phase separation and coarsening in one dimensional driven diffusive systems local dynamics leading to long range hamiltonians a driven system of three species of particles diffusing on a ring is studied in detail the dynamics is local and conserves the three densities a simple argument suggesting that the model should phase separate and break the translational symmetry is given we show that for the special case where the three densities are equal the model obeys detailed balance and the steady state distribution is governed by a hamiltonian with asymmetric long range interactions this provides an explicit demonstration of a simple mechanism for breaking of ergodicity in one dimension the steady state of finite size systems is studied using a generalized matrix product ansatz the coarsening process leading to phase separation is studied numerically and in a mean field model the system exhibits slow dynamics due to trapping in metastable states whose number is exponentially large in the system size the typical domain size is shown to grow logarithmically in time generalizations to a larger number of species are discussed

the group of automorphisms of a zero divisor graph based on rank one upper triangular matrices abstract let f q be a finite field with q elements n 2 a positive integer mat n q the set of all n n matrices over f q r n q the set of all rank one upper triangular matrices in mat n q the zero divisor graph of mat n q written as mat n q is a directed graph with vertex set all nonzero zero divisors of mat n q and there is a directed edge from a vertex a to a vertex b written as a b if and only if a b 0 in this paper we determine the automorphisms of an induced subgraph written as r n q of mat n q with vertex set r n q the main theorem of this article proves that a bijective map on r n q with n 3 is an automorphism of r n q if and only if x a x p 1 x i j p x x i j r n q where a x f q depends on x p is an invertible upper triangular matrix is an automorphism of the field f q x i j denotes the matrix whose i j entry is x i j

more on symplectic graphs modulo pn abstract meemark and prinyasart 10 proved by combinatorial method that the symplectic graph sp p n 2 modulo p n is strongly regular when 1 and sp p n 2 is arc transitive when p is an odd prime in this paper combining matrix method and elementary number theory we continue this research and prove that sp p n 2 is arc transitive for any prime p furthermore we determine the suborbits of the symplectic group modulo p n on sp p n 2 and show that sp p n 2 is a strictly deza graph when 2 and n 2

the structure of rings of quotients abstract for an arbitrary ring r we completely characterize when q r the maximal right ring of quotients of r is a direct product of indecomposable rings and when q r is a direct product of prime rings in terms of conditions on ideals of r our work generalizes decomposition results of goodearl for a von neumann regular right self injective ring and of jain lam and leroy for q r when r is right nonsingular to develop our results we define a useful dimension on bimodules and characterize the subset of ideals of r which are dense in ring direct summands of q r a structure theorem for r b q r the subring of q r generated by r e r r and e b q r is provided for a semiprime ring r our methods allow us to properly generalize rowen s theorem for semiprime pi rings we also apply our results to functional analysis to obtain a direct product decomposition of the local multiplier algebra m loc a of a c algebra a as a byproduct we obtain a complete description of a c algebra whose extended centroid is c as a consequence we show that a c algebra with only finitely many minimal prime ideals and satisfying a polynomial identity is finite dimensional

hulls of semiprime rings with applications to c algebras abstract for a ring r we investigate and determine minimal right essential overrings right ring hulls belonging to certain classes which are generated by r and subsets of the central idempotents of q r where q r is the maximal right ring of quotients of r we show the existence of and characterize a quasi baer hull and a right fi extending hull for every semiprime ring our results include i r b q r i e the subring of q r generated by r e r r and e b q r where b q r is the set of all central idempotents of q r is the smallest quasi baer and the smallest right fi extending right ring of quotients of a semiprime ring r with unity in this case various overrings of r b q r including all right essential overrings of r containing b q r are also quasi baer and right fi extending ii lying over going up and incomparability of prime ideals various regularity conditions and classical krull dimension transfer between r and r b q r and iii the existence of a boundedly centrally closed hull for every c algebra and a complete characterization for an intermediate c algebra between a c algebra a and its local multiplier c algebra m loc a to be boundedly centrally closed

