arXiv subjects

Uwe C. Täuber

Publications and source records attributed to Uwe C. Täuber.

51 records · Page 3Linked to original sources

arXiv2016

Non-equilibrium relaxation in a stochastic lattice Lotka-Volterra model

We employ Monte Carlo simulations to study a stochastic Lotka-Volterra model on a two-dimensional square lattice with periodic boundary conditions. If the (local) prey carrying capacity is finite, there exists an extinction threshold for the predator population that separates a stable active two-species coexistence phase from an inactive state wherein only prey survive. Holding all other rates fixed, we investigate the non-equilibrium relaxation of the predator density in the vicinity of the critical predation rate. As expected, we observe critical slowing-down, i.e., a power law dependence of the relaxation time on the predation rate, and algebraic decay of the predator density at the extinction critical point. The numerically determined critical exponents are in accord with the established values of the directed percolation universality class. Following a sudden predation rate change to its critical value, one finds critical aging for the predator density autocorrelation function that is also governed by universal scaling exponents. This aging scaling signature of the active-to-absorbing state phase transition emerges at significantly earlier times than the stationary critical power laws, and could thus serve as an advanced indicator of the (predator) population's proximity to its extinction threshold.

q-bio.PE↗

arXiv2013

Relaxation dynamics in type-II superconductors with point-like and correlated disorder

We employ an elastic line model to investigate the steady-state properties and non-equilibrium relaxation kinetics of magnetic vortex lines in disordered type-II superconductors using Langevin molecular dynamics (LMD). We extract the dependence of the mean vortex line velocity and gyration radius as well as the mean-square displacement in the steady state on the driving current, and measure the vortex density and height autocorrelations in the aging regime. We study samples with either randomly distributed point-like or columnar attractive pinning centers, which allows us to distinguish the complex relaxation features of interacting flux lines subject to extended vs. uncorrelated disorder. Additionally, we find that our new LMD findings match earlier Monte Carlo (MC) simulation data well, verifying that these two microscopically quite distinct simulation methods lead to macroscopically very similar results for non-equilibrium vortex matter.

cond-mat.supr-con↗

arXiv2011

Relaxation and Glassy Dynamics in Disordered Type-II Superconductors

We study the non-equilibrium relaxation kinetics of interacting magnetic flux lines in disordered type-II superconductors at low temperatures by means of a three-dimensional elastic line model and Monte Carlo simulations. Investigating the vortex density and height autocorrelation functions as well as the flux line mean-square displacement, we observe the emergence of glassy dynamics, caused by the competing effects of vortex pinning due to point defects and long-range repulsive interactions between the flux lines. Our systematic numerical study allows us to carefully disentangle the associated different relaxation mechanisms, and to assess their relative impact on the kinetics of vortex matter at low temperatures.

cond-mat.supr-con↗

arXiv2010

Spatial Rock-Paper-Scissors Models with Inhomogeneous Reaction Rates

We study several variants of the stochastic four-state rock-paper-scissors game or, equivalently, cyclic three-species predator-prey models with conserved total particle density, by means of Monte Carlo simulations on one- and two-dimensional lattices. Specifically, we investigate the influence of spatial variability of the reaction rates and site occupancy restrictions on the transient oscillations of the species densities and on spatial correlation functions in the quasi-stationary coexistence state. For small systems, we also numerically determine the dependence of typical extinction times on the number of lattice sites. In stark contrast with two-species stochastic Lotka-Volterra systems, we find that for our three-species models with cyclic competition quenched disorder in the reaction rates has very little effect on the dynamics and the long-time properties of the coexistence state. Similarly, we observe that site restriction only has a minor influence on the system's dynamical properties. Our results therefore demonstrate that the features of the spatial rock-paper-scissors system are remarkably robust with respect to model variations, and stochastic fluctuations as well as spatial correlations play a comparatively minor role.

q-bio.PE↗

arXiv2010

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.

cond-mat.stat-mech↗

arXiv2002

Random walks with imperfect trapping in the decoupled-ring approximation

We investigate random walks on a lattice with imperfect traps. In one dimension, we perturbatively compute the survival probability by reducing the problem to a particle diffusing on a closed ring containing just one single trap. Numerical simulations reveal this solution, which is exact in the limit of perfect traps, to be remarkably robust with respect to a significant lowering of the trapping probability. We demonstrate that for randomly distributed traps, the long-time asymptotics of our result recovers the known stretched exponential decay. We also study an anisotropic three-dimensional version of our model, where for sufficiently large transverse diffusion the system is described by the mean-field kinetics. We discuss possible applications of some of our findings to the decay of excitons in semiconducting organic polymer materials, and emphasize the crucial influence of the spatial trap distribution on the kinetics.

