Quantum thermodynamics of overdamped modes in local and spatially dispersive materials

Abstract

The quantum thermodynamical properties of (quasi-normal) overdamped electromagnetic modes (eddy currents) are investigated in the context of the magnetic Casimir-Polder interaction. The role of the material response in terms of spatially local and nonlocal material models is discussed. In particular, the focus is set on the system's entropy in the limit of low temperatures. In specific circumstances the spatially local (Drude) model reveals an "entropy defect", while spatial dispersion leads to a more regular behavior. We present a detailed description of this phenomenon and of the different mechanisms at work in the system with regard to the eddy modes' properties. Extensively discussing classical and quantum features, we relate our results to the wide range of literature and draw intriguing connections to seemingly distant fields as, e.g., the theory of magnetohydrodynamics and superconductivity.

Low-temperature behavior of the Casimir-Polder free energy and entropy for an atom interacting with graphene

“…On the theoretical side, it was shown that the Lifshitz theory comes into conflict with the Nernst heat theorem when the response of metals with perfect crystal lattices to low-frequency electromagnetic fluctuations is described by the Drude model. This was proven in different geometries for the Casimir interaction between nonmagnetic [44][45][46][47][48] and magnetic [49] metals and, very recently, for the Casimir-Polder interaction of both polarizable and magnetizable atoms interacting with metallic plate [50].…”

No-Slip Boundary Conditions for Electron Hydrodynamics and the Thermal Casimir Pressure

“…The only way to formally isolate the local Drude model is the "dirty limit," where τ → 0 at fixedλ p , v F . A discussion of the opposite case, that is typical for low temperatures, is provided by Reiche et al [14], Intravaia et al [26].…”

“…The first coincidence is that the typical thermal frequency is quite close to the Drude scattering rate k B T/h = 0.94/τ (gold at room temperature). (For a detailed study of the behaviour of Casimir pressure and entropy at low temperatures, see References [14,26].) The second coincidence is one of length scales.…”

“…The problem arises, however, that the Casimir force under realistic conditions also contains a temperature-dependent contribution (sometimes this is attributed to "real" rather than "virtual" particles) whose relevant frequencies peak in the infrared (hω ∼ k B T = 25.2 meV at room temperature, for example, Wien's displacement law) [9,10]. Its evaluation requires the knowledge of the infrared conductivity of a metal, but this has been the subject of great discussions-the "Drude vs. plasma" controversy [11][12][13][14][15].…”

Extended hydrodynamic description for nonequilibrium atom-surface interactions

“…An example is provided by the analysis of Casimir(-Polder) forces in systems involving spatially nonlocal material and non-trivial geometries beyond the analytically accessible cases. [62,63]. and the other is connected to Landau damping in the bulk,…”