Dynamical approach to the Casimir effect

Abstract

Casimir forces can appear between intrusions placed in different media driven by several fluctuation mechanisms, either in equilibrium or out of it. Herein, we develop a general formalism to obtain such forces from the dynamical equations of the fluctuating medium, the statistical properties of the driving noise, and the boundary conditions of the intrusions (which simulate the interaction between the intrusions and the medium). As a result, an explicit formula for the Casimir force over the intrusions is derived. This formalism contains the thermal Casimir effect as a particular limit and generalizes the study of the Casimir effect to such systems through their dynamical equations, with no appeal to their Hamiltonian, if any exists. In particular, we study the Casimir force between two infinite parallel plates with Dirichlet or Neumann boundary conditions, immersed in several media with finite correlation lengths (reaction--diffusion system, liquid crystals, and two coupled fields with non-Hermitian evolution equations). The driving Gaussian noises have vanishing or finite spatial or temporal correlation lengths; in the first case, equilibrium is reobtained and finite correlations produce nonequilibrium dynamics. The results obtained show that, generally, nonequilibrium dynamics leads to Casimir forces, whereas Casimir forces are obtained in equilibrium dynamics if the stress tensor is anisotropic.

12 pages, 1 figure

References in corpus (6)

• Casimir forces between arbitrary compact objects
• Fluctuation-Induced Casimir Forces in Granular Fluids
• Critical Casimir Effect in superfluid wetting films
• Relaxation phenomena at criticality
• Violation of action--reaction and self-forces induced by nonequilibrium fluctuations
• Generalized Casimir forces in non-equilibrium systems

Cited by in corpus (8)

• Critical Casimir Effect: Exact Results
• Forces exerted by a correlated fluid on embedded inclusions
• Out of equilibrium thermal Casimir effect in a model polarizable material
• Fluctuation Spectra and Force Generation in Non-equilibrium Systems
• Surface-induced non-equilibrium dynamics and critical Casimir forces for model B in film geometry
• Stochastic Quantization and Casimir Forces
• On the dynamics of the interaction between triggered active inclusions
• Stochastic Quantization and Casimir Forces: Pistons of Arbitrary Cross Section