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Dynamical approach to the Casimir effect

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Rodríguez López, P. and Brito, Ricardo and Soto, R. (2011) Dynamical approach to the Casimir effect. Physical Review E, 83 (3, Par). ISSN 1539-3755

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Official URL: http://pre.aps.org/pdf/PRE/v83/i3/e031102


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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.


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© American Physical Society.
This article has benefited from discussions with many colleagues: J. M. R. Parrondo, M. Clerc, N. van Kampen, O. Descalzi, F. Barra, A. Galindo, G. G. Alcaine, J. San Martin, and U. M. B. Marconi. P. R.-L. and R. B. are supported by the Spanish projects MOSAICO, UCM/PR34/07-15859, and MODELICO (Comunidad de Madrid). P. R.-L.'s research is also supported by a FPU MEC grant. The research is supported by Fondecyt Grants No. 1100100, No. 1070958, and No. 7070301, and Proyecto Anillo ACT 127.

Subjects:Sciences > Physics > Thermodynamics
ID Code:21240
Deposited On:13 May 2013 12:20
Last Modified:24 Jul 2018 10:58

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