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

Fluctuation-induced forces occur generically when long-range 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-range correlations appear more commonly in certain nonequilibrium systems with conservation laws. Consequently, a variety of nonequilibrium fluctuation phenomena, including fluctuation-induced forces, have been discovered and explored recently. Here we address a long-standing problem of nonequilibrium 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 nonlocal 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 nonequilibrium processes in critical fluids (e.g., fluctuation-mediated self-assembly or aggregation). In certain regimes, our results are applicable to active matter.