong optimality properties for this task properties of the multiple channel segmentation approach are analyzed in particular perturbations of textures from an ideal model are found to have important effects on the segmentation that can usually be ameliorated by simply preceding the segmentation process by a logarithmic operation and using a low pass postfilter prior to making region assignments the difficult problems of space variant textures and multiple component textures are also considered local spatial frequency estimation approaches are suggested that use the responses as constraints in estimating the locally emergent texture frequencies complex texture aggregates containing multiple shared frequency components can be analyzed if the textures are distinct and few in number

statistical description of small quantum systems beyond the weak coupling limit an explicit expression is derived for the statistical description of small quantum systems which are relatively weakly and directly coupled to only small parts of their environments the derived expression has a canonical form but is given by a renormalized self hamiltonian of the studied system which appropriately takes into account the influence of the system environment interaction in the case that the system has a narrow spectrum and the environment is sufficiently large the modification to the self hamiltonian usually has a mean field feature given by an environmental average of the interaction hamiltonian in other cases the modification may be beyond the mean field approximation

a contour based recovery of image flow iterative transformation method the authors present an iterative algorithm for the recovery of 2 d motion i e for the determination of a transformation that maps one image onto another the local ambiguity in measuring the motion of contour segments the aperture problem implies a reliance on measurements along the normal direction since the measured normal flow does not agree with the actual normal flow the full flow recovered from this erroneous flow also possesses substantial error and any attempt to recover the 3 d motion from such full flow fails the proposed method is based on the observation that a polynomial approximation of the image flow provides sufficient information for 3 d motion computation the use of an explicit flow model results in improved normal flow estimates through an iterative process the authors discuss the adequacy and the convergence of the algorithm the algorithm was tested on some synthetic and some simple natural time varying images the image flow recovered from this scheme is sufficiently accurate to be useful in 3 d structure and motion computation

universal time fluctuations in near critical out of equilibrium quantum dynamics out of equilibrium quantum systems display complex temporal patterns such time fluctuations are generically exponentially small in the system volume and therefore can be safely ignored in most of the cases however if one consider small quench experiments time fluctuations can be greatly enhanced we show that time fluctuations may become stronger than other forms of equilibrium quantum fluctuations if the quench is performed close to a critical point for sufficiently relevant operators the full distribution function of dynamically evolving observable expectation values becomes a universal function uniquely characterized by the critical exponents and the boundary conditions at regular points of the phase diagram and for nonsufficiently relevant operators the distribution becomes gaussian our predictions are confirmed by an explicit calculation on the quantum ising model

equilibration on average in quantum processes with finite temporal resolution we characterize the conditions under which a multitime quantum process with a finite temporal resolution can be approximately described by an equilibrium one by providing a generalization of the notion of equilibration on average where a system remains closed to a fixed equilibrium for most times to one which can be operationally assessed at multiple times we place an upper bound on a new observable distinguishability measure comparing a multitime process with a finite temporal resolution against a fixed equilibrium one while the same conditions on single time equilibration such as a large occupation of energy levels in the initial state remain necessary we obtain genuine multitime contributions depending on the temporal resolution of the process and the amount of disturbance of the observer s operations on it

simulation of fluid and particles flows asymptotic preserving schemes for bubbling and flowing regimes in this work we propose asymptotic preserving numerical schemes for the bubbling and flowing regimes of particles immersed in a fluid treated by two phase flow models the description comprises compressible euler equations for the dense phase fluid and a kinetic fokker planck equation for the disperse phase particles coupled through friction terms we show numerical simulations in the relevant case of gravity in the one dimensional case demonstrating the overall behavior of the schemes

spin and the thermal equilibrium distribution of wave functions consider a quantum system s weakly interacting with a very large but finite system b called the heat bath and suppose that the composite s b is in a pure state with participating energies between e and e with small then it is known that for most the reduced density matrix of s is approximately equal to the canonical density matrix that is the reduced density matrix is universal in the sense that it depends only on s s hamiltonian and the temperature but not on b s hamiltonian on the interaction hamiltonian or on the details of it has also been pointed out that s can also be attributed a random wave function whose probability distribution is universal in the same sense this distribution is known as the scrooge measure or gaussian adjusted projected gap measure we regard it as the thermal equilibrium distribution of wave functions the relevant concept of the wave function of a subsystem is known as the conditional wave function in this paper we develop analogous considerations for particles with spin one can either use some kind of conditional wave function or more naturally the conditional density matrix which is in general different from the reduced density matrix we ask what the thermal equilibrium distribution of the conditional density matrix is and find the answer that for most the conditional density matrix is approximately deterministic in fact approximately equal to the canonical density matrix

irreversibility and entropy production in transport phenomena iv symmetry integrated intermediate processes and separated variational principles for multi currents abstract the mechanism of entropy production in transport phenomena is discussed again by emphasizing the role of symmetry of non equilibrium states and also by reformulating einstein s theory of brownian motion to derive entropy production from it this yields conceptual reviews of the previous papers m suzuki physica a 390 2011 1904 391 2012 1074 392 2013 314 separated variational principles of steady states for multi external fields x i and induced currents j i are proposed by extending the principle of minimum integrated entropy production found by the present author for a single external field the basic strategy of our theory on steady states is to take in all the intermediate processes from the equilibrium state to the final possible steady states in order to study the irreversible physics even in the steady states as an application of this principle gransdorff prigogine s evolution criterion inequality or stability condition d x p d r i j i d x i 0 is derived in the stronger form d q i d r j i d x i 0 for individual force x i and current j i even in nonlinear responses which depend on all the external forces x k nonlinearly this is called separated evolution criterion some explicit demonstrations of the present general theory to simple electric circuits with multi external fields are given in order to clarify the physical essence of our new theory and to realize the condition of its validity concerning the existence of the solutions of the simultaneous equations obtained by the separated variational principles it is also instructive to compare the two results obtained by the new variational theory and by the old scheme based on the instantaneous entropy production this seems to be suggestive even to the energy problem in the world