exact solution of a 1d asymmetric exclusion model using a matrix formulation several recent works have shown that the one dimensional fully asymmetric exclusion model which describes a system of particles hopping in a preferred direction with hard core interactions can be solved exactly in the case of open boundaries here the authors present a new approach based on representing the weights of each configuration in the steady state as a product of noncommuting matrices with this approach the whole solution of the problem is reduced to finding two matrices and two vectors which satisfy very simple algebraic rules they obtain several explicit forms for these non commuting matrices which are in the general case infinite dimensional their approach allows exact expressions to be derived for the current and density profiles finally they discuss briefly two possible generalizations of their results the problem of partially asymmetric exclusion and the case of a mixture of two kinds of particles

growth and zeros of meromorphic solution of some linear difference equations abstract in this paper we study growth and zeros of linear difference equations p n z f z n p 1 z f z 1 p 0 z f z f z where f z p n z p 0 z are polynomials with f p n p 0 0 and satisfy deg p n p 0 max deg p j j 0 n 1 the corresponding homogeneous equation of the above equation is also investigated

the asymmetric exclusion process and brownian excursions we consider the totally asymmetric exclusion process tasep in one dimension in its maximal current phase we show by an exact calculation that the non gaussian part of the fluctuations of density can be described in terms of the statistical properties of a brownian excursion numerical simulations indicate that the description in terms of a brownian excursion remains valid for more general one dimensional driven systems in their maximal current phase

z4 kerdock codes orthogonal spreads and extremal euclidean line sets when m is odd spreads in an orthogonal vector space of type omega 2m 2 2 are related to binary kerdock codes and extremal line sets in rr 2 m 1 with prescribed angles spreads in a 2m dimensional binary symplectic vector space are related to kerdock codes over zz 4 and extremal line sets in cc 2 m with prescribed angles these connections involve binary real and complex geometry associated with extraspecial 2 groups a geometric map from symplectic to orthogonal spreads is shown to induce the gray map from a corresponding zz 4 kerdock code to its binary image these geometric considerations lead to the construction for any odd composite m of large numbers of zz 4 kerdock codes they also produce new zz 4 linear kerdock and preparata codes 1991 mathematics subject classification primary 94b60 secondary 51m15 20c99

phase transitions in an exactly soluble one dimensional exclusion process we consider an exclusion process with particles injected with rate at the origin and removed with rate at the right boundary of a one dimensional chain of sites the particles are allowed to hop onto unoccupied sites to the right only for the special case of 1 the model was solved previously by derridaet al here we extend the solution to general the phase diagram obtained from our exact solution differs from the one predicted by the mean field approximation

wigner weyl correspondence in quantum mechanics for continuous and discrete systems a dirac inspired view drawing inspiration from dirac s work on functions of non commuting observables we develop an approach to phase space descriptions of operators and the wigner weyl correspondence in quantum mechanics complementary to standard formulations this involves a two step process introducing phase space descriptions based on placing position dependences to the left of momentum dependences or the other way around then carrying out a natural transformation to eliminate a kernel which appears in the expression for the trace of the product of two operators the method works uniformly for both continuous cartesian degrees of freedom and for systems with finite dimensional state spaces it is interesting that the kernel encountered is naturally expressible in terms of geometric phases and its removal involves extracting its square root in a suitable manner

lattice gas models in contact with stochastic reservoirs local equilibrium and relaxation to the steady state extending the results of a previous work we consider a class of discrete lattice gas models in a finite interval whose bulk dynamics consists of stochastic exchanges which conserve the particle number and with stochastic dynamics at the boundaries chosen to model infinite particle reservoirs at fixed chemical potentials we establish here the local equilibrium structure of the stationary measures for these models further we prove as a law of large numbers that the time dependent empirical density field converges to a deterministic limit process which is the solution of the initial boundary value problem for a nonlinear diffusion equation

