# Dynamics of the critical Casimir force for a conserved order parameter after a critical quench

## TL;DR

This paper investigates the non-equilibrium dynamics of critical Casimir forces in conserved-parameter fluids after a quench to the critical point, revealing oscillatory behaviors and complex transient regimes influenced by initial conditions and geometry.

## Contribution

It provides a detailed analysis of non-equilibrium critical Casimir forces with conserved order parameters, highlighting oscillatory time-dependences and transient phenomena not previously understood.

## Key findings

- Oscillatory time-dependent Casimir forces observed.
- Transient regimes depend on initial conditions and geometry.
- Results applicable to active matter in certain regimes.

## Abstract

Fluctuation-induced forces occur generically when long-ranged correlations (e.g., in fluids) are confined by external bodies. In classical systems, such correlations require specific conditions, e.g., a medium close to a critical point. On the other hand, long-ranged correlations appear more commonly in certain non-equilibrium systems with conservation laws. Consequently, a variety of non-equilibrium fluctuation phenomena, including fluctuation-induced forces, have been discovered and explored recently. Here, we address a long-standing problem of non-equilibrium critical Casimir forces emerging after a quench to the critical point in a confined fluid with order-parameter-conserving dynamics and non-symmetry-breaking boundary conditions. The interplay of inherent (critical) fluctuations and dynamical non-local effects (due to density conservation) gives rise to striking features, including correlation functions and forces exhibiting oscillatory time-dependences. Complex transient regimes arise, depending on initial conditions and the geometry of the confinement. Our findings pave the way for exploring a wealth of non-equilibrium processes in critical fluids (e.g., fluctuation-mediated self-assembly or aggregation). In certain regimes, our results are applicable to active matter.