violation of the fluctuation dissipation theorem in glassy systems basic notions and the numerical evidence this review reports on the research done during past years on violations of the fluctuation dissipation theorem fdt in glassy systems it is focused on the existence of a quasi fluctuation dissipation theorem qfdt in glassy systems and the current supporting knowledge gained from numerical simulation studies it covers a broad range of non stationary aging and stationary driven systems such as structural glasses spin glasses coarsening systems ferromagnetic models at criticality trap models models with entropy barriers kinetically constrained models sheared systems and granular media the review is divided into four main parts 1 an introductory section explaining basic notions related to the existence of the fdt in equilibrium and its possible extension to the glassy regime qfdt 2 a description of the basic analytical tools and results derived in the framework of some exactly solvable models 3 a detailed report of the current evidence in favour of the qfdt and 4 a brief digression on the experimental evidence in its favour this review is intended for inexpert readers who want to learn about the basic notions and concepts related to the existence of the qfdt as well as for the more expert readers who may be interested in more specific results

generic features of the fluctuation dissipation relation in coarsening systems the integrated response function in phase ordering systems with scalar vector conserved and nonconserved order parameter is studied at various space dimensionalities assuming scaling of the aging contribution ensuremath chi ag t t w t w ensuremath a ensuremath chi stackrel ifmmode hat else fi ensuremath chi t t w we obtain by numerical simulations and analytical arguments the phenomenological formula describing the dimensionality dependence of a ensuremath chi in all cases considered the primary result is that a ensuremath chi vanishes continuously as d approaches the lower critical dimensionality d l this implies that i the existence of a nontrivial fluctuation dissipation relation and ii the failure of the connection between statics and dynamics are generic features of phase ordering at d l

finite size scaling properties of the damage distance and dynamical critical exponent for the ising model abstract with the damage spreading method scaling properties of the damage distance on the ising model with heat bath dynamics are studied numerically with the parallel flipping scheme the scaling curves fall on two curves which depend on the odd or even lattice sizes the both scaling curves give the consistent dynamical exponent as z 2 16 0 04 for d 2 and z 2 09 0 05 for d 3 respectively by shifting one of them two curves overlap each other perfectly meanwhile all the scaling curves obtained by single spin flipping processes with different odd or even lattice sizes fall on a single curve from which the consistent dynamical critical exponent with the parallel scheme is obtained z 2 18 0 02 for d 2 and z 2 08 0 04 for d 3

short time critical dynamics of the ising model studied within the n fold algorithm abstract the short time behaviour of the critical two dimensional ising model is studied for the bortz kalos lebowitz n fold way algorithm bkl algorithm for square lattices of linear sizes l 110 128 140 170 and 200 we calculate the short time critical behaviour for the bkl algorithm and also for the heat bath algorithm comparison of these results shows that although power law scaling form emerges from the early times of the dynamics there are noticeable differences which do not produce negligible effects on the estimates of critical exponents the observed universality of short time critical behaviour supplements our fundamental knowledge of critical phenomena however short time dynamics seem to be related only approximately with equilibrium critical properties therefore any attempt to estimate equilibrium critical exponents from the short time regime would be superfluous except for the purpose of comparison because these exponents have been determined very precisely by different methods

universality of the off equilibrium response function in the kinetic ising chain the off equilibrium response function chi t t w and autocorrelation function c t t w of an ising chain with spin exchange dynamics are studied numerically and compared with the same quantities in the case of spin flip dynamics it is found that even though these quantities are different in the two cases the parametric plot of chi t t w versus c t t w is the same while this result could be expected in higher dimensionality where chi c is related to the equilibrium state it is far from trivial in the one dimensional case where this relation does not hold the origin of the universality of chi c is traced back to the optimization of domains position with respect to the perturbing external field this mechanism is investigated resorting to models with a single domain moving in a random environment

interest rates in quantum finance the wilson expansion and hamiltonian interest rate instruments form a major component of the capital markets the libor market model lmm is the finance industry standard interest rate model for both libor and euribor which are the most important interest rates the quantum finance formulation of the libor market model is given in this paper and leads to a key generalization all the libors for different future times are imperfectly correlated a key difference between a forward interest rate model and the lmm lies in the fact that the lmm is calibrated directly from the observed market interest rates the short distance wilson expansion phys rev 179 1499 1969 of a gaussian quantum field is shown to provide the generalization of ito calculus in particular the wilson expansion of the gaussian quantum field a t x driving the libors yields a derivation of the libor drift term that incorporates imperfect correlations of the different libors the logarithm of libor phi t x is defined and provides an efficient and compact representation of the quantum field theory of the libor market model the lagrangian and feynman path integrals of the libor market model of interest rates are obtained as well as a derivation given by its hamiltonian the hamiltonian formulation of the martingale condition provides an exact solution for the nonlinear drift of the libor market model the quantum finance formulation of the lmm is shown to reduce to the industry standard bruce gatarek musiela jamshidian model when the forward interest rates are taken to be exactly correlated

