Casimir Effect at Finite Temperature

Tadaki, Shin–ichi; Takagi, Shin

doi:10.1143/ptp.75.262

Cited by 33 publications

(38 citation statements)

References 4 publications

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“…It was also shown by Gundersen and Ravndal [18] that the scaled free energy associated with massless fermions fields at finite temperature submitted to MIT boundary conditions satisfy the relation given by equation (38) and therefore exhibts temperature inversion symmetry. Tadaki and Takagi [22] have calculated Casimir free energies for a massless scalar field obeying Dirichlet or Neumann boundary conditions on both plates and found this symmetry. However, if the massless scalar field must satisfy mixed boundary conditions, say, Dirichlet boundary conditions on one plate and Neumann boundary conditions on the other, the temperature inversion symmetry is lost.…”

Section: Temperature Inversion Symmetrymentioning

confidence: 97%

Zeta function method and repulsive Casimir forces for an unusual pair of plates at finite temperature

1999

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We apply the generalized Zeta function method to compute the Casimir energy and pressure between an unusual pair of parallel plates at finite temperature, namely, a perfectely conducting plate (ǫ → ∞) and an infinitely permeable one (µ → ∞). The high and low temperature limits of these quantities are discussed. Relationships between high and low temperature limits for the free energy are established by means of a modified version of the temperature inversion symmetry.

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Section: Temperature Inversion Symmetrymentioning

confidence: 97%

Zeta function method and repulsive Casimir forces for an unusual pair of plates at finite temperature

1999

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“…To name a few, we mention the "mode summation technique" [12,13,17,18] (which was the method originally used by Casimir), analyses of Green's functions and of the energy-momentum tensor in the presence of boundaries [20,21,22,23,24,25,26] and zeta function techniques [27,28]. These techniques possess flexibility which permits, among other things, the handling of temperature dependence (in vacuum and in dielectrics) [20,21,26,29,30,31,32,34], of fields with finite mass [31,35], various geometrical setups [5,6,7,8,22,24,25,32,33,36,37], and a better insight into the Casimir force (macroscopic) in relation to microscopic "long range forces" [14].…”

Section: Introductionmentioning

confidence: 99%

“…These techniques possess flexibility which permits, among other things, the handling of temperature dependence (in vacuum and in dielectrics) [20,21,26,29,30,31,32,34], of fields with finite mass [31,35], various geometrical setups [5,6,7,8,22,24,25,32,33,36,37], and a better insight into the Casimir force (macroscopic) in relation to microscopic "long range forces" [14].…”

Section: Introductionmentioning

confidence: 99%

Casimir Effect: The Classical Limit

Feinberg¹,

Mann²,

Revzen³

2002

The Ninth Marcel Grossmann Meeting

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We analyze the high temperature (or classical) limit of the Casimir effect. A useful quantity which arises naturally in our discussion is the "relative Casimir energy", which we define for a configuration of disjoint conducting boundaries of arbitrary shapes, as the difference of Casimir energies between the given configuration and a configuration with the same boundaries infinitely far apart. Using path integration techniques, we show that the relative Casimir energy vanishes exponentially fast in temperature. This is consistent with a simple physical argument based on Kirchhoff's law. As a result the "relative Casimir entropy", which we define in an obviously analogous manner, tends, in the classical limit, to a finite asymptotic value which depends only on the geometry of the boundaries. Thus the Casimir force between disjoint pieces of the boundary, in the classical limit, is entropy driven and is governed by a dimensionless number characterizing the geometry of the cavity. Contributions to the Casimir thermodynamical quantities due to each individual connected component of the boundary exhibit logarithmic deviations in temperature from the behavior just described. These logarithmic deviations seem to arise due to our difficulty to separate the Casimir energy (and the other thermodynamical quantities) from the "electromagnetic" self-energy of each of the connected components of the boundary in a well defined manner. Our approach to the Casimir effect is not to impose sharp boundary conditions on the fluctuating field, but rather take into consideration its interaction with the plasma of "charge carriers" in the boundary, with the plasma frequency playing the role of a physical UV cutoff. This also allows us to analyze deviations from a perfect conductor behavior.

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“…A few other papers on this kind of symmetry have also been published [7,8,9,10,11]. Until the publication of Ref.…”

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confidence: 99%

“…Temperature inversion symmetry also appeared in the Brown-Maclay work [6] where they related directly the zero-temperature Casimir energy to the energy density of blackbody radiation at temperature T . A few other papers on this kind of symmetry have also been published [7,8,9,10,11]. Until the publication of Ref.…”

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confidence: 99%

Temperature inversion symmetry in the Casimir effect with an antiperiodic boundary condition

et al. 2003

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We present explicitly another example of a temperature inversion symmetry in the Casimir effect for a nonsymmetric boundary condition. We also give an interpretation for our result. PACS numbers: 11.10.Wx, 12.20.Ds, This brief report was motivated by a recent paper published by Santos et al. [1], in which they discuss the temperature inversion symmetry in the Casimir effect [2] for mixed boundary conditions (for a detailed discussion on the Casimir effect see [3,4] and references therein). In an earlier paper, Ravndal and Tollefsen [5] showed that for the usual setup of two parallel plates a simple inversion symmetry arises in the Casimir effect at finite temperature. Temperature inversion symmetry also appeared in the Brown-Maclay work[6] where they related directly the zero-temperature Casimir energy to the energy density of blackbody radiation at temperature T . A few other papers on this kind of symmetry have also been published [7,8,9,10,11]. Until the publication of Ref. [1], this kind of inversion symmetry had appeared only in calculations of Casimir energy involving symmetric boundary conditions. In 1999, Santos et al. [1] showed, for the case of a massless scalar field submitted to mixed boundary conditions (Dirichlet-Neumann), that the Helmholtz free energy per unit area could be written as a sum of two terms, each of them obeying separately a temperature inversion symmetry. Our purpose here is to present another kind of nonsymmetric boundary condition for which there exists such a symmetry. We show * Electronic address: acap@if.ufrj.br † Electronic address: britto@if.ufrj.br ‡ Electronic address: fabiopr@if.ufrj.br § Electronic address: siqueira@if.ufrj.br

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Casimir Effect at Finite Temperature

Cited by 33 publications

References 4 publications

Zeta function method and repulsive Casimir forces for an unusual pair of plates at finite temperature

Zeta function method and repulsive Casimir forces for an unusual pair of plates at finite temperature

Casimir Effect: The Classical Limit

Temperature inversion symmetry in the Casimir effect with an antiperiodic boundary condition

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