conformal invariance and critical dynamics the author discusses the behaviour of dynamic correlation functions under conformal transformations in particular the exact form of the dynamic scaling function at the critical point for an arbitrary isotropic two dimensional model is obtained with either conserved or nonconserved order parameter

applications of field theoretic renormalization group methods to reaction diffusion problems we review the application of field theoretic renormalization group rg methods to the study of fluctuations in reaction diffusion problems we first investigate the physical origin of universality in these systems before comparing rg methods to other available analytic techniques including exact solutions and smoluchowski type approximations starting from the microscopic reaction diffusion master equation we then pedagogically detail the mapping to a field theory for the single species reaction ka a k we employ this particularly simple but non trivial system to introduce the field theoretic rg tools including the diagrammatic perturbation expansion renormalization and callan symanzik rg flow equation we demonstrate how these techniques permit the calculation of universal quantities such as density decay exponents and amplitudes via perturbative dc d expansions with respect to the upper critical dimension dc with these basics established we then provide an overview of more sophisticated applications to multiple species reactions disorder effects l evy flights persistence problems and the influence of spatial boundaries we also analyse field theoretic approaches to non equilibrium phase transitions separating active from absorbing states we focus particularly on the generic directed percolation universality class as well as on the most prominent exception to this class even offspring branching and annihilating random walks finally we summarize the state of the field and present our perspective on outstanding problems for the future

classification of phase transitions in reaction diffusion models equilibrium phase transitions are associated with rearrangements of minima of a lagrangian potential treatment of nonequilibrium systems requires doubling of degrees of freedom which may be often interpreted as a transition from the coordinate to the phase space representation as a result one has to deal with the hamiltonian formulation of the field theory instead of the lagrangian one we suggest a classification scheme of phase transitions in reaction diffusion models based on the topology of the phase portraits of corresponding hamiltonians in models with an absorbing state such a topology is fully determined by intersecting curves of zero energy we identify four families of topologically distinct classes of phase portraits stable upon renormalization group transformations

critical phenomena at surfaces in a model of nonequilibrium phase transitions critical phenomena at surfaces are studied in a simple two dimensional model of non equilibrium phase transitions belonging to the class of interacting particle systems the mean field renormalization group approach and numerical simulations are used to determine the phase diagram for this system and some of the critical exponents associated with ordinary special extraordinary and surface phase transitions

representations of the schrodinger group and matrix orthogonal polynomials the representations of the schrodinger group in one space dimension are explicitly constructed in the basis of the harmonic oscillator states these representations are seen to involve matrix orthogonal polynomials in a discrete variable that have charlier and meixner polynomials as building blocks the underlying lie theoretic framework allows for a systematic derivation of the structural formulas recurrence relations difference equations rodrigues formula etc that these matrix orthogonal polynomials satisfy

dynamic correlations in domain growth a 1 n expansion the authors consider the dynamics of the n component ginzburg landau model with nonconserved order parameter model a following a quench from a high temperature equilibrium state to zero temperature the two time correlation function of the order parameter field is found in the 1 n expansion to have the asymptotic scaling form ck t t t d2 t t lambda 2 f k2t k2t for t t with f 0 0 constant the form of the new exponent lambda which is a non trivial function of n and d was given explicitly to o 1 n in a recent letter the purpose of this study is to present a more detailed account of the calculation leading to the o 1 n form for lambda they also examine the role of thermal fluctuations in the ordered phase and the effect of long range initial correlations on the ordering process

on holographic realization of logarithmic galilean conformal algebra we study two dimensional logarithmic galilean conformal algebra lgca by making use of a contraction of topologically massive gravity at critical point we observe that using a naive contraction at the critical point fails to give a well defined theory though contracting the theory while we are approaching the critical point leads to a well behaved expression for two point functions of the energy momentum tensors of lgca

a monte carlo study of scaling and universality in 2d directed percolation monte carlo data for the pair correlation function is obtained on five different lattices for the directed percolation problem in two dimensions scaling is tested and found to hold beyond 20 lattice spacings for all models evidence is found to support the universality of the scaling function the values of the exponents gamma v sub and vperpendicular to v sub are extracted from the data the results for all models are summarised by gamma v sub 1 305 or 0 007 and vperpendicular to v sub 0 629 or 0 010 comparison is made with estimates derived by other means