exact results for one dimensional cellular automata with different types of updates we study two common types of time noncontinuous updates for one dimensional stochastic cellular automata with arbitrary nearest neighbor interactions and arbitrary open boundary conditions we first construct the stationary states using the matrix product formalism this construction then allows to prove a general connection between the stationary states which are produced by the two different types of updates using this connection we derive explicit relations between the densities and correlation functions for these different stationary states

competition between multiple totally asymmetric simple exclusion processes for a finite pool of resources using monte carlo simulations and a domain wall theory we discuss the effect of coupling several totally asymmetric simple exclusion processes taseps to a finite reservoir of particles this simple model mimics directed biological transport processes in the presence of finite resources such as protein synthesis limited by a finite pool of ribosomes if all taseps have equal length we find behavior which is analogous to a single tasep coupled to a finite pool for the more generic case of chains with different lengths several unanticipated regimes emerge a generalized domain wall theory captures our findings in good agreement with simulation results

exact solution of a cellular automaton for traffic we present an exact solution of a probabilistic cellular automaton for traffic with open boundary conditions e g cars can enter and leave a part of a highway with certain probabilities the model studied is the asymmetric exclusion process asep with simultaneous updating of all sites it is equivalent to a special case vmax 1 of the nagel schreckenberg model for highway traffic which has found many applications in real time traffic simulations the simultaneous updating induces additional strong short range correlations compared to other updating schemes the stationary state is written in terms of a matrix product solution the corresponding algebra which expresses a system size recursion relation for the weights of the configurations is quartic in contrast to previous cases in which the algebra is quadratic we derive the phase diagram and compute various properties such as density profiles two point functions and the fluctuations in the number of particles cars in the system the current and the density profiles can be mapped onto the asep with other time discrete updating procedures through use of this mapping our results also give new results for these models

representations of the quadratic algebra and partially asymmetric diffusion with open boundaries we consider the one dimensional partially asymmetric exclusion model with open boundaries the model describes a system of hard core particles that hop stochastically in both directions with different rates at both boundaries particles are injected and extracted by means of the method of derrida et al the stationary probability measure can be expressed as a matrix product state involving two matrices forming a fock like representation of a general quadratic algebra we obtain the representations of this algebra which were unknown in the mathematical literature and use the two dimensional one to derive exact expressions for the density profile and correlation functions using the correspondence between the stochastic model and a quantum spin chain we obtain exact correlation functions for a spin heisenberg xxz chain with non diagonal boundary terms generalizations to other reaction diffusion models are discussed

partially asymmetric simple exclusion model in the presence of an impurity on a ring we study a generalized two species model on a ring the original model mallick k 1996 j phys a math gen 29 5375 describes ordinary particles hopping exclusively in one direction in the presence of an impurity the impurity hops with a rate different from that of ordinary particles and can be overtaken by them here we let the ordinary particles also hop backward with rate q using the matrix product ansatz we obtain the relevant quadratic algebra a finite dimensional representation of this algebra enables us to compute the stationary bulk density of the ordinary particles as well as the speed of impurity on a set of special surfaces of the parameter space we will obtain the phase structure of this model in the accessible region and show how the phase structure of the original model is modified in the infinite volume limit this model presents a shock in one of its phases

local inhomogeneity in asymmetric simple exclusion processes with extended objects totally asymmetric simple exclusion processes tasep with particles which occupy more than one lattice site and with a local inhomogeneity far away from the boundaries are investigated these non equilibrium processes are relevant for the understanding of many biological and chemical phenomena the steady state phase diagrams currents and bulk densities are calculated using a simple approximate theory and extensive monte carlo computer simulations it is found that the phase diagram for tasep with a local inhomogeneity is qualitatively similar to homogeneous models although the phase boundaries are significantly shifted the complex dynamics is discussed in terms of domain wall theory for driven lattice systems

