Recently D. A. R. Dalvit and S. K. Lamoreaux arXiv:0805.1676 [Phys. Rev. Lett. v.101, 163203 (2008)] suggested the modification of the reflection coefficients in the Lifshitz theory taking into account the screening effects and diffusion currents. We demonstrate that the suggested modification is thermodynamically and experimentally inconsistent.
We develop a new theory for Casimir-Lifshitz and Casimir-Polder interactions with semiconductor surfaces that takes into account charge drift in the bulk material. The corresponding frequency-dependent dispersion relations describe a crossover between Lifshitz results for dielectrics and for good conductors. In the quasi-static limit, our calculated reflection amplitudes coincide with those recently computed to account for Debye screening in the thermal Lifshitz force with conducting surfaces with small density of carriers.
We show that the claims expressed in the Comment arXiv:0810.3244v1 by R.S. Decca et al against our paper, D.A.R. Dalvit and S.K. Lamoreaux, Phys. Rev. Lett. {\bf 101}, 163203 (2008), are wrong and manifestly inconsistent with basic principles of statistical physics.
The low-temperature behavior of the Casimir-Polder free energy and entropy for an atom near a dielectric plate are found on the basis of the Lifshitz theory. The obtained results are shown to be thermodynamically consistent if the dc conductivity of the plate material is disregarded. With inclusion of dc conductivity, both the standard Lifshitz theory (for all dielectrics) and its generalization taking into account screening effects (for a wide range of dielectrics) violate the Nernst heat theorem. The inclusion of the screening effects is also shown to be inconsistent with experimental data o…
The Casimir-Polder interaction of an atom with a metallic wall is investigated in the framework of the Lifshitz theory. It is demonstrated that in some temperature (separation) region the Casimir-Polder entropy takes negative values and goes to zero when the temperature vanishes. This result is obtained both for an ideal metal wall and for real metal walls. Simple analytical representations for the Casimir-Polder free energy and force are also obtained. These results are used to make a comparison between the phenomenological potential used in the theoretical description of quantum reflection a…
We review recent results on the low-temperature behaviors of the Casimir-Polder and Casimir free energy an entropy for a polarizable atom interacting with a graphene sheet and for two graphene sheets, respectively. These results are discussed in the wide context of problems arising in the Lifshitz theory of van der Waals and Casimir forces when it is applied to metallic and dielectric bodies. After a brief treatment of different approaches to theoretical description of the electromagnetic response of graphene, we concentrate on the derivation of response function in the framework of thermal qu…
We consider Casimir-Polder and Casimir forces with finite dissipation by coupling heat baths to the dipoles introducing, this way, dissipation from 'first principles'. We derive a representation of the free energy as an integral over real frequencies, which can be viewd as an generalization of the 'remarkable formula' introduced by Ford et. al. 1985. For instance, we obtain a nonperturbative representation for the atom-atom and atom-wall interactions. We investigate several limiting cases. From the limit $T\to0$ we show that the third law of thermodynamics cannot be violated within the given a…
Casimir-Polder interactions are considered in an inhomogeneous, dispersive background. We consider both the interaction between a polarizable atom and a perfectly conducting wall, and between such an atom and a plane interface between two different inhomogeneous dielectric media. Renormalization is achieved by subtracting the interaction with the local inhomogeneous medium by itself. The results are expressed in general form, and generalize the Dzyaloshinskii-Lifshitz-Pitaevskii interaction between a spatially homogeneous dielectric interface and a polarizable atom.
The van der Waals and Casimir-Polder interaction energy of an atom with an infinitely thin sphere with finite conductivity is investigated in the framework of the hydrodynamic approach at finite temperature. This configuration models the real interaction of an atom with fullerene. The Lifshitz approach is used to find the free energy. We find the explicit expression for the free energy and perform the analysis of it for i) high and low temperatures, ii) large radii of sphere and ii) short separation between an atom and sphere. At low temperatures the thermal part of the free energy approaches …
The analytic expressions for the free energy and entropy of the Casimir-Polder interaction between a polarizable and magnetizable atom and a graphene sheet are found in the limiting case of low temperature. In so doing, the response of graphene to electromagnetic fluctuations is described in the framework of the Dirac model by means of the polarization tensor in (2+1)-dimensional space-time. It is shown that the dominant contribution to the low-temperature behavior is given by an explicit dependence of the polarization tensor on temperature as a parameter. We demonstrate that the Lifshitz theo…
The Lifshitz-type formulas for the free energy and Casimir-Polder force acting between an atom possessing a permanent magnetic moment and a wall made of different materials are derived. Simple model allowing analytic results is considered where the atomic magnetic susceptibility is frequency-independent and wall is made of ideal metal. Numerical computations of the Casimir-Polder force are performed for H atom interacting with walls made of ideal metal, nonmagnetic (Au) and ferromagnetic (Fe) metals and of ferromagnetic dielectric. It is shown that for the first three wall materials the inclus…
We find the low-temperature behavior of the Casimir-Polder free energy and entropy for an atom interacting with real graphene sheet possessing nonzero energy gap and chemical potential. Employing the formalism of the polarization tensor, it is shown that the Casimir-Polder entropy goes to zero by the power law with vanishing temperature, i.e., the Nernst heat theorem is satisfied. This result is discussed in connection with the problems connected with account of free charge carriers in the Lifshitz theory.
