It is demonstrated that the general theory of Casimir and van der Waals forces describes the interaction-induced equilibrium thermodynamic potentials of the damped harmonic oscillator bilinearly coupled to the environment. An extended model for a damped oscillator is suggested along the lines of the general theory of Casimir and van der Waals forces, and the corresponding thermodynamic quantities obtained. While the original model involves a heat bath consisting of a large number of free oscillators having infinitesimal damping functions, the extended model allows any generally admissible frequency and temperature dependent dissipative susceptibilities of the heat bath constituents, influenced by the additional dissipative environmental channels that are not directly linked to the system oscillator. Consequently, the results obtained are applicable to the frequency and temperature dependent damping function of the system oscillator.
The van der Waals and Casimir interactions of a hydrogen atom (molecule) with a single-walled and a multiwalled carbon nanotubes are compared. It is shown that the macroscopic concept of graphite dielectric permittivity is already applicable for nanotubes with only two or three walls. The absorption of hydrogen atoms by a nanotube at separations below one nanometer is considered. The lateral force due to exchange repulsion moves the atom to a position above the cell center, where it is absorbed by the nanotube because the repulsive force cannot balance the van der Waals attraction.
We study the behavior of the critical Casimir force and its interplay with the van der Waals force acting between two parallel slabs separated at a distance $L$ from each other confining a non-polar simple fluid or a binary liquid mixture. The surfaces of the slabs are coated by thin layers exerting strong preference to the liquid phase of the fluid, or one of the components of the mixture. The slabs influence the fluid by long-range competing dispersion potentials. Under such conditions one usually expects {\it attractive} Casimir force governed by universal scaling function to which the disp…
In this work the induced van der Waals interaction between a pair of neutral atoms or molecules is considered by use of a statistical mechanical method. Commonly this interaction is obtained by standard quantum mechanical perturbation theory to second order. However, the latter is restricted to electrostatic interactions between charges and dipole moments. So with radiating dipole-dipole interaction where retardation effects are important for large separations of the particles, other methods are needed, and the resulting induced interaction is the Casimir-Polder interaction usually obtained by…
This paper is a continuation of a previous one [Jancovici and Samaj, 2004 J. Stat. Mech. P08006] dealing with classical Casimir phenomena in semi-infinite wall geometries. In that paper, using microscopic Coulomb systems, the long-ranged Casimir force due to thermal fluctuations in conducting walls was shown to be screened by the presence of an electrolyte between the walls into some residual short-ranged force. Here, we aim to extend the study of the screening (cancellation) phenomena to universal Casimir terms appearing in the large-size expansions of the grand potentials for microscopic Cou…
We derive a first--principles method of determining the van der Waals or Casimir pressure in a dissipative and dispersive planar multilayered system by calculating the Maxwell stress tensor in a fictitious layer of vacuum, that is eventually made to vanish, introduced in the structure. This is illustrated by calculating the van der Waals pressure in a thin film with dissipative properties embedded between two semi--infinite media.
It is shown that the criticism by Raabe and Welsch of the Dzyaloshinskii-Lifshitz-Pitaevskii theory of the van der Waals-Casimir forces inside a medium is based on misunderstandings. It is explained why and at which conditions one can use the ''Minkowski-like '' stress tensor for calculations of the forces. The reason, why approach of Raabe and Welsch is incorrect, is discussed.
We present the results of a one-loop calculation of the effect of a van der Waals type interaction potential $\sim | {\bf x} |^{-d-σ}$ on the critical Casimir force and specific heat of confined $^4$He near the superfluid transition. We consider a $^4$He film of thickness $L$. In the region $L \gtrsim ξ$ (correlation length) we find that the van der Waals interaction causes a leading non-universal non-scaling contribution of $O (ξ^2 L^{-d-σ})$ to the critical temperature dependence of the Casimir force above $T_λ$ that dominates the universal scaling contribution $\sim e^{- L/ξ}$ predicted by …
We consider systems confined to a $d$-dimensional slab of macroscopic lateral extension and finite thickness $L$ that undergo a continuous bulk phase transition in the limit $L\to\infty$ and are describable by an O(n) symmetrical Hamiltonian. Periodic boundary conditions are applied across the slab. We study the effects of long-range pair interactions whose potential decays as $b x^{-(d+σ)}$ as $x\to\infty$, with $2<σ<4$ and $2<d+σ\leq 6$, on the Casimir effect at and near the bulk critical temperature $T_{c,\infty}$, for $2<d<4$. For the scaled reduced Casimir force per unit cross-sectional a…
We discuss repulsive Casimir forces between dielectric materials with non trivial magnetic susceptibility. It is shown that considerations based on naive pair-wise summation of Van der Waals and Casimir Polder forces may not only give an incorrect estimate of the magnitude of the total Casimir force, but even the wrong sign of the force when materials with high dielectric and magnetic response are involved. Indeed repulsive Casimir forces may be found in a large range of parameters, and we suggest that the effect may be realized in known materials. The phenomenon of repulsive Casimir forces ma…
Recently Philbin et al. (New J. Phys. 11 (2009) 033035; arXiv:0904.2148v3) presented a new theory of the van der Waals friction. Contrary to the previous theories they claimed that there is no "quantum friction" at zero temperature. We show that this theory is incorrect.
