solutions of the yang baxter equation for isotropic quantum spin chains the author considers solutions of the yang baxter equation such that the logarithmic derivative of the transfer matrix yields a quantum spin hamiltonian which is isotropic in spin space i e su 2 invariant four such solutions are known for each value of the spin s for s 1 2 they degenerate into the same solution and for s 1 they only give three different solutions for s or 6 he shows that these are the only solutions which are su 2 invariant except for s 3 when there is a fifth solution

subduction coefficients of brauer algebras and racah coefficients of o n and sp 2 m ii racah coefficients irreducible representations of brauer algebras are discussed in the non standard basis a method for evaluating subduction coefficients sdcs i e the transformation coefficients between standard and non standard bases of brauer algebras is outlined non trivial sdcs of for are derived racah coefficients of o n and sp 2m can be derived from subduction coefficients of brauer algebras by using the schur weyl duality relation between and o n or sp 2m

growth of order in vector spin systems scaling and universality the growth of order in vector spin systems with nonconserved order parameter model a is considered following an instantaneous quench from infinite to zero temperature the results of numerical simulations in spatial dimension d 2 and spin dimension 2n5 are presented for n4 a scaling regime where a characteristic length scale l t emerges is entered for sufficiently long times with l t t12 the autocorrelation function a t decays with time as a t t d lambda 2 and the exponent lambda n agrees well with the predictions of the 1 n expansion the cases n 2 and 3 are more complicated due to the non trivial role played by topological singularities i e vortices n 2 and polyakov solitons n 3 for n4 universal amplitudes and scaling functions characterizing the energy relaxation and the equal time correlation function are identified it is argued that for d3 where an ordered phase exists at low temperature such universal quantities characterize the entire ordered phase

generalized vector coherent state theory of sp 2n r vector operators and of sp 2n r contains implies u n reduced wigner coefficients sp 2n r contains implies u n reduced wigner coefficients coupling a positive discrete series unitary irreducible representation with the 2n dimensional non unitary irreducible representation characterized by 1 are evaluated by making use of generalized vector coherent state techniques general formulae are given in terms of the k matrix elements of vector coherent state theory and of some u n 6j or 9j type recoupling coefficients explicit analytic expressions are obtained in some important special cases such results should allow a determination of wsp 2n r approximately w n p 2n r and osp p 2n r matrix representations to be completed because both the w n generators and the osp p 2n r odd generators transform under the sp 2n r irrep 1

reaction diffusion processes described by three state quantum chains and integrability the master equation of one dimensional three species reaction diffusion processes is mapped onto an imaginary time schrodinger equation in many cases the hamiltonian obtained is that of an integrable quantum chain with known properties within this approach we search for three state integrable quantum chains with known spectra and which are related to diffusive reactive systems two integrable models are found to appear naturally in this context the uqsu 2 invariant model with external fields and the three state uqsu p m invariant perk schultz models with external fields a non local similarity transformation which brings the hamiltonian governing the chemical processes to the known standard forms is described leading in the case of periodic boundary conditions to a generalization of the dzialoshinsky moriya interaction for n state hamiltonians n 2

comparison theorems and orbit counting in hyperbolic geometry in this article we address an interesting problem in hyperbolic geometry this is the problem of comparing different quantities associated to the fundamental group of a hyperbolic manifold e g word length displacement in the universal cover etc asymptotically our method involves a tnixture of ideas from both thermodynamic ergodic theory and the automaton associated to strongly markov groups 0 introduction in 5 cannon showed that for fundamental groups of many manifolds of negative curvature including for example compact manifolds the generating function for word length is a rational function to explain the implications of this property we recall that the growth of the quantity n n card g fe r igl n was studied by milnor in his fundamental paper 13 where he obtained estimates using comparison with the growth of volume in the universal cover cannon used purely combinatorial methods to show that the generating function is rational in particular this implies that we can find constants ybi and ci and positive integers ki i 1 n such that n n 1 1 cinkitn the key step in cannon s approach was to associate to the grol1p an automaton in this article we shall augment this with the notion of weighting this allows us to draw upon the well known theory of thermodynamic formalism to prove a number of new results which can be viewed as weighted analogues of the above results it has long been understood that this approach must havew close connections with symbolic dynamics markov partitions subshifts of finite type cf 1 20 21 and in particular the work of bourdon 4 and by extension to the whole paraphernalia of the area of dynamical systems collectively called thermodynamic formalism in this article we shall elaborate on this connection as an integral part of our analysis let teln for some n 2 denote n dimensional hyperbolic space i e the unique n dimensional simply connected complete riemannian manifold wi th all sectional received by the editors may 23 1995 1991 mathematics subject classification primary 20f32 22e40 58e40 secondary 11f72 20f10 58f20