cond-mat.stat-mech↗

arXiv1998

Non-equilibrium critical behavior of O(n)-symmetric systems: Effect of reversible mode-coupling terms and dynamical anisotropy

Phase transitions in non-equilibrium steady states of O(n)-symmetric models with reversible mode couplings are studied using dynamic field theory and the renormalization group. The systems are driven out of equilibrium by dynamical anisotropy in the noise for the conserved quantities, i.e., by constraining their diffusive dynamics to be at different temperatures T^\par and T^\perp in d_\par- and d_\perp-dimensional subspaces, respectively. In the case of the Sasv'ari-Schwabl-Sz'epfalusy (SSS) model for planar ferro- and isotropic antiferromagnets, we assume a dynamical anisotropy in the noise for the non-critical conserved quantities that are dynamically coupled to the non-conserved order parameter. We find the equilibrium fixed point (with isotropic noise) to be stable with respect to these non-equilibrium perturbations, and the familiar equilibrium exponents therefore describe the asymptotic static and dynamic critical behavior. Novel critical features are only found in extreme limits, where the ratio of the effective noise temperatures T^\par/T^\perp is either zero or infinite. On the other hand, for model J for isotropic ferromagnets with a conserved order parameter, the dynamical noise anisotropy induces effective long-range elastic forces, which lead to a softening only of the d_\perp-dimensional sector in wavevector space with lower noise temperature T^\perp < T^\par. The ensuing static and dynamic critical behavior is described by power laws of a hitherto unidentified universality class, which, however, is not accessible by perturbational means for d_\par \geq 1. We obtain formal expressions for the novel critical exponents in a double expansion about the static and dynamic upper critical dimensions and d_\par, i.e., about the equilibrium theory.

cond-mat.stat-mech↗

arXiv1998

Multicritical behavior in coupled directed percolation processes

We study a hierarchy of directed percolation (DP) processes for particle species A, B, ..., unidirectionally coupled via the reactions A -> B, ... When the DP critical points at all levels coincide, multicritical behavior emerges, with density exponents β^{(k)} which are markedly reduced at each hierarchy level k >= 2. We compute the fluctuation corrections to β^{(2)} to O(ε= 4-d) using field-theoretic renormalization group techniques. Monte Carlo simulations are employed to determine the new exponents in dimensions d <= 3.

cond-mat.stat-mech↗

arXiv1997

Superfluid Bosons and Flux Liquids: Disorder, Thermal Fluctuations, and Finite-Size Effects

The influence of different types of disorder (both uncorrelated and correlated) on the superfluid properties of a weakly interacting or dilute Bose gas, as well as on the corresponding quantities for flux line liquids in high-temperature superconductors at low magnetic fields are reviewed, investigated and compared. We exploit the formal analogy between superfluid bosons and the statistical mechanics of directed lines, and explore the influence of the different "imaginary time" boundary conditions appropriate for a flux line liquid. For superfluids, we discuss the density and momentum correlations, the condensate fraction, and the normal-fluid density as function of temperature for two- and three-dimensional systems subject to a space- and time-dependent random potential as well as conventional point-, line-, and plane-like defects. In the case of vortex liquids subject to point disorder, twin boundaries, screw dislocations, and various configurations of columnar damage tracks, we calculate the corresponding quantities, namely density and tilt correlations, the ``boson'' order parameter, and the tilt modulus. The finite-size corrections due to periodic vs. open "imaginary time" boundary conditions differ in interesting and important ways. Experimental implications for vortex lines are described briefly.

cond-mat.supr-con↗

arXiv1997

`Real' vs `Imaginary' Noise in Diffusion-Limited Reactions

Reaction-diffusion systems which include processes of the form A+A->A or A+A->0 are characterised by the appearance of `imaginary' multiplicative noise terms in an effective Langevin-type description. However, if `real' as well as `imaginary' noise is present, then competition between the two could potentially lead to novel behaviour. We thus investigate the asymptotic properties of the following two `mixed noise' reaction-diffusion systems. The first is a combination of the annihilation and scattering processes 2A->0, 2A->2B, 2B->2A, and 2B->0. We demonstrate (to all orders in perturbation theory) that this system belongs to the same universality class as the single species annihilation reaction 2A->0. Our second system consists of competing annihilation and fission processes, 2A->0 and 2A->(n+2)A, a model which exhibits a transition between active and absorbing phases. However, this transition and the active phase are not accessible to perturbative methods, as the field theory describing these reactions is shown to be non-renormalisable. This corresponds to the fact that there is no stationary state in the active phase, where the particle density diverges at finite times. We discuss the implications of our analysis for a recent study of another active / absorbing transition in a system with multiplicative noise.

