We study the Casimir-Lifshitz interaction out of thermal equilibrium, with particular attention devoted to the surface-surface and surface-atom configurations. A systematic investigation of the contributions to the force coming from the propagating and evanescent components of the electromagnetic radiation is performed. The large distance behaviors of such interactions is discussed, and both analytical and numerical results are compared with the equilibrium ones. A detailed analysis of the crossing between the surface-surface and the surface-rarefied body, and finally the surface-atom force is shown, and a complete derivation and discussion of the recently predicted non-additivity effects and new asymptotic behaviors is presented.
The Casimir force and free energy at low temperatures has been the subject of focus for some time. We calculate the temperature correction to the Casimir-Lifshitz free energy between two parallel plates made of dielectric material possessing a constant conductivity at low temperatures, described through a Drude-type dielectric function. For the transverse magnetic (TM) mode such a calculation is new. A further calculation for the case of the TE mode is thereafter presented which extends and generalizes previous work for metals. A numerical study is undertaken to verify the correctness of the a…
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.
We investigate the force acting between two parallel plates held at different temperatures. The force reproduces, as limiting cases, the well known Casimir-Lifshitz surface-surface force at thermal equilibrium and the surface-atom force out of thermal equilibrium recently derived by M. Antezza \emph{et al.}, Phys. Rev. Lett. {\bf 95}, 113202 (2005). The asymptotic behavior of the force at large distances is explicitly discussed. In particular when one of the two bodies is a rarefied gas the force is not additive, being proportional to the square root of the density. Nontrivial cross-over regio…
We study the field theoretical model of a scalar field in presence of spacial inhomogeneities in form of one and two finite width mirrors (material slabs). The interaction of the scalar field with the defect is described with position-dependent mass term. Within this model we derive the interaction of two finite width mirrors, establish the correspondence of the model to the Lifshitz formula and construct limiting procedure to obtain finite self-energy of a single mirror without any normalization condition.
Recently J.N. Munday and F. Capasso [Phys. Rev. A {\bf 75}, 060102(R) (2007); arXiv:0705.3793] claimed that they have performed a precision measurement of the Casimir force between a sphere and a plate coated with Au, both immersed in ethanol. The measurement results were claimed to be consistent with the Lifshitz theory. We demonstrate that the calculation of the Casimir force between the smooth bodies following the authors prescription has a discrepancy up to 25% with respect to authors result. We show also that the attractive electrostatic force only due to the surface potential differences…
Recently, the premelting and formation of ice due to the Casimir-Lifshitz interaction, proposed in early 1990s by Elbaum and Schick [Phys. Rev. Lett. 66, 1713-1716 (1991)], have been generalized to diverse practical scenarios, yielding novel physical intuitions and possibilities of application for those phenomena. The properties of materials, in particular, the electrical permittivity and permeability, exert significant influences on the Casimir-Cifshitz energies and forces, and hence on the corresponding premelting and formation of ice. To address these influences in detail and explore the re…
We present here detailed measurements of the Casimir-Lifshitz force between two gold surfaces, performed for the first time in both gas (nitrogen) and liquid (ethanol) enviroments with the same apparatus and on the same spot of the sample. Furthermore, we study the role of double-layer forces in the liquid, and we show that these electrostatic effects are important. The later contributions were precisely subtracted to recover the genuine Casimir force, and the experimental results are compared with calculations using Lifshitz theory. Our measurements demonstrate that a carefull account of the …
We discuss the limitations of the applicability of the Lifshitz formula to describe the temperature dependence of the Casimir force between two bulk lossy metals. These limitations follow from the finite sizes of the interacting bodies. Namely, Lifshitz's theory is not applicable when the characteristic wavelengths of the fluctuating fields, responsible for the temperature-dependent terms in the Casimir force, is longer than the sizes of the samples. As a result of this, the widely discussed linearly decreasing temperature dependence of the Casimir force can be observed only for dirty and/or l…
The physical reasons why the Drude dielectric function is not compatible with the Lifshitz formula, as opposed to the generalized plasma-like permittivity, are presented. Essentially, the problem is connected with the finite size of metal plates. It is shown that the Lifshitz theory combined with the generalized plasma-like permittivity is thermodynamically consistent.