adsorption and collapse of self avoiding walks in three dimensions a monte carlo study we consider self avoiding walks on the simple cubic lattice with a unit degree vertex at the origin and confined to the half space in addition the walks interact with the plane z 0 and have a vertex vertex interaction within the walk so that the walk can adsorb at the surface z 0 and also undergo collapse we investigate the interaction between collapse and adsorption using monte carlo methods and explore the form of the phase diagram

exact evaluation of the collapse phase boundary for two dimensional directed polymers the phase boundary of the collapsed phase for a directed polymer on a square lattice in the presence of an attractive wall and monomer monomer interactions is calculated exactly using transfer matrix techniques the position of the multicritical point is also identified

more on coupling coefficients for the most degenerate representations of so n we present explicit closed form expressions for the general group theoretical factor appearing in the topology of a high temperature expansion of so n symmetric lattice models this object which is closely related to 6j symbols for the most degenerate representation of so n is discussed in detail

transfer matrix study of the adsorption of a flexible self avoiding polymer chain in two dimensions the authors model the polymer as a self avoiding walk on a semi infinite square lattice with an energy contribution in from each step along the lattice boundary the critical adsorption temperature ta and the ordinary and special surface exponents of the walk above and at the adsorption temperature respectively are estimated with transfer matrix finite size scaling methods for the adsorption temperature they obtain exp in kta 2 041 or 0 002 and for the crossover and susceptibility exponents of the special transition phi sp 0 501 or 0 003 and gamma 1sp 1 454 or 0 004

a hierarchy of coupled burgers systems possessing a hereditary structure a hierarchy of typical integrable coupled burgers systems is proposed by introducing a special spectral problem involving q dependent variables u0 u1 uq 1 these systems possess a hereditary structure and may reduce to a hierarchy of burgers equations under the reduction ui 0 0 or i or q 2 it is shown that their flows and lax operators commute mutually but each system is not hamiltonian

riemann liouville fractional integration and reduced distributions on hyperspheres using properties of dirichlet s iterated integral formula the author shows how the riemann liouville fractional integral unifies arbitrary moment calculations for reduced distributions on hyperspheres a whole class of problems of this type is then reduced to readily identifiable integral transforms the work is applied to quantum inference and connections made to random matrix theory aspects of nuclear physics and quantum chaos

quantum maps from transfer operators abstract the selberg zeta function s s yields an exact relationship between the periodic orbits of a fully chaotic hamiltonian system the geodesic flow on surfaces of constant negative curvature and the corresponding quantum system the spectrum of the laplace beltrami operator on the same manifold it was found that for certain manifolds s s can be exactly ewritten as the fredholm grothendieck determinant det 1 t s where ts is a generalization of the ruelle perron frobenius transfer operator we present an alternative derivation of this result yielding a method to find not only the spectrum but also the eigenfunctions of the laplace beltrami operator in terms of eigenfunctions of ts various properties of the transfer operator are investigated both analytically and numerically for several systems

the algebraic structures of isospectral lax operators and applications to integrable equations for a general spectral operator the author establishes types of algebraic structures of the spaces of the corresponding isospectral lax operators which essentially form the theoretical basis of the lax operator method furthermore the author introduces the concepts of tau algebras and master algebras to describe time polynomial dependent symmetries of nonlinear integrable equations finally the author applies the theory of lax operators to the kp hierarchy of integrable equations as an illustrative example and thus obtain the master symmetry algebra of the kp hierarchy

keller osserman a priori estimates and the harnack inequality for quasilinear elliptic and parabolic equations with absorption term abstract in this article we study quasilinear equations model of which are i 1 n u x i p i 2 u x i x i f u 0 u 0 u t i 1 n u m i 1 p i 1 u x i p i 2 u x i x i f u 0 u 0 despite of the lack of comparison principle we prove a priori estimates of keller osserman type particularly under some natural assumptions on the function f for nonnegative solutions of p laplace equation with absorption term we prove an estimate of the form 0 u x 0 f s d s c r p u p x 0 x 0 b 8 r x 0 with constant c independent of u using this estimate we give a simple proof of the harnack inequality we prove a similar result for the evolution p laplace equation with absorption

