Saddles and dynamics in a solvable mean-field model

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.

7 pages, 8 figures

References in corpus (10)

• The relationship between fragility, configurational entropy and the potential energy landscape of glass forming liquids
• Inherent Structure Entropy of Supercooled Liquids
• Crossover to Potential Energy Landscape Dominated Dynamics in a Model Glass-forming Liquid
• Saddles in the energy landscape probed by supercooled liquids
• Saddle Points and Dynamics of Lennard-Jones Clusters, Solids and Supercooled Liquids
• Energy landscape of a Lennard-Jones liquid: Statistics of stationary points
• Structural relaxation in Morse clusters: Energy landscapes
• Instantaneous Normal Mode Analysis of Supercooled Water
• Quasi-saddles as relevant points of the potential energy surface in the dynamics of supercooled liquids
• Role of saddles in mean-field dynamics above the glass transition

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• Topological properties of the mean field phi^4 model
• Dynamics and geometric properties of the k-Trigonometric model
• Mode-locking transitions in nano-structured weakly disordered lasers