optimal liouville type theorems for noncooperative elliptic schrodinger systems and applications we study multi component elliptic schrodinger systems arising in nonlinear optics and bose einstein condensation phenomena we prove new liouville type nonexistence theorems as well as a priori bounds decay and singularity estimates this is shown under an optimal sobolev growth restriction on the nonlinearities thus improving on recent results of dancer et al and of tavares et al these systems are of non cooperative form and hence cannot be tackled by maximum principle methods such as moving planes instead we rely on a delicate combination of rellich pohozaev type identities sobolev and interpolation inequalities on sn 1 and feedback and measure arguments we also extend our results to a rather general class of gradient type systems

bifurcations of radially symmetric solutions in a coupled elliptic system with critical growth in rd for d 3 4 abstract we consider a system of coupled elliptic partial differential equations with critical growth in r d for d 3 4 and study bifurcations of three families of radially symmetric bounded solutions we reduce the problems of the three families to those of three symmetric homoclinic orbits in a four dimensional reversible system of ordinary differential equations and show that transcritical or pitchfork bifurcations of the three families occur at infinitely many parameter values numerical computations are also given to demonstrate our theoretical results

on the identification of quasiprimary scaling operators in local scale invariance the relationship between physical observables defined in lattice models and the associated quasi primary scaling operators of the underlying field theory is revisited in the context of local scale invariance we argue that this relationship is only defined up to a time dependent amplitude and derive the corresponding generalizations of predictions for two time response and correlation functions applications to non equilibrium critical dynamics of several systems with a fully disordered initial state and vanishing initial magnetization including the glauber ising model the frederikson andersen model and the ising spin glass are discussed the critical contact process and the parity conserving non equilibrium kinetic ising model are also considered

equivalence between poisson representation and fock space formalism for birth death processes the equivalence between the poisson representation and the fock space formalism both used to derive coarse grained equations from the master equation for non equilibrium systems is explicitly demonstrated

logarithmic correlators in nonrelativistic conformal field theory we show how logarithmic terms may arise in the correlators of fields which belong to the representation of the schrodinger virasoro algebra or the affine galilean conformal algebra gca we show that in gca only scaling operator can have a jordan form and rapidity cannot we observe that in both algebras logarithmic dependence appears along the time direction alone

meta conformal invariance and the boundedness of two point correlation functions the covariant two point functions derived from ward identities in direct space can be affected by consistency problems and can become unbounded for large time or space separations this difficulty arises for several extensions of dynamical scaling for example schrodinger invariance conformal galilei invariance or meta conformal invariance but not for standard ortho conformal invariance for meta conformal invariance in dimensions which acts as a dynamical symmetry of a simple advection equation these difficulties can be cured by going over to a dual space and an extension of these dynamical symmetries through the construction of a new generator in the cartan sub algebra this provides a canonical interpretation of meta conformally covariant two point functions as correlators galilei conformal correlators can be obtained from meta conformal invariance through a simple contraction in contrast by an analogus construction schrodinger covariant two point functions are causal response functions all these two point functions are bounded at large separations for sufficiently positive values of the scaling exponents

exact exponent λ of the autocorrelation function for a soluble model of coarsening the exponent lambda that describes the decay of the autocorrelation function a t in a phase ordering system a t sim l d lambda where d is the dimension and l the characteristic length scale at time t is calculated exactly for the time dependent ginzburg landau equation in d 1 we find lambda 0 399 383 5 ldots we also show explicitly that a small bias of positive domains over negative gives a magnetization which grows in time as m t sim l mu and prove that for the 1d ginzburg landau equation mu lambda exemplifying a general result

symmetry based determination of space time functions in nonequilibrium growth processes we study the space time correlation and response functions in nonequilibrium growth processes described by linear stochastic langevin equations exploiting exclusively the existence of space and time dependent symmetries of the noiseless part of these equations we derive expressions for the universal scaling functions of two time quantities which are found to agree with the exact expressions obtained from the stochastic equations of motion the usefulness of the space time functions is illustrated through the investigation of two atomistic growth models the family model and the restricted family model which are shown to belong to a unique universality class in 1 1 and 2 1 space dimensions this corrects earlier studies which claimed that in 2 1 dimensions the two models belong to different universality classes