dynamic scaling of disordered ising systems the critical dynamics of site disordered three dimensional ising systems has been studied by conventional local dynamics simulations investing 1015 single spin flips the author has verified that the correlation functions of disordered ising systems obey dynamic scaling behaviour the dynamic scaling functions have been calculated the critical exponent z appears to be strongly dependent on the degree of disorder the author has shown that this dependence arises from a crossover phenomenon which has been detected in the static critical behaviour the dynamical exponent has been estimated to be z 2 4 or 0 1 which is surprisingly near to the renormalization group result in o in 1 2

slow relaxation in the large n model for phase ordering the basic features of the slow relaxation phenomenology arising in phase ordering processes are obtained analytically in the large n model through the exact separation of the order parameter into the sum of thermal and condensation components the aging contribution in the response function x a g t t w is found to ohey a pattern of behavior under variation of dimensionality qualitatively similar to the one observed in ising systems there exists a critical dimensionality d 4 above which x a g t t w is proportional to the defect density d t while for d 4 it vanishes more slowly than d t and at d 2 does not vanish as in the ising case this behavior can be understood in terms of the dependence on dimensionality of the interplay between the defect density and the effective response associated to a single defect

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

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

critical exponents for the percolation problem and the yang lee edge singularity gives details of a calculation of critical exponents for a class of field theory models that have an interaction cubic in the fields the results have already been reported give the exponents to third order in epsilon where epsilon 6 d and d is the dimensionality of space the class of models includes the percolation problem and the yang lee edge singularity so the authors give explicit results for the exponents to order epsilon 3 in these cases by resummation methods based on the symptotic behaviour of the epsilon expansion they obtain numerical estimates for these exponents for a number of interesting values of d

renormalization group operator product expansion and anomalous scaling in models of turbulent advection recent progress on the anomalous scaling in models of turbulent heat and mass transport is reviewed with the emphasis on the approach based on the field theoretic renormalization group rg and operator product expansion ope in that approach the anomalous scaling is established as a consequence of the existence in the corresponding field theoretic models of an infinite number of dangerous composite fields operators with negative critical dimensions which are identified with the anomalous exponents this allows one to calculate the exponents in a systematic perturbation expansion similar to the e expansion in the theory of critical phenomena the rg and ope approach is presented in a self contained way for the example of a passive scalar field temperature concentration of an impurity etc advected by a self similar gaussian velocity ensemble with vanishing correlation time the so called kraichnan s rapid change model where the anomalous exponents are known up to order o e3 effects of anisotropy compressibility and the correlation time of the velocity field are discussed passive advection by non gaussian velocity field governed by the stochastic navier stokes equation and passively advected vector e g magnetic fields are considered

computation of the critical exponents of percolation computes the critical indices of percolation using a method in which the integrals are computed at fixed dimension at the order of two loops following this method the authors obtain the series giving the critical exponents expanded with respect to the coupling constant while in the epsilon expansion method the expansion of the series is performed with respect to the coupling constant and to the number of dimensions d thus the authors think that they have obtained better control of the position of the fixed point at a dimension not too near to size they are also able to improve the numerical values of the exponents at d 3

universality in dynamic critical phenomena we use heat bath dynamics to evaluate the dynamic critical exponent z and the dynamic finite size scaling function of an ising model on square planar triangular and honeycomb lattices we find convincing evidence that z is universal and by choosing an aspect ratio and a nonuniversal metric factor for the scaled time of each lattice we can obtain a universal dynamic finite size scaling function for the ising model on the planar lattices our results suggest many interesting problems for further research s1063 651x 97 15408 3

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

the dynamical critical exponent of the two three and five dimensional kinetic ising model abstract we present monte carlo simulation results for the dynamical critical exponent z of the two three and five dimensional kinetic ising model we used glauber as well as metropolis dynamics both type of dynamics lead to the same z values in two and three dimensions the z values were calculated from the magnetization relaxation from an ordered state into the equilibrium state at tc for very large systems up to 169984 2 3072 3 and 48 5 for the two dimensional case we obtain z 2 21 0 03 and for the three dimensional case z 2 08 0 03 for the five dimensional glauber case the requirement z 2 gives a critical point j kbtc 0 11391 from monte carlo simulations whereas new series expansions with four more terms give 0 113935 0 000015 for this ratio

a remark on possible violations of the pauli principle recently ignatiev and kuzmin 1988 developed a theoretical model to implement small violations of the pauli principle the authors remark that the pauli principle is unique among discrete symmetries and that in consequence any apparent violation actually signals new physical degrees of freedom with no violation of the pauli principle they construct an algebraic model which incorporates the algebra of ignatiev and kuzmin and leads to the same apparent violations yet preserves the pauli principle their algebra is that of a jordan pair an algebraic concept which provides a natural framework for structures that do not assume bilinear commutation relations

