Some applications of recent theories of disordered systems

TL;DR

This thesis explores the equilibrium properties of glassy systems and recent theories of nonequilibrium stationary states, including the fluctuation relation, through theoretical analysis and numerical simulations.

Contribution

It provides a comprehensive review and new insights into glass phenomenology, replica-based glass transition studies, and the application of the chaotic hypothesis to nonequilibrium systems.

Findings

Replica trick and HNC approximation elucidate the glass transition in Hard Sphere liquids.

Correlation between fragility and vibrational properties in p-spin models established.

Fluctuation relation successfully tested in Lennard-Jones particle systems under external driving.

Abstract

This Ph.D. thesis is divided in two parts. The first one concerns the equilibrium properties of glassy systems. Some aspects of the phenomenology of glasses and of theories attempting to describe them are reviewed in chapter 1. A study of the glass transition of the Hard Sphere liquid based on a replica trick and on the HNC approximation (following Mezard and Parisi) is presented in chapter 2 (cond-mat/0506445). A study of the correlation between fragility and vibrational properties of the minima of the energy landscape in p-spin mean field models is presented in chapter 3 (cond-mat/0401450). The second part of the thesis concerns some recent attempts - reviewed in chapter 4 - to build a statistical theory of a class of nonequilibrium stationary states, based on the "chaotic hypothesis" of Cohen and Gallavotti. In chapter 5 the fluctuation relation, that follows from the chaotic hypothesis for reversible systems, is succesfully tested at the non-Gaussian level in a numerical simulation of a system of particles interacting via a Lennard-Jones--like potential and subjected to an external driving force and to an isokinetic constraint (cond-mat/0412455). In chapter 7 an extension of the fluctuation relation to non-equilibrium relaxational systems driven by external forces (whose dynamics is discussed in chapter 6) is investigated in a simple case (cond-mat/0504750) and the results are compared with numerical simulations on binary Lennard-Jones mixtures (cond-mat/0403579). All the results collected in this thesis already appeared on cond-mat. They are presented here in a (kind of) self-consistent way.