Mode-coupling approach for the slow dynamics of a liquid on a spherical substrate

TL;DR

This paper extends mode-coupling theory to liquids on spherical substrates, revealing that curvature influences slow dynamics similarly to Euclidean space but with quantitative discrepancies.

Contribution

It derives MCT equations for spherical geometry and analyzes how curvature affects the slow dynamics of liquids, highlighting both qualitative similarities and quantitative differences.

Findings

MCT equations adapted for spherical geometry

Curvature influences relaxation slowdown

Quantitative predictions differ from actual dynamics

Abstract

We study the dynamics of a one-component liquid constrained on a spherical substrate, a 2-sphere, and investigate how the mode-coupling theory (MCT) can describe the new features brought by the presence of curvature. To this end we have derived the MCT equations in a spherical geometry. We find that, as seen from the MCT, the slow dynamics of liquids in curved space at low temperature does not qualitatively differ from that of glass-forming liquids in Euclidean space. The MCT predicts the right trend for the evolution of the relaxation slowdown with curvature but is dramatically off at a quantitative level.