nonequilibrium critical relaxation with coupling to a conserved density the authors study nonequilibrium critical relaxation properties of model c purely dissipative relaxation of an order parameter coupled to a conserved density starting from a macroscopically prepared initial state with short range correlations using a field theoretic renormalization group approach they show that all the stages of growth of the correlation length display universal behaviour governed by a new critical exponent theta this exponent is calculated to second order in in 4 d where d is the spatial dimension of the system

critical dynamics of the three dimensional ising model a monte carlo study extensive monte carlo simulations have been performed to analyze the dynamical behavior of the three dimensional ising model with local dynamics we have studied the equilibrium correlation functions and the power spectral densities of odd and even observables the exponential relaxation times have been calculated in the asymptotic one exponential time region we find that the critical exponentz 2 09 0 02 characterizes the algebraic divergence with lattice size for all observables the influence of scaling corrections has been analyzed we have determined integrated relaxation times as well their dynamical exponentzint agrees withz for correlations of the magnetization and its absolute value but it is different for energy correlations we have applied a scaling method to analyze the behavior of the correlation functions this method verifies excellent scaling behavior and yields a dynamical exponentzscal which perfectly agrees withz

three dimensional randomly dilute ising model monte carlo results we perform a high statistics simulation of the three dimensional randomly dilute ising model on cubic lattices l 3 with l le 256 we choose a particular value of the density x 0 8 for which the leading scaling corrections are suppressed we determine the critical exponents obtaining nu 0 683 3 eta 0 035 2 beta 0 3535 17 and alpha 0 049 9 in agreement with previous numerical simulations we also estimate numerically the fixed point values of the four point zero momentum couplings that are used in field theoretical fixed dimension studies although these results somewhat differ from those obtained using perturbative field theory the field theoretical estimates of the critical exponents do not change significantly if the monte carlo result for the fixed point is used finally we determine the six point zero momentum couplings relevant for the small magnetization expansion of the equation of state and the invariant amplitude ratio r xi that expresses the universality of the free energy density per correlation volume we find r xi 0 2885 15

on the crossover to universal criticality in dilute ising systems monte carlo simulations of the critical behaviour of disordered ising systems have led to concentration dependent critical exponents which seem to violate universality we apply the renormalization group to investigate the crossover effects which cause the observed behaviour we improve the three loop expansion of the callan symanzik and wilson functions by a pade borel approximation and solve the flow equations for various initial points the exponents found in the simulations can be related to regions in the space of coupling coefficients away from the fixed point

bond percolation and the yang lee edge singularity problems in three dimensions field theories with a trilinear interaction are used to describe both the random bond percolation problem and the yang lee edge singularity problems in three dimensions at criticality renormalisation group functions are calculated to order four for the exponents eta omega and the beta function and to order five for the remaining critical exponents estimations of the critical coupling constant and the exponents for percolation theory are found by summing conformal transformations of the borel transformed series

concrete construction and properties of the difference equation derived from the cellular automaton using the filtration technique following the proposal of a filtration technique by nobe satsuma and tokihiro we concretely construct partial difference equations which preserve any time evolution patterns of cellular automaton ca stably by the filtration technique we illustrate how to develop a method of filtration for applying to the typical two spatial dimensional ca rule the game of life and verify that the filtration method provides the stable difference equation associated with the ca compared with the inverse ultradiscretization besides in order to discuss whether the filtration technique can lead one to partial differential equations from ca rules we show a derivation of the burgers equation from rule 184 ca via the discrete burgers equation constructed by the filtration method as an example

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

the becker doring equations with exponentially size dependent rate coefficients this paper is concerned with an analysis of the becker doring equations which lie at the heart of a number of descriptions of non equilibrium phase transitions and related complex dynamical processes the becker doring theory describes growth and fragmentation in terms of stepwise addition or removal of single particles to or from clusters of similar particles and has been applied to a wide range of problems of physicochemical and biological interest within recent years here we consider the case where the aggregation and fragmentation rates depend exponentially on cluster size these choices of rate coefficients at least qualitatively correspond to physically realistic molecular clustering scenarios such as occur in for example simulations of simple fluids new similarity solutions for the constant monomer becker doring system are identified and shown to be generic in the case of aggregation and fragmentation rates that depend exponentially on cluster size

universality in the off equilibrium critical dynamics of the three dimensional diluted ising model we study the off equilibrium critical dynamics of the three dimensional diluted ising model we compute the dynamical critical exponent z and we show that it is independent of the dilution only when we take into account the scaling corrections to the dynamics finally we will compare our results with the experimental data

critical behaviour in aperiodic systems the author considers layered systems with aperiodically modulated couplings and study the effect of inhomogeneity on the critical behaviour using scaling arguments a relevance irrelevance type criterion is formulated and for relevant inhomogeneities the scaling form of singular quantities is determined the author has performed exact calculations for the surface magnetization of aperiodic quantum ising chains and for a 1 1 dimensional directed polymer in a longitudinal aperiodic environment the results for both systems are in accord with scaling considerations for a marginal aperiodicity the critical exponents are found to be non universal