lie bialgebra structures on the deformative schrodinger virasoro algebras in this paper we investigate lie bialgebra structures on the deformative schrodinger virasoro algebras mainly using the techniques introduced recently which indicate that all cases considered in this paper except one behave different from their centerless ones

e2 sl2 for most laurent polynomial rings it is not known whether or not sl2 r and e2 r are equal for r z t t 1 zthe ring of rational integers orforr k t1 t 1 t2 t2j1 k a field e2 s is the subgroup of sl2 s generated by the elementary matrices o 1 a e s we discuss this question for related laurent polynomial rings r s tj tl 1 tk tk our results show that for most laurent polynomial rings r sl2 r e2 r and moreover any generating set for s12 r must contain infinitely many elements not in e2 r suslin 9 has proved that for n 2 3 and arbitrary k sln r e r forr equal to z tl t11 tk tkjl ork tj t1 1 tk tk by contrast we state

positive solutions for a weakly coupled nonlinear schrodinger system abstract existence of a nontrivial solution is established via variational methods for a system of weakly coupled nonlinear schrodinger equations the main goal is to obtain a positive solution of minimal action if possible with all vector components not identically zero generalizations for nonautonomous systems are considered

non local representations of the ageing algebra in higher dimensions the ageing lie algebra and especially its local representations for a dynamical exponent z 2 have played an important role in the description of systems undergoing simple ageing after a quench from a disordered state to the low temperature phase here the construction of representations of for generic values of z is described for any space dimension d 1 generalizing upon earlier results for d 1 the mechanism for the closure of the lie algebra is explained the lie algebra generators contain higher order differential operators or the riesz fractional derivative co variant two time response functions are derived some simple applications to the exactly solvable models of phase separation or interface growth with conserved dynamics are discussed

least energy solitary waves for a system of nonlinear schrodinger equations in mathbb r n in this paper we consider systems of coupled schrodinger equations which appear in nonlinear optics the problem has been considered mostly in the one dimensional case here we make a rigorous study of the existence of least energy standing waves solitons in higher dimensions we give conditions on the parameters of the system under which it possesses a solution with least energy among all multi component solutions conditions under which the system does not have positive solutions and the associated energy functional cannot be minimized on the natural set where the solutions lie

ageing without detailed balance in the bosonic contact and pair contact processes exact results ageing in systems without detailed balance is studied in the exactly solvable bosonic contact process and the critical bosonic pair contact process the two time correlation function and the two time response function are explicitly found in the ageing regime the dynamical scaling of these is analysed and exact results for the ageing exponents and the scaling functions are derived for the critical bosonic pair contact process the autocorrelation and autoresponse exponents agree but the ageing exponents a and b are shown to be distinct

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

conformal carroll groups conformal extensions of levy leblond s carroll group based on geometric properties analogous to those of newton cartan space time are proposed the extensions are labeled by an integer k this framework includes and extends our recent study of the bondi metzner sachs bms and newman unti nu groups the relation to conformal galilei groups is clarified conformal carroll symmetry is illustrated by carrollian photons motion both in the newton cartan and carroll spaces may be related to that of strings in the bargmann space

super schrodinger algebra in ads cft we discuss extended super schrodinger algebras obtained as subalgebras of the superconformal algebra psu 2 2 4 the schrodinger algebra with two spatial dimensions can be embedded into so 4 2 in the superconformal case the embedded algebra may be enhanced to the so called super schrodinger algebra in fact we find an extended super schrodinger subalgebra of psu 2 2 4 it contains 24 supercharges i e 3 4 of the original supersymmetries and the generators of so 6 as well as the generators of the original schrodinger algebra in particular the 24 supercharges come from 16 rigid supersymmetries and half of 16 superconformal ones moreover this superalgebra contains a smaller super schrodinger subalgebra which is a supersymmetric extension of the original schrodinger algebra and so 6 by eight supercharges half of 16 rigid supersymmetries it is still a subalgebra even if there are no so 6 generators we also discuss super schrodinger subalgebras of the superconformal algebras osp 8 4 and

