Casimir effect between two spheres at small separations

Teo, Lee-Peng

doi:10.1103/physrevd.85.045027

Cited by 35 publications

(56 citation statements)

References 30 publications

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“…Together with (50) and (21), we find that the small separation leading term of the Casimir interaction always agrees with the proximity force approximation. This is true at any temperature.…”

Section: Cassupporting

confidence: 81%

“…However, the computation of the next-to-leading order term is often tedious, but it captures important information of the Casimir interaction such as the response of the system to the curvature of the surfaces, and it also gives a rough idea of how accurate the leading term is. Using the idea first developed in [29], such computations have been performed for various geometric configurations [29,30,[44][45][46][47][48][49][50][51][52]. In this section, we will compute the small separation asymptotic expansions of the Casimir interaction at any temperature.…”

Section: Small Separation Asymptotic Behavior Of the Casimir Intermentioning

confidence: 99%

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Finite temperature Casimir interaction between spheres in(D+1)-dimensional spacetime: Exact computations and asymptotic expansions

Teo

2014

Phys. Rev. D

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We consider the finite temperature Casimir interaction between two Dirichlet spheres in ðD þ 1Þ-dimensional Minkowski spacetime. The Casimir interaction free energy is derived from the zero temperature Casimir interaction energy via the Matsubara formalism. In the high temperature region, the Casimir interaction is dominated by the term with zero Matsubara frequency, and it is known as the classical term since this term is independent of the Planck constant ℏ. Explicit expression of the classical term is derived and it is computed exactly using appropriate similarity transforms of matrices. We then compute the small separation asymptotic expansion of this classical term up to the next-to-leading order term. For the remaining part of the finite temperature Casimir interaction with nonzero Matsubara frequencies, we obtain its small separation asymptotic behavior by applying certain prescriptions to the corresponding asymptotic expansion at zero temperature. This gives us a leading term that is shown to agree precisely with the proximity force approximation at any temperature. The next-to-leading order term at any temperature is also derived and it is expressed as an infinite sum over integrals. To obtain the asymptotic expansion at the low and medium temperature regions, we apply the inverse Mellin transform techniques. In the low temperature region, we obtain results that agree with our previous work on the zero temperature Casimir interaction.

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Section: Cassupporting

confidence: 81%

Section: Small Separation Asymptotic Behavior Of the Casimir Intermentioning

confidence: 99%

Finite temperature Casimir interaction between spheres in(D+1)-dimensional spacetime: Exact computations and asymptotic expansions

Teo

2014

Phys. Rev. D

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“…(23), which is attractive for all separations and temperatures. While this proceeding was on review process, a related work was published 20 .…”

Section: Casimir Energy and Entropy Between Perfect Metal Spheres 483mentioning

confidence: 99%

Casimir Energy and Entropy Between Perfect Metal Spheres

Rodriguez-López

2012

Int. J. Mod. Phys. Conf. Ser.

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We calculate the Casimir energy and entropy for two perfect metal spheres in the large and short separation limit. We obtain nonmonotonic behavior of the Helmholtz free energy with separation and temperature, leading to parameter ranges with negative entropy, and also nonmonotonic behavior of the entropy with temperature and with the separation between the spheres. The appearance of this anomalous behavior of the entropy is discussed as well as its thermodynamic consequences.

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“…The idea of the derivation is to similar to perturbation in quantum field theory. Later the method has been generalized to compute the small separation asymptotic behavior of the Casimir interaction energy in various settings [32,41,42,[44][45][46][47][48][49][50][51].…”

Section: Small Separation Asymptotic Behaviormentioning

confidence: 99%

Scalar cylinder-plate and cylinder-cylinder Casimir interaction in higher dimensional spacetime

Teo

2015

Phys. Rev. D

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We study the cylinder-plate and the cylinder-cylinder Casimir interaction in the (D + 1)-dimensional Minkowski spacetime due to the vacuum fluctuations of massless scalar fields. Different combinations of Dirichlet (D) and Neumann (N) boundary conditions are imposed on the two interacting objects. For the cylinder-cylinder interaction, we consider the case where one cylinder is inside the other, and the case where the two cylinders are outside each other. By computing the transition matrices of the objects and the translation matrices that relate different coordinate systems, the explicit formulas for the Casimir interaction energies are derived. From these formulas, we compute the large separation and small separation asymptotic behaviors of the Casimir interaction. For the cylinder-plate interaction with R ≪ L, where R is the radius of the cylinder and L is the distance from the center of the cylinder to the plate, the order of decay of the Casimir interaction only depends on the boundary conditions imposed on the cylinder. The orders are L −D+1 / ln(L) and L −D−1 / ln L respectively for Dirichlet and Neumann boundary conditions on the cylinder. For two cylinders with radii R1 and R2 lying parallelly outside each other, the orders of decay of therespectively for DD, DN/ND and NN boundary conditions, where L is the distance between the centers of the cylinders. The more interesting and important characteristic of Casimir interaction appears at small separation. Using perturbation technique, we compute the small separation asymptotic expansions of the Casimir interaction energies up to the next-to-leading order terms. The leading terms coincide with the respective results obtained using proximity force approximation, which is of order d −D+1/2 , where d is the distance between the two objects. The results on the next-toleading order terms are more interesting and important. We find some universal behaviors. It is also noticed that for the case of Dirichlet-Dirichlet cylinder-plate interaction, the next-to-leading order term agrees with that obtained using derivative expansion. Hence, based on our results on other boundary conditions and on the cylinder-cylinder interaction, we postulate a formula for the derivative expansion to expand the Casimir interaction energy up to the next-to-leading order terms for DD, DN, ND and NN boundary conditions, for the interaction between two curved surfaces in (D + 1)-dimensional Minkowski spacetime. It is found that the postulate agrees with our previous results on the sphere-sphere interactions except when D = 4.

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Casimir effect between two spheres at small separations

Cited by 35 publications

References 30 publications

Finite temperature Casimir interaction between spheres in(D+1)-dimensional spacetime: Exact computations and asymptotic expansions

Finite temperature Casimir interaction between spheres in(D+1)-dimensional spacetime: Exact computations and asymptotic expansions

Casimir Energy and Entropy Between Perfect Metal Spheres

Scalar cylinder-plate and cylinder-cylinder Casimir interaction in higher dimensional spacetime

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