Analysis of Glassy Landscapes Using Diffusion Maps

Carmeline Dsilva, Princeton University

The glass transition is one of the most puzzling phenomena in solid-state physics. Molecular motion slows dramatically, and yet, unlike in crystallization, the molecules do not assume a unique, ordered structure. The links between the detailed structure and connectivity of a system’s potential energy surface and this dynamical slowdown are the subject of intense exploration and speculation.

We explore the structure of the glass potential energy landscape using diffusion maps, a nonlinear dimensionality reduction technique. Through molecular dynamics simulations, we collect data about the minima (or “basins”) and saddles (“transition states”) of the glass energy landscape. We then analyze the resulting network of basins and transition states using diffusion maps, trying to obtain a low-dimensional embedding of the energy landscape and to search for persistent connectivity patterns in the discovered network of minima.

Abstract Author(s): Carmeline J. Dsilva, Ioannis G. Kevrekidis