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.
Bibliographical noteFunding Information:
This work was supported by the Technion VPR Fund, by the Fund for Promotion of Research at the Technion, by the Fund for Promotion of Sponsored Research at the Technion, and by the Technion-Haifa University Joint Research Fund. J.F.’s research has been supported in part by the Israeli Science Foundation Grant 307/98 (090-903). Special thanks are due to our colleagues Constantin Brif, Hiroshi Ezawa, Oded Kenneth, Israel Klich, Koichi Nakamura, Amos Ori, Shmuel Nussinov, Lev Pitaevski, Guy Ramon, Giuseppe Vitiello, and Joshua Zak for informative comments. Finally, J.F. thanks Roger Balian for a useful discussion.
ASJC Scopus subject areas
- Physics and Astronomy (all)