the effect of attractive monomer monomer interactions on adsorption of a polymer chain the authors have used transfer matrix techniques to study a model of polymer adsorption and collapse they consider the conventional model of a self avoiding walk with attractive nearest neighbour interactions on the square lattice and introduce adsorbing boundaries the numerical results are consistent with the existence of a multicritical point where the adsorption and collapse transitions coincide and suggest that the adsorption transition of a collapsed polymer chain in first order there is also clear evidence that the collapse transition lowers the adsorption temperature estimates of the surface scaling dimensions at the ordinary theta transition support the conjecture of seno and stella 1988 that the surface critical behaviour at the theta and theta points belong to different universality classes

boundaries of markov partitions the core of a markov partition is the nonwandering set of the map restricted to the boundary of the partition we show that the core of a markov partition is always a finitely presented system then we show that every one sided sofic system occurs as the core of a markov partition for an n fold covering map on the circle and every two sided sofic system occurs as the core of a markov partition for a hyperbolic automorphism of the two dimensional torus

induced measures in the space of mixed quantum states we analyse several product measures in the space of mixed quantum states in particular we study measures induced by the operation of partial tracing the natural rotationally invariant measure on the set of all pure states of a n k composite system induces a unique measure in the space of n n mixed states or in the space of k k mixed states if the reduction takes place with respect to the first subsystem for k n the induced measure is equal to the hilbert schmidt measure which is shown to coincide with the measure induced by singular values of non hermitian random gaussian matrices pertaining to the ginibre ensemble we compute several averages with respect to this measure and show that the mean entanglement of n n pure states behaves as lnn 1 2

ageing properties of critical systems in the past few years systems with slow dynamics have attracted considerable theoretical and experimental interest ageing phenomena are observed during this everlasting non equilibrium evolution a simple instance of such a behaviour is provided by the dynamics that takes place when a system is quenched from its high temperature phase to the critical point the aim of this review is to summarize the various numerical and analytical results that have been recently obtained for this case particular emphasis is put on the field theoretical methods that can be used to provide analytical predictions for the relevant dynamical quantities fluctuation dissipation relations are discussed and in particular the concept of fluctuation dissipation ratio fdr is reviewed emphasizing its connection with the definition of a possible effective temperature the renormalization group approach to critical dynamics is summarized and the scaling forms of the time dependent non equilibrium correlation and response functions of a generic observable are discussed from them the universality of the associated fdr follows as an amplitude ratio it is then possible to provide predictions for ageing quantities in a variety of different models in particular the results for models a b and c dynamics of the o n ginzburg landau hamiltonian and model a dynamics of the weakly dilute ising magnet and of the 3 theory are reviewed and compared with the available numerical results and exact solutions the effect of a planar surface on the ageing behaviour of model a dynamics is also addressed within the mean field approximation

the embedding e0 and the spectrum dependent r matrix for q f4 the explicit embedding forms of e0 for the minimal representations of the quantum f4 e6 and e7 are obtained in this paper in terms of jimbo s method the spectrum dependent r matrices both trigonometric and rational for those representations are computed

renyi wehrl entropies as measures of localization in phase space we generalize the concept of the wehrl entropy of quantum states which gives a basis independent measure of their localization in phase space we discuss the minimal values and the typical values of these r enyi wehrl entropies for pure states for spin systems according to lieb s conjecture the minimal values are provided by the spin coherent states though lieb s conjecture remains unproven we give new proofs of partial results that may be generalized for other systems we also investigate random pure states and calculate the mean r enyi wehrl entropies averaged over the natural measure in the space of pure quantum states

extended covariance for the lagrange equations of motion a geometric analysis the infinitesimal transformations which leave the lagrangian structure of the equations of motion unchanged are intrinsically characterized a new condition is given with which to obtain alternative lagrangians

solitary wave solutions of nonlinear evolution and wave equations using a direct method and macsyma the direct algebraic method for constructing travelling wave solutions on nonlinear evolution and wave equations has been generalized and systematized the class of solitary wave solutions is extended to analytic rather than rational functions of the real exponential solutions of the linearized equation expanding the solutions in an infinite series in these real exponentials an exact solution of the nonlinear pde is obtained whenever the series can be summed methods for solving the nonlinear recursion relation for the coefficients of the series and for summing the series in closed form are discussed the algorithm is now suited to solving nonlinear equations by any symbolic manipulation program this direct method is illustrated by constructing exact solutions of a generalized kdv equation the kuramoto sivashinski equation and a generalized fisher equation

