supports of derivations free factorizations and ranks of fixed subgroups in free groups for f a free group of finite rank it is shown that the fixed subgroup of any set b of endomorphisms of f has rank rank f generalizing a recent result of dicks and ventura the proof involves the combinatorics of derivations of groups some related questions are examined

heat fluctuation distribution from non equilibrium states a non equilibrium state is described by parameters alpha j aj which are ensemble averages of dynamical phase functions aj gamma by using a projection operator technique of zwanzig 1961 one can derive from the classical liouville equation an integro differential equation for g vj the amplitude for the probability that the aj have respective values vj these previously derived results are applied to the heat flux aj in a fluid and an approximate differential equation derived for g v j where j aj the first moment of this equation yields the catteneo vernotte equation 1958 with a set of auxiliary assumptions which are also employed in solving the equation for g the author obtains g g 0 1 g v j where g 0 kappa pi mu 3 2 exp mu v j 2 kappa is the einstein distribution and g is a sum of products of scalar combinations of j v j and del t and laguerre polynomials ln 12 z2 where z identical to mu kappa 1 2 v j the einstein distribution g 0 gives correctly nu 2 to o j2 when del t 0 but not in the presence of a temperature gradient

generalized deformed algebras f a1 and their applications generalized deformation of a1 is proposed some generalized deformed algebras f a1 and their unitary representations are discussed in detail f a1 involves not only lie algebras su 2 su 1 1 e2 and boson algebra as special cases but also quantum algebras suq 2 suq 1 1 q boson algebra and a large class of other nonlinear algebras it is found that these algebras can be mapped from one type to another by generalized deforming functionals in some cases possible applications in physical problems are outlined some examples are also given as illustrations

quantum algebra deforming maps clebsch gordan coefficients coproducts r and u matrices quantum algebra deforming maps explicitly define comultiplications that differ from the usual noncocommutative coproducts map induced coproducts are connected to the usual ones by similarity transformations u that may be expressed either in terms of clebsch gordan coefficients or in a universal operator form the product of two such u matrices yields the r matrix for a fixed value of the spectral parameter which bears on the yang baxterization of u as well as r all this is explicitly illustrated for the tensor product 1 2 j of su 2 q using several deforming maps whose coproducts are continuously connected by similarity transformations to form a two parameter manifold some observations are made on the general structure of u and r matrices and of coproduct manifolds based on the solutions of hierarchies of partial difference equations applications of deforming maps and u matrices to the physics of spin chains are outlined

bipartite and tripartite entanglement of truncated harmonic oscillator coherent states via beam splitters we introduce a special class of truncated weyl heisenberg algebra and discuss the corresponding hilbertian and analytical representations subsequently we study the effect of a quantum network of beam splitting on coherent states of this nonlinear class of harmonic oscillators we particularly focus on quantum networks involving one and two beam splitters and examine the degree of bipartite as well as tripartite entanglement using the linear entropy

on nonlinear angular momentum theories their representations and associated hopf structures nonlinear sl 2 algebras subtending generalized angular momentum theories are studied in terms of undeformed generators and bases we construct their unitary irreducible representations in such a general context the linear sl 2 case as well as its q deformation are easily recovered as specific examples two other physically interesting applications corresponding to the so called higgs and quadratic algebras are also considered we show that these two nonlinear algebras can be equipped with a hopf structure

elementary derivation of nonlinear transport equations from statistical mechanics exact closed nonlinear transport equations for a set of macroscopic variablesa are derived from classical statistical mechanics the derivation involves only simple manipulations of the liouville equation and makes no use of projection operators or graphical expansions it is based on the chapman enskog idea of separating the distribution function into a constrained equilibrium part obtained from information theory and a small remainder the resulting exact transport equations involve time convolutions over the past history of botha t anda t however if the variablesa provide a complete macroscopic description the equations may be simplified this is accomplished by a systematic expansion procedure of chapman enskog type in which the small parameter is the natural parameter of slowness relevant to the problem when carried out to second order this expansion leads to approximate nonlinear transport equations that are local in time these equations are valid far from equilibrium they contain nonlinear i e state dependent transport coefficients given by integrals of time correlation functions in the constrained equilibrium ensemble earlier results are recovered when the equations are linearized about equilibrium as an illustrative application of the formalism an expression is derived for the nonlinear i e velocity dependent friction coefficient for a heavy particle in a bath of light particles