a quantum anharmonic oscillator model for the stock market abstract a financially interpretable quantum model is proposed to study the probability distributions of the stock price return the dynamics of a quantum particle is considered an analog of the motion of stock price then the probability distributions of price return can be computed from the wave functions that evolve according to schrodinger equation instead of a harmonic oscillator in previous studies a quantum anharmonic oscillator is applied to the stock in liquid market the leptokurtic distributions of price return can be reproduced by our quantum model with the introduction of mixed state and multi potential the trend following dominant market in which the price return follows a bimodal distribution is discussed as a specific case of the illiquid market

the response of glassy systems to random perturbations a bridge between equilibrium and off equilibrium we discuss the response of aging systems with short range interactions to a class of random perturbations although these systems are out of equilibrium the limit value of the free energy at long times is equal to the equilibrium free energy by exploiting this fact we define a new order parameter function and we relate it to the ratio between response and fluctuation which is in principle measurable in an aging experiment for a class of systems possessing stochastic stability we show that this new order parameter function is intimately related to the static order parameter function describing the distribution of overlaps between clustering states the same method is applied to investigate the geometrical organization of pure states we show that the ultrametric organization in the dynamics implies static ultrametricity and we relate these properties to static separability i e the property that the measure of the overlap between pure states is essentially unique our results especially relevant for spin glasses pave the way to an experimental determination of the order parameter function

the minimal length uncertainty and the quantum model for the stock market abstract we generalize the recently proposed quantum model for the stock market by zhang and huang to make it consistent with the discrete nature of the stock price in this formalism the price of the stock and its trend satisfy the generalized uncertainty relation and the corresponding generalized hamiltonian contains an additional term proportional to the fourth power of the trend we study a driven infinite quantum well where information as the external field periodically fluctuates and show that the presence of the minimal trading value of stocks results in a positive shift in the characteristic frequencies of the quantum system the connection between the information frequency and the transition probabilities is discussed finally

finite size scaling and critical exponents in critical relaxation we simulate the critical relaxation process of the two dimensional ising model with the initial state both completely disordered or completely ordered results of a new method to measure both the dynamic and static critical exponents are reported based on the finite size scaling for the dynamics at the early time from the time dependent binder cumulant the dynamical exponent z is extracted independently while the static exponents beta nu and nu are obtained from the time evolution of the magnetization and its higher moments

non equilibrium critical relaxation of the three dimensional ising model abstract the non equilibrium relaxation process at the critical point is studied using monte carlo simulation for the ferromagnetic ising model on a cubic lattice it was observed that the time dependent magnetization decayed following a power law t from the all up initial condition three kinds of single spin flip dynamics were studied for several lattices up to 1536 3 the system size dependences are also studied the value of was estimated to be 0 250 2 this value of leads to the estimation of the dynamical exponent z to be 2 06 2 if we assume z where and denote the critical exponents for spontaneous magnetization and correlation length in equilibrium state respectively and 0 515 the result of the non equilibrium relaxation in the ordered phase is also given

energy relaxation in ising models starting with all spins parallel simulations show the energy to relax at the critical point as t 1 z with z near 2 2 for 1699802 no logarithm and 2 1 for 28003

non equilibrium dynamics of the ising model for t less than equal totc the growth of order in ising models with nonconserved order parameter is considered for quenches to final temperatures tf 0 and tf tc the results of numerical simulations in spatial dimension d 2 are presented in all cases a scaling regime is entered for sufficiently long times where the characteristic length scale is the domain size l t approximately t12 for tf 0 and the nonequilibrium correlation length xi t approximately t1z for tf tc the equal time correlation function has the expected scaling forms f r l t and r d 2 eta fc r xi t for tf 0 and tc respectively the scaling function fc x has interesting short distance behaviour which is elucidated using scaling arguments and by in and 1 n expansions the t 0 scaling function f x depends on whether the spin correlations present in the initial conditions are of long or short range as does the exponent which describes the decay of the autocorrelation function a t si t si o approximately l t results for a quench from the equilibrium critical state to tf 0 are consistent with theoretical predictions

a far from equilibrium fluctuation dissipation relation for an ising glauber like model we derive an exact expression of the response function to an infinitesimal magnetic field for an ising glauber like model with arbitrary exchange couplings the result is expressed in terms of thermodynamic averages and does not depend on the initial conditions or on the dimension of the space the response function is related to time derivatives of a complicated correlation function and so the expression is a generalization of the equilibrium fluctuation dissipation theorem in the special case of this model correspondence with the ising glauber model is discussed a discrete time version of the relation is implemented in monte carlo simulations and then used to study the ageing regime of the ferromagnetic two dimensional ising glauber model quenched from the paramagnetic phase to the ferromagnetic one our approach has the originality to give direct access to the response function and the fluctuation dissipation ratio

