Dynamical Behaviour of Low Autocorrelation Models

TL;DR

This paper studies the dynamical behavior of low autocorrelation binary sequences, revealing a glass transition characterized by diverging relaxation times and aging phenomena, indicating complex non-ergodic dynamics.

Contribution

It demonstrates the existence of a purely dynamical glass transition in low autocorrelation models and characterizes its first order nature through aging phenomena.

Findings

Presence of a glass transition at temperature T_G

Diverging relaxation times near T_G with exponent ~2

Aging phenomena below T_G

Abstract

We have investigated the nature of the dynamical behaviour in low autocorrelation binary sequences. These models do have a glass transition $T_G$ of a purely dynamical nature. Above the glass transition the dynamics is not fully ergodic and relaxation times diverge like a power law $\tau\sim (T-T_G)^{-\gamma}$ with $\gamma$ close to $2$. Approaching the glass transition the relaxation slows down in agreement with the first order nature of the dynamical transition. Below the glass transition the system exhibits aging phenomena like in disordered spin glasses. We propose the aging phenomena as a precise method to determine the glass transition and its first order nature.