Recently Yampol'skii et al. [Phys. Rev. A v.82, 032511 (2010)] advocated that Lifshitz theory is not applicable when the characteristic wavelength of the fluctuating electromagnetic field, responsible for the thermal correction to the Casimir force, is larger than the size of the metal test bodies. It was claimed that this is the case in experiments which exclude Lifshitz theory combined with the Drude model. We calculate the wavelengths of the evanescent waves giving the dominant contribution to the thermal correction and we find that they are much smaller than the sizes of the test bodies. T…
It was recently found that thermodynamic anomalies which arise in the Casimir effect between metals described by the Drude model can be attributed to the interaction of fluctuating Foucault (or eddy) currents [Phys. Rev. Lett. 103, 130405 (2009)]. We show explicitly that the two leading terms of the low-temperature correction to the Casimir free energy of interaction between two plates, are identical to those pertaining to the Foucault current interaction alone, up to a correction which is very small for good metals. Moreover, a mode density along real frequencies is introduced, showing that t…
The experimental demonstration of the modification of the Casimir force between a gold coated sphere and a single-crystal Si membrane by light pulses is performed. The specially designed and fabricated Si membrane was irradiated with 514 nm laser pulses of 5 ms width in high vacuum leading to a change of the charge-carrier density. The difference in the Casimir force in the presence and in the absence of laser radiation was measured by means of an atomic force microscope as a function of separation at different powers of the absorbed light. The total experimental error of the measured force di…
It is shown that the violation of the positiveness of the entropy due to the Casimir-Lifshitz interaction claimed in several papers is an artifact related to an improper interpretation of the "Casimir entropy", which actually is a difference of two positive terms. It is explained that at definite condition this "Casimir entropy" must be negative. A direct derivation of the low temperature behavior of the surface entropy of a metallic surface in conditions of the anomalous skin effect is given and singular temperature dependency of this quantity is discussed. In conclusion a hydrodynamic exampl…
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.
The new approach to the theoretical description of the thermal Casimir force between real metals is presented. It uses the plasma-like dielectric permittivity that takes into account the interband transitions of core electrons. This permittivity precisely satisfies the Kramers-Kronig relations. The respective Casimir entropy is positive and vanishes at zero temperature in accordance with the Nernst heat theorem. The physical reasons why the Drude dielectric function, when substituted in the Lifshitz formula, is inconsistent with electrodynamics are elucidated. The proposed approach is the sing…
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…
Casimir interactions between macroscopic objects are strongly influenced by their geometrical features as shape and orientation as well as by their material properties. The effect of geometry is commonly obtained from the proximity approximation (PA). Here we present a path integral quantization for the electromagnetic field in the presence of deformed metallic surfaces. From the resulting effective action the Casimir force between the surfaces can be calculated without the PA. For corrugated surfaces the force is obtained both perturbatively for small deformations and by a numerical approach …
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.
In this letter we consider the fluctuation induced force exerted between two plates separated by a distance $L$ in a fluid with a temperature gradient. We predict that, for a range of distances $L$, this non-equilibrium force is anomalously large compared to other Casimir forces. The physical reason is that correlations in a non-equilibrium fluid are generally of longer range than other correlations, even than those near an equilibrium critical point. This giant Casimir force is related to a divergent Burnett coefficient that characterizes an Onsager cross effect between the pressure and the t…
We calculate the Casimir stresses in a thin layer of active fluid with nematic order. By using a stochastic hydrodynamic approach for an active fluid layer of finite thickness $L$, we generalize the Casimir stress for nematic liquid crystals in thermal equilibrium to active systems. We show that the active Casimir stress differs significantly from its equilibrium counterpart. For contractile activity, the active Casimir stress, although attractive like its equilibrium counterpart, diverges logarithmically as $L$ approaches a threshold of the spontaneous flow instability from below. In contrast…