evenly distributed unitaries on the structure of unitary designs we clarify the mathematical structure underlying unitary t designs these are sets of unitary matrices evenly distributed in the sense that the average of any tth order polynomial over the design equals the average over the entire unitary group we present a simple necessary and sufficient criterion for deciding if a set of matrices constitutes a design lower bounds for the number of elements of 2 designs are derived we show how to turn mutually unbiased bases into approximate 2 designs whose cardinality is optimal in leading order designs of higher order are discussed and an example of a unitary 5 design is presented we comment on the relation between unitary and spherical designs and outline methods for finding designs numerically or by searching character tables of finite groups further we sketch connections to problems in linear optics and questions regarding typical entanglement

relationships between characteristic functions of δnf and f abstract in this paper we obtain the accurate relationships between the characteristic functions of a finite order meromorphic function f z and its forward differences n f z where f z has two borel exceptional values

galois quantum systems irreducible polynomials and riemann surfaces finite quantum systems in which the position and momentum take values in the galois field gf pl are studied ideas from the subject of field extension are transferred in the context of quantum mechanics the frobenius automorphisms in galois fields lead naturally to the frobenius formalism in a quantum context the hilbert space splits into frobenius subspaces which are labeled with the irreducible polynomials associated with the ypl y the frobenius maps transform unitarily the states of a galois quantum system and leave fixed all states in some of its galois subsystems where the position and momentum take values in subfields of gf pl an analytic representation of these systems in the l sheeted complex plane shows deeper links between galois theory and riemann surfaces

galois quantum systems a finite quantum system in which the position and momentum take values in the galois field gf p is constructed from a smaller quantum system in which the position and momentum take values in using field extension the galois trace is used in the definition of the fourier transform the heisenberg weyl group of displacements and the sp 2 gf p group of symplectic transformations are studied a class of transformations inspired by the frobenius maps in galois fields is introduced the relationship of this galois quantum system with its subsystems in which the position and momentum take values in subfields of gf p is discussed

an extended weyl wigner transformation for special finite spaces abstract we extend the weyl wigner transformation to those particular degrees of freedom described by a finite number of states using a technique of constructing operator bases developed by schwinger discrete transformation kernels are presented instead of continuous coordinate momentum pair system and systems such as the one dimensional canonical continuous coordinate momentum pair system and the two dimensional rotation system are described by special limits expressions are explicitly given for the spin one half case

geometrical description of quantal state determination under the assumption that every quantal measurement may give data about the post measurement state of the inspected ensemble the problem of the state determination is reconsidered it is shown that orthogonal decomposition of the set of complex n n hermitian matrices into the commutative subsets allows operators to be found such that post measurement information on these observables allows a partial in some cases total determination of the pre measurement state to be effected

entanglement bell inequality and all that we start from the geometrical observation that a finite set of pure states correspond to some points on a sphere and their convex span cannot be the whole set of states if we call the left over entangled we can pursue this picture from the simplest case of a two dimensional hilbert space to the usual alice and bob game of entangled states and then move to bigger systems and finely to quantum field theory where almost everything is entangled on the way we encounter more or less known old friends up from the shell structure of states to the monogamy of squashed entanglement we study how entanglement can be concentrated on a small slice and how it depends on the particular factorization of the hilbert space

lower current large deviations for zero range processes on a ring we study lower large deviations for the current of totally asymmetric zero range processes on a ring with concave current density relation we use an approach by jensen and varadhan which has previously been applied to exclusion processes to realize current fluctuations by travelling wave density profiles corresponding to non entropic weak solutions of the hyperbolic scaling limit of the process we further establish a dynamic transition where large deviations of the current below a certain value are no longer typically attained by non entropic weak solutions but by condensed profiles where a non zero fraction of all the particles accumulates on a single fixed lattice site this leads to a general characterization of the rate function which is illustrated by providing detailed results for four generic examples of jump rates including constant rates decreasing rates unbounded sublinear rates and asymptotically linear rates our results on the dynamic transition are supported by numerical simulations using a cloning algorithm

generalized circulant densities and a sufficient condition for separability in a series of papers with kossakowski the first author has examined properties of densities for which the positive partial transpose ppt property can be readily checked these densities were also investigated from a different perspective by baumgartner hiesmayr and narnhofer in this paper we show how the support of such densities can be expressed in terms of lines in a finite geometry and how the same structure lends itself to checking the necessary ppt condition and to a novel sufficient condition for separability

