Numerical studies of Lifshitz interactions between dielectrics

Pasquali, Samuela; Maggs, A. C.

doi:10.1103/physreva.79.020102

Cited by 15 publications

(24 citation statements)

References 17 publications

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“…Until recently, most works on the subject had been restricted to simple geometries, such as parallel plates or similar approximations thereof. However, new theoretical methods capable of computing the force in arbitrary geometries have already begun to explore the strong geometry dependence of the force and have demonstrated a number of interesting effects [6][7][8][9][10][11][12][13][14][15]. A substantial motivation for the study of this effect is from recent progress in the field of nanotechnology, especially in the fabrication of micro-electro-mechanical systems (MEMS), where Casimir forces have been observed [16] and may play a significant role in "stiction" and other phenomena involving small surface separations.…”

Section: Introductionmentioning

confidence: 99%

Casimir forces in the time domain: Applications

et al. 2010

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Citation McCauley, Alexander P. et al. "Casimir forces in the time domain: Applications." Physical Review A 81.1 (2010): 012119.Our previous article [Phys. Rev. A 80, 012115 (2009)] introduced a method to compute Casimir forces in arbitrary geometries and for arbitrary materials that was based on a finite-difference time-domain (FDTD) scheme. In this article, we focus on the efficient implementation of our method for geometries of practical interest and extend our previous proof-of-concept algorithm in one dimension to problems in two and three dimensions, introducing a number of new optimizations. We consider Casimir pistonlike problems with nonmonotonic and monotonic force dependence on sidewall separation, both for previously solved geometries to validate our method and also for new geometries involving magnetic sidewalls and/or cylindrical pistons. We include realistic dielectric materials to calculate the force between suspended silicon waveguides or on a suspended membrane with periodic grooves, also demonstrating the application of perfectly matched layer (PML) absorbing boundaries and/or periodic boundaries. In addition, we apply this method to a realizable three-dimensional system in which a silica sphere is stably suspended in a fluid above an indented metallic substrate. More generally, the method allows off-the-shelf FDTD software, already supporting a wide variety of materials (including dielectric, magnetic, and even anisotropic materials) and boundary conditions, to be exploited for the Casimir problem.

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Section: Introductionmentioning

confidence: 99%

Casimir forces in the time domain: Applications

et al. 2010

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“…New computational methods for Casimir interactions [3][4][5][6][7][8] have become important in order to model nonplanar micromechanical systems where unusual Casimir effects have been predicted, and there has been increasing interest in T > 0 corrections [9][10][11][12][13][14][15][16][17][18][19], especially in recently identified systems where these effects are non-negligible [12]. Although T > 0 effects are easy to incorporate in the imaginary frequency domain, where they merely turn an integral into a sum over Matsubara frequencies [20], they are nontrivial in time domain because of the singularity of the zero-frequency contribution, and we show that a naive approach leads to incorrect results.…”

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confidence: 99%

Calculation of nonzero-temperature Casimir forces in the time domain

et al. 2011

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We show how to compute Casimir forces at nonzero temperatures with time-domain electromagnetic simulations, for example using a finite-difference time-domain (FDTD) method. Compared to our previous zero-temperature time-domain method, only a small modification is required, but we explain that some care is required to properly capture the zero-frequency contribution. We validate the method against analytical and numerical frequency-domain calculations, and show a surprising high-temperature disappearance of a non-monotonic behavior previously demonstrated in a piston-like geometry.Comment: 5 pages, 2 figures, submitted to Physical Review A Rapid Communicatio

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“…Realistic, general numerical methods to solve for Casimir forces were simply unavailable; solutions were limited to special high-symmetry geometries (and often to special materials like perfect metals) that are amenable to analytical and semi-analytical approaches. This is not to say that there were not, in principle, decadesold theoretical frameworks capable of describing fluctuations for arbitrary geometries and materials, but practical techniques for evaluating these theoretical descriptions on a computer have only been demonstrated in the last few years [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. In almost all cases, these approaches turn out to be closely related to computational methods from classical EM, which is fortunate because it means that Casimir computations can exploit decades of progress in computational classical EM once the relationship between the problems becomes clear.…”

Section: Introductionmentioning

confidence: 99%

Numerical Methods for Computing Casimir Interactions

Johnson

2011

Lecture Notes in Physics

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We review several different approaches for computing Casimir forces and related fluctuation-induced interactions between bodies of arbitrary shapes and materials. The relationships between this problem and well known computational techniques from classical electromagnetism are emphasized. We also review the basic principles of standard computational methods, categorizing them according to three criteria-choice of problem, basis, and solution technique-that can be used to classify proposals for the Casimir problem as well. In this way, mature classical methods can be exploited to model Casimir physics, with a few important modifications.

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Numerical studies of Lifshitz interactions between dielectrics

Cited by 15 publications

References 17 publications

Casimir forces in the time domain: Applications

Casimir forces in the time domain: Applications

Calculation of nonzero-temperature Casimir forces in the time domain

Numerical Methods for Computing Casimir Interactions

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