general solutions for multispin two time correlation and response functions in the glauber ising chain the kinetic glauber ising spin chain is one of the very few exactly solvable models of non equilibrium statistical mechanics nevertheless existing solutions do not yield tractable expressions for two time correlation and response functions of observables involving products of more than one or two spins we use a new approach to solve explicitly the full hierarchy of differential equations for the correlation and response functions from this general solution follow closed expressions for arbitrary multispin two time correlation and response functions for the case where the system is quenched from equilibrium at ti 0 to some arbitrary t 0 by way of application we give the results for two and four spin two time correlation and response functions from the standard mapping these also imply new exact results for two time particle correlation and response functions in one dimensional diffusion limited annihilation

ito versus stratonovich a survey is given of the facts and fancies concerning the nonlinear langevin or ito equation actually it is merely a pre equation which becomes an equation when an interpretation rule is added the rules of ito and stratonovich differ but both are mathematically consistent and therefore equally admissible conventions the reason why they seem to lead to physical differences is that the langevin approach used to arrive at the equation involves a tacit assumption for systems with external noise this assumption can be justified and it is then clear that the stratonovich rule applies systems with internal noise however can only be properly described by a master equation and the ito stratonovich controversy never enters afterward one is free to model the resulting fluctuations either with an ito or a stratonovich scheme but that does not lead to any new information

random initial conditions and nonlinear relaxation the author studies the effect of randomness in the initial conditions on the deterministic diffusion equation with nonlinear terms physically this describes among other things the time development of a system quenched from a high temperature to the vicinity of the critical point in the approximation where the effects of thermal noise are neglected he considers the case of a non conserved order parameter with o n symmetry and shows that the nonlinearities are irrelevant for the large time behaviour for dimension d 2 the model is investigated for d 2 using the renormalization group and in expansion it is found to all orders in in that the local fluctuations in the order parameter scale like t 12 and have a universal distribution the time dependence of the response function describing the dependence on the initial condition is characterized by another exponent which is computed to o in 2 these results are checked in the exactly soluble cases of n to infinity and d 0

non equilibrium relaxation and interface energy of the ising model abstract from the non equilibrium critical relaxation study of the two dimensional ising model the dynamical critical exponent z is estimated to be 2 165 0 010 for this model the relaxation in the ordered phase of this model is consistent with exp t behavior the interface energy of the three dimensional ising model is studied and the critical exponent of the correlation length and the critical amplitude of the surface tension 0 are estimated to be 0 6250 0 0025 and 1 42 0 04 respectively a dynamic monte carlo renormalization group method is successfully applied to the equilibrium properties of the three dimensional ising model

path integral for equities dynamic correlation and empirical analysis abstract this paper develops a model to describe the unequal time correlation between rate of returns of different stocks a non trivial fourth order derivative lagrangian is defined to provide an unequal time propagator which can be fitted to the market data a calibration algorithm is designed to find the empirical parameters for this model and different de noising methods are used to capture the signals concealed in the rate of return the detailed results of this gaussian model show that the different stocks can have strong correlation and the empirical unequal time correlator can be described by the model s propagator this preliminary study provides a novel model for the correlator of different instruments at different times

a finite dimensional quantum model for the stock market abstract we present a finite dimensional version of the quantum model for the stock market proposed in c zhang and l huang a quantum model for the stock market physica a 389 2010 5769 our approach is an attempt to make this model consistent with the discrete nature of the stock price and is based on the mathematical formalism used in the case of the quantum systems with finite dimensional hilbert space the rate of return is a discrete variable corresponding to the coordinate in the case of quantum systems and the operator of the conjugate variable describing the trend of the stock return is defined in terms of the finite fourier transform the stock return in equilibrium is described by a finite gaussian function and the time evolution of the stock price directly related to the rate of return is obtained by numerically solving a schrodinger type equation

price volume multifractal analysis and its application in chinese stock markets abstract an empirical research on chinese stock markets is conducted using statistical tools first the multifractality of stock price return series r i r i ln p t 1 ln p t and trading volume variation series v i v i ln v t 1 ln v t is confirmed using multifractal detrended fluctuation analysis furthermore a multifractal detrended cross correlation analysis between stock price return and trading volume variation in chinese stock markets is also conducted it is shown that the cross relationship between them is also found to be multifractal second the cross correlation between stock price p i and trading volume v i is empirically studied using cross correlation function and detrended cross correlation analysis it is found that both shanghai stock market and shenzhen stock market show pronounced long range cross correlations between stock price and trading volume third a composite index r based on price and trading volume is introduced compared with stock price return series r i and trading volume variation series v i r variation series not only remain the characteristics of original series but also demonstrate the relative correlation between stock price and trading volume finally we analyze the multifractal characteristics of r variation series before and after three financial events in china namely price limits reform of non tradable shares and financial crisis in 2008 in the whole period of sample to study the changes of stock market fluctuation and financial risk it is found that the empirical results verified the validity of r