We use the density matrix formalism in order to calculate the energy level shifts, in second order on interaction, of an atom in the presence of a perfectly conducting wall in the dipole approximation. The thermal corrections are also examined when $\hbar ω_0/k_B T = k_0 λ_T \gg 1$, where ${$ω_0=k_0 c$}$ is the dominant transition frequency of the atom and $λ_T$ is the thermal length. When the distance $z$ between the atom and the wall is larger than $λ_T$ we find the well known result obtained from Lifshitz's formula, whose leading term is proportional to temperature and is independent of $c$…
This Resource Letter provides a guide to the literature on van der Waals and Casimir-Polder forces. Journal articles, books, and other documents are cited on the following topics: van der Waals forces, retarded dispersion forces or Casimir-Polder forces between atoms or molecules, Casimir-Polder forces between a molecule and a dielectric or conducting body, the summation of Casimir-Polder forces as leading to the Casimir and Lifshitz forces between conducting and dielectric bodies, Casimir friction, applications to nanotechnology, the nature of the quantum vacuum, and experimental tests of the…
Recently the Lifshitz theory of dispersion forces was extended for the case of an atom (molecule) interacting with a plane surface of a uniaxial crystal or with a long solid cylinder or cylindrical shell made of isotropic material or uniaxial crystal. The obtained results are applicable to nanosystems. In particular, we investigate the Casimir-Polder interaction between hydrogen atoms (molecules) and multi-wall carbon nanotubes. It is demonstrated that the hydrogen atoms located inside multiwall carbon nanotubes have a lower free energy compared to those located outside. We also perform compar…
Casimir and Casimir-Polder repulsion have been known for more than 50 years. The general "Lifshitz" configuration of parallel semi-infinite dielectric slabs permits repulsion if they are separated by a dielectric fluid that has a value of permittivity that is intermediate between those of the dielectric slabs. This was indirectly confirmed in the 1970s, and more directly by Capasso's group recently. It has also been known for many years that electrically and magnetically polarizable bodies can experience a repulsive quantum vacuum force. More amenable to practical application are situations wh…
The Lifshitz theory of dispersion forces leads to thermodynamic and experimental inconsistencies when the role of drifting charge carriers is included in the model of the dielectric response. Recently modified reflection coefficients were suggested that take into account screening effects and diffusion currents. We demonstrate that this theoretical approach leads to a violation of the third law of thermodynamics (Nernst's heat theorem) for a wide class of materials and is excluded by the data from two recent experiments. The physical reason for its failure is explained by the violation of ther…
The interaction between drifting carriers and traveling electromagnetic waves is considered within the context of the classical Boltzmann transport equation to compute the Casimir-Lifshitz force between media with small density of charge carriers, including dielectrics and intrinsic semiconductors. We expand upon our previous work [Phys. Rev. Lett. {\bf 101}, 163203 (2008)] and derive in some detail the frequency-dependent reflection amplitudes in this theory and compute the corresponding Casimir free energy for a parallel plate configuration. We critically discuss the the issue of verificatio…
Theory of the Casimir effect is presented in several examples. Casimir - Polder type formulas, Lifshitz theory and theory of the Casimir effect for two gratings separated by a vacuum slit are derived. Equations for the electromagnetic field in the presence of a medium and dispersion are discussed. Casimir effect for systems with a layer of 2+1 fermions is studied.
We extend our previous work [Phys. Rev. Lett. {\bf 100}, 183602 (2008)] on the generalization of the Casimir-Lifshitz theory to treat anisotropic magnetodielectric media, focusing on the forces between metals and magnetodielectric metamaterials and on the possibility of inferring magnetic effects by measurements of these forces. We present results for metamaterials including structures with uniaxial and biaxial magnetodielectric anisotropies, as well as for structures with isolated metallic or dielectric properties that we describe in terms of filling factors and a Maxwell Garnett approximatio…
The physical origin of the Casimir force is connected with the existence of zero-point and thermal fluctuations. The Casimir effect is very general and finds applications in various fields of physics. This review is limited to the rapid progress at the intersection of experiment and theory that has been achieved in the last few years. It includes a critical assessment of the proposed approaches to the resolution of the puzzles arising in the applications of the Lifshitz theory of the van der Waals and Casimir forces to real materials. All the primary experiments on the measurement of the Casim…
The Casimir-Polder-Lifshitz force felt by an atom near the surface of a substrate is calculated out of thermal equilibrium in terms of the dielectric function of the material and of the atomic polarizability. The new force decays like $1/z^3$ at large distances (i.e. slower than at equilibrium), exhibits a sizable temperature dependence and is attractive or repulsive depending on whether the temperature of the substrate is higher or smaller than the one of the environment. Our predictions can be relevant for experiments with ultracold atomic gases. Both dielectric and metal substrates are cons…