subconstituents of symplectic graphs modulo pn abstract the two subconstituents of symplectic graphs modulo p n denoted by sp 2 z p n where n are positive integers are studied the first subconstituent is shown to be a 3 deza graph except the trivial case 1 when it is strongly regular and when 2 the second subconstituent is shown to be a strictly deza graph the parameters of these graphs are determined moreover the chromatic number and the full automorphism group of these two subconstituents are given

entropy of open lattice systems we investigate the behavior of the gibbs shannon entropy of the stationary nonequilibrium measure describing a one dimensional lattice gas of l sites with symmetric exclusion dynamics and in contact with particle reservoirs at different densities in the hydrodynamic scaling limit l the leading order o l behavior of this entropy has been shown by bahadoran to be that of a product measure corresponding to strict local equilibrium we compute the first correction which is o 1 the computation uses a formal expansion of the entropy in terms of truncated correlation functions for this system the k th such correlation is shown to be o l k 1 this entropy correction depends only on the scaled truncated pair correlation which describes the covariance of the density field it coincides in the large l limit with the corresponding correction obtained from a gaussian measure with the same covariance

suborbits of a point stabilizer in the orthogonal group on the last subconstituent of orthogonal dual polar graphs abstract as one of the serial papers on suborbits of point stabilizers in classical groups on the last subconstituent of dual polar graphs the corresponding problem for orthogonal dual polar graphs over a finite field of odd characteristic is discussed in this paper we determine all the suborbits of a point stabilizer in the orthogonal group on the last subconstituent and calculate the length of each suborbit moreover we discuss the quasi strongly regular graphs and the association schemes based on the last subconstituent respectively

exact stationary distribution of an asymmetric simple exclusion process with langmuir kinetics and memory reservoirs we present exact stationary distribution of the asymmetric simple exclusion process with langmuir kinetics and its related model on a ring the distribution is expressed in simple factorized forms that is supported by detailed balance conditions satisfied in the attachment and detachment transitions using the equations we derive the density of particles the current and the variance of particle numbers in each lane the expressions for the density are well associated with the ones found in equilibrium theories moreover a simple relation between the variance of particle number and the current is proved

yang lee zeros for a nonequilibrium phase transition equilibrium systems which exhibit a phase transition can be studied by investigating the complex zeros of the partition function this method pioneered by yang and lee has been widely used in equilibrium statistical physics we show that an analogous treatment is possible for a nonequilibrium phase transition into an absorbing state by investigating the complex zeros of the survival probability of directed percolation processes we demonstrate that the zeros provide information about universal properties moreover we identify certain nontrivial points where the survival probability for bond percolation can be computed exactly

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

the quantum group suq 2 and a q analogue of the boson operators a new realisation of the quantum group suq 2 is constructed by means of a q analogue to the jordan schwinger mapping determining thereby both the complete representation structure and q analogues to the wigner and racah operators to achieve this realisation a new elementary object is defined a q analogue to the harmonic oscillator the uncertainty relation for position and momentum in a q harmonic oscillator is quite unusual

two way traffic flow exactly solvable model of traffic jam we study completely asymmetric two channel exclusion processes in one dimension it describes a two way traffic flow with cars moving in opposite directions the interchannel interaction makes cars slow down in the vicinity of approaching cars in the other lane particularly we consider in detail the system with a finite density of cars on one lane and a single car on the other when the interchannel interaction reaches a critical value a traffic jam occurs which turns out to be of first order phase transition we derive exact expressions for the average velocities the current the density profile and the k point density correlation functions we also obtain the exact probability of two cars being in one lane of distance r apart provided there is a finite density of cars on the other lane and show that the two cars form a weakly bound state in the jammed phase

construction of a matrix product stationary state from solutions of a finite size system stationary states of stochastic models which have n states per site in matrix product form are considered first we give a necessary condition for the existence of a finite m dimensional matrix product stationary state for any n m second we give a method to construct the matrices from the stationary