chaotic sets of continuous and discontinuous maps abstract this paper discusses li yorke chaotic sets of continuous and discontinuous maps with particular emphasis to shift and subshift maps scrambled sets and maximal scrambled sets are introduced to characterize li yorke chaotic sets the orbit invariant for a scrambled set is discussed some properties about maximality equivalence and uniqueness of maximal scrambled sets are also discussed it is shown that for shift maps the set of all scrambled pairs has full measure and chaotic sets of some discontinuous maps such as the gauss map interval exchange transformations and a class of planar piecewise isometries are studied finally some open problems on scrambled sets are listed and remarked

combinatorics of transformations from standard to non standard bases in brauer algebras transformation coefficients between standard bases for irreducible representations of the brauer centralizer algebra and split bases adapted to the subalgebra f1 f2 f are considered after providing the suitable combinatorial background based on the definition of the i coupling relation on nodes of the subduction grid we introduce a generalized version of the subduction graph which extends the one given in chilla 2006 j phys a math gen 39 7657 for symmetric groups thus we can describe the structure of the subduction system arising from the linear method and give an outline of the form of the solution space an ordering relation on the grid is also given and then as in the case of symmetric groups the choices of the phases and of the free factors governing the multiplicity separations are discussed

the asymmetric simple exclusion process an integrable model for non equilibrium statistical mechanics the asymmetric simple exclusion process asep plays the role of a paradigm in non equilibrium statistical mechanics we review exact results for the asep obtained by the bethe ansatz and put emphasis on the algebraic properties of this model the bethe equations for the eigenvalues of the markov matrix of the asep are derived from the algebraic bethe ansatz using these equations we explain how to calculate the spectral gap of the model and how global spectral properties such as the existence of multiplets can be predicted an extension of the bethe ansatz leads to an analytic expression for the large deviation function of the current in the asep that satisfies the gallavotti cohen relation finally we describe some variants of the asep that are also solvable by the bethe ansatz

collapsing and adsorbing polygons the adsorption transition in the phase diagram of a self interacting lattice polygon is examined the polygon has a nearest neighbour contact fugacity and the interaction between the polygon and an impenetrable wall is modelled by a visit fugacity which is conjugate to the number of vertices of the polygon incident with the wall the partition function of this model is z c y z d p v cp c v c y v z c where p c v c is the number of polygons with c nearest neighbour contacts v visits to the wall and n edges and counted up to translations parallel to the wall the limiting free energy of this model is f c y z d limn 1 1 logz c y z and it is known to be a non analytic function of y for each z 1 for all z2 0 1

response of non equilibrium systems with long range initial correlations the long time dynamics of the d dimensional spherical model with a non conserved order parameter and quenched from an initial state with long range correlations is studied through the exact calculation of the two time autocorrelation and autoresponse functions in the ageing regime these are given in terms of non trivial universal scaling functions of both time variables at criticality five distinct types of ageing are found depending on the form of the initial correlations while at low temperatures only a single type of ageing exists the autocorrelation and autoresponse exponents are shown to be generically different and to depend on the initial conditions the scaling form of the two time response functions agrees with a recent prediction coming from conformal invariance

symmetry groups of attractors for maps equivariant under the action of a finite group on n the possible symmetries of fixed points are known and correspond to the isotropy subgroups this paper investigates the possible symmetries of arbitrary possibly chaotic attractors and finds that the necessary conditions of melbourne dellnitz golubitsky 15 are sufficient at least for continuous maps

dynamic correlations in phase ordering the 1 n expansion reconsidered the ordering dynamics of a system with a non conserved order parameter is considered following a quench into the ordered phase from high temperature newman and bray 1990 have set up an expansion in powers of 1 n for the o n model to obtain correlation functions and the two time exponent lambda but their calculation contains a simplifying assumption which is incorrect tight upper and lower bounds for lambda are obtained as a function of the space dimension d these bounds exclude the result of newman and bray although the dependence of lambda on d is qualitatively very similar comparison with simulations shows that the first order 1 n calculation does not agree with numerical results as well as previously thought

