Humboldt-Universität zu Berlin - Faculty of Mathematics and Natural Sciences - Statistical Physics and Nonlinear Dynamics & Stochastic Processes

Humboldt-Universität zu Berlin | Faculty of Mathematics and Natural Sciences | Department of Physics | Statistical Physics and Nonlinear Dynamics & Stochastic Processes | AllEvents | 1. Fluctuation-dissipation relation in a random-field model & 2. Aspects of anomalous diffusion in crowded media

1. Fluctuation-dissipation relation in a random-field model & 2. Aspects of anomalous diffusion in crowded media

by R. Toral and M. Weiss
  • What TSP Termin
  • When Jul 13, 2011 from 03:00 to 03:00 (Europe/Berlin / UTC200)
  • Where NEW15 - 3'101
  • Attendees R. Toral, M. Weiss
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"Fluctuation-dissipation relation in a random-field model" by R. Toral:

"We address a mean-field zero-temperature Ginzburg-Landau, or phi-4,
model subjected to quenched additive noise, which has been used recently
as a framework for analyzing collective effects induced by diversity. We
first make use of a self-consistent theory to calculate the phase
diagram of the system, predicting the onset of an order-disorder
critical transition at a critical value of the quenched noise intensity,
with critical exponents that follow Landau theory of thermal phase
transitions. We subsequently perform a numerical integration of the
system's dynamical variables in order to compare the analytical results
(valid in the thermodynamic limit and associated to the ground state of
the global Lyapunov potential) with the stationary state of the (finite
size) system. In the region of the parameter space where metastability
is absent (and therefore the stationary state coincides with the ground
state of the Lyapunov potential), a finite-size scaling analysis of the
order parameter fluctuations suggests that the magnetic susceptibility
diverges quadratically in the vicinity of the transition, what
constitutes a violation of the fluctuation-dissipation relation. We
derive an effective Hamiltonian and accordingly argue that its
functional form does not allow to straightforwardly relate the order
parameter fluctuations to the linear response of the system, at odds
with equilibrium theory. In the region of the parameter space where the
system is susceptible to have a large number of metastable states (and
therefore the stationary state does not necessarily correspond to the
ground state of the global Lyapunov potential), we numerically find a
phase diagram that strongly depends on the initial conditions of the
dynamical variables. We conclude that structural diversity can induce
both the creation and annihilation of order in a nontrivial way."