disordered totally asymmetric simple exclusion process exact results we study the effect of quenched spatial disorder on the current carrying steady states of a totally asymmetric simple exclusion process with spatially disordered jump rates expressions for the steady state weights and the current are derived for this model in one dimension these solutions are exploited to study analytically the exact symmetries of the system in particular we confirm the recent numerical observation of tripathy and barma phys rev e 58 1911 1998 that the magnitude of the steady state current is left invariant when the direction of all the allowed particle jumps are reversed

nonequilibrium stationary states and equilibrium models with long range interactions it was recently suggested by blythe and evans that a properly defined steady state normalization factor can be seen as a partition function of a fictitious statistical ensemble in which the transition rates of the stochastic process play the role of fugacities in analogy with the lee yang description of phase transition of equilibrium systems they studied the zeros in the complex plane of the normalization factor in order to find phase transitions in nonequilibrium steady states we show that like for equilibrium systems the densities associated with the rates are nondecreasing functions of the rates and therefore one can obtain the location and nature of phase transitions directly from the analytical properties of the densities we illustrate this phenomenon for the asymmetric exclusion process we actually show that its normalization factor coincides with an equilibrium partition function of a walk model in which the densities have a simple physical interpretation

the asymmetric exclusion process comparison of update procedures the asymmetric exclusion process asep has attracted a lot of interest not only because of its many applications e g in the context of the kinetics of biopolymerization and traffic flow theory but also because it is a paradigmatic model for nonequilibrium systems here we study the asep for different types of updates namely random sequential sequential sublattice parallel and parallel in order to compare the effects of the different update procedures on the properties of the stationary state we use large scale monte carlo simulations and analytical methods especially the so called matrix product ansatz mpa we present in detail the exact solution for the model with sublattice parallel and sequential updates using the mpa for the case of parallel update which is important for applications like traffic flow theory we determine the phase diagram the current and density profiles based on monte carlo simulations we furthermore suggest an mpa for that case and derive the corresponding matrix algebra

bilinear forms graphs over residue class rings abstract we investigate the bilinear forms graph over the residue class ring modulo p s where p is a prime number and s is a positive integer first we prove that the bilinear forms graph is a connected vertex transitive graph when p 2 is distance regular if and only if s 1 next we completely determine the valency of a vertex the clique number the independence number and the chromatic number of the bilinear forms graph respectively finally we show that both and the complement of are not cores and their cores are complete

exact solution of an exclusion process with three classes of particles and vacancies we present an exact solution for an asymmetric exclusion process on a ring with three classes of particles and vacancies using a matrix product ansatz we find exact expressions for the weights of the configurations in the stationary state the solution involves tensor products of quadratic algebras

ring hulls and applications our goal is to develop methods that enable one to select a class k of rings and then to describe all right essential overrings or all right rings of quotients of a given ring r which lie in k our major method of attack is to determine the existence and or uniqueness of right ring hulls of r in k and to use these to characterize the right essential overrings of r which are in k some applications are 1 a characterization of the right rings of quotients of the 2 by 2 upper triangular matrix ring over a pid which are either baer or right extending 2 a characterization of a continuous ring hull for a commutative ring whose singular ideal has finite uniform dimension 3 a characterization of the right extending rings which have the 2 by 2 matrix ring over a given division ring for their maximal right ring of quotients 4 a characterization of the intermediate right extending rings between the 2 by 2 upper triangular matrix ring and the 2 by 2 matrix ring over a large class of local right finitely extending rings 5 a characterization of the classical right ring of quotients as a ring hull from a certain class of rings

suborbits of a point stabilizer in the unitary group on the last subconstituent of hermitean dual polar graphs let be a dual polar graph in a unitary space it is well known that a point stabilizer in the unitary group is transitive on the last subconstituent of in this paper we determine all the suborbits of this action calculate its rank and the length of each suborbit note that the induced subgraph on is quasi strongly regular as an application of our results all its parameters are computed