symbolic dynamics for geodesic floes the subject of symbolic dynamics is of central importance in the modern theory of dynamical systems the use of symbolic sequences to study dynamical properties of geodesies originates in the work of koebe 21 22 and morse 24 25 and is already foreshadowed in hadamard 15 and jordan 19 the method of koebe and of morse is to code a geodesic on a surface m of negative curvature by recording the order in which it traverses a given set of labelled curves on m the treatment of morse allows variable curvature but assumes at least two boundary components whereas koebe assumes constant curvature but allows infinite connectivity and nonorientability and treats the more difficult case of a closed surface this last case is handled by recording crossings of a fixed pants decomposition anticipating the thurston parameterization of simple curves as described in 11 both koebe and morse used their codings to demonstrate the existence of countably many closed geodesies and of everywhere dense transitive geodesies morse further constructed the first nonsynthetic example of a recurrent nonperiodic discontinuous motion in modern terminology a minimal nowhere dense set later 26 morse treated the special closed surfaces of genus g associated to tesselations of the disc d by regular 4 gons each edge of a region in such a tesselation may be labelled by the isometry which glues it to another side of the same region in forming the quotient sin face m the set of isometries appearing as labels generate tti m thus any geodesic is coded as a doubly infinite sequence of generators of iri m the same method applies quite generally to tesselations associated to any fuchsian group we call the sequences thus obtained cutting sequences and refer to generating sets of this kind as geometric the difficulty of course is to determine precisely the class of sequences which occur for a surface with boundary one obtains exactly reduced sequences in the generators in generalthe problem4s gompligated1 henge the difficulties encountered in 26 see also theorem 3 below there is another method of coding geodesies using certain boundary expansions for points at infinity in the universal cover of m for the modular surface h sl 2 2 the appropriate expansions are continued fractions and for the symmetrical genus g surfaces above they are the nielsen boundary expansions of 27

painleve analysis of the generalized burgers huxley equation a complete painleve test 1900 is applied to the generalized burgers huxley equation using the version of the painleve analysis recently developed by weiss tabor and carnevale 1983 for partial nonlinear differential equations in so doing the authors are able to find a complete set of new solutions as well as recovering some previous particular solutions already found by using ad hoc methods which have been recently published

adsorption and collapse of self avoiding walks at a defect plane we consider self avoiding walks and polygons on the simple cubic lattice with a vertex vertex interaction i e a contact interaction which also interact with a defect plane z 0 the walks or polygons can undergo a collapse transition and can also adsorb at the defect plane for the polygon case we prove that the limiting free energy exists and show that there is an adsorption transition for each finite value of the vertex vertex interaction we use monte carlo methods to investigate the form of the phase diagram for the walk problem

statistical regularities of self intersection counts for geodesics on negatively curved surfaces let s be a compact surface with constant negative curvature 1 from among all closed geodesics on of length t choose one at random and letnt be the number of its self intersections we prove that for a certain constant 0 the random variable nt t t has a limit distribution as t we conjecture that for surfaces of variable negative curvature the order of magnitude of typical variations is t rather than t we also prove analogous results for generic geodesics that is geodesics whose initial tangent vectors are chosen randomly according to normalized liouville measure date november 10 2011 1991 mathematics subject classification primary 57m05 secondary 53c22 37d40

universality class for domain growth in random magnets a 2d ising model with random ferromagnetic bonds is studied by monte carlo simulation following a quench from t infinity to t tc the domain size grows as l t approximately in t to x at late times the data are consistent with the theoretical prediction chi 4 the exponent defined by si 0 si t approximately l t and the scaling functions for the spatial correlations are very close to those of the pure system suggesting that pure and random systems belong to the same universality class

adsorbing and collapsing trees self interacting branched polymers interacting with a wall can be modelled by lattice trees in a half space with a nearest neighbour contact fugacity and a visit fugacity conjugate to the number of visits the tree makes to the wall which is the boundary of the half space we show that there is a limiting free energy in this model and that it is a non analytic function of the visit fugacity for every finite and fixed value of the contact fugacity this implies the existence of an adsorption transition in this model and there is a critical curve in the phase diagram which separates the phase of desorbed trees from a phase of adsorbed trees moreover we show that for all finite values of the contact fugacity and the adsorption transition occurs at a strictly attractive value of the interaction between the tree and the wall

finite length scaling of collapsing directed walks we study the finite length scaling of self interacting partially directed self avoiding walks utilising enumeration data up to a total length of 6000 steps this facilitates the evaluation of the numerical techniques available for calculating exponents at the point and in the collapsed phase of walk type models another consequence is the conjecture of a new scaling theory for the collapsed region of the phase diagram and the suggestion that this should be applicable to the wider range of undirected problems including interacting saw we provide a phenomenological picture of the phase transition in terms of the condensation of droplets that allows us to understand the various length scales involved in the problem pacs numbers 05 50 q 05 70 fh 61 41 e email prel aleks brak tonyg mundoe maths mu oz au

time dependent symmetries of variable coefficient evolution equations and graded lie algebras polynomial in time dependent symmetries are analysed for polynomial in time dependent evolution equations graded lie algebras especially virasoro algebras are used to construct nonlinear variable coefficient evolution equations both in 1 1 dimensions and in 2 1 dimensions which possess higher degree polynomial in time dependent symmetries the theory also provides a kind of new realization of graded lie algebras some illustrative examples are given