A novel approach for calculating Casimir forces between periodically deformed objects is developed. This approach allows, for the first time, a rigorous non-perturbative treatment of the Casimir effect for disconnected objects beyond Casimir's original two-plate configuration. The approach takes into account the collective nature of fluctuation induced forces, going beyond the commonly used pairwise summation of two-body van der Waals forces. As an application of the method, we exactly calculate the Casimir force due to scalar field fluctuations between a flat and a rectangular corrugated plat…
We study systems in which both long-ranged van der Waals and critical Casimir interactions are present. We study the interplay between these forces, as well as the {\it total} force (TF) between a spherical colloid particle and a thick planar slab, and between two spherical colloid particles. We do that using general scaling arguments and mean-field type calculations utilizing the Derjaguin and the surface integration approaches. They both are based on data of the forces between two parallel slabs separated at a distance $L$ from each other, confining the fluctuating fluid medium characterized…
Relaxation of the thermal Casimir or van der Waals force for a model dielectric medium is investigated. We start with a model of interacting polarization fields with a dynamics that leads to a frequency dependent dielectric constant of the Debye form. In the static limit the usual zero frequency Matsubara mode component of the Casimir force is recovered. We then consider the out of equilibrium relaxation of the van der Waals force to its equilibrium value when two initially uncorrelated dielectric bodies are brought into sudden proximity. It is found that the spatial dependence of the out of e…
The properties of fluctuation induced interactions like van der Waals and Casimir-Lifshitz forces are of interest in a plethora of fields ranging from biophysics to nanotechnology. Here we describe a general approach to compute these interactions. It is based on a combination of methods from statistical physics and scattering theory. We showcase how it is exquisitely suited to analyze a variety of previously unexplored phenomena. Examples are given to show how the interplay of geometry and material properties helps to understand and control these forces.
We study the geometry dependence of the Casimir energy for deformed metal plates by a path integral quantization of the electromagnetic field. For the first time, we give a complete analytical result for the deformation induced change in Casimir energy δ\cal E in an experimentally testable, nontrivial geometry, consisting of a flat and a corrugated plate. Our results show an interesting crossover for δ\cal E as a function of the ratio of the mean plate distance H, to the corrugation length λ: For λ\ll H we find a {\em slower} decay \sim H^{-4}, compared to the H^{-5} behavior predicted by the …
We compute fluctuation-induced (Casimir) forces for classical systems after a temperature quench. Using a generic coarse-grained model for fluctuations of a conserved density, we find that transient forces arise even if the initial and final states are force-free. In setups reminiscent of Casimir (planar walls) and van der Waals (small inclusions) interactions, we find comparable exact universal expressions for the force. Dynamical details only scale the time axis of transient force curves. We propose that such quenches can be achieved, for instance, in experiments on active matter, employing …
A new general expression is derived for the fluctuating electromagnetic field outside a metal surface, in terms of its surface impedance. It provides a generalization to real metals of Lifshitz theory of molecular interactions between dielectric solids. The theory is used to compute the radiative heat transfer between two parallel metal surfaces at different temperatures. It is shown that a measurement of this quantity may provide an experimental resolution of a long-standing controversy about the effect of thermal corrections on the Casimir force between real metal plates.
After a review of the standard calculation of the Casimir force between two metallic plates at zero and non-zero temperatures, we present the study of microscopic models to determine the large-distance asymptotic force in the high-temperature regime. Casimir's conducting plates are modelized by plasmas of interacting charges at temperature T. The charges are either classical, or quantum-mechanical and coupled to a (classical) radiation field. In these models, the force obtained is twice weaker than that arising from standard treatments neglecting the microscopic charge fluctutations inside the…
We investigate the dynamics of thermal Casimir interactions between plates described within a living conductor model, with embedded mobile anions and cations, whose density field obeys a stochastic partial differential equation which can be derived starting from the Langevin equations of the individual particles. This model describes the thermal Casimir interaction in the same way that the fluctuating dipole model describes van der Waals interactions. The model is analytically solved in a Debye-Hückel-like approximation. We identify several limiting dynamical regimes where the time dependence …
We present a simple general proof that Casimir force cannot originate from the vacuum energy of electromagnetic (EM) field. The full QED Hamiltonian consists of 3 terms: the pure electromagnetic term $H_{\rm em}$, the pure matter term $H_{\rm matt}$ and the interaction term $H_{\rm int}$. The $H_{\rm em}$-term commutes with all matter fields because it does not have any explicit dependence on matter fields. As a consequence, $H_{\rm em}$ cannot generate any forces on matter. Since it is precisely this term that generates the vacuum energy of EM field, it follows that the vacuum energy does not…
If the damping of a simple harmonic oscillator from a thermally random force is sufficiently strong, then the oscillator may become unstable. For a photon oscillator (radiatively damped by electric dipole moments), the instability leads to a low temperature Hepp-Lieb-Preparata super-radiant phase transition. The stable oscillator regime is described by the free energy of the conventional Casimir effect. The unstable (strongly damped) oscillator has a free energy corresponding to Dicke super-radiance.