affine extension of galilean conformal algebra in 2 1 dimensions we show that a class of nonrelativistic algebras including noncentrally extended schrodinger algebra and galilean conformal algebra gca has an affine extension in 2 1 hitherto unknown this extension arises out of the conformal symmetries of the two dimensional complex plane we suggest that this affine form may be the symmetry that explains the relaxation of some classical phenomena toward their critical point this affine algebra admits a central extension and maybe realized in the bulk the bulk realization suggests that this algebra may be derived by looking at the asymptotic symmetry of an anti de sitter ads theory this suggests that ads cft conformal field theory duality may take on a special form in four dimensions

schrodinger invariance and strongly anisotropic critical systems the extension of strongly anisotropic or dynamical scaling to local scale invariance is investigated for the special case of an anisotropy or dynamical exponent z 2 the group of local scale transformation considered is the schrodinger group which can be obtained as the nonrelativistic limit of the conformal group the requirement of schrodinger invariance determines the two point function in the bulk and reduces the three point function to a scaling form of a single variable scaling forms are also derived for the two point function close to a free surface which can be either spacelike or timelike these results are reproduced in several exactly solvable statistical systems namely the kinetic ising model with glauber dynamics lattice diffusion lifshitz points in the spherical model and critical dynamics of the spherical model with a nonconserved order parameter for generic values of evidence from higher order lifshitz points in the spherical model and from directed percolation suggests a simple scaling form of the two point function

entire nonradial solutions for non cooperative coupled elliptic system with critical exponents in r3 abstract we consider the following coupled elliptic system s n u 1 u n 2 n 2 u 2 n 2 v n n 2 in r n v 2 v n 2 n 2 v 2 n 2 u n n 2 in r n u v 0 u v d 1 2 r n where n 3 1 2 are two positive constants and 0 is the coupling constant when n 3 we prove the existence of infinitely many positive nonradial solutions

phase transitions and correlations in the bosonic pair contact process with diffusion exact results the variance of the local density of the pair contact process with diffusion is investigated in a bosonic description at the critical point of the absorbing phase transition where the average particle number remains constant it is shown that for a lattice dimension d 2 the variance exhibits a phase transition for high enough diffusion constants it asymptotically approaches a finite value while for low diffusion constants the variance diverges exponentially in time this behaviour also appears in the density correlation function implying that the correlation time is negative yet one has dynamical scaling with a dynamical exponent calculated to be z 2

multiple bound states of nonlinear schrodinger systems this paper is concerned with existence of bound states for schrodinger systems which have appeared as several models from mathematical physics we establish multiplicity results of bound states for both small and large interactions this is done by different approaches depending upon the sizes of the interaction parameters in the systems for small interactions we give a new approach to deal with multiple bound states the novelty of our approach lies in establishing a certain type of invariant sets of the associated gradient flows for large interactions we use a minimax procedure to distinguish solutions by analyzing their morse indices

lowest weight representations of super schrodinger algebras in one dimensional space lowest weight modules in particular verma modules over the n 1 2 super schrodinger algebras in 1 1 dimensional spacetime are investigated the reducibility of the verma modules is analyzed via explicitly constructed singular vectors the classification of the irreducible lowest weight modules is given for both massive and massless representations a vector field realization of the n 1 2 super schrodinger algebras is also presented

simple harish chandra modules over super schrodinger algebra in 1 1 dimensional spacetime the n 1 super schrodinger algebra s 1 1 in 1 1 dimensional spacetime contains a subalgebra isomorphic to osp 1 2 module let v be a simple weight module for the n 1 super schrodinger algebra s 1 1 but not a simple osp 1 2 module let supp v if v is neither a highest weight module nor a lowest weight module for s 1 1 we prove that supp v z and all non trivial weight spaces of v have the same dimension we prove that if v is a harish chandra module then it is a highest weight module or lowest weight module or a twisted localization of a highest weight module

automorphisms and verma modules for generalized schrodinger virasoro algebras abstract let f be a field of characteristic 0 g an additive subgroup of f f satisfying g and 2 g we define a class of infinite dimensional lie algebras which are called generalized schrodinger virasoro algebras and denoted by gsv g in this paper the automorphism group and irreducibility of verma modules for gsv g are completely determined

