Dynamical approach to the Casimir effect

Area of Science:

• Physics
• Statistical Mechanics
• Soft Matter Physics

Background:

• Casimir forces arise from fluctuations in media, traditionally studied in equilibrium.
• Existing formalisms often rely on Hamiltonian descriptions, limiting applicability to systems with known Hamiltonians.

Purpose of the Study:

• To develop a general formalism for calculating Casimir forces from dynamical equations.
• To extend the study of Casimir effects to non-equilibrium systems and media without explicit Hamiltonians.

Main Methods:

• Deriving Casimir forces from the dynamical equations of fluctuating media and noise properties.
• Analyzing boundary conditions of intrusions to model medium-intrusions interaction.
• Investigating systems like reaction-diffusion, liquid crystals, and non-Hermitian fields.

Main Results:

• An explicit formula for Casimir force is derived.
• The formalism includes the thermal Casimir effect as a limit.
• Non-equilibrium dynamics generally lead to Casimir forces, unlike equilibrium dynamics which require anisotropic stress tensors.

Conclusions:

• The dynamical formalism provides a unified approach to Casimir forces in diverse physical systems.
• It successfully generalizes Casimir effect studies beyond equilibrium and Hamiltonian-based methods.
• Non-equilibrium fluctuations play a crucial role in generating Casimir forces.