the tricritical behavior of self interacting partially directed walks we present the thermodynamics of two variations of the interacting partially directed self avoiding walk problem by discussing versions where the length of the walks assume real as well as a integral values while the discrete model has been considered previously to varying degrees of success the continuous model we now define has not the examination of the continuous model leads to theexact derivation of several exponents for the discrete model some of these exponents can be calculated using a continued fraction representation for both models the crossover exponent is found to be 2 3 moreover we confirm the tricritical nature of the collapse transition in the generalized ensemble and calculate the full scaling form of the generating function additionally the similarities noticed previously to other models but left unexplored are explained with the aid of necklacing arguments

fractional strings hypothesis and non simple laced integrable models the author discusses the ground state and some elementary excitations of the bp non simple laced integrable models the zeros of the associated bethe ansatz equations are characterized by a special distribution in the complex plane which is different from the usual string hypothesis the introduction of this new solution makes it possible to calculate exactly various properties in the thermodynamic limit the finite size corrections to the eigenspectrum strongly suggest that the bp wess zumino witten novikov models are the underlying conformal field theory for these non simple laced models

branching annihilating random walks in one dimension some exact results we derive a self duality relation for a one dimensional model of branching and annihilating random walkers with an even number of offspring on nearest neighbour sites with the duality relation and by deriving further exact results in some limiting cases involving fast diffusion we obtain new information on the location and nature of the phase transition line between an active stationary state non zero density and an absorbing state extinction of all particles thus clarifying some so far open problems in these limits the transition is mean field like but on the active side of the phase transition line the fluctuation in the number of particles deviates from its mean field value we also show that well within the active region of the phase diagram a finite system approaches the absorbing state very slowly on a time scale which diverges exponentially in system size in the absence of particle diffusion the branching process with infinite annihilation rate is strongly non ergodic

almost sure invariance principle for sequential and non stationary dynamical systems we establish almost sure invariance principles a strong form of approximation by brownian motion for non stationary time series arising as observations on dynamical systems our examples include observations on sequential expanding maps perturbed dynamical systems non stationary sequences of functions on hyperbolic systems as well as applications to the shrinking target problem in expanding systems

random unitary matrices methods of constructing random matrices typical of circular unitary and circular orthogonal ensembles are presented we generate numerically random unitary matrices and show that the statistical properties of their spectra level spacing distribution number variance and eigenvectors entropy participation ratio eigenvector statistics confer to the predictions of the random matrix theory for both cue and coe

infinitely many symmetries of the davey stewartson equation using a formal series symmetry method for the davey stewartson equation dse we find that there exist two sets of infinitely many formal series symmetries of the dse however different from the kadomtsev petviashvili equation kpe we failed to get infinitely many truncated symmetries only six truncated symmetries can be obtained simply from the formal series symmetries

anisotropy in field assisted diffusion on a gasket fractal the random walk on the two dimensional gasket fractal has been studied with various forms of constant bias fields applied using the monte carlo method crossover from anomalous diffusion to drift was observed in the horizontal and upward bias fields while crossover from anomalous to normal diffusion was found in the downward bias field the scaling relation r bs t approximately tkf bstk was confirmed and the scaling exponent of f x approximately xbeta at large x was obtained as beta 1 175 or 0 004 for the horizontal bias field and beta 0 319 or 0 002 for the downward bias field in good agreement with the theoretical work by parrondo et al 1990

non abelian pseudopotentials and conservation laws of reaction diffusion equations the authors apply the wahlquist estabrook technique to reaction diffusion equations a representation for non abelian pseudopotentials is obtained an infinite hierarchy of conservation laws is derived from these pseudopotentials the class of equations associated with such pseudopotentials is determined and examples are presented

weil petersson metrics manhattan curves and hausdorff dimension in this note we want to relate the weil petersson metric on teichm uller space to the boundary correspondence between the actions on the boundary of fuchsian groups consider the space of riemann metrics g on a compact surface v with negative euler characteristic this can be endowed with a number of natural riemannian metrics of particular interest is the weil petersson metric whose definition was proposed by weil in 1958 based on earlier work of petersson cf 18 there is a particularly intuitive equivalent definition of the weil petersson metric using the second derivative of lengths of typical closed geodesics due to thurston and wolpert 19

phenomenological renormalisation of the self avoiding walk in two dimensions phenomenological renormalisation is used to calculate the exponent v and the connective constant of the self avoiding walk problem on a square lattice a transfer matrix technique is developed for the polymer problem the results indicate that flory s value v 0 75 is true in two dimensions to extremely high accuracy

