Perturbative approach to calculating the Casimir force in fluctuating scalar and vector fields

Abstract

Based on a perturbative approach, a series expansion in susceptibility function of the medium is obtained for the Casimir force between arbitrary shaped objects foliated in a scalar or vector fluctuating field in arbitrary dimensions. Finite-temperature corrections are derived and the results are compared in first order with weak coupling regime in scattering method. The generalization to a massive vector field is also investigated.

From Brownian Motion Formalism to Fluctuation-Induced Force in a General Fluctuating Medium

“…The operator ô can be a general linear operator. For example, when the fluctuating field is the electromagnetic field, then ô = ∂ 2 t + ∇ × ∇×, [16,17]. The fluctuating field can be assumed as a scalar, vector, tensor or a spinor field interacting linearly with material fields and the only modification in each case is a rearrangement of indices on fields and coupling functions in the total Lagrangian density.…”

“…Fluctuation-induced forces are ubiquitous phenomena in a wide variety of systems in physics and chemistry [1][2][3]. Since the seminal paper of Casimir [4] on fluctuation induced force between two parallel plates made of perfect conductors due to vacuum fluctuations of electromagnetic field and its generalization to the case of dielectric slabs by Lifshitz [5,6], an extensive work has been down on fluctuation-induced forces [7][8][9][10][11][13][14][15][16][17]. Alongside the theoretical works, experimental high precision verifications of the Casimir force have been achieved [18][19][20][21][22][23][24].…”

Induced Casimir Force between Heavy Particles Substituted in an Oscillator Chain

“…This model has been applied to a variety of different problems in atomic and molecular physics and condensed matter, where dissipation on energy or phase are important or even when the medium is an amplifying one. Some important examples are: quantum Brownian motion of an oscillator in a dissipative medium [18], quantum tunneling with dissipation [8,15], electromagnetic field quantization in a magnetodielectric medium [19][20][21], Casimir energy for separated objects in vacuum electromagnetic field [1,[22][23][24], dissipative optomechanical models [25], and dissipation in quantum optics [26].…”

Perturbative Approach to Calculating the Correlation Function of bi-isotropic Metamaterials

“…Path integrals in quantum electrodynamic field theory play a much more important role due to several reasons. They provide Green's functions with an easy road to quantization and expressions, which are related to many physical quantities [8][9][10]. In addition, the close relationship between statistical mechanics and quantum field theory is reflected in the path integral methods.…”