Glass and jamming transition of simple liquids: static and dynamic theory

TL;DR

This paper develops a comprehensive theoretical framework combining field theory, replica theory, and mean-field approaches to analyze the glass and jamming transitions in simple liquids with various interaction potentials.

Contribution

It introduces a unified, self-contained theoretical approach to study static and dynamic aspects of glass and jamming transitions, bridging previous methods and providing quantitative predictions.

Findings

Resolved technical issues in dynamic field-theoretic analysis.

Established exact comparisons between Mode-Coupling and replica theories.

Derived a quantitative mean-field theory of the jamming transition.

Abstract

We study the glass and jamming transition of finite-dimensional models of simple liquids: hard- spheres, harmonic spheres and more generally bounded pair potentials that modelize frictionless spheres in interaction. At finite temperature, we study their glassy dynamics via field-theoretic methods by resorting to a mapping towards an effective quantum mechanical evolution, and show that such an approach resolves several technical problems encountered with previous attempts. We then study the static, mean-field version of their glass transition via replica theory, and set up an expansion in terms of the corresponding static order parameter. Thanks to this expansion, we are able to make a direct and exact comparison between historical Mode-Coupling results and replica theory. Finally we study these models at zero temperature within the hypotheses of the random-first-order-transition theory, and are able to derive a quantitative mean-field theory of the jamming transition. The theoretic methods of field theory and liquid theory used in this work are presented in a mostly self-contained, and hopefully pedagogical, way. This manuscript is a corrected version of my PhD thesis, defended in June, 29th, under the advisorship of Fr\'ed\'eric van Wijland, and also contains the result of collaborations with Ludovic Berthier and Francesco Zamponi. The PhD work was funded by a CFM-JP Aguilar grant, and conducted in the Laboratory MSC at Universit\'e Denis Diderot--Paris 7, France.