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

triangular matrix representations in this paper we develop the theory of generalized triangular matrix representation in an abstract setting this is accomplished by introducing the concept of a set of left triangulating idempotents these idempotents determine a generalized triangular matrix representation for an algebra the existence of a set of left triangulating idempotents does not depend on any specific conditions on the algebras however if the algebra satisfies a mild finiteness condition then such a set can be refined to a complete set of left triangulating idempotents in which each diagonal subalgebra has no nontrivial generalized triangular matrix representation we then apply our theory to obtain new results on generalized triangular matrix representations including extensions of several well known results

some general features of matrix product states in stochastic systems we will prove certain general relations in the matrix product ansatz mpa for one dimensional stochastic systems which are true in both random and sequential updates we will derive general mpa expressions for the currents and current correlators and find the conditions in the mpa formalism under which the correlators are site independent or completely vanishing

one dimensional partially asymmetric simple exclusion process on a ring with a defect particle the effect of a moving defect particle for the one dimensional partially asymmetric simple exclusion process on a ring is considered the current of the ordinary particles the speed of the defect particle and the density profile of the ordinary particles are calculated exactly the phase diagram for the correlation length is identified as a by product the average and the variance of the particle density of the one dimensional partially asymmetric simple exclusion process with open boundaries are also computed

triangular matrix representations of ring extensions in this paper we investigate the class of piecewise prime pwp rings which properly includes all piecewise domains hence all right hereditary rings which are semiprimary or right noetherian for a pwp ring we determine a large class of ring extensions which have a generalized triangular matrix representation for which the diagonal rings are prime

nonequilibrium steady states of matrix product form a solver s guide we consider the general problem of determining the steady state of stochastic nonequilibrium systems such as those that have been used to model among other things biological transport and traffic flow we begin with a broad overview of this class of driven diffusive systems which includes exclusion processes focusing on interesting physical properties such as shocks and phase transitions we then turn our attention specifically to those models for which the exact distribution of microstates in the steady state can be expressed in a matrix product form in addition to a gentle introduction to this matrix product approach how it works and how it relates to similar constructions that arise in other physical contexts we present a unified pedagogical account of the various means by which the statistical mechanical calculations of macroscopic physical quantities are actually performed we also review a number of more advanced topics including nonequilibrium free energy functionals the classification of exclusion processes involving multiple particle species existence proofs of a matrix product state for a given model and more complicated variants of the matrix product state that allow various types of parallel dynamics to be handled we conclude with a brief discussion of open problems for future research

on the ubiquity of matrix product states in one dimensional stochastic processes with boundary interactions abstract recently it has been shown that the zero energy eigenstate corresponding to the stationary state of a stochastic hamiltonian with nearest neighbour interaction in the bulk and single site boundary terms can generically be written in the form of a so called matrix product state we generalize this result to stochastic hamiltonians with arbitrary but finite interaction range as an application two different particle hopping models with three site bulk interaction are studied for these models which can be interpreted as cellular automata for traffic flow we present exact solutions for periodic boundary conditions and some suitably chosen boundary interactions

finite dimensional representations of the quadratic algebra applications to the exclusion process we study the one dimensional partially asymmetric simple exclusion process asep with open boundaries that describes a system of hard core particles hopping stochastically on a chain coupled to reservoirs at both ends derrida and coworkers showed in 1993 that the stationary probability distribution of this model can be represented as a trace on a quadratic algebra closely related to the deformed oscillator algebra we construct all finite dimensional irreducible representations of this algebra this enables us to compute the stationary bulk density as well as all correlation lengths for the asep on a set of special curves of the phase diagram

an exact solution of a one dimensional asymmetric exclusion model with open boundaries a simple asymmetric exclusion model with open boundaries is solved exactly in one dimension the exact solution is obtained by deriving a recursion relation for the steady state if the steady state is known for all system sizes less thann then our equation 8 gives the steady state for sizen using this recursion we obtain closed expressions 48 for the average occupations of all sites the results are compared to the predictions of a mean field theory in particular for infinitely large systems the effect of the boundary decays as the distance to the power 1 2 instead of the inverse of the distance as predicted by the mean field theory

