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

Abstract

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

Casimir force on a piston at finite temperature in Randall-Sundrum models

“…The quantum field theory shares many of the effects at finite temperature. Thermal influence on the Casimir effect is manifest in many cases [10,18,27,[52][53][54][55][56][57]. The influence of a sufficiently high temperature can even change conclusions completely.…”

Study of temperature inversion symmetry for the twisted Wess–Zumino model

“…As it can be easily seen from relation (2), he used periodic boundary conditions, corresponding to the compact dimension and periodic for the 'temperature dimension' (consistent with the KMS relations). In previous and later results [3][4][5][6][7][8], the symmetries, which the function (1) has, were studied and calculations for other fields, such as fermions and gauge fields, with various boundary conditions, were done. Studying thermodynamical quantities of fields in such topological spaces is of great importance (for example in microelectronics where characteristic distances become small [9]).…”