Anomalous dynamical scaling in anharmonic chains and plasma models with multiparticle collisions

TL;DR

This paper investigates the anomalous scaling behavior of equilibrium correlations in one-dimensional anharmonic and plasma models, confirming some theoretical predictions but also revealing violations and crossovers in scaling regimes.

Contribution

It compares two models with three conservation laws, verifying nonlinear fluctuating hydrodynamics predictions and identifying regimes where expected scaling is violated.

Findings

Confirmed nonlinear fluctuating hydrodynamics predictions for structure factors.

Observed violations of expected current correlation scaling in some regimes.

Demonstrated crossover behavior in the plasma model by varying coupling constants.

Abstract

We study the anomalous dynamical scaling of equilibrium correlations in one dimensional systems. Two different models are compared: the Fermi-Pasta-Ulam chain with cubic and quartic nonlinearity and a gas of point particles interacting stochastically through the multiparticle collision dynamics. For both models -that admit three conservation laws- by means of detailed numerical simulations we verify the predictions of nonlinear fluctuating hydrodynamics for the structure factors of density and energy fluctuations at equilibrium. Despite this, violations of the expected scaling in the currents correlation are found in some regimes, hindering the observation of the asymptotic scaling predicted by the theory. In the case of the gas model this crossover is clearly demonstrated upon changing the coupling constant.