the dynamics of pythagorean triples we construct a piecewise onto 3 to 1 dynamical system on the positive quadrant of the unit circle such that for rational points which correspond to normalized primitive pythagorean triples the associated ternary expansion is finite and is equal to the address of the ppt on barning s 1963 ternary tree of ppts while irrational points have infinite expansions the dynamical system is conjugate to a modified euclidean algorithm the invariant measure is identified and the system is shown to be conservative and ergodic we also show based on a result of aaronson and denker 1999 that the dynamical system can be obtained as a factor map of a cross section of the geodesic flow on a quotient space of the hyperbolic plane by the group 2 a free subgroup of the modular group with two generators

correlations for pairs of closed geodesics in this article we consider natural counting problems for closed geodesics on negatively curved surfaces we present asymptotic estimates for pairs of closed geodesics the differences of whose lengths lie in a prescribed family of shrinking intervals related pair correlation problems have been studied in both quantum chaos and number theory

symbolic dynamics for the modular surface and beyond in this expository article we describe the two main methods of representing geodesics on surfaces of constant negative curvature by symbolic sequences and their development a geometric method stems from a 1898 work of j hadamard and was developed by m morse in the 1920s it consists of recording the successive sides of a given fundamental region cut by the geodesic and may be applied to all finitely generated fuchsian groups another method of arithmetic nature uses continued fraction expansions of the end points of the geodesic at infinity and is even older it comes from the gauss reduction theory introduced to dynamics by e artin in a 1924 paper this method was used to exhibit dense geodesics on the modular surface for 80 years these classical works have provided inspiration for mathematicians and a testing ground for new methods in dynamics geometry and combinatorial group theory we present some of the ideas results old and recent and interpretations that illustrate the multiple facets of the subject

on lyapunov exponent and sensitivity sensitive dependence on initial conditions is widely understood as being the central idea of chaos for a large class of transformations of the interval we prove that positiveness of the lyapunov exponent implies the sensitivity property we also provide bounds for the sensitivity constant

generalized continued fractions1research supported by garc src kosef 1 the invariant measures for the transformations x f x on the unit interval are studied where i f c 2 ii f or p p 0 0 241485

correlations of length spectra for negatively curved manifolds in this paper we obtain asymptotic estimates for pairs of closed geodesics on negatively curved manifolds the differences of whose lengths lie in a prescribed family of shrinking intervals where the geodesics are ordered with respect to a discrete length in certain cases this discrete length can be taken to be the word length with respect to a set of generators for the fundamental group

the algebraic structure of zero curvature representations and application to coupled kdv systems the author first establishes an algebraic structure related to zero curvature representations and propose a new approach for calculating symmetry algebras of integrable systems then he deduces a hierarchy of nonisospectral flows associated with coupled kdv systems from a spectral problem with the laurent polynomial dependent form of the spectral parameter furthermore the commutator relations of lax operators corresponding to isospectral and nonisospectral flows are worked out according to this algebraic structure and thus a symmetry algebra for coupled kdv systems is engendered from this general theory

adsorption and collapse of self avoiding walks and polygons in three dimensions we consider self avoiding walks and polygons on the simple cubic lattice confined to the half space and interacting with the plane z 0 in addition there is a short range vertex vertex interaction in the walk or polygon which can lead to a collapse transition we explore the interaction between collapse and adsorption in these systems and discuss the form of the phase diagram key results include a proof of the existence of an adsorption transition for polygons for every value of the vertex vertex interaction a corresponding proof for walks when the vertex vertex interaction term is repulsive and a proof that if polygons exhibit a collapse transition then the phase boundary between the expanded and desorbed phase and the collapsed and desorbed phase must be a straight line

on quantum deformations of the simplest lie parasuperalgebra quantum deformations of the simplest lie parasuperalgebra psqm 2 are constructed by taking advantage of the well known representations of suq 2 c as a particular result the authors show that the fundamental witten superalgebra sqm 2 cannot be deformed

self consistent screening approximation for critical dynamics we generalize bray s self consistent screening approximation to describe the critical dynamics of the theory in order to obtain the dynamical exponent z we have to make an ansatz for the form of the scaling functions which fortunately can be restricted by general arguments numerical values of z for d 3 and n 1 10 are obtained using two different ansatz and differ by a very small amount in particular the value of obtained for the three dimensional ising model agrees well with recent monte carlo simulations

