Casimir forces in modulated systems

Dzyaloshinskiǐ, I. E.; Kats, E. I.

doi:10.1088/0953-8984/16/32/003

Cited by 5 publications

(5 citation statements)

References 19 publications

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“…Analogous oscillatory effects with respect to the factor q 0 L for anisotropic modulated systems have recently been obtained in [10]. It can be easily seen that the pressure F(L, T ) can be expressed in terms of the energy per unit area G(L, T ) where…”

Section: A Modulated System With a Homogeneous Layer Embedded In Itsupporting

confidence: 52%

“…Even today a direct generalization of the Lifshitz approach [4] is still actual for anisotropic, multilayered and other complex systems [8,9]. A good example in this direction is the calculation of the Casimir forces in modulated systems made recently in [10]. Here an appropriate perturbation scheme has been formulated and valuable estimations for the chemical potential in cholesteric liquid crystalline films have been obtained.…”

Section: Introductionmentioning

confidence: 99%

“…A brief exposition of general theory will be given in section 2 and appendix A. Section 3 is devoted to isotropic modulated systems interacting across a homogeneous layer of finite thickness L. In order to find the van der Waals interaction energy in closed form here we use the regular perturbation theory for small modulations (as in [10]). In section 4 a biophysical example is given for two symmetrical plane-parallel systems 'lipid/water/lipid' and 'water/lipid/water' by taking into account the thin transition layer between water and lipid substances where the dielectric permittivity is continuously varying function of the position.…”

Section: Introductionmentioning

confidence: 99%

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van der Waals interactions between bodies having inhomogeneous dielectric permittivities

Genchev¹

2006

J. Phys.: Condens. Matter

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We present analytical results for the contribution of electromagnetic fluctuations in the distribution of interaction energy and pressure in isotropic systems whose properties depend only on one spatial coordinate. If we neglect the continuous inhomogeneity introduced here and consider the simplest case of two macroscopic homogeneous bodies separated by a homogeneous film our result reduces to the well-known Lifshitz formula. As a first application of theory, a one-dimensional modulated system with a homogeneous layer embedded in it is considered and a suitable perturbation theory for this system is developed. In the main part of this paper we limit the calculations to the non-retarded case, that is only the calculation of van der Waals interaction energy is given. As a second application of theory we consider the van der Waals interaction between two semi-infinite media across a planar region within which there is a thin film having an arbitrary variation of the dielectric permittivity. The importance of the precise evaluation of the transverse magnetic surface mode dispersion relation in inhomogeneous media is elucidated. For concreteness the influence of the transition layer between water and lipid in a symmetrical configuration is considered in some detail. The zero-frequency term and the dispersion-only contribution to the Hamaker coefficient are given analytically using some approximations and modelling of the dielectric constants reasonable for these dielectrics at room temperature. As a whole the results indicate the necessity of performing Lifshitz-type calculations on realistic inhomogeneous layered models, as are the models described here, for accurate interaction energy modelling. Of course further work is needed for real justification of the continuous variation of dielectric permittivities across phase interfaces.

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Section: A Modulated System With a Homogeneous Layer Embedded In Itsupporting

confidence: 52%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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van der Waals interactions between bodies having inhomogeneous dielectric permittivities

Genchev¹

2006

J. Phys.: Condens. Matter

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“…• two-dimensional Ising model [154][155][156]162] • fluctuations confined by membranes [81,82,86,89,153,169,[299][300][301] • liquid crystals [71,72,105,[302][303][304][305][306][307][308][309][310] • O(n ≥ 2) vector models below T c [207,208,286,287] • three-dimensional Ising model [182,192] • non-equilibrium fluctuation-induced forces in fluids [94-96, 98, 99, 101, 311, 312].…”

Section: Casimir-like Effects Off Criticalitymentioning

confidence: 99%

Critical Casimir Effect: Exact Results

Dantchev¹,

Dietrich²

2022

Preprint

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In any medium there are fluctuations due to temperature or due to the quantum nature of its constituents. If a material body is immersed into such a medium, its shape and the properties of its constituents modify the fluctuations in the surrounding medium. If in the same medium there is a second body, modifications of the fluctuation due to the first one influence the modifications due to the second one. This mutual influence results in a force between these bodies. If the excitations of the medium, which mediate the effective interaction between the bodies, are massless, this force is longranged and nowadays known as a Casimir force. If the fluctuating medium consists of the confined electromagnetic field in vacuum, one speaks of the quantum mechanical Casimir effect. In the case that the order parameter of material fields fluctuates -such as differences of number densities or concentrations -and that the corresponding fluctuations of the order parameter are long-ranged, one speaks of the critical Casimir effect. This holds, e.g., in the case of systems which undergo a second-order phase transition and which are thermodynamically located near the corresponding critical point, or for systems with a continuous symmetry exhibiting Goldstone mode excitations. Here we review the currently available exact results concerning the critical Casimir effect in systems encompassing the one-dimensional Ising, XY, and Heisenberg models, the two-dimensional Ising model, the Gaussian and the spherical models, as well as the mean field results for the Ising and the XY model. Special attention is paid to the influence of the boundary conditions on the behavior of the Casimir force. We present results both for the case of classical critical fluctuations if the system possesses a critical point at a non-zero temperature, as well as the case of quantum systems undergoing a continuous phase transition at zero temperature as function of certain parameters. As confinements we consider the film, the sphere -plane, and the sphere -sphere geometries. We discuss systems governed by short-ranged, by subleading long-ranged (i.e., of the van der Waals type), and by leading long-ranged interactions. In order to put the critical Casimir effect into the proper context and in order to make the review as self-contained as possible, basic facts about the theory of phase transitions, the theory of critical phenomena in classical and quantum systems, and finite-size scaling theory are recalled. Whenever possible, a discussion of the relevance of the exact results towards an understanding of available experiments is presented. Hints about eventually applying the results towards their potential use in devices are also given.

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“…As the separation between the two flat surfaces is decreased, the Casimir force increases rapidly and monotonically. Lifshitz extended the analysis to real materials by considering the polarization fluctuations within the interacting bodies and calculated the force in terms of the dielectric properties of the material 2,3 . In the past two decades, advances in mechanical transducers and atomic force microscopes have enabled precision measurements of the Casimir force [4][5][6][7][8][9][10][11][12][13][14][15][16][17] .…”

Section: Introductionmentioning

confidence: 99%

Strong geometry dependence of the Casimir force between interpenetrated rectangular gratings

Wang

Tang

et al. 2021

Nat Commun

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Quantum fluctuations give rise to Casimir forces between two parallel conducting plates, the magnitude of which increases monotonically as the separation decreases. By introducing nanoscale gratings to the surfaces, recent advances have opened opportunities for controlling the Casimir force in complex geometries. Here, we measure the Casimir force between two rectangular silicon gratings. Using an on-chip detection platform, we achieve accurate alignment between the two gratings so that they interpenetrate as the separation is reduced. Just before interpenetration occurs, the measured Casimir force is found to have a geometry dependence that is much stronger than previous experiments, with deviations from the proximity force approximation reaching a factor of ~500. After the gratings interpenetrate each other, the Casimir force becomes non-zero and independent of displacement. This work shows that the presence of gratings can strongly modify the Casimir force to control the interaction between nanomechanical components.

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Casimir forces in modulated systems

Cited by 5 publications

References 19 publications

van der Waals interactions between bodies having inhomogeneous dielectric permittivities

van der Waals interactions between bodies having inhomogeneous dielectric permittivities

Critical Casimir Effect: Exact Results

Strong geometry dependence of the Casimir force between interpenetrated rectangular gratings

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