hydrodynamics of stationary non equilibrium states for some stochastic lattice gas models we consider discrete lattice gas models in a finite interval with stochastic jump dynamics in the interior which conserve the particle number and with stochastic dynamics at the boundaries chosen to model infinite particle reservoirs at fixed chemical potentials the unique stationary measures of these processes support a steady particle current from the reservoir of higher chemical potential into the lower and are non reversible we study the structure of the stationary measure in the hydrodynamic limit as the microscopic lattice size goes to infinity in particular we prove as a law of large numbers that the empirical density field converges to a deterministic limit which is the solution of the stationary transport equation and the empirical current converges to the deterministic limit given by fick s law

hydrodynamics and large deviation for simple exclusion processes we prove the hydrodynamical limit for weakly asymmetric simple exclusion processes a large deviation property with respect to this limit is established for the symmetric case we treat also the situation where a slow reaction creation and annihilation of particles is present

exact large deviation functional of a stationary open driven diffusive system the asymmetric exclusion process we consider the asymmetric exclusion process asep in one dimension on sites i 1 n in contact at sites i 1 and i n with infinite particle reservoirs at densities a and b as a and b are varied the typical macroscopic steady state density profile x x a b obtained in the limit n l b a exhibits shocks and phase transitions here we derive an exact asymptotic expression for the probability of observing an arbitrary macroscopic profile rho x text p n rho x sim exp l mathcal f a b rho x rho a rho b so that mathcal f is the large deviation functional a quantity similar to the free energy of equilibrium systems we find as in the symmetric purely diffusive case q 1 treated in an earlier work that mathcal f is in general a non local functional of x unlike the symmetric case however the asymmetric case exhibits ranges of the parameters for which mathcal f rho x is not convex and others for which mathcal f rho x has discontinuities in its second derivatives at x x in the latter ranges the fluctuations of order 1 sqrt n in the density profile near x are then non gaussian and cannot be calculated from the large deviation function

non orthogonal wigner like mapping we have developed a general method for construction of wigner like mapping to the phase space associated with a non orthogonal set of mutually unbiased equally separated bases explicit expressions of the wigner functions in terms of measurements in non orthogonal bases are given and the limit cases are analyzed

extended reduction criterion and lattice states we study a particular class of states of a bipartite system consisting of two four level parties by means of an adapted extended reduction criterion we associate their entanglement properties to the geometric patterns of a planar lattice consisting of 16 points

existence of finite order meromorphic solutions as a detector of integrability in difference equations abstract the existence of sufficiently many finite order in the sense of nevanlinna meromorphic solutions of a difference equation appears to be a good indicator of integrability it is shown that out of a large class of second order difference equations the only equation that can admit a sufficiently general finite order meromorphic solution is the difference painleve ii equation the proof given relies on estimates obtained by arguments related to singularity confinement the existence of meromorphic solutions of a general class of first order difference equations is also proven by a simple method based on banach s fixed point theorem

current fluctuations in stochastic systems with long range memory we propose a method to calculate the large deviations of current fluctuations in a class of stochastic particle systems with history dependent rates long range temporal correlations are seen to alter the speed of the large deviation function in analogy with long range spatial correlations in equilibrium systems we give some illuminating examples and discuss the applicability of the gallavotti cohen fluctuation theorem

variations on a theme of heisenberg pauli and weyl the parentage between weyl pairs the generalized pauli group and the unitary group is investigated in detail we start from an abstract definition of the heisenberg weyl group on the field and then switch to the discrete heisenberg weyl group or generalized pauli group on a finite ring the main characteristics of the latter group an abstract group of order d3 noted pd are given conjugacy classes and irreducible representation classes or equivalently lie algebra of dimension d3 associated with pd leaving the abstract sector a set of weyl pairs in dimension d is derived from a polar decomposition of su 2 closely connected to angular momentum theory then a realization of the generalized pauli group pd and the construction of generalized pauli matrices in dimension d are revisited in terms of weyl pairs finally the lie algebra of the unitary group u d is obtained as a subalgebra of the lie algebra associated with pd this leads to a development of the lie algebra of u d in a basis consisting of d2 generalized pauli matrices in the case where d is a power of a prime integer the lie algebra of su d can be decomposed into d 1 cartan subalgebras