the structure of the torelli group i a finite set of generators for j this is the first of three papers concerning the so called torelli group let m mg be a compact orientable surface of genus g having n boundary components and let 9 xg be its mapping class group that is the group of orientation preserving diffeomorphisms of m which are 1 on the boundary am modulo isotopies which fix 3m pointwise this group is also known to the complex analysts as the teichmuller group or modular group if n 0 or 1 let further 4 jg be the subgroup of d1 which acts trivially on h1 m z the topologists have no traditional name for a but the analysts tell me it was known classically and is called the torelli group several interesting problems and conjectures exist concerning f the principal one can be found in kirby s problem list k and asks if gg is finitely generated in this first paper we shall answer the question affirmatively for both gg 0 and fgg when g 3 and shall give a fairly simple set of generators two other conjectures were made by the author the first involves the subgroup j of f which is generated by twists on nulhomologous simple closed curves ji produces a surjective homomorphism t fgg 1 a3h1 m z which kills c and it is conjectured there that in fact 5y ker t the proof of this is the content of the second paper in the third paper we use the results of the second to compute the abelianization f f explicitly thereby verifying another conjecture in ji the first reasonably simple but infinite set of generators for fg0 was produced by powell in p his generators consist of two types a twists on bounding simple closed curves b opposite twists on a bounding pair of disjoint homologous simple closed curves each of which are nonbounding using his result the author showed in j2 that the maps of the second type which we call bp maps for bounding pair are actually sufficient to generate both kg 0 and fg 1 for g 3 and in fact that we need only those whose two curves bound a genus one subsurface of m note that for g 2 all bp maps are trivial and hence the result fails in this case in the finite set of generators produced in this paper only

theory of phase ordering kinetics the theory of phase ordering dynamics that is the growth of order through domain coarsening when a system is quenched from the homogeneous phase into a broken symmetry phase is reviewed with the emphasis on recent developments interest will focus on the scaling regime that develops at long times after the quench how can one determine the growth laws that describe the time dependence of characteristic length scales and what can be said about the form of the associated scaling functions particular attention will be paid to systems described by more complicated order parameters than the simple scalars usually considered for example vector and tensor elds the latter are needed for example to describe phase ordering in nematic liquid crystals on which there have been a number of recent experiments the study of topological defects domain walls vortices strings and monopoles provides a unifying framework for discussing coarsening in these dia erent systems

on two dimensional directed percolation extended series expansions for the mean size and the first and second moments of the pair connectedness for both bond and site percolation on the directed square and triangular lattices have been obtained analysis based on differential approximants allows the critical percolation probabilities and exponents to be estimated and as a result the critical exponents are conjectured to be gamma 41 18 nu perpendicular to 79 72 and nu sub 26 15 scaling then gives beta 199 720 alpha 299 360 and delta 1839 199

classification of finite irreducible conformal modules over some lie conformal algebras related to the virasoro conformal algebra in this paper we classify all finite irreducible conformal modules over a class of lie conformal algebras w b with b related to the virasoro conformal algebra explicitly any finite irreducible conformal module over w b is proved to be isomorphic to m with 0 or 0 if b 0 or m with 0 if b 0 as a byproduct all finite irreducible conformal modules over the heisenberg virasoro conformal algebra and the w 2 2 lie conformal algebra are classified finally the same thing is done for the schrodinger virasoro conformal algebra

sharp thresholds of blow up and global existence for the coupled nonlinear schrodinger system in this paper we establish two new types of invariant sets for the coupled nonlinear schrodinger system in the euclidean n space rn and derive two sharp thresholds of blow up and global existence for its solutions some analogous results for the nonlinear schrodinger system posed on the hyperbolic space hn and on the standard 2 sphere s2 are also presented our arguments and constructions are improvements of some previous works on this direction at the end we give some heuristic analysis about the strong instability of the solitary waves the relation between the two types of thresholds is a very interesting problem and we leave it as an open problem for further study

clustering of diffusing organisms recently a brownian bugs model has been proposed as a possible explanation for the clustering of organisms such as planktons w r young a j roberts and g stuhne nature london 412 328 2001 in this model diffusing organisms die and give birth with equal probabilities and are independent of each other the clustering phenomenon is due to the discreteness of birth and death events and cannot be explained in the framework of the continuous model of population dynamics we show by exact calculation that at dimensions smaller than or equal to 2 this simple mechanism is enough to provoke aggregations of the organisms at dimensions higher than 2 the clustering phenomenon disappears but reproductive fluctuations can still be large compared to diffusive ones

