Saddles and dynamics in a solvable mean-field model

TL;DR

This paper applies the saddle-approach to a solvable mean-field model, revealing a strong link between saddle properties and system dynamics, and confirming the approach's usefulness in understanding interacting systems.

Contribution

It demonstrates the effectiveness of the saddle-approach in analyzing a mean-field model, connecting saddle properties with dynamical behavior across temperatures.

Findings

Saddle order and diffusivity share similar temperature dependence.

Both exhibit Arrhenius behavior at low temperatures.

Saddle-approach effectively interprets dynamics in interacting systems.

Abstract

We use the saddle-approach, recently introduced in the numerical investigation of simple model liquids, in the analysis of a mean-field solvable system. The investigated system is the k-trigonometric model, a k-body interaction mean field system, that generalizes the trigonometric model introduced by Madan and Keyes [J. Chem. Phys. 98, 3342 (1993)] and that has been recently introduced to investigate the relationship between thermodynamics and topology of the configuration space. We find a close relationship between the properties of saddles (stationary points of the potential energy surface) visited by the system and the dynamics. In particular the temperature dependence of saddle order follows that of the diffusivity, both having an Arrhenius behavior at low temperature and a similar shape in the whole temperature range. Our results confirm the general usefulness of the saddle-approach in the interpretation of dynamical processes taking place in interacting systems.