an exact formula for the statistics of the current in the tasep with open boundaries we study the totally asymmetric exclusion process on a finite one dimensional lattice with open boundaries i e in contact with two reservoirs at different potentials the total time integrated current through the system is a random variable that scales linearly with time in the long time limit we conjecture a parametric representation for the generating function of the cumulants of the current which is related to the large deviation function by laplace transform this formula is valid for all system sizes and for all values of the boundary coupling parameters

wigner functions and separability for finite systems a discussion of discrete wigner functions in phase space related to mutually unbiased bases is presented this approach requires mathematical assumptions which limits it to systems with density matrices defined on complex hilbert spaces of dimension pn where p is a prime number with this limitation it is possible to define a phase space and wigner functions in close analogy to the continuous case that is we use a phase space that is a direct sum of n two dimensional vector spaces each containing p2 points this is in contrast to the more usual choice of a two dimensional phase space containing p2n points a useful aspect of this approach is that we can relate complete separability of density matrices and their wigner functions in a natural way we discuss this in detail for bipartite systems and present the generalization to arbitrary numbers of subsystems when p is odd special attention is required for two qubits p 2 and our technique fails to establish the separability property for more than two qubits finally we give a brief discussion of hamiltonian dynamics in the language developed in the paper

density large deviations for multidimensional stochastic hyperbolic conservation laws we investigate the density large deviation function for a multidimensional conservation law in the vanishing viscosity limit when the probability concentrates on weak solutions of a hyperbolic conservation law conservation law when the conductivity and dif fusivity matrices are proportional i e an einstein like relation is satisfied the problem has been solved in 4 when this proportionality does not hold we compute explicitly the large deviation function for a step like density profile and we show that the associated optimal current has a non trivial structure we also derive a lower bound for the large deviation function valid for a general weak solution and leave the general large deviation function upper bound as a conjecture

universal large deviation function of the kardar parisi zhang equation in one dimension using the bethe ansatz we calculate the whole large deviation function of the displacement of particles in the asymmetric simple exclusion process asep on a ring when the size of the ring is large the central part of this large deviation function takes a scaling form independent of the density of particles we suggest that this scaling function found for the asep is universal and should be characteristic of all the systems described by the kardar parisi zhang equation in 1 1 dimension simulations done on two simple growth models are in reasonable agreement with this conjecture

an angular momentum approach to quadratic fourier transform hadamard matrices gauss sums mutually unbiased bases the unitary group and the pauli group the construction of unitary operator bases in a finite dimensional hilbert space is reviewed through a nonstandard approach combining angular momentum theory and representation theory of su 2 a single formula for the bases is obtained from a polar decomposition of su 2 and is analyzed in terms of cyclic groups quadratic fourier transforms hadamard matrices and generalized gauss sums weyl pairs generalized pauli operators and their application to the unitary group and the pauli group naturally arise in this approach

tomographically complete sets of orthonormal bases in finite systems quantum systems where the position and momentum are in the ring d is an odd integer are considered a tomographically complete set of bases i e a set of bases such that probabilities from tomography experiments corresponding to these bases can be used for the calculation of an arbitrary density matrix is considered such a set of bases is constructed by considering a factorization of a system with dimension d p1p2 where p1 p2 are prime numbers in terms of two subsystems with dimensions p1 and p2 appropriate combination of the mutually unbiased bases in the subsystems leads to a tomographically complete set of bases in the full system this set leads to probabilities along all the lines through the origin 0 0 in the phase space with exactly d points it is shown that the number of these lines is d the dedekind function the general theory is exemplified with examples

current reservoirs in the simple exclusion process we consider the symmetric simple exclusion process in the interval n n with additional birth and death processes respectively on n k n k 0 and n n k the exclusion is speeded up by a factor n2 births and deaths by a factor n assuming propagation of chaos a property proved in a companion paper de masi et al http arxiv org abs 1104 3447 we prove convergence in the limit n to the linear heat equation with dirichlet condition on the boundaries the boundary conditions however are not known a priori they are obtained by solving a non linear equation the model simulates mass transport with current reservoirs at the boundaries and the fourier law is proved to hold

