Casimir Effect: The Classical Limit

Abstract

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.

latex, 56 pages, one eps figure. Major improvements of presentation (especially in Section 2). No change in the conclusions. Connection with the works of Balian et al. on the Casimir effect is clarified. Abstract changed, typos corrected

References in corpus (5)

• Zeta Functions and the Casimir Energy
• Gauge Theories with Cayley-Klein $SO(2;j)$ and $SO(3;j)$ Gauge Groups
• Casimir force between partially transmitting mirrors
• Casimir's energy of a conducting sphere and of a dilute dielectric ball
• Causality, stability and passivity for a mirror in vacuum

Cited by in corpus (55)

• The Casimir force between real materials: experiment and theory
• Opposites Attract - A Theorem About The Casimir Force
• Casimir forces in a T operator approach
• Does the Transverse Electric Zero Mode Contribute to the Casimir Effect for a Metal?
• Thermal quantum field theory and the Casimir interaction between dielectrics
• Experiment and theory in the Casimir effect
• Comment on "On the temperature dependence of the Casimir effect"
• Van der Waals and Casimir interactions between two graphene sheets
• Theory of the Casimir interaction for graphene-coated substrates using the polarization tensor and comparison with experiment
• Present status of controversies regarding the thermal Casimir force
• Thermal Casimir effect in ideal metal rectangular boxes
• Casimir Effects: an Optical Approach II. Local Observables and Thermal Corrections
• Lifshitz theory of atom-wall interaction with applications to quantum reflection
• The Casimir Problem of Spherical Dielectrics: Numerical Evaluation for General Permittivities
• Quantum field theory on toroidal topology: algebraic structure and applications
• Analytic approach to the thermal Casimir force between metal and dielectric
• Thermal correction to the Casimir force, radiative heat transfer, and an experiment
• High temperature asymptotics of thermodynamic functions of electromagnetic field subjected to boundary conditions on a sphere and cylinder
• Finite Temperature Casimir Effect in Kaluza-Klein Spacetime
• Temperature dependence of the magnetic Casimir-Polder interaction
• Thermal Casimir effect for neutrino and electromagnetic fields in closed Friedmann cosmological model
• Thermofield Dynamics and Casimir Effect for Fermions
• Generalized Bogoliubov Transformation for Confined Fields: Applications in Casimir Effect
• Interplay between geometry and temperature for inclined Casimir plates
• Finite temperature Casimir effect for massive scalar field in spacetime with extra dimensions
• Classical Casimir-Polder force between polarizable microparticles and thin films including graphene
• Screening of classical Casimir forces by electrolytes in semi-infinite geometries
• Classical Casimir interaction in the plane-sphere geometry
• Classical limit of the Casimir interaction for thin films with applications to graphene
• Geothermal Casimir phenomena for the sphere-plate and cylinder-plate configurations
• Long-range magnetic interaction due to the Casimir effect
• Casimir Energies: Temperature Dependence, Dispersion, and Anomalies
• Casimir effect for a dilute dielectric ball at finite temperature
• Geothermal Casimir Phenomena
• Casimir energies with finite-width mirrors
• Small object limit of Casimir effect and the sign of the Casimir force
• Temperature dependence of the plasmonic Casimir interaction
• Perturbative zero-point energy for a cylinder of elliptical section
• Classical Casimir free energy for two Drude spheres of arbitrary radii: A plane-wave approach
• On the entanglement of a quantum field with a dispersive medium
• Finite temperature Casimir pistons for electromagnetic field with mixed boundary conditions and its classical limit
• On the Casimir entropy between 'perfect crystals'
• Numerical methods for fluctuation driven interactions between dielectrics
• Local thermal behaviour of a massive scalar field near a reflecting wall
• High Temperature Asymptotics in Terms of Heat Kernel Coefficients: Boundary Conditions with Spherical and Cylindrical Symmetries
• Thermal Casimir Effect for Rectangular Cavities inside D+1-dimensional Minkowski Spacetime Revisited
• Comment on "Casimir energies with finite-width mirrors"
• Electromagnetic Response of the Electron Gas and the Thermal Casimir Pressure Anomaly
• Classical limit of the Casimir entropy for scalar massless field
• Casimir type effects for scalar fields interacting with material slabs
• "Screening" of universal van der Waals - Casimir terms by Coulomb gases in a fully-finite two-dimensional geometry
• Generalized Bogoliubov Transformation, Fermion Field and Casimir Effect in a Box
• Casimir effect in the boundary state formalism
• Semiclassical Casimir Energies at Finite Temperature
• Casimir effect with dielectric matter in salted water and implications at the cell scale