Finite-size effects on current correlation functions

TL;DR

This paper investigates finite-size effects on current correlation functions in one-dimensional systems, revealing recurrence phenomena and sound mode collisions that influence decay rates, and proposes a method for accurate evaluation.

Contribution

It uncovers mechanisms behind finite-size effects on current correlation functions and introduces a procedure for correct decay rate estimation in such systems.

Findings

Global energy CCF decays as ~ t^{-2/3} in diatomic hard-core gas

In Fermi-Pasta-Ulam-β model, decay is close to ~ t^{-1/2}

Recurrence and sound mode collisions significantly affect CCF decay behaviors

Abstract

We study why the calculation of current correlation functions (CCFs) still suffers from finite size effects even when the periodic boundary condition is taken. Two important one dimensional, momentum conserving systems are investigated as examples. Intriguingly, it is found that the state of a system recurs in the sense of microcanonical ensemble average, and such recurrence may result in oscillations in CCFs. Meanwhile, we find that the sound mode collisions induce an extra time decay in a current so that its correlation function decays faster (slower) in a smaller (larger) system. Based on these two unveiled mechanisms, a procedure for correctly evaluating the decay rate of a CCF is proposed, with which our analysis suggests that the global energy CCF decays as $\sim t^{-\frac{2}{3}}$ in the diatomic hard-core gas model and in a manner close to $\sim t^{-\frac{1}{2}}$ in the Fermi-Pasta-Ulam-$\beta$ model.