Nonequilibrium critical dynamics of the relaxational models C and D

We investigate the critical dynamics of the $n$-component relaxational models C and D which incorporate the coupling of a nonconserved and conserved order parameter S, respectively, to the conserved energy density rho, under nonequilibrium conditions by means of the dynamical renormalization group. Detailed balance violations can be implemented isotropically by allowing for different effective temperatures for the heat baths coupling to the slow modes. In the case of model D with conserved order parameter, the energy density fluctuations can be integrated out. For model C with scalar order parameter, in equilibrium governed by strong dynamic scaling (z_S = z_rho), we find no genuine nonequilibrium fixed point. The nonequilibrium critical dynamics of model C with n = 1 thus follows the behavior of other systems with nonconserved order parameter wherein detailed balance becomes effectively restored at the phase transition. For n >= 4, the energy density decouples from the order parameter. However, for n = 2 and n = 3, in the weak dynamic scaling regime (z_S <= z_rho) entire lines of genuine nonequilibrium model C fixed points emerge to one-loop order, which are characterized by continuously varying critical exponents. Similarly, the nonequilibrium model C with spatially anisotropic noise and n < 4 allows for continuously varying exponents, yet with strong dynamic scaling. Subjecting model D to anisotropic nonequilibrium perturbations leads to genuinely different critical behavior with softening only in subsectors of momentum space and correspondingly anisotropic scaling exponents. Similar to the two-temperature model B the effective theory at criticality can be cast into an equilibrium model D dynamics, albeit incorporating long-range interactions of the uniaxial dipolar type.Comment: Revtex, 23 pages, 5 eps figures included (minor additions), to appear in Phys. Rev.

Pair Contact Process with Diffusion: Failure of Master Equation Field Theory

We demonstrate that the `microscopic' field theory representation, directly derived from the corresponding master equation, fails to adequately capture the continuous nonequilibrium phase transition of the Pair Contact Process with Diffusion (PCPD). The ensuing renormalization group (RG) flow equations do not allow for a stable fixed point in the parameter region that is accessible by the physical initial conditions. There exists a stable RG fixed point outside this regime, but the resulting scaling exponents, in conjunction with the predicted particle anticorrelations at the critical point, would be in contradiction with the positivity of the equal-time mean-square particle number fluctuations. We conclude that a more coarse-grained effective field theory approach is required to elucidate the critical properties of the PCPD.Comment: revtex, 8 pages, 1 figure include

Kinetics of phase-separation in the critical spherical model and local scale-invariance

The scaling forms of the space- and time-dependent two-time correlation and response functions are calculated for the kinetic spherical model with a conserved order-parameter and quenched to its critical point from a completely disordered initial state. The stochastic Langevin equation can be split into a noise part and into a deterministic part which has local scale-transformations with a dynamical exponent z=4 as a dynamical symmetry. An exact reduction formula allows to express any physical average in terms of averages calculable from the deterministic part alone. The exact spherical model results are shown to agree with these predictions of local scale-invariance. The results also include kinetic growth with mass conservation as described by the Mullins-Herring equation.Comment: Latex2e with IOP macros, 28 pp, 2 figures, final for

Nonequilibrium steady states of driven magnetic flux lines in disordered type-II superconductors

We investigate driven magnetic flux lines in layered type-II superconductors subject to various configurations of strong point or columnar pinning centers by means of a three-dimensional elastic line model and Metropolis Monte Carlo simulations. We characterize the resulting nonequilibrium steady states by means of the force-velocity / current-voltage curve, static structure factor, mean vortex radius of gyration, number of double-kink and half-loop excitations, and velocity / voltage noise spectrum. We compare the results for the above observables for randomly distributed point and columnar defects, and demonstrate that the three-dimensional flux line structures and their fluctuations lead to a remarkable variety of complex phenomena in the steady-state transport properties of bulk superconductors.Comment: 23 pages, IOP style, 18 figures include

