critical exponents from power spectra we have simulated the two and three dimensional ising models at their respective critical points with a conventional monte carlo algorithm from the power spectrum of the magnetization autocorrelations we have determined the dynamic critical exponents and obtained the valuesz 2 16 2 19 andz 2 05 in agreement with the results quoted in the literature we have also studied the power spectrum for the kardar parisi zhang and sun guo grant equations describing interface dynamics arguments similar to what was recently used to conclude thatz 4 for model b in critical dynamics were applied to the sun guo grant growth model and the known exact values for the roughening and dynamic exponents were obtained from an analysis of the corresponding power spectrum in self organized critical sand models one obtains a recently proposed hyperscaling relation

quantum communication with coherent states quantum communication is studied under the cutoff rate criterion for transmission of m coherent states of real amplitude m 2 7 comparison with other measurement operators of interest such as the number and the quasi classical operators is made the effect of quantization of the decision level on the cutoff rate is considered

on compound state and mutual information in quantum information theory corresp a quantum mechanical compound state of an input state and its output state generated through a communication channel is constructed the mutual information of quantum communication theory is defined by using the compound state and its fundamental properties are studied

simulation of the three dimensional ising model on the creutz cellular automaton abstract the three dimensional ising model is simulated on the creutz cellular automaton the values computed for the critical temperature and the static critical exponents within the framework of the finite size scaling theory are in agreement with their values obtained by different methods

test of three dimensional q2r ising algorithm simulation results of q2r cellular automata on the simple cubic lattice are compared with usual monte carlo simulations of the ising model curie temperature spontaneous magnetisation and specific heat agree but at low temperatures the susceptibility and the distribution of local energies differ

critical slowing down in ising model for creutz algorithm abstract dynamical critical exponents for the two dimensional ising model are computed on a cellular automaton from the relaxations of the time displaced correlation and auto correlation functions for the order parameter and the internal energy at the critical temperatures and from the nonlinear relaxation time for the order parameter near the critical temperature the analysis of the data within the frame of the dynamical finite size scaling hypothesis gives z m z e 2 20 and z a m 1 91 and z a e 0 19 for the linear dynamical exponents corresponding respectively to the relaxations of the correlation and the autocorrelation functions for the order parameter and the internal energy and nl m 2 07 for the nonlinear dynamical exponent for the order parameter these values verify the scaling relations between the dynamical exponents

on the dynamic exponent of the two dimensional ising model the authors use the method of damage spreading to measure the time taken for the equilibrium damage the magnetization to disappear in finite systems 10 or 2 27

dynamical finite size scaling function of the four dimensional ising model for creutz algorithm abstract dynamical critical exponents for the four dimensional ising model are computed on a cellular automaton from the relaxations of the time displaced correlation for the order parameter and the internal energy at the critical temperatures the analysis of the data within the frame of the dynamical finite size scaling hypothesis gives the linear dynamical critical exponents for the order parameter and the internal energy in our calculation the linear dynamical critical exponents are found z m z h i 2 04 at t c z m 1 99 z h i 2 00 at t c l the values of z m z h i 2 04 obtained for t c verify the dynamical finite size scaling for which it was adopted four dimensional ising model

critical behavior of the two dimensional ising model with next nearest neighbor antiferromagnetic interaction on the creutz cellular automaton the two dimensional ising model with nearest and next nearest neighbor antiferromagnetic interactions of ratio r is simulated on the creutz cellular automaton the values of the critical temperature and the critical exponents for o r are estimated within the framework of the finite size scaling theory the dependence of tc on r agrees with the crossover scaling theory for 1 75 the results for 0 r are compatible with ising critical behavior

on hyperboloidal cauchy data for vacuum einstein equations and obstructions to smoothness of scri the relationship between the geometric properties of hyperboloidal cauchy data for vacuum einstein equations at the conformal boundary of the initial data surface and between the space time geometry is analyzed in detail we prove that a necessary condition for existence of a smooth or a polyhomogeneous scri i e a scri around which the metric is expandable in terms ofr j log i r rather than in terms ofr j is the vanishing of the shear of the conformal boundary of the initial data surface we derive the boundary constraints which have to be satisfied by an initial data set for compatibility with friedrich s conformal framework we show that a sufficient condition for existence of a smooth scri not necessarily complete is the vanishing of the shear of the conformal boundary of the initial data surface and smoothness up to boundary of the conformally rescaled initial data we also show that the occurrence of some log terms in an asymptotic expansion at the conformal boundary of solutions of the constraint equations is related to the non vanishing of the weyl tensor at the conformal boundary

on the regularity of solutions to the yamabe equation and the existence of smooth hyperboloidal initial data for einstein s field equations the regularity of the solutions to the yamabe problem is considered in the case of conformally compact manifolds and negative scalar curvature the existence of smooth hyperboloidal initial data for einstein s field equations is demonstrated

dynamical properties of the two and three dimensional ising models by damage spreading the method of damage spreading is used to measure the dynamic exponent z for both the two and three dimensional ising models with heat bath dynamics the authors also measure a new exponent alpha describing the rate at which a damage cloud grows they report values of z 2 24 or 0 04 and alpha 0 77 or 0 11 in two dimensions and z 2 202 or 0 03 and alpha 0 92 or 0 10 in three dimensions

