Statistical Mechanics
Novel effective ergodicity breaking phase transition in a driven-dissipative system (1903.12652v1)
Sakib Matin, Chon-Kit Pun, Harvey Gould, W. Klein
2019-03-29
We show that the Olami-Feder-Christensen model exhibits an effective ergodicity breaking transition as the noise is varied. Above the critical noise, the average stress on each site converges to the global average. Below the critical noise, the stress on individual sites becomes trapped in different limit cycles. We use ideas from the study of dynamical systems and compute recurrence plots and the recurrence rate. We identify the order parameter as the recurrence rate averaged over all sites and find numerical evidence that the transition can be characterized by exponents that are consistent with hyperscaling.
The Power Light Cone of the Discrete Bak-Sneppen, Contact and other local processes (1903.12607v1)
Tom Bannink, Harry Buhrman, András Gilyén, Mario Szegedy
2019-03-29
We consider a class of random processes on graphs that include the discrete Bak-Sneppen (DBS) process and the several versions of the contact process (CP), with a focus on the former. These processes are parametrized by a probability
that controls a local update rule. Numerical simulations reveal a phase transition when
goes from 0 to 1. Analytically little is known about the phase transition threshold, even for one-dimensional chains. In this article we consider a power-series approach based on representing certain quantities, such as the survival probability or the expected number of steps per site to reach the steady state, as a power-series in
of the chain grows. This is a phenomenon that has been used in the physics community but was not yet proven. We show that for local events
of which the support is a distance
apart we have
. The stabilization allows for the (exact) computation of coefficients for arbitrary large systems which can then be analyzed using the wide range of existing methods of power series analysis.
Exponentially fast dynamics of chaotic many-body systems (1802.08265v2)
Fausto Borgonovi, Felix M. Izrailev, Lea F. Santos
2018-02-22
We demonstrate analytically and numerically that in isolated quantum systems of many interacting particles, the number of many-body states participating in the evolution after a quench increases exponentially in time, provided the eigenstates are delocalized in the energy shell. The rate of the exponential growth is defined by the width
of the local density of states (LDOS) and is associated with the Kolmogorov-Sinai entropy for systems with a well defined classical limit. In a finite system, the exponential growth eventually saturates due to the finite volume of the energy shell. We estimate the time scale for the saturation and show that it is much larger than
. Numerical data obtained for a two-body random interaction model of bosons and for a dynamical model of interacting spin-1/2 particles show excellent agreement with the analytical predictions.
Out-of-equilibrium dynamical equations of infinite-dimensional particle systems. II. The anisotropic case under shear strain (1903.12572v1)
Elisabeth Agoritsas, Thibaud Maimbourg, Francesco Zamponi
2019-03-29
As an extension of the isotropic setting presented in the companion paper [J. Phys. A 52, 144002 (2019)], we consider the Langevin dynamics of a many-body system of pairwise interacting particles in
. The dynamics is then controlled by a single one-dimensional effective stochastic process which depends on three distinct strain-dependent kernels -- self-consistently determined by the process itself -- encoding the effective restoring force, friction and noise terms due to the particle interactions. From there one can compute dynamical observables such as particle mean-square displacements and shear stress fluctuations, and eventually aim at providing an exact
benchmark for liquid and glass rheology. As an application of our results, we derive dynamically the 'state-following' equations that describe the static response of a glass to a finite shear strain until it yields.
Equivalence of position-position auto-correlations in the Slicer Map and the Lévy-Lorentz gas (1709.04980v3)
Claudio Giberti, Lamberto Rondoni, Muhammad Tayyab, Juergen Vollmer
2017-09-14
The Slicer Map is a one-dimensional non-chaotic dynamical system that shows sub-, super-, and normal diffusion as a function of its control parameter. In a recent paper [Salari et al., CHAOS 25, 073113 (2015)] it was found that the moments of the position distributions as the Slicer Map have the same asymptotic behaviour as the L'evy-Lorentz gas, a random walk on the line in which the scatterers are randomly distributed according to a L'evy-stable probability distribution. Here we derive analytic expressions for the position-position correlations of the Slicer Map and, on the ground of this result, we formulate some conjectures about the asymptotic behaviour of position-position correlations of the L'evy-Lorentz gas, for which the information in the literature is minimal. The numerically estimated position-position correlations of the L'evy-Lorentz show a remarkable agreement with the conjectured asymptotic scaling.
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