Coarsening of Disordered Quantum Rotors under a Bias Voltage

We solve the dynamics of an ensemble of interacting rotors coupled to two leads at different chemical potential letting a current flow through the system and driving it out of equilibrium. We show that at low temperature the coarsening phase persists under the voltage drop up to a critical value of the applied potential that depends on the characteristics of the electron reservoirs. We discuss the properties of the critical surface in the temperature, voltage, strength of quantum fluctuations and coupling to the bath phase diagram. We analyze the coarsening regime finding, in particular, which features are essentially quantum mechanical and which are basically classical in nature. We demonstrate that the system evolves via the growth of a coherence length with the same time-dependence as in the classical limit, $R(t) \simeq t^{1/2}$ -- the scalar curvature driven universality class. We obtain the scaling function of the correlation function at late epochs in the coarsening regime and we prove that it coincides with the classical one once a prefactor that encodes the dependence on all the parameters is factorized. We derive a generic formula for the current flowing through the system and we show that, for this model, it rapidly approaches a constant that we compute.Comment: 53 pages, 12 figure

Logarithmic roughening in a growth process with edge evaporation

Roughening transitions are often characterized by unusual scaling properties. As an example we investigate the roughening transition in a solid-on-solid growth process with edge evaporation [Phys. Rev. Lett. 76, 2746 (1996)], where the interface is known to roughen logarithmically with time. Performing high-precision simulations we find appropriate scaling forms for various quantities. Moreover we present a simple approximation explaining why the interface roughens logarithmically.Comment: revtex, 6 pages, 7 eps figure

A field theoretic approach to master equations and a variational method beyond the Poisson ansatz

We develop a variational scheme in a field theoretic approach to a stochastic process. While various stochastic processes can be expressed using master equations, in general it is difficult to solve the master equations exactly, and it is also hard to solve the master equations numerically because of the curse of dimensionality. The field theoretic approach has been used in order to study such complicated master equations, and the variational scheme achieves tremendous reduction in the dimensionality of master equations. For the variational method, only the Poisson ansatz has been used, in which one restricts the variational function to a Poisson distribution. Hence, one has dealt with only restricted fluctuation effects. We develop the variational method further, which enables us to treat an arbitrary variational function. It is shown that the variational scheme developed gives a quantitatively good approximation for master equations which describe a stochastic gene regulatory network.Comment: 13 pages, 2 figure

Ageing in the contact process: Scaling behavior and universal features

We investigate some aspects of the ageing behavior observed in the contact process after a quench from its active phase to the critical point. In particular we discuss the scaling properties of the two-time response function and we calculate it and its universal ratio to the two-time correlation function up to first order in the field-theoretical epsilon-expansion. The scaling form of the response function does not fit the prediction of the theory of local scale invariance. Our findings are in good qualitative agreement with recent numerical results.Comment: 20 pages, 3 figure

Nonequilibrium relaxation and scaling properties of the two-dimensional Coulomb glass in the aging regime

We employ Monte Carlo simulations to investigate the two-time density autocorrelation function for the two-dimensional Coulomb glass. We find that the nonequilibrium relaxation properties of this highly correlated disordered system can be described by a full aging scaling ansatz. The scaling exponents are non-universal, and depend on temperature and charge density.Comment: 6 pages, 3 figures included; revised version: corrected exponents, and some additional explanations and references added; to appear in EP

Ageing without detailed balance: local scale invariance applied to two exactly solvable models

I consider ageing behaviour in two exactly solvable reaction-diffusion systems. Ageing exponents and scaling functions are determined. I discuss in particular a case in which the equality of two critical exponents, known from systems with detailed balance, does not hold any more. Secondly it is shown that the form of the scaling functions can be understood by symmetry considerations.Comment: 6 pages, contribution to the summer school "Ageing and the Glass Transition" held in Luxemburg in September 05. Published versio