Aging and effective temperatures in the low temperature mode-coupling equations

TL;DR

This paper explores the dynamics of mean-field disordered models in the glassy phase at low temperatures, focusing on aging phenomena and the rigorous definition of effective temperatures through time-scale-dependent measurements.

Contribution

It provides a theoretical framework for understanding aging and effective temperatures in low-temperature mode-coupling equations for disordered systems.

Findings

The system never reaches equilibrium, retaining memory of initial conditions.

Effective temperature can be rigorously defined via time-scale-dependent thermometer readings.

The approach links aging dynamics with thermalization concepts in disordered models.

Abstract

The low-temperature generalization of the mode-coupling equations corresponds to the dynamics of mean-field disordered models in the glassy phase. The system never achieves equilibrium, preserving the memory of the time elapsed after the quench throughout its evolution. A concept of effective temperature can be made quite rigorous in this context by considering readings of thermometers in different time-scales and the thermalization of weakly coupled subsystems.