For the first time we present analytical results for the contribution of electromagnetic fluctuations into thermodynamic properties of modulated systems, like cholesteric or smectic liquid crystalline films. In the case of small dielectric anisotropy we have derived explicit analytical expressions for the chemical potential of such systems. Two limiting cases were specifically considered: (i) the Van der Waals (VdW) limit, i.e., in the case when the retardation of the electromagnetic interactions can be neglected; and (ii) the Casimir limit, i.e. when the effects of retardation becomes conside…
We review recent results obtained in the physics of the thermal Casimir force acting between two dielectrics, dielectric and metal, and between metal and semiconductor. The detailed derivation for the low-temperature behavior of the Casimir free energy, pressure and entropy in the configuration of two real dielectric plates is presented. For dielectrics with finite static dielectric permittivity it is shown that the Nernst heat theorem is satisfied. Hence, the Lifshitz theory of the van der Waals and Casimir forces is demonstrated to be consistent with thermodynamics. The nonzero dc conductivi…
The Casimir-Lifhitz force acts between neutral material bodies and is due to the fluctuations (around zero) of the electrical polarizations of the bodies. This force is a macroscopic manifestation of the van der Waals forces between atoms and molecules. In addition to being of fundamental interest, the Casimir-Lifshitz force plays an important role in surface physics, nanotechnology and biophysics. There are two different approaches in the theory of this force. One is centered on the fluctuations inside the bodies, as the source of the fluctuational electromagnetic fields and forces. The secon…
We present a general method to study the non-equilibrium behavior of Casimir type fluctuation induced forces for classical free scalar field theories. In particular we analyze the temporal evolution of the force towards its equilibrium value when the field dynamics is given by a general class of over damped stochastic dynamics (including the model A and model B class). The steady state force is also analyzed for systems which have non-equilibrium steady states, for instance where they are driven by colored noise. The key to the method is that out of equilibrium force is computed by specifying …
Understanding the force between charged surfaces immersed in an electrolyte solution is a classic problem in soft matter and liquid-state theory. Recent experiments showed that the force decays exponentially but the characteristic decay length in a concentrated electrolyte is significantly larger than what liquid-state theories predict based on analysing correlation functions in the bulk electrolyte. Inspired by the classical Casimir effect, we consider an alternative mechanism for force generation, namely the confinement of density fluctuations in the electrolyte by the walls. We show analyti…
We consider the Bose gas on a $d$-dimensional anisotropic lattice employing the imperfect (mean-field) gas as a prototype example. We study the dimensional crossover arising as a result of varying the dispersion relation at finite temperature $T$. We analyze in particular situations where one of the relevant effective dimensionalities is located at or below the lower critical dimension, so that the Bose-Einstein condensate becomes expelled from the system by anisotropically modifying the lattice parameters controlling the kinetic term in the Hamiltonian. We clarify the mechanism governing this…
We study the thermal Casimir effect between two thick slabs composed of plane-parallel layers of random dielectric materials interacting across an intervening homogeneous dielectric. It is found that the effective interaction at long distances is self averaging and its value is given by a that between non-random media with the effective dielectric tensor of the corresponding random media. The behavior at short distances becomes random (sample dependent) and is dominated by the local values of the dielectric constants proximal to each other across the homogeneous slab. These results are extende…
We calculate the effect of the interaction between an optically active material and a Bose-Einstein condensate on the collective oscillations of the condensate. We provide explicit expressions for the frequency shift of the center of mass oscillation in terms of the potential generated by the substrate and of the density profile of the gas. The form of the potential is discussed in details and various regimes (van der Waals-London, Casimir-Polder and thermal regimes) are identified as a function of the distance of atoms from the surface. Numerical results for the frequency shifts are given for…
The Casimir force between macroscopic bodies depends strongly on their shape and orientation. To study this geometry dependence in the case of two deformed metal plates, we use a path integral quantization of the electromagnetic field which properly treats the many-body nature of the interaction, going beyond the commonly used pairwise summation (PWS) of van der Waals forces. For arbitrary deformations we provide an analytical result for the deformation induced change in Casimir energy, which is exact to second order in the deformation amplitude. For the specific case of sinusoidally corrugate…
