### Abstract

Original language | Undefined |
---|---|

Article number | 10.1088/0305-4470/39/21/S79 |

Pages (from-to) | 6777-6784 |

Number of pages | 8 |

Journal | Journal of physics A: mathematical and general |

Volume | 39 |

Issue number | Technical |

DOIs | |

Publication status | Published - 10 May 2006 |

### Keywords

- METIS-237880
- IR-66833
- EWI-8946

### Cite this

*Journal of physics A: mathematical and general*,

*39*(Technical), 6777-6784. [10.1088/0305-4470/39/21/S79]. https://doi.org/10.1088/0305-4470/39/21/S79

}

*Journal of physics A: mathematical and general*, vol. 39, no. Technical, 10.1088/0305-4470/39/21/S79, pp. 6777-6784. https://doi.org/10.1088/0305-4470/39/21/S79

**The casimir free energy in high- and low-temperature limits.** / Svetovoy, Vitaly; Esquivel, R.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - The casimir free energy in high- and low-temperature limits

AU - Svetovoy, Vitaly

AU - Esquivel, R.

N1 - 10.1088/0305-4470/39/21/S79

PY - 2006/5/10

Y1 - 2006/5/10

N2 - The problem with the temperature dependence of the Casimir force is investigated. We analyse high-temperature limit analytically making calculations at real frequencies. The purpose is to answer the questionwhy there is no continuous transition between real and ideal metals and why the result does not depend on the relaxation frequency. It is found that the contribution of evanescent s polarized fields is finite even for an infinitely small relaxation frequency (plasma model) and exactly cancels the contribution of propagating fields. For the ideal metal the evanescent fields do not contribute at all. The lowtemperature limit is analysed to establish behaviour of the entropy at T → 0. It is stressed that the nonlocal effects are important in this limit because the mean free path for electrons becomes larger than the field penetration depth. In this limit vF /a plays the role of the relaxation frequency, where vF is the Fermi velocity and a is the distance between plates. It is indicated that the Leontovich approximate impedance cannot be used for calculations because it is good for the description of propagating but not evanescent fields. It is found that due to nonlocality the Casimir entropy approaches zero at T → 0 when s polarization does not contribute to the classical part of the Casimir force.

AB - The problem with the temperature dependence of the Casimir force is investigated. We analyse high-temperature limit analytically making calculations at real frequencies. The purpose is to answer the questionwhy there is no continuous transition between real and ideal metals and why the result does not depend on the relaxation frequency. It is found that the contribution of evanescent s polarized fields is finite even for an infinitely small relaxation frequency (plasma model) and exactly cancels the contribution of propagating fields. For the ideal metal the evanescent fields do not contribute at all. The lowtemperature limit is analysed to establish behaviour of the entropy at T → 0. It is stressed that the nonlocal effects are important in this limit because the mean free path for electrons becomes larger than the field penetration depth. In this limit vF /a plays the role of the relaxation frequency, where vF is the Fermi velocity and a is the distance between plates. It is indicated that the Leontovich approximate impedance cannot be used for calculations because it is good for the description of propagating but not evanescent fields. It is found that due to nonlocality the Casimir entropy approaches zero at T → 0 when s polarization does not contribute to the classical part of the Casimir force.

KW - METIS-237880

KW - IR-66833

KW - EWI-8946

U2 - 10.1088/0305-4470/39/21/S79

DO - 10.1088/0305-4470/39/21/S79

M3 - Article

VL - 39

SP - 6777

EP - 6784

JO - Journal of physics A: mathematical and theoretical

JF - Journal of physics A: mathematical and theoretical

SN - 1751-8113

IS - Technical

M1 - 10.1088/0305-4470/39/21/S79

ER -