generalization of thermodynamic potentials including information in this work we analyze the connection between information theory and thermodynamics three different potentials are presented all related to the kullback leibler divergence these potentials represent three different conditions of energy and information exchange between a reservoir and a subsystem the first potential describes a situation where the two systems are exchanging energy without any external control the second potential considers the situation where the reservoir can get information through the state of another secondary system about the internal state of the subsystem this information can then be used by a maxwell demon to increase the free energy of the subsystem in this second scenario it is assumed that the energy cost of the information probe and the maxwell demon are at the expense of the reservoir finally a third case is considered where the information obtained through the secondary system is used not only to manipulate an internal maxwell demon but to perform directly work over the subsystem this last case involves a direct modification of the hamiltonian of the subsystem

on a non equilibrium partition function for heat conduction the authors provide a physical interpretation for the lagrange multipliers associated with heat conduction in an information theoretical description of non equilibrium systems such an identification is based on the generalised gibbs equation of extended irreversible thermodynamics

distorted heisenberg algebra and coherent states for isospectral oscillator hamiltonians the dynamical algebra associated with a family of isospectral oscillator hamiltonians is studied through the analysis of its representation in the basis of energy eigenstates it is shown that this representation becomes similar to that of the standard heisenberg algebra and it is dependent on a parameter omega or 0 we call it the distorted heisenberg algebra where omega is the distortion parameter the corresponding coherent states for an arbitrary omega are derived and some particular examples are discussed in detail a prescription to produce the squeezing by adequately selecting the initial state of the system is given

temporally stable coherent states for infinite well and poschl teller potentials this article is a direct illustration of a construction of coherent states which has been recently proposed by two of us jpg and jk we have chosen the example of a particle trapped in an infinite square well and also in poschl teller potentials of the trigonometric type in the construction of the corresponding coherent states we take advantage of the simplicity of the solutions which ultimately stems from the fact they share a common su 1 1 symmetry a la barut girardello many properties of these states are then studied both from mathematical and from physical points of view

examples of retracts in free groups that are not the fixed subgroup of any automorphism let n be an arbitrary cardinal and let fn be a free group of rank n the flxed subgroup of an endomorphismof fn is the subgroup of elements in fn flxed by in this paper the relationship between the family of flxed subgroups of endomorphisms of fn and the family of flxed subgroups of automorphisms of fn will be studied we prove that these two families of subgroups do not coincide for n 3 by showing an inflnite sequence of explicit examples of retracts of fn and so flxed subgroups of endomorphisms of fn which are not flxed subgroups of any automorphism of fn

on equalizers of sections abstract let g and m be groups and a b g g m group theoretic sections of the natural projection g m g we use the almost stability theorem pro trees and new folding sequence techniques to show that if g is finitely generated then the equalizer of a and b is a free factor of g which answers a question of g m bergman

two examples in the galois theory of free groups abstract let f be a free group and let h be a subgroup of f the galois monoid end h f consists of all endomorphisms of f which fix every element of h the galois group aut h f consists of all automorphisms of f which fix every element of h the end f closure and the aut f closure of h are the fixed subgroups fix end h f and fix aut h f respectively martino and ventura considered examples where fix aut h f fix end h f h we obtain for two of their examples explicit descriptions of end h f aut h f and fix aut h f and hence give much simpler verifications that fix aut h f fix end h f in these cases