vector coherent state theory of the noncompact orthosymplectic superalgebras i general theory vector coherent states are defined for the positive discrete series irreducible representations of the non compact orthosymplectic superalgebras osp p 2n r where p 2m or 2m 1 an orthonormal bargmann berezin basis symmetry adapted to osp p 2n r so p sp 2n r so p u n is constructed and used to develop the k matrix theory for osp p 2n r a general method is provided for determining the conditions of existence of star representations and of grade star representations in the osp 2 2n r case and the branching rule for their decomposition into a direct sum of so p sp 2n r irreducible representations as a by product it also enables the matrix elements of the odd generators between basis states of lowest weight so p u n irreducible representations to be calculated in a straightforward way

two dimensional self avoiding walk with hydrogen like bonding phase diagram and critical behaviour the phase diagram for a two dimensional self avoiding walk model on the square lattice incorporating attractive short ranged interactions between parallel sections of walk is derived using numerical transfer matrix techniques the model displays a collapse transition in contrast to the standard point model the transition is first order the phase diagram in the full fugacity temperature plane displays an additional transition line when compared to the point model as well as a critical transition at finite temperature in the hamiltonian walk limit

hamiltonian structure of discrete soliton systems we describe an approach for investigating the hamiltonian structures of the lattice isospectral evolution equations associated with a general discrete spectral problem by using the so called implicit representations of the isospectral flows we demonstrate the existence of the recursion operator l which is a strong and hereditary symmetry of the flows it is then proven that every equation in the isospectral hierarchy possesses the hamiltonian structure if l has a skew symmetric factorization and the first equation ut k 0 in the hierarchy satisfies some simple condition we obtain related properties such as the implectic symplectic factorization of l the liouville complete integrability and the multi hamiltonian structures of the isospectral hierarchy four examples are given

the statistical mechanics of random copolymers random copolymers are polymers with two or more types of monomer where the monomer sequence is determined by some random process once determined the sequence is fixed so random copolymers are an example of a system with quenched randomness we review the statistical mechanics of random copolymers focusing on self avoiding walk models where there are two types of monomers a and b which are randomly distributed along the polymer chain theoretical approximate and numerical results are reviewed for models of the random copolymer adsorption localization and collapse phase transitions we concentrate on what is known about the existence of phase transitions the morita approximation and results about self averaging we also discuss in less detail the replica trick and numerical methods including monte carlo methods exact enumeration and transfer matrix methods important open problems are identified throughout and highlighted in the conclusions

free energy as a geometric invariant the free energy plays a fundamental role in statistical and condensed matter physics a related notion of free energy plays an important role in the study of hyperbolic dynamical systems in this paper we introduce and study a natural notion of free energy for surfaces with variable negative curvature this geometric free energy encodes a new type of marked length spectrum of closed geodesics which lies between the well known marked length spectrum marked by the corresponding element of the fundamental group and the unmarked length spectrum we prove that the free energy parametrizes the boundary of the domain of convergence of a poincare series which also encodes this spectrum we also show that this new length spectrum or equivalently the geometric free energy is not an isometry invariant in the final section we use tools from multifractal analysis to effect a fine asymptotic comparison of word length and geodesic length of closed geodesics we hope that our geometric understanding of free energy will provide new insight into this fundamental physical and dynamical quantity

the monge metric on the sphere and geometry of quantum states topological and geometrical properties of the set of mixed quantum states in the n dimensional hilbert space are analysed assuming that the corresponding classical dynamics takes place on the sphere we use the vector su 2 coherent states and the generalized husimi distributions to define the monge distance between two arbitrary density matrices the monge metric has a simple semiclassical interpretation and induces a non trivial geometry among all pure states the distance from the maximally mixed state proportional to the identity matrix admits the largest value for the coherent states while the delocalized chaotic states are close to this contrasts the geometry induced by the standard trace hilbert schmidt or bures metrics for which the distance from is the same for all pure states we discuss possible physical consequences including unitary time evolution and the process of decoherence we introduce also a simplified monge metric defined in the space of pure quantum states and more suitable for numerical computation

hamiltonian and quasi hamiltonian structures associated with semi direct sums of lie algebras the trace variational identity is generalized to zero curvature equations associated with non semi simple lie algebras or equivalently lie algebras possessing degenerate killing forms an application of the resulting generalized variational identity to a class of semi direct sums of lie algebras in the akns case furnishes hamiltonian and quasi hamiltonian structures of the associated integrable couplings three examples of integrable couplings for the akns hierarchy are presented one hamiltonian and two quasi hamiltonian

interacting partially directed walks a model of polymer collapse abstract a survey of the results that have been obtained to date on the partially directed walk model of the polymer collapse transition is presented