The Casimir free energy in high- and low-temperature limits

Svetovoy, V. B.; Esquivel, R.

doi:10.1088/0305-4470/39/21/s79

Cited by 30 publications

(34 citation statements)

References 40 publications

(49 reference statements)

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“…For pure metals, where the anomalous skin effect theory must be used, the situation is quite interesting. As it was shown by Svetovoy and Esquivel [8], in this case |∂S C /∂l| ∝ T , while |S C | ∝ T 2/3 (see next section). Thus |S C | ≫ |∂S C /∂l|.…”

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confidence: 70%

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Casimir-Lifshitz Forces and Entropy

Pitaevskiĭ

2010

Int. J. Mod. Phys. A

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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 example of the entropy of a liquid film is considered. It occurs that the entropy of a film of finite thickness and a liquid half-space behave differently at T → 0.PACS numbers: 34.35.+a,42.50.Nn, PHYSICAL MEANING AND PROPERTIES OF THE "CASIMIR ENTROPY"Recently much attention has been devoted to the calculation of the entropy related to the Casimir-Lifshitz forces [1][2][3][4][5][6][7][8]. The common point of these papers is the calculation of the so-called "Casimir entropy", which is defined as

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confidence: 70%

“…Recently much attention has been devoted to the calculation of the entropy related to the Casimir-Lifshitz forces [1][2][3][4][5][6][7][8]. The common point of these papers is the calculation of the so-called "Casimir entropy", which is defined as…”

Section: Physical Meaning and Properties Of The "Casimir Entropy"mentioning

confidence: 99%

Casimir-Lifshitz Forces and Entropy

Pitaevskiĭ

2010

Int. J. Mod. Phys. A

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“…It is not clear for the moment how realistic is this suggestion but in this paper it is shown that the repulsion can dominate at least for the thermal part of the force.The thermal force also revealed interesting cancelations between EW and PW contributions. At large distances significant cancelations are realized for dielectrics [12] and metals [14]. The cancelation is reduced in the non-equilibrium situation when the temperatures of the bodies are different [12].…”

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confidence: 99%

Evanescent character of the repulsive thermal Casimir force

Svetovoy

2007

Phys. Rev. A

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The physical origin of the negative thermal correction to the Casimir force between metals is clarified. For this purpose the asymptotic behavior of the thermal Casimir force is analyzed at large and small distances in the real frequency representation. Contributions from propagating and evanescent waves are considered separately. At large distances they cancel each other in substantial degree so that only the attractive Lifshitz limit survives. At smaller separations the repulsive evanescent contribution of s-polarization dominates in the case of two metals or a metal and a high-permittivity dielectric. Common origin and order of magnitude of the repulsion in these two cases demonstrate naturalness of the controversial large thermal correction between metals. DOI: 10.1103/PhysRevA.76.062102 PACS number͑s͒: 12.20.Ds, 42.50.Lc, 42.50.Pq Over the last decade there was a growing interest in the Casimir force ͓1͔ that was measured in a series of recent experiments ͓2͔. Particularly the thermal part of the force was a subject of active and often controversial discussion ͑see ͓3͔ for a review͒. Here we concentrate on the thermal force, which does not include the zero point fluctuations. The repulsion discussed in this paper has the meaning of a negative thermal correction to the force at zero temperature, but the total force is always attractive ͓4͔. At large distances a ӷបc / T ͑k B =1͒, the thermal force is given by the Lifshitz limit ͓4-6͔where a is the distance between parallel plates and T is the temperature of the system. This formula was derived for two dielectric plates with the static dielectric constants 1 and 2 . The force between two ideal metals can be found from Eq. ͑1͒ as the limit 1,2 → ϱ that gives F Lif = T ͑3͒ / 8 a 3 . This equation became one of the points of controversy ͓7,8͔ because direct calculation of the thermal force between ideal metals ͓9͔ gave the result, which is two times larger. This contradiction found its resolution ͓10,11͔. At large distances only low frequency electromagnetic ͑EM͒ fluctuations contribute to the force. In this limit the s-polarized EM field degenerates to a pure magnetic one, which penetrates freely via a nonmagnetic metal ͓11͔. On the contrary, the ppolarized field is pure electric and reflected by the metal. For the ideal metal both polarizations are reflected and the force will be two times larger. In this sense the ideal metal is rather the limit case of a superconductor than of a normal metal ͓12͔.The difference between ideal and real metals manifests itself also at small distances a បc / T. The force between ideal metals is attractive and small ͓9͔. On the contrary, the force between real metals is relatively large and repulsive ͓7͔. This difference did not yet find a clear physical explanation.In this paper it is demonstrated that at distances a Շបc / T the evanescent contribution of s-polarization to the thermal Casimir force dominates for two metals or in the case of a metal and a high-permittivity dielectric. For both material configurations the force...

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“…For the class I materials the calculations were performed in [12] but the distance dependent leading term was presented in [24]: F % À0:0193T 2 a! 2 p @v F c 2 ;…”

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Application of the Lifshitz Theory to Poor Conductors

Svetovoy

2008

Phys. Rev. Lett.

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The Lifshitz formula for dispersive forces is generalized to the materials, which cannot be described with the local dielectric response. The principal nonlocality of poor conductors is related to the finite screening length of the penetrating field and collisional relaxation; at low temperatures the role of collisions plays the Landau damping. Spatial dispersion makes the theory self-consistent. Our predictions are compared with the recent experiment. It is demonstrated that at low temperatures Casimir-Lifshitz entropy disappears as T in the case of degenerate plasma and as T2 for the nondegenerate one.

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The Casimir free energy in high- and low-temperature limits

Cited by 30 publications

References 40 publications

Casimir-Lifshitz Forces and Entropy

Casimir-Lifshitz Forces and Entropy

Evanescent character of the repulsive thermal Casimir force

Application of the Lifshitz Theory to Poor Conductors

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