synchronous asymmetric exclusion processes for a fully synchronous asymmetric exclusion process with open or closed boundaries only partial analytic results are known owing to the appearance of strong short range correlations which invalidate simple mean field approximations here we present a new method for calculating basic properties of nonequilibrium steady states and calculate densities fluxes travel times spatial and temporal correlation functions phase diagrams profiles and widths of boundary layers and interfaces between phases in coexistence as well as their microstructures this paper is based on two new elements i a microscopic characterization of order parameters and local configurations in the relevant phases based on the microdynamics of the model and ii an improved mean field approximation which neglects certain four point and higher order correlation functions it is conjectured that the density profiles obtained here are exact up to terms that are exponentially small in the system size

spectral degeneracies in the totally asymmetric exclusion process we study the spectrum of the markov matrix of the totally asymmetric exclusion process tasep on a one dimensional periodic lattice at arbitrary filling although the system does not possess obvious symmetries except translation invariance the spectrum presents many multiplets with degeneracies of high order when the size of the lattice and the number of particles obey some simple arithmetic rules this behaviour is explained by a hidden symmetry property of the bethe ansatz assuming a one to one correspondence between the solutions of the bethe equations and the eigenmodes of the markov matrix we derive combinatorial formulae for the orders of degeneracy and the number of multiplets these results are confirmed by exact diagonalisations of small size systems this unexpected structure of the tasep spectrum suggests the existence of an underlying large invariance group

matrix product states of three families of one dimensional interacting particle systems abstract the steady states of three families of one dimensional non equilibrium models with open boundaries first proposed in n j phys 5 2003 145 1 are studied using a matrix product formalism it is shown that their associated quadratic algebras have two dimensional representations provided that the transition rates lie on specific manifolds of parameters exact expressions for the correlation functions of each model have also been obtained we have also studied the steady state properties of one of these models first introduced in j phys a math gen a 36 2003 74 with more details by introducing a canonical ensemble we calculate the canonical partition function of this model exactly using the yang lee theory of phase transitions we spot a second order phase transition from a power law to a jammed phase the density profile of particles in each phase has also been studied a simple generalization of this model in which both the left and the right boundaries are open has also been introduced it is shown that double shock structures may evolve in the system under certain conditions

traffic of molecular motors through tube like compartments the traffic of molecular motors through open tube like compartments is studied using lattice models these models exhibit boundary induced phase transitions related to those of the asymmetric simple exclusion process asep in one dimension the location of the transition lines depends on the boundary conditions at the two ends of the tubes three types of boundary conditions are studied a periodic boundary conditions which correspond to a closed torus like tube b fixed motor densities at the two tube ends where radial equilibrium holds locally and c diffusive motor injection at one end and diffusive motor extraction at the other end in addition to the phase diagrams we also determine the profiles for the bound and unbound motor densities using mean field approximations and monte carlo simulations our theoretical predictions are accessible to experiments

exact solution of the master equation for the asymmetric exclusion process using the bethe ansatz we obtain the exact solution of the master equation for the totally asymmetric exclusion process on an infinite one dimensional lattice we derive explicit expressions for the conditional probabilitiesp x1 xn t y1 yn 0 of findingn particles on lattices sitesx1 xn at timet with initial occupationy1 yn at timet 0

phase transition in the abc model recent studies have shown that one dimensional driven systems can exhibit phase separation even if the dynamics is governed by local rules the mathrm abc model which comprises three particle species that diffuse asymmetrically around a ring shows anomalous coarsening into a phase separated steady state in the limiting case in which the dynamics is symmetric and the parameter q describing the asymmetry tends to one no phase separation occurs and the steady state of the system is disordered in the present work we consider the weak asymmetry regime q mathrm exp ensuremath ensuremath beta n where n is the system size and study how the disordered state is approached in the case of equal densities we find that the system exhibits a second order phase transition at some nonzero ensuremath beta c the value of ensuremath beta c 2 ensuremath pi sqrt 3 and the optimal profiles can be obtained by writing the exact large deviation functional for nonequal densities we write down mean field equations and analyze some of their predictions