aging properties of an anomalously diffusing particule we report new results about the two time dynamics of an anomalously diffusing classical particle as described by the generalized langevin equation with a frequency dependent noise and the associated friction the noise is defined by its spectral density proportional to 1 at low frequencies with 0 1 subdiffusion or 1 2 superdiffusion using laplace analysis we derive analytic expressions in terms of mittag leffler functions for the correlation functions of the velocity and of the displacement while the velocity thermalizes at large times slowly in contrast to the standard brownian motion case 1 the displacement never attains equilibrium it ages we thus show that this feature of normal diffusion is shared by a subdiffusive or superdiffusive motion we provide a closed form analytic expression for the fluctuation dissipation ratio characterizing aging

non equilibrium relaxation at a tricritical point we study the purely relaxational tricritical dynamics of a non conserved order parameter model a in the upper critical dimension dc 3 and in 3 epsilon dimensions we are especially interested in the relaxation starting from a macroscopically prepared initial state with a small correlation length using the methods of renormalized field theory we obtain the scaling behaviour of the correlation and response functions and study the nonlinear relaxation of the order parameter m t in three dimensions m t displays a crossover from the purely logarithmic short time behaviour m t approximately in t t0 a to a t 14 power law with logarithmic corrections for dimensions d 3 we obtain the exponents which govern the tricritical relaxation at lowest non trivial order in epsilon 3 d the dynamic scaling exponent z is calculated at second order in epsilon

monte carlo simulations of the violation of the fluctuation dissipation theorem in domain growth processes numerical simulations of various domain growth systems are reported in order to compute the parameter describing the violation of fluctuation dissipation theorem fdt in aging phenomena we compute two time correlation and response functions and find that as expected from the exact solution of a certain mean field model equivalent to the o n model in three dimensions in the limit of n going to infinity this parameter is equal to one no violation of fdt in the quasiequilibrium regime short separation of times and zero in the aging regime

renewal modulation and superstatistics in times series we consider two different approaches to which we refer to as renewal and modulation to generate time series with a nonexponential distribution of waiting times we show that different time series with the same waiting time distribution are not necessarily statistically equivalent and might generate different physical properties renewal generates aging and anomalous scaling while modulation yields no significant aging and either ordinary or anomalous diffusion according to the dynamic prescription adopted we show in fact that the physical realization of modulation generates two classes of events the events of the first class are determined by the persistent use of the same exponential time scale for an extended lapse of time and consequently are numerous the events of the second class are identified with the abrupt changes from one to another exponential prescription and consequently are rare the events of the second class although rare determine the scaling of the diffusion process and for this reason we term them as crucial events according to the prescription adopted to produce modulation the distribution density of the time distances between two consecutive crucial events might have or not a diverging second moment in the former case the resulting diffusion process although going through a transition regime very extended in time will eventually become anomalous in conclusion modulation rather than ruling out the action of renewal events produces crucial events hidden by clouds of exponential events thereby setting the challenge for their identification

dynamical relaxation and universal short time behavior of finite systems a system belonging to the dynamic universality class of model a is considered in a block v ld geometry with periodic boundary conditions the relaxation of the order parameterm t from an initial value m i is investigated at the bulk critical temperature we demonstrate that a proper scaling description of the problem involves two characteristic times tl lz andtl m i z x wherez is the familiar dynamic bulk exponent while xi is an independent new bulk exponent discovered recently previous analyses of the problem either were restricted tot ti or tacitly used the incorrect assumption thatxi v thus the short time regimet ti with universal dependence on m i was missed as a concrete example we study the exact solution in the large n limit

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

scaling of the linear response function from zero field cooled and thermoremanent magnetization in phase ordering kinetics in this paper we investigate the relation between the scaling properties of the linear response function r t s of the thermoremanent magnetization trm and of the zero field cooled zfc magnetization in the context of phase ordering kinetics we explain why the retrieval of the scaling properties of r t s from those of trm and zfc magnetization is not trivial preasymptotic contributions generate a long crossover in trm while zfc magnetization is affected by a dangerous irrelevant variable lack of understanding of both these points has generated some confusion in the literature the full picture relating the exponents of all the quantities involved is explicitly illustrated in the framework of the large n model following this scheme an assessment of the present status of numerical simulations for the ising model can be made we reach the conclusion that on the basis of the data available up to now statements on the scaling properties of r t s can be made from zfc magnetization but not from trm from zfc data for the ising model with d 2 3 4 we confirm the previously found linear dependence on dimensionality of the exponent a entering r t s ensuremath sim s ensuremath 1 a f t s we also find evidence that a recently derived form of the scaling function f x using local scale invariance arguments m henkel m pleimling c godr eche and j m luck phys rev lett 87 265701 2001 does not hold for the ising model

critical phenomena at perfect and non perfect surfaces the effect of imperfections on surface critical properties is studied for ising models with nearest neighbour ferromagnetic couplings on simple cubic lattices in particular results of monte carlo simulations for flat perfect surfaces are compared to those for flat surfaces with random weak or strong interactions between neighbouring spins in the surface layer and for surfaces with steps of monoatomic height surface critical exponents at the ordinary transition in particular are found to be robust against these perturbations

