Out-of-equilibrium relaxation of the thermal Casimir effect in a model polarizable material

Correlation Decoupling of Casimir Interaction in an Electrolyte Driven by External Electric Fields

It is well established that the long-range van der Waals or thermal Casimir interaction between two semi-infinite dielectrics separated by a distance H is screened by an intervening electrolyte. Here we show how this interaction is modified when an electric field of strength E is applied parallel to the dielectric boundaries, leading to a nonequilibrium steady state with a current. The presence of the field induces a long-range thermal repulsive interaction, scaling just like the thermal Casimir interaction between dielectrics without the intervening electrolyte, i.e., as 1/H^{3}. At small E the effect is of order E^{2}, while at large fields it saturates to an E independent value. We explain the results in terms of a decoupling mechanism between the charge density fluctuations of cations and anions at large applied fields.

Particles with nonlinear electric response: Suppressing van der Waals forces by an external field

We study the classical thermal component of Casimir, or van der Waals, forces between point particles with highly anharmonic dipole Hamiltonians when they are subjected to an external electric field. Using a model for which the individual dipole moments saturate in a strong field (a model that mimics the charges in a neutral, perfectly conducting sphere), we find that the resulting Casimir force depends strongly on the strength of the field, as demonstrated by analytical results. For a certain angle between the external field and center-to-center axis, the fluctuation force can be tuned and suppressed to arbitrarily small values. We compare the forces between these particles with those between particles with harmonic Hamiltonians and also provide a simple formula for asymptotically large external fields, which we expect to be generally valid for the case of saturating dipole moments.

Relaxation of the thermal Casimir force between net neutral plates containing Brownian charges

We investigate the dynamics of thermal Casimir interactions between plates described within a living conductor model, with embedded mobile anions and cations, whose density field obeys a stochastic partial differential equation which can be derived starting from the Langevin equations of the individual particles. This model describes the thermal Casimir interaction in the same way that the fluctuating dipole model describes van der Waals interactions. The model is analytically solved in a Debye-Hückel-like approximation. We identify several limiting dynamical regimes where the time dependence of the thermal Casimir interactions can be obtained explicitly. Most notably we find a regime with diffusive scaling, even though the charges are confined to the plates and do not diffuse into the intervening space, which makes the diffusive scaling difficult to anticipate and quite unexpected on physical grounds.