# Diverging time scale in the dimensional crossover for liquids in strong confinement

## TL;DR

This study investigates the transition from three-dimensional to two-dimensional behavior in confined dense hard-sphere liquids, revealing a diverging time scale and exponential decay of transversal kinetic energy correlations.

## Contribution

It provides a detailed analysis of the 3D to 2D crossover, including a new analytic theory that accurately describes the diverging time scale in strong confinement.

## Key findings

- Decoupling of transverse and lateral dynamics with increasing confinement
- Diverging time scale separating 2D and 3D behaviors
- Exponential decay of transversal kinetic energy correlations

## Abstract

We study a strongly interacting dense hard-sphere system confined between two parallel plates by event-driven molecular dynamics simulations to address the fundamental question of the nature of the 3D to 2D crossover. As the fluid becomes more and more confined the dynamics of the transverse and lateral degrees of freedom decouple, which is accompanied by a diverging time scale separating 2D from 3D behavior. Relying on the time-correlation function of the transversal kinetic energy the scaling behavior and its density-dependence is explored. Surprisingly, our simulations reveal that its time-dependence becomes purely exponential such that memory effects can be ignored. We rationalize our findings quantitatively in terms of an analytic theory which becomes exact in the limit of strong confinement.