on the range of validity of the 6 e expansion for percolation in 6 epsilon dimensions the critical properties of percolation can be computed starting from a phi 3 theory having the same symmetry of the one state potts model the authors argue that this fixed point must be unstable with respect to a phi 4 interaction in two dimensions therefore a phi 4 perturbation is relevant this suggestion is confirmed by an explicit two loops computation

quantum finance hamiltonian for coupon bond european and barrier options coupon bond european and barrier options are financial derivatives that can be analyzed in the hamiltonian formulation of quantum finance forward interest rates are modeled as a two dimensional quantum field theory and its hamiltonian and state space is defined european and barrier options are realized as transition amplitudes of the time integrated hamiltonian operator the double barrier option for a financial instrument is knocked out terminated with zero value if the price of the underlying instrument exceeds or falls below preset limits the barrier option is realized by imposing boundary conditions on the eigenfunctions of the forward interest rates hamiltonian the price of the european coupon bond option and the zero coupon bond barrier option are calculated it is shown that is general the constraint function for a coupon bond barrier option can to a good approximation be linearized a calculation using an overcomplete set of eigenfunctions yields an approximate price for the coupon bond barrier option which is given in the form of an integral of a factor that results from the barrier condition times another factor that arises from the payoff function

the dynamic critical exponent of dilute and pure ising systems a massive dynamic field theory is employed to calculate the critical exponent z of the three dimensional dilute ising model to two loop order without expansion in square root 4 d with result z approximately 2 191 applying the same method to the pure ising model at three loop order we find z 2 022 for d 3 and z 2 124 for d 2

a bayesian analysis of monte carlo correlation times for the two dimensional ising model abstract we present a new bayesian analysis of the high accuracy data of nightingale and blote for the correlation times of the two dimensional ising model to determine the value of the dynamical critical exponent we demonstrate the crucial role played by the nightingale blote assumption that odd terms disappear in their expression for the correlation time as a function of the size of the system we obtain differing results for the existence of logarithmic corrections and the value of the dynamical critical exponent depending on whether or not that assumption is valid

damage spreading and critical exponents for model a ising dynamics using damage spreading and heat bath dynamics we study the ising model in 2 and 3 dimensions with non conservative dynamics our algorithm differs in some important points from previous ones which makes it rather efficient we give estimates for the exponent z which seem to be the most precise published so far 2 172 0 006 for d 2 2 032 0 004 for d 3 we also give precise estimates of the exponent introduced by janssen et al z phys b 73 1989 539 and of analogous but in principle independent exponents we find surprisingly that some of the latter agree with and give an explanation for this

quantum spatial periodic harmonic model for daily price limited stock markets abstract we investigate the behaviors of stocks in daily price limited stock markets by purposing a quantum spatial periodic harmonic model the stock price is considered to be oscillating and damping in a quantum spatial periodic harmonic oscillator potential well a complicated non linear relation including inter band positive correlation and intra band negative correlation between the volatility and trading volume of a stock is numerically derived with the energy band structure of the model concerned the effectiveness of price limit is re examined with some observed characteristics of price limited stock markets in china studied by applying our quantum model

a quantum model for the stock market abstract beginning with several basic hypotheses of quantum mechanics we give a new quantum model in econophysics in this model we define wave functions and operators of the stock market to establish the schrodinger equation for stock price based on this theoretical framework an example of a driven infinite quantum well is considered in which we use a cosine distribution to simulate the state of stock price in equilibrium after adding an external field into the hamiltonian to analytically calculate the wave function the distribution and the average value of the rate of return are shown

chaotic behavior of an extended system abstract some general aspects of spatiotemporal chaos are considered with emphasis on long range correlations and response an attempt is made to characterize the statistical steady state of a chaotic system by analogy with the description of a system near thermal equilibrium the one dimensional kuramoto sivashinsky equation is considered as an example and our present understanding of its statistical behavior is reviewed

long time traces of the initial condition in relaxation phenomena near criticality the time evolution of systems relaxing towards thermal equilibrium is examined near the critical temperature t c with special attention paid to the role of the initial value m i of the order parameter phi to this end the n component model a for a cube of length l is investigated the common belief that all memory of m i is necessarily lost after a microscopic time span is shown to be unfounded general arguments and the exact solution of the limit n to infty show that m i leaves its traces in both the linear and nonlinear long time relaxation of phi near or at t c specifically for linear relaxation near t c or at t c with l infty the amplitude of the exponential decay depends on m i and the short time exponent theta x i x phi z provided t i sim m i z x i is comparable to or larger than other time scales here x i is the scaling dimension of m i z is the dynamic bulk exponent and x phi is the usual equilibrium scaling dimension of phi

