Transient Casimir Forces from Quenches in Thermal and Active Matter

We compute fluctuation-induced (Casimir) forces for classical systems after a temperature quench. Using a generic coarse-grained model for fluctuations of a conserved density, we find that transient forces arise even if the initial and final states are force free. In setups reminiscent of Casimir (planar walls) and van der Waals (small inclusions) interactions, we find comparable exact universal expressions for the force. Dynamical details only scale the time axis of transient force curves. We propose that such quenches can be achieved, for instance, in experiments on active matter, employing tunable activity or interaction protocols.

Figure 1

The transient force $F$ between two parallel plates from Eq. (7), as a function of rescaled time $t^{*}=\mu m_{0}t{L}^{-2}$. The dotted lines indicate the long-time asymptotes. The force is always attractive.

Figure 2

The force [Eq. (11)] between two embedded objects, which are small compared to their separation, as a function of dimensionless time $t^{*}=\mu m_{0}t{L}^{-2}$. Dotted lines in the insets are long-time asymptotes as given.