non linear heat conduction in dense fluids in a dense fluid with very large heat flow j the thermal conductivity lambda lambda 0 lambda 2j2 an estimate of lambda 2 lambda 0 is made for hard spheres with mass and diameter appropriate to ar and density just below the gas solid transition this estimate indicates that fourier s law will hold in the form appropriate to low j if j or approximately 109 w m 2 and that the j dependence of pressure and internal energy is of the same order as that of lambda the calculation utilises an earlier derivation from the classical liouville equation which expresses lambda at high density in terms of the thermodynamic pressure the latter can be calculated with the aid of reciprocity and integrability conditions of extended non equilibrium thermodynamics which treats j as a state variable

morse like squeezed coherent states and some of their properties using the f deformed oscillator formalism we introduce a class of squeezed coherent states for a morse potential system morse like squeezed coherent states defined as approximate eigenstates of a linear combination of f deformed ladder operators for the states thus constructed we analyze their statistical properties their uncertainty relations their wigner function and their temporal evolution on phase space

examination of phenomenological coefficient matrices within the canonical model of field theory of thermodynamics the field equations of linear irreversible thermodynamics have been deduced from hamilton s principle the hamiltonian formalism has been considered as a theory of conservative systems without dissipative processes in this paper we present the field equations of linear irreversible thermodynamics that are deduced from a hamiltonian principle first we present the canonical mathematical model for purely dissipative transport processes then introducing a lie algebra of the potentials with the help of an algebraic type transformation we examine the physical processes in this algebra we expect that two kinds of descriptions of the same physical situation develop into two such descriptions in time which describe the same physical situations as well since the given transformation is a dynamical transformation it leaves the lagrangian invariant in the sense of the above mentioned expectation we expect that the entropy density function and the entropy production density function which pertains to the same physical situation have to be invariant under that transformation which leaves the lagrangian invariant it is shown that these are satisfied if the phenomenological coefficient matrices are symmetric s1063 651x 97 08305 0

approach of spherical harmonics to the representation of the deformed su 1 1 algebra the m shifting generators of su 2 algebra together with a pair of l shifting ladder symmetry operators have been used in the space of all spherical harmonics ylm in order to introduce a new set of operators expressing the transitions between them it is shown that the space of spherical harmonics whose l 2m or l 2m is given presents negative and positive irreducible representations of a deformed su 1 1 algebra respectively these internal symmetries also suggest new algebraic methods to construct the spherical harmonics in the framework of the spectrum generating algebras

information theoretic extended entropy for steady heat condition a phase space distribution for a far from equilibrium steady state in which thermodynamic temperature t and heat flux j are specified is calculated by maximising the information theoretic entropy when this distribution is used to calculate free energy f the latter is obtained as a function of the distribution moduli which in turn are calculated from a consistency condition as functions of j and t the coefficient of the o j2 term in f can be expressed in terms of the radial distribution function g2 and three particle distribution g3 a numerical estimate is made for a hard sphere model of liquid ar at 87 k and high density using the percus yevick solution for g2 and the kirkwood superposition for g3 the estimate confirms the conclusion of an earlier theory that non linear effects at liquid density are negligible except possibly for unrealistically large j fluctuation theory is invoked to make an estimate of the negligibly small o j4 term in f

coherent states for isospectral oscillator hamiltonians coherent states for a family of isospectral oscillator hamiltonians are derived from a suitable choice of annihilation and creation operators the fock bargmann representation is also considered

coherent states for systems with discrete and continuous spectrum for a system with one degree of freedom coherent states that are parametrized by classical canonical action angle variables are introduced these states also possess continuity of labelling a resolution of unity and temporal stability the insistence on canonical action angle variables strongly restricts any remaining arbitrariness in the coherent state definition such states are introduced for semibounded hamiltonian operators having either a discrete or a continuous spectrum hamiltonians that have both discrete and continuous parts in their spectrum are also discussed