entanglement reflected in wigner functions we construct an abelian algebra built by maximally entangled pure states the partial transposition maps this algebra for odd dimensions into a full matrix algebra ppt states are in one to one correspondence to states with a positive definite wigner function special extremal ppt states correspond to projections of various dimensions in particular we recover the projections corresponding to a complete set of mutually unbiased bases in prime dimensions

peres horodecki separability criterion for continuous variable systems the peres horodecki criterion of positivity under partial transpose is studied in the context of separability of bipartite continuous variable states the partial transpose operation admits in the continuous case a geometric interpretation as mirror reflection in phase space this recognition leads to uncertainty principles stronger than the traditional ones to be obeyed by all separable states for all bipartite gaussian states the peres horodecki criterion turns out to be a necessary and sufficient condition for separability

computation of current cumulants for small nonequilibrium systems we analyze a systematic algorithm for the exact computation of the current cumulants in stochastic nonequilibrium systems recently discussed in the framework of full counting statistics for mesoscopic systems this method is based on identifying the current cumulants from a rayleigh schrodinger perturbation expansion for the generating function here it is derived from a simple path distribution identity and extended to the joint statistics of multiple currents for a possible thermodynamical interpretation we compare this approach to a generalized onsager machlup formalism we present calculations for a boundary driven kawasaki dynamics on a one dimensional chain both for attractive and repulsive particle interactions

characterizing entanglement via uncertainty relations we derive a family of necessary separability criteria for finite dimensional systems based on inequalities for variances of observables we show that every pure bipartite entangled state violates some of these inequalities furthermore a family of bound entangled states and true multipartite entangled states can be detected the inequalities also allow us to distinguish between different classes of true tripartite entanglement for qubits we formulate an equivalent criterion in terms of covariance matrices this allows us to apply criteria known from the regime of continuous variables to finite dimensional systems

large deviation functional of the weakly asymmetric exclusion process we obtain the large deviation functional of a density profile for the asymmetric exclusion process of l sites with open boundary conditions when the asymmetry scales like l 1 we recover as limiting cases the expressions derived recently for the symmetric ssep and the asymmetric asep cases in the asep limit the nonlinear differential equation one needs to solve can be analysed by a method which resembles the wkb method

quantum systems with finite hilbert space galois fields in quantum mechanics a galois quantum system in which the position and momentum take values in the galois field gf pl is considered it is comprised of l component systems which are coupled in a particular way and is described by a certain class of hamiltonians displacements in the gf pl gf pl phase space and the corresponding heisenberg weyl group are studied symplectic transformations are shown to form the sp 2 gf pl group wigner and weyl functions are defined and their properties are studied frobenius symmetries which are based on frobenius automorphisms in the theory of galois fields are a unique feature of these systems for l 2 if they commute with the hamiltonian there are constants of motion which are discussed an analytic representation in the l sheeted complex plane provides an elegant formalism that embodies the properties of frobenius transformations the difference between a galois quantum system and other finite quantum systems where the position and momentum take values in the ring is discussed

fluctuations in the weakly asymmetric exclusion process with open boundary conditions we investigate the fluctuations around the average density profile in the weakly asymmetric exclusion process with open boundaries in the steady state we show that these fluctuations are given in the macroscopic limit by a centered gaussian field and we compute explicitly its covariance function we use two approaches the first method is dynamical and based on fluctuations around the hydrodynamic limit we prove that the density fluctuations evolve macroscopically according to an autonomous stochastic equation and we search for the stationary distribution of this evolution the second approach which is based on a representation of the steady state as a sum over paths allows one to write the density fluctuations in the steady state as a sum over two independent processes one of which is the derivative of a brownian motion the other one being related to a random path in a potential

hudson s theorem for finite dimensional quantum systems we show that on a hilbert space of odd dimension the only pure states to possess a non negative wigner function are stabilizer states the clifford group is identified as the set of unitary operations which preserve positivity the result can be seen as a discrete version of hudson s theorem hudson established that for continuous variable systems the wigner function of a pure state has no negative values if and only if the state is gaussian turning to mixed states it might be surmised that only convex combinations of stabilizer states give rise to non negative wigner distributions we refute this conjecture by means of a counterexample further we give an axiomatic characterization which completely fixes the definition of the wigner function and compare two approaches to stabilizer states for hilbert spaces of prime power dimensions in the course of the discussion we derive explicit formulas for the number of stabilizer codes defined on such systems