the noncommutative space of stochastic diffusion systems in the matrix product ground states approach to n species diffusion processes the stationary probability distribution is expressed as a matrix product state with respect to a quadratic algebra determined by the dynamics of the process we show that the quadratic algebra defines a noncommutative space with a glq n quantum group action as its symmetry boundary processes account for the appearance of parameter dependent linear terms in the algebraic relations we argue that for systems with boundary conditions the diffusion algebras are also obtained either by a shift of basis in the n dimensional quantum plane or by an appropriate change of basis in a lower dimensional one which leads to a reduction of the glq n symmetry

simple lie algebras and graphs abstract kaplansky introduced several classes of central simple lie algebras in characteristic 2 we view these algebras in terms of graphs and we classify them using a theorem of shult characterizing graphs with the cotriangle condition there is also a connection with fischer s theorem on groups generated by 3 transpositions uniqueness of these algebras is phrased in terms of their cohomology and a lower bound for dim h 1 of these algebras is given

projective planes graphs and simple algebras abstract let x be a projective plane of order n a flag x0 l0 in x determines a graph f which is used to construct a central simple jordan algebra a of dimension n3 1 over a field k of characteristic 2 with x2 0 for all x a when n is even the group of all algebra automorphisms of a is isomorphic to the symplectic group sp n3 k we also imbed every finite connected graph g whose adjacency matrix is non singular mod 2 in a strongly regular graph g and we construct a central simple lie algebra over z 2 z from g in particular f gives a central simple lie algebra

matrix product ground states for exclusion processes with parallel dynamics we show in the example of a one dimensional asymmetric exclusion process that stationary states of models with parallel dynamics may be written in a matrix product form the corresponding algebra is quadratic and involves three different matrices using this formalism we prove previous conjectures for the equal time correlation functions of the model

large deviation of the density profile in the steady state of the open symmetric simple exclusion process we consider an open one dimensional lattice gas on sites i 1 n with particles jumping independently with rate 1 to neighboring interior empty sites the simple symmetric exclusion process the particle fluxes at the left and right boundaries corresponding to exchanges with reservoirs at different chemical potentials create a stationary nonequilibrium state sns with a steady flux of particles through the system the mean density profile in this state which is linear describes the typical behavior of a macroscopic system i e this profile occurs with probability 1 when n the probability of microscopic configurations corresponding to some other profile x x i n has the asymptotic form exp n f f is the large deviation functional in contrast to equilibrium systems for which f eq is just the integral of the appropriately normalized local free energy density the f we find here for the nonequilibrium system is a nonlocal function of this gives rise to the long range correlations in the sns predicted by fluctuating hydrodynamics and suggests similar non local behavior of f in general sns where the long range correlations have been observed experimentally

exact results for a fully asymmetric exclusion process with sequential dynamics and open boundaries an exact and rigorous calculation of the current and density profile in the steady state of the one dimensional fully asymmetric simple exclusion process with open boundaries and forward ordered sequential dynamics is presented the method is based on a matrix product representation of the steady state probability distribution the main idea is to choose a suitable representation in which the scalar products describing the current and local density profile for a chain of arbitrary finite size depend only on the elements in a finite number of rows and columns this makes possible the use of a truncated finite dimensional representation of the matrices and vectors involved after performing the calculations we lift the truncation by letting its dimensionality go to infinity in this limit the results become exact for any size of the chain by rescaling one of the infinitedimensional matrix representations found in the work of derrida et al j phys a 26 1493 1993 for their algebra we obtain a symmetric propagator matrix its truncated version is diagonalized by orthogonal transformation for easy calculation of the relevant scalar products an interpretation of the phase transitions between the different phases is given in terms of eigenvalue splitting from a bounded quasicontinuous spectrum a precise description of the local density profiles is given for all values of the parameters it is shown that the leading order asymptotic form of the position dependent terms in the local density changes within the low and high density phases signaling the presence of a higher order transition