on automorphism fixed subgroups of a free group abstract let f be a finitely generated free group and let n denote its rank a subgroup h of f is said to be automorphism fixed or auto fixed for short if there exists a set s of automorphisms of f such that h is precisely the set of elements fixed by every element of s similarly h is 1 auto fixed if there exists a single automorphism of f whose set of fixed elements is precisely h we show that each auto fixed subgroup of f is a free factor of a 1 auto fixed subgroup of f we show also that if and only if n 3 then there exist free factors of 1 auto fixed subgroups of f which are not auto fixed subgroups of f a 1 auto fixed subgroup h of f has rank at most n by the bestvina handel theorem and if h has rank exactly n then h is said to be a maximum rank 1 auto fixed subgroup of f and similarly for auto fixed subgroups hence a maximum rank auto fixed subgroup of f is a maximum rank 1 auto fixed subgroup of f we further prove that if h is a maximum rank 1 auto fixed subgroup of f then the group of automorphisms of f which fix every element of h is free abelain of rank at most n 1 all of our results apply also to endomorphisms

integral equations versus internal variables in the search for an effectively hyperbolic thermal transport equation to obtain a thermal wave equation predicting finite phase velocity in the infinite frequency limit grad s 13 moment method and extended thermodynamics have added a term linear in the time derivative of the heat flux to fourier s law when nonlocal effects are added via a term linear in the heat flux laplacian the problem of nonhyperbolicity and infinite phase velocity recurs one approach postulates an infinite hierarchy of coupled equations each of which describes time evolution of a flux appearing in the preceding hierarchy equation this is shown to disagree in the high frequency limit with an evolution equation derived by projection operators from the liouville equation in which memory and nonlocal effects are represented by integrals over time and space nonlocal effects disappear in the infinite frequency limit of the latter but not of the former

quasi equilibrium closure hierarchies for the boltzmann equation abstract after boltzmann and gibbs the notion of disorder in statistical physics relates to ensembles not to individual states this disorder is measured by the logarithm of ensemble volume the entropy but recent results about measure concentration effects in analysis and geometry allow us to return from the ensemble based point of view to a state based one at least partially in this paper the order disorder problem is represented as a problem of relation between distance and measure the effect of strong order disorder separation for multiparticle systems is described the phase space could be divided into two subsets one of them set of disordered states has almost zero diameter the second one has almost zero measure the symmetry with respect to permutations of particles is responsible for this type of concentration dynamics of systems with strong order disorder separation has high average acceleration squared which can be interpreted as evolution through a series of collisions acceleration dominated dynamics the time arrow direction from order to disorder follows from the strong order disorder separation but inverse for systems in space of symmetric configurations with sticky boundaries the way back from disorder to order is typical natural selection recommendations for mining of molecular dynamics results are also presented

topology of finite graphs this paper derives from a course in group theory which i gave at berkeley in 1982 i wanted to prove the standard theorems on free groups and discovered that after a few preliminaries the notion of locally injective map or immersion of graphs was very useful this enables one to see in an effective easy algorithmic way just what happens with finitely generated free groups one can understand in this way 1 howson s theorem that if a and b are finitely generated subgroups of a free group then a b is finitely generated and 2 m hall s theorem that finitely generated subgroups of free groups are closed in the profinite topology during this course s m gersten came up with a simple proof of h neumann s inequality on the ranks in howson s theorem one of the ideas in gersten s proof was to use core graphs graphs with no trees hanging on subsequently i found that some consequences of a paper of greenberg s could be proved using core graphs and covering translations of immersions the most striking such result is that if a and b are finitely generated subgroups of a free group and if a c b is of finite index in both a and b then a b is of finite index in a v b the subgroup generated by a ub

nonlinear coherent states for nonlinear systems in this work we construct nonlinear coherent states for hamiltonians with linear and quadratic terms in the number operator by the generalization of two definitions as eigenstates of a deformed annihilation operator and as those states obtained by the application of a deformed displacement operator on the vacuum state we evaluate their temporal dependence analyze its dispersion relations and some of their statistical properties for two model hamiltonians one supporting a finite number of bound states and the other supporting an infinite number of bound states