difference analogue of the lemma on the logarithmic derivative with applications to difference equations the lemma on the logarithmic derivative of a meromorphic function has many applications in the study of meromorphic functions and ordinary dierential equa tions in this paper a dierence analogue of the logarithmic derivative lemma is presented and then applied to prove a number of results on meromorphic solutions of complex dierence equations these results include a dierence analogue of the clunie lemma as well as other results on the value distribution of solutions

discrete phase space approach to mutually orthogonal latin squares we show there is a natural connection between latin squares and commutative sets of monomials defining geometric structures in finite phase space of prime power dimensions a complete set of such monomials defines a mutually unbiased basis mub and may be associated with a complete set of mutually orthogonal latin squares mols we translate some possible operations on the monomial sets into isomorphisms of latin squares and find a general form of permutations that map between latin squares corresponding to unitarily equivalent mutually unbiased sets

discrete wigner distribution for two qubits a characterization of entanglement properties we study the properties of the discrete wigner distribution for two qubits introduced by wotters in particular we analyse the entanglement properties within the wigner distribution picture by considering the negativity of the wigner function wf and the correlations of the marginal distribution we show that a state is entangled if at least one among the values assumed by the corresponding discrete wf is smaller than a certain critical negative value then based on the partial transposition criterion we establish a relation between the separability of a density matrix and the non negativity of the wfs relevant both to such a density matrix and to the partially transposed thereof finally we derive a simple inequality involving the covariance matrix elements of a given wf which appears to provide a separability criterion stronger than the one based on the local uncertainty relations

eigenvalues and eigenvectors of the finite fourier transform the eigenvalues and eigenvectors of the n n unitary matrix of finite fourier transform whose j k element is 1 n 1 2 exp 2 i n jk i 1 1 2 is determined in doing so a multitude of identities some of which may be new are encountered a conjecture is advanced

antishocks in the asep with open boundaries conditioned on low current we study the time evolution of the asep on a finite lattice with l sites and open boundaries conditioned on an atypically low current up to a finite time t by an exact computation we show that for a one parameter family of boundary densities and a special value of the conditioned current an initial product measure with an antishock at site k evolves into a convex combination of such antishocks at sites k the weights p k t k 0 are shown to be the transition probabilities of simple biased random walk with reflecting boundaries we compute explicitly these transition rates our result implies that the antishock remains microscopically stable under the locally conditioned dynamics

exact probability function for bulk density and current in the asymmetric exclusion process we examine the asymmetric simple exclusion process with open boundaries a paradigm of driven diffusive systems having a nonequilibrium steady state transition we provide a full derivation and expanded discussion and digression on results previously reported briefly in m depken and r stinchcombe phys rev lett 93 040602 2004 in particular we derive an exact form for the joint probability function for the bulk density and current both for finite systems and also in the thermodynamic limit the resulting distribution is non gaussian and while the fluctuations in the current are continuous at the continuous phase transitions the density fluctuations are discontinuous the derivations are done by using the standard operator algebraic techniques and by introducing a modified version of the original operator algebra as a by product of these considerations we also arrive at a very simple way of calculating the normalization constant appearing in the standard treatment with the operator algebra like the partition function in equilibrium systems this normalization constant is shown to completely characterize the fluctuations albeit in a very different manner

open asep in the weakly asymmetric regime we consider asep on a bounded interval and on a half line with sources and sinks on the full line bertini and giacomin in 1997 proved convergence under weakly asymmetric scaling of the height function to the solution of the kpz equation we prove here that under similar weakly asymmetric scaling of the sources and sinks as well the bounded interval asep height function converges to the kpz equation on the unit interval with neumann boundary conditions on both sides different parameter for each side and likewise for the half line asep to kpz on a half line this result can be interpreted as showing that the kpz equation arises at the triple critical point maximal current high density low density of the open asep 2018 wiley periodicals inc