cond-mat.stat-mech↗

arXiv1997

Field Theory of Branching and Annihilating Random Walks

We develop a systematic analytic approach to the problem of branching and annihilating random walks, equivalent to the diffusion-limited reaction processes 2A->0 and A->(m+1)A, where m>=1. Starting from the master equation, a field-theoretic representation of the problem is derived, and fluctuation effects are taken into account via diagrammatic and renormalization group methods. For d>2, the mean-field rate equation, which predicts an active phase as soon as the branching process is switched on, applies qualitatively for both even and odd m, but the behavior in lower dimensions is shown to be quite different for these two cases. For even m, and d~2, the active phase still appears immediately, but with non-trivial crossover exponents which we compute in an expansion in eps=2-d, and with logarithmic corrections in d=2. However, there exists a second critical dimension d_c'~4/3 below which a non-trivial inactive phase emerges, with asymptotic behavior characteristic of the pure annihilation process. This is confirmed by an exact calculation in d=1. The subsequent transition to the active phase, which represents a new non-trivial dynamic universality class, is then investigated within a truncated loop expansion. For odd m, we show that the fluctuations of the annihilation process are strong enough to create a non-trivial inactive phase for all d<=2. In this case, the transition to the active phase is in the directed percolation universality class.

cond-mat.stat-mech↗

arXiv1996

Theory of Branching and Annihilating Random Walks

A systematic theory for the diffusion--limited reaction processes $A + A \to 0$ and $A \to (m+1) A$ is developed. Fluctuations are taken into account via the field--theoretic dynamical renormalization group. For $m$ even the mean field rate equation, which predicts only an active phase, remains qualitatively correct near $d_c = 2$ dimensions; but below $d_c' \approx 4/3$ a nontrivial transition to an inactive phase governed by power law behavior appears. For $m$ odd there is a dynamic phase transition for any $d \leq 2$ which is described by the directed percolation universality class.

cond-mat.stat-mech↗

arXiv1996

Critical Behavior of O(n)-symmetric Systems With Reversible Mode-coupling Terms: Stability Against Detailed-balance Violation

We investigate nonequilibrium critical properties of $O(n)$-symmetric models with reversible mode-coupling terms. Specifically, a variant of the model of Sasvári, Schwabl, and Szépfalusy is studied, where violation of detailed balance is incorporated by allowing the order parameter and the dynamically coupled conserved quantities to be governed by heat baths of different temperatures $T_S$ and $T_M$, respectively. Dynamic perturbation theory and the field-theoretic renormalization group are applied to one-loop order, and yield two new fixed points in addition to the equilibrium ones. The first one corresponds to $Θ= T_S / T_M = \infty$ and leads to model A critical behavior for the order parameter and to anomalous noise correlations for the generalized angular momenta; the second one is at $Θ= 0$ and is characterized by mean-field behavior of the conserved quantities, by a dynamic exponent $z = d / 2$ equal to that of the equilibrium SSS model, and by modified static critical exponents. However, both these new fixed points are unstable, and upon approaching the critical point detailed balance is restored, and the equilibrium static and dynamic critical properties are recovered.

cond-mat.stat-mech↗

arXiv1996

Localized Flux Lines and the Bose Glass

Columnar defects provide effective pinning centers for magnetic flux lines in high--$T_{\rm c}$ superconductors. Utilizing a mapping of the statistical mechanics of directed lines to the quantum mechanics of two--dimensional bosons, one expects an entangled flux liquid phase at high temperatures, separated by a second--order localization transition from a low--temperature ``Bose glass'' phase with infinite tilt modulus. Recent decoration experiments have demonstrated that below the matching field the repulsive forces between the vortices may be sufficiently large to produce strong spatial correlations in the Bose glass. This is confirmed by numerical simulations, and a remarkably wide soft ``Coulomb gap'' at the chemical potential is found in the distribution of pinning energies. At low currents, the dominant transport mechanism in the Bose glass phase proceeds via the formation of double kinks between not necessarily adjacent columnar pins, similar to variable--range hopping in disordered semiconductors. The strong correlation effects originating in the long--range vortex interactions drastically reduce variable--range hopping transport.

cond-mat↗

arXiv1994

Coulomb Gap and Correlated Vortex Pinning in Superconductors

The positions of columnar pins and magnetic flux lines determined from a decoration experiment on BSCCO were used to calculate the single--particle density of states at low temperatures in the Bose glass phase. A wide Coulomb gap is found, with gap exponent $s \approx 1.2$, as a result of the long--range interaction between the vortices. As a consequence, the variable--range hopping transport of flux lines is considerably reduced with respect to the non--interacting case, the effective Mott exponent being enhanced from $p_0 = 1/3$ to $p_{\rm eff} \approx 0.5$ for this specific experiment.

cond-mat↗