quantum brst charge for quadratically nonlinear lie algebras we consider the construction of a nilpotent brst charge for extensions of the virasoro algebra of the form ta tb fabctc vabcdtctd classical algebras in terms of poisson brackets and ta tb habi fabctc vabcd tctd quantum algebras in terms of commutator brackets normal ordering of the product tctd is understood in both cases we assume that the set of generators ta splits into a set hi generating an ordinary lie algebra and remaining generators s such that only thevij are nonvanishing in the classical case a nilpotent brst charge can always be constructed for the quantum case we derive a condition which is necessary and sufficient for the existence of a nilpotent brst charge non trivial examples are the spin 3 algebra with central chargec 100 and theso n extended superconformal algebras with levels 2 n 3

applications of reciprocity to non linear extended thermodynamics kinetic equations abstract reciprocity relations and integrability conditions can be used in non linear extended irreversible thermodynamics to calculate forces and phenomenological coefficients uniquely in terms of parameters in kinetic equations derived from a model one assumes a set of n even variables i and corresponding i with an equation from the model for i independent thermodynamic forces terms are assumed known comparison of powers of in the model equation with corresponding powers in the canonical onsager casimir formalism yields equations to determine all quantities in the latter save the higher dependence of entropy which is affected by uncertainties in measurement by introducing a phenomenological ansatz one can relate these higher entropy terms to corresponding terms in the model equation a numerical illustration is made for a relaxing scalar structural parameter appropriate to a simple liquid

nonlinear reciprocity and the maximum entropy formalism abstract the maximum entropy formalism calculates a phase space distribution p x which maximizes the information theoretic entropy subject to specified values of internal energy and state variables i and i i 1 n the latter are averages calculated from p of dynamical functions ai and ai ilai respectively where l is the liouville operator from p one extracts a fluctuation distribution g a v for the values of the a and a a kinetic equation for the fluctuation distribution has been derived by grabert using projection operators appropriate to a system in thermal contact with its surroundings and g is proposed as an ansatz for its solution from the first moments of the kinetic equation after introduction therein of g one extracts phenomenological equations for ai and hi whose terms can be grouped to exhibit onsager symmetry even when nonlinear terms are included the groupings can be affected exactly but not uniquely

onsager reciprocity in the nonlinear regime a system is assumed in the framework of extended non equilibrium thermodynamics to be described by state variables i which are ensemble averages of dynamical functions ai and their time derivatives i gai a fokker planck type equation is derived by the zwanzig projection operator technique for g a v the amplitude of the probability that a a and a v the first moments of this equation give the phenomenological equations which can be cast in onsager casimir canonical form with forces and coefficients exhibiting reciprocity and non linear in both and variables it is necessary to assume that g is sharply peaked in equilibrium and that a markovian approximation holds for the particular sets of variables and time scale chosen the arguments are illustrated by applying them to heat conduction in a liquid or solid

phase operators temporally stable phase states mutually unbiased bases and exactly solvable quantum systems we introduce a one parameter generalized oscillator algebra that covers the case of the harmonic oscillator algebra and discuss its finite and infinite dimensional representations according to the sign of the parameter we define an hamiltonian operator associated with and examine the degeneracies of its spectrum for the finite when 0 and the infinite when 0 representations of we construct the associated phase operators and build temporally stable phase states as eigenstates of the phase operators to overcome the difficulties related to the phase operator in the infinite dimensional case and to avoid the degeneracy problem for the finite dimensional case we introduce a truncation procedure which generalizes the one used by pegg and barnett for the harmonic oscillator this yields a truncated generalized oscillator algebra where s denotes the truncation order we construct two types of temporally stable states for as eigenstates of a phase operator and as eigenstates of a polynomial in the generators of two applications are considered in this paper the first concerns physical realizations of and in the context of one dimensional quantum systems with finite morse system or infinite poschl teller system discrete spectra the second deals with mutually unbiased bases used in quantum information

generalized deformed oscillator corresponding to the modified poschl teller energy spectrum a generalized deformed oscillator with eigenvalues equal to the eigenvalues of the schrodinger equation with the modified poschl teller potential is constructed for special values of the potential depth the deformed oscillator algebra has a finite dimensional irreducible representation the polynomial representation and the associate deformed operations of integration and differentiation are studied the results of this study are general and they can be applied directly to the case of the q deformed oscillator with q being a root of unity