fluctuation statistics in networks a stochastic path integral approach we investigate the statistics of fluctuations in a classical stochastic network of nodes joined by connectors the nodes carry generalized charge that may be randomly transferred from one node to another our goal is to find the time evolution of the probability distribution of charges in the network the building blocks of our theoretical approach are 1 known probability distributions for the connector currents 2 physical constraints such as local charge conservation and 3 a time scale separation between the slow charge dynamics of the nodes and the fast current fluctuations of the connectors we integrate out fast current fluctuations and derive a stochastic path integral representation of the evolution operator for the slow charges the statistics of charge fluctuations may be found from the saddle point approximation of the action once the probability distributions on the discrete network have been studied the continuum limit is taken to obtain a statistical field theory we find a correspondence between the diffusive field theory and a langevin equation with gaussian noise sources leading nevertheless to nontrivial fluctuation statistics to complete our theory we demonstrate that the cascade diagrammatics recently introduced by nagaev naturally follows from the stochastic path integral by generalizing the principle of minimal correlations we extend the diagrammatics to calculate current correlation functions for an arbitrary network one primary application of this formalism is that of full counting statistics fcs the motivation for why it was developed in the first place we stress however that the formalism is suitable for general classical stochastic problems as an alternative approach to the traditional master equation or doi peliti technique the formalism is illustrated with several examples both instantaneous and time averaged charge fluctuation statistics in a mesoscopic chaotic cavity as well as the fcs and new results for a generalized diffusive wire

thermodynamic formula for the cumulant generating function of time averaged current the cumulant generating function of time averaged current is studied from an operational viewpoint specifically for interacting brownian particles under nonequilibrium conditions we show that the first derivative of the cumulant generating function is equal to the expectation value of the current in a modified system with an extra force added where the modified system is characterized by a variational principle the formula reminds us of einstein s fluctuation theory in equilibrium statistical mechanics furthermore since the formula leads to the fluctuation dissipation relation when the linear response regime is focused on it is regarded as an extension of the linear response theory to that valid beyond the linear response regime the formula is also related to previously known theories such as the donsker varadhan theory the additivity principle and the least dissipation principle but it is not derived from them examples of its application are presented for a driven brownian particle on a ring subject to a periodic potential

the kpz limit of asep with boundary it was recently proved in corwin and shen cpam cs16 that under weakly asymmetric scaling the height functions for asep with sources and sinks converges to the hopf cole solution of the kpz equation with inhomogeneous neumann boundary conditions in their assumptions cs16 chose positive values for the neumann boundary condition and they assumed initial data which is close to stationarity by developing more extensive heat kernel estimates we clarify and extend their results to negative values of the neumann boundary parameters and we also show how to generalize their results to empty initial data which is very far from stationarity combining our result with barraquand et al duke math j bbcw17 we obtain the laplace transform of the one point distribution for half line kpz and use this to confirm t1 3 scale goe tracy widom long time fluctuations at the origin

the angle angular momentum quantum phase space the angle angular momentum quantum phase space is considered and the corresponding heisenberg weyl group is studied when 2j 1 is a power of a prime z 2j 1 is a galois field and stronger results can be proved sl 2 z 2j 1 transformations are explicitly constructed and various properties of the displacement operators are studied central extensions of the abelian group by z 2j 1 are studied and they provide all the ways of constructing the heisenberg weyl group from g and z 2j 1

mutually unbiased bases generalized spin matrices and separability abstract a collection of orthonormal bases for a complex d dimensional hilbert space is called mutually unbiased mub if for any two vectors v and w from different bases the square of the inner product equals 1 d v w 2 1 d the mub problem is to prove or disprove the existence of a maximal set of d 1 bases it has been shown in ann phys 191 1989 363 that such a collection exists if d is a power of a prime number p we revisit this problem and use d d generalizations of the pauli spin matrices to give a constructive proof of this result specifically we give explicit representations of commuting families of unitary matrices whose eigenvectors solve the mub problem additionally we give formulas from which the orthogonal bases can be readily computed we show how the techniques developed here provide a natural way to analyze the separability of the bases the techniques used require properties of algebraic field extensions and the relevant part of that theory is included in the appendix