simulation of nonlinear interest rates in quantum finance libor market model abstract the simulation of the libor market model lmm is extensively studied in the framework of quantum finance the imperfectly correlated libor rates are simulated based on a gaussian quantum field and a recursion equation of nontrivial stochastic drift the libor options are studied using both the simulation method and the analytical formula the caplet price of simulation is compared with black s caplet formula which can be exactly derived from the lmm the invariance of caplet price for different forward bond numeraire is verified by using the simulation the simulation results for coupon bond options and swaptions are compared with the approximate price which are limited for the reason that the approximate price is derived using the small volatility expansion the simulation method is shown to have great potential in the application of pricing interest rate instruments

ageing phenomena without detailed balance the contact process the long time dynamics of the 1d contact process suddenly brought out of an uncorrelated initial state is studied through a light cone transfer matrix renormalization group approach at criticality the system undergoes ageing which is characterized through the dynamical scaling of the two times autocorrelation and autoresponse functions the observed non equality of the ageing exponents a and b excludes the possibility of a finite fluctuation dissipation ratio in the ageing regime the scaling form of the critical autoresponse function is in agreement with the prediction of local scale invariance

aging in ferromagnetic systems at criticality near four dimensions we study the off equilibrium response and correlation functions and the corresponding fluctuation dissipation ratio for a purely dissipative relaxation of an o n symmetric vector model model a below its upper critical dimension the scaling behavior of these quantities is analyzed and the associated universal functions are determined at first order in ensuremath epsilon 4 ensuremath d in the high temperature phase and at criticality a nontrivial limit of the fluctuation dissipation ratio is found in the aging regime x ensuremath infty 1 2 1 ensuremath ensuremath epsilon 4 n 2 n 8 o ensuremath epsilon 2

a quantum statistical approach to simplified stock markets we use standard perturbation techniques originally formulated in quantum statistical mechanics in the analysis of a toy model of a stock market which is given in terms of bosonic operators in particular we discuss the probability of transition from a given value of the portfolio of a certain trader to a different one this computation can also be carried out using some kind of feynman graphs adapted to the present context

fluctuation dissipation ratio in the one dimensional kinetic ising model the exact relation between the response function r t t and the two time correlation function c t t is derived analytically in the one dimensional kinetic ising model subjected to a temperature quench the fluctuation dissipation ratio x t t is found to depend on time through c t t in the time region where scaling c t t f t t holds the crossover from the nontrivial form x c t t to x t t identical with1 takes place as the waiting time t w is increased from below to above the equilibration time t eq

quantum brownian motion model for the stock market abstract it is believed by the majority today that the efficient market hypothesis is imperfect because of market irrationality using the physical concepts and mathematical structures of quantum mechanics we construct an econophysical framework for the stock market based on which we analogously map massive numbers of single stocks into a reservoir consisting of many quantum harmonic oscillators and their stock index into a typical quantum open system a quantum brownian particle in particular the irrationality of stock transactions is quantitatively considered as the planck constant within heisenberg s uncertainty relationship of quantum mechanics in an analogous manner we analyze real stock data of shanghai stock exchange of china and investigate fat tail phenomena and non markovian behaviors of the stock index with the assistance of the quantum brownian motion model thereby interpreting and studying the limitations of the classical brownian motion model for the efficient market hypothesis from a new perspective of quantum open system dynamics

critical dynamics of stochastic models with energy conservation model c we calculate the field theoretic functions of the generalized dynamical model c in which a conserved secondary density is coupled to a nonconserved complex order parameter in two loop order we show that the fixed points in this extended model are equal to the fixed points obtained in model c with a real order parameter which has been introduced by halperin hohenberg and ma our results correct long standing errors in the field theoretic functions in model c published by several authors leading also to different fixed point values w for the ratio of the two time scales involved the stability regions of the fixed points which remained partially unclear considered in a phase diagram whose axes are the spatial dimension d and number of order parameter components n are now clarified especially an anomalous region found by previous authors in which the scaling properties remained unsolved does not exist there are only two regions one with a finite fixed point w where the dynamical exponent z of the order parameter is z 2 alpha nu and another region where w 0 and z is equal to the model a value

non equilibrium critical relaxation with reversible mode coupling the non equilibrium critical relaxation of systems in which the order parameter couples reversibly to conserved densities is investigated the initial state which may be macroscopically prepared by a quench from a temperature t tc to the critical temperature tc is characterized by short range correlations in the case where the order parameter itself is conserved the relaxation shows universal scaling if on the other hand the order parameter is not conserved the scaling is governed by a new exponent which depends on the width of the initial distribution of the conserved fields however the response function of the conserved fields still shows universal scaling

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

a non perturbative approach to critical dynamics this paper is devoted to a non perturbative renormalization group nprg analysis of model a which stands as a paradigm for the study of critical dynamics the nprg formalism has appeared as a valuable theoretical tool to investigate non equilibrium critical phenomena yet the simplest and nontrivial models for critical dynamics have never been studied using nprg techniques in this paper we focus on model a taking this opportunity to provide a pedagogical introduction to nprg methods for dynamical problems in statistical physics the dynamical exponent z is computed in d 3 and d 2 and is found to be in close agreement with results from other methods