a six vertex model as a diffusion problem derivation of correlation functions a cellular automaton which describes diffusion of particles with exclusion in one dimension is shown to be equivalent to a six vertex model on a critical line the arrow arrow correlation function of the six vertex model is calculated exactly on this line using a transfer matrix method

symmetry results for elliptic schrodinger systems on half spaces abstract in this paper we prove some symmetry and monotonicity results for classical positive solutions for elliptic schrodinger systems on half spaces with the neumann type condition our methods employ the alexandrov serrin method of moving planes combined with hopf s lemma at a corner

classification of harish chandra modules over some lie algebras related to the virasoro algebra abstract in this paper we provide a uniform method to thoroughly classify all harish chandra modules over some lie algebras related to the virasoro algebras we first classify such modules over the lie algebra w s for s 0 1 2 with this result and method we can also do such works for some lie algebras related to the virasoro algebra including the several kinds of schrodinger virasoro lie algebras which are open up to now

classification of finite irreducible conformal modules over a class of lie conformal algebras of block type abstract we classify finite irreducible conformal modules over a class of infinite lie conformal algebras b p of block type where p is a nonzero complex number in particular we obtain that a finite irreducible conformal module over b p may be a nontrivial extension of a finite conformal module over vir if p 1 where vir is a virasoro conformal subalgebra of b p as a byproduct we also obtain the classification of finite irreducible conformal modules over a series of finite lie conformal algebras b n for n 1

on the non relativistic structure of the ads cft superalgebras the property of the conformal algebra to contain the schrodinger algebra in one less space dimension is extended to the supersymmetric case more precisely we determine the non relativistic counterpart of any field theory admissible superconformal algebra even if each type of superalgebra provides a different solution its basis decomposition into two copies of the super schrodinger algebra differing only by their super heisenberg part remains valid in all cases so generalizing a feature already observed in the non supersymmetric conformal case

response functions in phase ordering kinetics we discuss the behavior of response functions in phase ordering kinetics within the perturbation theory approach developed earlier at zeroth order the results agree with previous gaussian theory calculations at second order the nonequilibrium exponents lambda and lambda r are changed but remain equal

whittaker modules for the schrodinger witt algebra in this paper whittaker modules for the schrodinger witt algebra sv are defined the whittaker vectors and the irreducibility of the whittaker modules are studied sv has a triangular decomposition according to its cartan subalgebra h sv sv h sv for any lie algebra homomorphism sv c we can define whittaker modules of type when is nonsingular the whittaker vectors the irreducibility and the classification of whittaker modules are completely determined when is singular by constructing some special whittaker vectors we find that the whittaker modules are all reducible moreover we get some more precise results for special

radial fredholm perturbation in the two dimensional ising model and gap exponent relation we consider concentric circular defects in the two dimensional ising model which are distributed according to a generalized fredholm sequence i e at exponentially increasing radii this type of aperiodicity does not change the bulk critical behaviour but introduces a marginal extended perturbation the critical exponent of the local magnetization is obtained through finite size scaling using a corner transfer matrix approach in the extreme anisotropic limit it varies continuously with the amplitude of the modulation and is closely related to the magnetic exponent of the radial hilhorst van leeuwen model through a conformal mapping of the system onto a strip the gap exponent relation is shown to remain valid for such an aperiodic defect

ground state of n coupled nonlinear schrodinger equations in mathbb r n n leq 3 we establish some general theorems for the existence and nonexistence of ground state solutions of steady state n coupled nonlinear schrodinger equations the sign of coupling constants ij s is crucial for the existence of ground state solutions when all ij s are positive and the matrix is positively definite there exists a ground state solution which is radially symmetric however if all ij s are negative or one of ij s is negative and the matrix is positively definite there is no ground state solution furthermore we find a bound state solution which is non radially symmetric when n 3