mutually unbiased bases containing a complex hadamard matrix of schmidt rank three constructing four six dimensional mutually unbiased bases mubs is an open problem in quantum physics and measurement we investigate the existence of four mubs including the identity and a compl

symplectic transformations and quantum tomography in finite quantum systems quantum systems where the position and momentum are in the ring zd d is an odd integer are considered symplectic transformations are studied and the order of sp 2 zd is calculated quantum tomography is also discussed it is shown that measurements used in the inverse radon transform need to be made on j2 d lines where j2 d is the jordan totient function

current large deviations for asymmetric exclusion processes with open boundaries we study the large deviation functional of the current for the weakly asymmetric simple exclusion process in contact with two reservoirs we compare this functional in the large drift limit to the one of the totally asymmetric simple exclusion process in particular to the jensen varadhan functional conjectures for generalizing the jensen varadhan functional to open systems are also stated

exact joint density current probability function for the asymmetric exclusion process we study the asymmetric simple exclusion process with open boundaries and derive the exact form of the joint probability function for the occupation number and the current through the system we further consider the thermodynamic limit showing that the resulting distribution is non gaussian and that the density fluctuations have a discontinuity at the continuous phase transition while the current fluctuations are continuous the derivations are performed by using the standard operator algebraic approach and by the introduction of new operators satisfying a modified version of the original algebra

static large deviations for a reaction diffusion model we consider the superposition of a symmetric simple exclusion dynamics speeded up in time with a spin flip dynamics in a one dimensional interval with periodic boundary conditions we prove the large deviations principle for the empirical measure under the stationary state we deduce from this result that the stationary state is concentrated on the stationary solutions of the hydrodynamic equation which are stable

generation of bases with definite factorization for an n qubit system and mutually unbiased sets construction we propose a systematic procedure to construct all the possible bases with a definite factorization structure eigenstates of n commuting monomials constructed as products of pauli operators for an n qubit system as well as the possibility of collecting them into mutually unbiased sets we also discuss an algorithm for the determination of basis separability and propose a criteria for complementarity between such bases the results are applied to generate non isomorphic complete sets of mutually unbiased bases

cyclic quantum error correcting codes and quantum shift registers we transfer the concept of linear feedback shift registers to quantum circuits it is shown how to use these quantum linear shift registers for encoding and decoding cyclic quantum error correcting codes

geometrical approach to the discrete wigner function in prime power dimensions we analyse the wigner function in prime power dimensions constructed on the basis of the discrete rotation and displacement operators labelled with elements of the underlying finite field we separately discuss the case of odd and even characteristics and analyse the algebraic origin of the non uniqueness of the representation of the wigner function explicit expressions for the wigner kernel are given in both cases

current fluctuations in the one dimensional symmetric exclusion process with open boundaries we calculate the first four cumulants of the integrated current of the one dimensional symmetric simple exclusion process of n sites with open boundary conditions for large system size n the generating function of the integrated current depends on the densities a and b of the two reservoirs and on the fugacity z the parameter conjugated to the integrated current through a single parameter based on our expressions for these first four cumulants we make a conjecture which leads to a prediction for all the higher cumulants in the case a 1 and b 0 our conjecture gives the same universal distribution as the one obtained by lee levitov and yakovets for one dimensional quantum conductors in the metallic regime

spectra of phase point operators in odd prime dimensions and the extended clifford group we analyze the role of the extended clifford group in classifying the spectra of phase point operators within the framework laid out by gibbons et al phys rev a 70 062101 2004 for setting up wigner distributions on discrete phase spaces based on finite fields to do so we regard the set of all the discrete phase spaces as a symplectic vector space over the finite field auxiliary results include a derivation of the conjugacy classes of esl 2 fn

geometrical approach to mutually unbiased bases we propose a unifying phase space approach to the construction of mutually unbiased bases for a two qubit system it is based on an explicit classification of the geometrical structures compatible with the notion of unbiasedness these consist of bundles of discrete curves intersecting only at the origin and satisfying certain additional properties we also consider the feasible transformations between different kinds of curves and show that they correspond to local rotations around the bloch sphere principal axes we suggest how to generalize the method to systems in dimensions that are powers of a prime