cauchy problems for the conformal vacuum field equations in general relativity cauchy problems for einstein s conformal vacuum field equations are reduced to cauchy problems for first order quasilinear symmetric hyperbolic systems the hyperboloidal initial value problem where cauchy data are given on a spacelike hypersurface which intersects past null infinity at a spacelike two surface is discussed and translated into the conformally related picture it is shown that for conformal hyperboloidal initial data of classhs s 4 there is a unique up to questions of extensibility development which is a solution of the conformal vacuum field equations of classhs it provides a solution of einstein s vacuum field equations which has a smooth structure at past null infinity

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

microcanonical simulations with a large number of demons we generalize the microcanonical algorithm developed by creutz et al 1986 and make a detailed comparison with the exact solution in the case of a two dimensional ising model at finite volume we present a new numerical method to compute the temperature in the microcanonical ensemble this allows us to define a thermalization criterion to estimate the point where the differences between canonical and microcanonical results are the smallest this criterion is shown to work well in the case of the two dimensional ising system

entanglement information rate distortion of a quantum gaussian source quantum distortion operator is introduced based on canonical operators as the lower bound of quantum information rate distortion the entanglement information rate distortion is achieved by gaussian map for gaussian source the entanglement information rate distortion function is calculated for one mode gaussian source it is achieved by a nontrivial unitary transformation the rate distortion is achievable at zero distortion point in contrast to the distortion defined via fidelity our definition of the distortion makes it possible to calculate the entanglement information rate distortion function for gaussian source

simulation of time exponent in 2d glauber kinetic ising model abstract simulations of the magnetization relaxation of large square lattices at the curie point give a dynamical exponent near 2 2 somewhat higher than expected

invariant in cellular automata for a subclass of the set of reversible cellular automata the author gives the form of an exact time invariant quantity which can be seen as a kind of energy with the ergodic assumption this is a model of two interacting ising spin systems

the effect of the increase of linear dimensions on exponents obtained by finite size scaling relations for the six dimensional ising model on the creutz cellular automaton the six dimensional ising model is simulated on the creutz cellular automaton using the finite size lattices with the linear dimension 4

the test of the finite size scaling relations for the six dimensional ising model on the creutz cellular automaton the six dimensional ising model is simulated on the creutz cellular automaton using the finite size lattices with the linear dimension 4 l 10 the exponents in the finite size scaling relations for the magnetic susceptibility and the order parameter at the infinite lattice critical temperature are computed to be 3 00 12 and 1 47 10 using 6 l 10 respectively which are in very good agreement with the theoretical predictions of and the critical temperature for the infinite lattice is found to be 10 835 5 using 4 l 10 which is also in very good agreement with the precise results the finite size scaling relation for the magnetic susceptibility at the infinite lattice critical temperature is also valid for the maxima of the magnetic susceptibilities of the finite size lattices the finite size scaling plots of the magnetic susceptibility and the order parameter verify the finite size scaling relations about the infinite lattice critical temperature

spectral methods in general relativistic astrophysics we present spectral methods developed in our group to solve three dimensional partial differential equations the emphasis is laid on equations arising from astrophysical problems in the framework of general relativity

calculating initial data for the conformal einstein equations by pseudo spectral methods abstract we present a numerical scheme for determining hyperboloidal initial data sets for the conformal field equations by using pseudo spectral methods this problem is to split into two parts the first step is the determination of a suitable conformal factor which transforms from an initial data set in physical space time to a hyperboloidal hypersurface in the ambient conformal manifold this is achieved by solving the yamabe equation a nonlinear second order equation the second step is a division by the conformal factor of certain fields which vanish on i the zero set of the conformal factor the challenge there is to numerically obtain a smooth quotient both parts are treated by pseudo spectral methods the nonlinear equation is solved iteratively while the division problem is treated by transforming the problem to the coefficient space solving it there by the qr factorisation of a suitable matrix and then transforming back these hyperboloidal initial data can be used to generate general relativistic space times by evolution with the conformal field equations

computation of correlation functions of the two dimensional ising model abstract the spin spin and energy energy correlation functions of the two dimensional ising model are computer on the creutz cellular automaton from the data for the spin spin correlation functions the values of the critical exponents and are obtained they are in agreement with their theoretical values

the asymptotic characteristic initial value problem for einstein s vacuum field equations as an initial value problem for a first order quasilinear symmetric hyperbolic system the asymptotic characteristic initial value problem for einstein s vacuum field equations where data are given on an incoming null hypersurface and on part of past null infinity is reduced to a characteristic initial value problem for a first order quasilinear symmetric hyperbolic system of differential equations for which existence and uniqueness of solutions can be shown it is delineated how the same method can be applied to the standard cauchy problems for einstein s vacuum and conformal vacuum equations

rate distortion and detection in quantum communication several relations between the rate distortion function and the probability of error in detection are studied in the context of quantum communication theory both of these criteria are associated with the same fidelity function