out of equilibrium properties of the semi infinite kinetic spherical model we study the ageing properties of the semi infinite kinetic spherical model at the critical point and in the ordered low temperature phase for both dirichlet and neumann boundary conditions the surface fluctuation dissipation ratio and the scaling functions of two time surface correlation and response functions are determined explicitly in the dynamical scaling regime in the low temperature phase our results show that for the case of dirichlet boundary conditions the value of the non equilibrium surface exponent b1 differs from the usual bulk value of systems undergoing phase ordering

super galilean conformal algebra in ads cft galilean conformal algebra gca is an inonu wigner iw contraction of a conformal algebra while newton hooke string algebra is an iw contraction of an anti de sitter ads algebra which is the isometry of an ads space it is shown that the gca is a boundary realization of the newton hooke string algebra in the bulk ads the string lies along the direction transverse to the boundary and the worldsheet is ads2 the one dimensional conformal symmetry so 2 1 and rotational symmetry so d contained in the gca are realized as the symmetry on the ads2 string worldsheet and rotational symmetry in the space transverse to the ads2 in adsd 2 respectively it follows from this correspondence that 32 supersymmetric gcas can be derived as iw contractions of superconformal algebras psu 2 2 4 osp 8 4 and osp 8 4 we also derive less supersymmetric gcas from su 2 2 2 osp 4 4 osp 2 4 and osp 8 2

local scale invariances in the bosonic contact and pair contact processes local scale invariance for ageing systems without detailed balance is tested through studying the dynamical symmetries of the critical bosonic contact process and the critical bosonic pair contact process their field theoretical actions can be split into a schrodinger invariant term and a pure noise term it is shown that the two time response and correlation functions are reducible to certain multipoint response functions which depend only on the schrodinger invariant part of the action for the bosonic contact process the representation of the schrodinger group can be derived from the free diffusion equation whereas for the bosonic pair contact process a new representation of the schrodinger group related to a nonlinear schrodinger equation with dimensionful couplings is constructed the resulting predictions of local scale invariance for the two time responses and correlators are completely consistent with the exactly known results in both models

on non linear partial differential equations with an infinite dimensional conditional symmetry abstract the invariance of non linear partial differential equations under a certain infinite dimensional lie algebra a n z in n spatial dimensions is studied the special case a 1 2 was introduced in j stat phys 75 1994 1023 and contains the schrodinger lie algebra sch 1 as a lie subalgebra it is shown that there is no second order equation which is invariant under the massless realizations of a n z however a large class of strongly non linear partial differential equations is found which are conditionally invariant with respect to the massless realization of a n z such that the well known monge ampere equation is the required additional condition new exact solutions are found for some representatives of this class

lie bialgebra structures on the schrodinger virasoro lie algebra in this paper we shall investigate lie bialgebra structures on the schrodinger virasoro algebra l we found out that not all lie bialgebra structures on the schrodinger virasoro algebra are triangular coboundary which is different from the related known results of some other lie algebras related to the virasoro algebra

kinetics of the long range spherical model the kinetic spherical model with long range interactions is studied after a quench to t tc or to t tc for the two time response and correlation functions of the order parameter as well as for composite fields such as the energy density the ageing exponents and the corresponding scaling functions are derived the results are compared to the predictions which follow from local scale invariance

more on symmetries of the schrodinger equation besides the usual and well known lie symmetries of the schrodinger equation the authors study higher order symmetry operators and point out their impact on classes of solvable potentials when time independent interactions take place for one dimensional space systems they consider the case of nth order symmetry operators and more particularly the third order context

cellular automata and statistical mechanical models we elaborate on the analogy between the transfer matrix of usual lattice models and the master equation describing the time development of cellular automata transient and stationary properties of probabilistic automata are linked to surface and bulk properties respectively of restricted statistical mechanical systems it is demonstrated that methods of statistical physics can be successfully used to describe the dynamic and the stationary behavior of such automata some exact results are derived including duality transformations exact mappings disorder and linear solutions many examples are worked out in detail to demonstrate how to use statistical physics in order to construct cellular automata with desired properties this approach is considered to be a first step toward the design of fully parallel probabilistic systems whose computational abilities rely on the cooperative behavior of their components

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

representations of the schrodinger virasoro algebras in this paper it is proved that an irreducible weight module with finite dimensional weight spaces over the schrodinger virasoro algebras is a highest lowest weight module or a uniformly bounded module furthermore indecomposable modules of the intermediate series over these algebras are completely determined