### Abstract

Rapidly convergent expansions of a one-loop contribution to the partition function of quantum fields with ellipsoid constant-energy surface dispersion law are derived. The omega-potential is naturally decomposed into three parts: the quasiclassical contribution, the contribution from the branch cut of the dispersion law, and the oscillating part. The low- and high-temperature expansions of the quasiclassical part are obtained. An explicit expression and a relation of the contribution from the cut with the Casimir term and vacuum energy are established. The oscillating part is represented in the form of the Chowla-Selberg expansion of the Epstein zeta function. Various resummations of this expansion are considered. The general procedure developed is then applied to two models: massless particles in a box both at zero and nonzero chemical potential, and electrons in a thin metal film. Rapidly convergent expansions of the partition function and average particle number are obtained for these models. In particular, the oscillations of the chemical potential of conduction electrons in graphene and a thin metal film due to a variation of size of the crystal are described.

Original language | English |
---|---|

Pages (from-to) | 2658-2693 |

Number of pages | 36 |

Journal | Annals of Physics |

Volume | 326 |

Issue number | 10 |

DOIs | |

Publication status | Published - Oct 2011 |

Externally published | Yes |

### Fingerprint

### Keywords

- Casimir effect
- Chemical potential oscillations
- Chowla-Selberg expansion
- High-temperature expansion

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Annals of Physics*,

*326*(10), 2658-2693. https://doi.org/10.1016/j.aop.2011.07.004

**One-loop omega-potential of quantum fields with ellipsoid constant-energy surface dispersion law.** / Kazinski, P. O.; Shipulya, M. A.

Research output: Contribution to journal › Article

*Annals of Physics*, vol. 326, no. 10, pp. 2658-2693. https://doi.org/10.1016/j.aop.2011.07.004

}

TY - JOUR

T1 - One-loop omega-potential of quantum fields with ellipsoid constant-energy surface dispersion law

AU - Kazinski, P. O.

AU - Shipulya, M. A.

PY - 2011/10

Y1 - 2011/10

N2 - Rapidly convergent expansions of a one-loop contribution to the partition function of quantum fields with ellipsoid constant-energy surface dispersion law are derived. The omega-potential is naturally decomposed into three parts: the quasiclassical contribution, the contribution from the branch cut of the dispersion law, and the oscillating part. The low- and high-temperature expansions of the quasiclassical part are obtained. An explicit expression and a relation of the contribution from the cut with the Casimir term and vacuum energy are established. The oscillating part is represented in the form of the Chowla-Selberg expansion of the Epstein zeta function. Various resummations of this expansion are considered. The general procedure developed is then applied to two models: massless particles in a box both at zero and nonzero chemical potential, and electrons in a thin metal film. Rapidly convergent expansions of the partition function and average particle number are obtained for these models. In particular, the oscillations of the chemical potential of conduction electrons in graphene and a thin metal film due to a variation of size of the crystal are described.

AB - Rapidly convergent expansions of a one-loop contribution to the partition function of quantum fields with ellipsoid constant-energy surface dispersion law are derived. The omega-potential is naturally decomposed into three parts: the quasiclassical contribution, the contribution from the branch cut of the dispersion law, and the oscillating part. The low- and high-temperature expansions of the quasiclassical part are obtained. An explicit expression and a relation of the contribution from the cut with the Casimir term and vacuum energy are established. The oscillating part is represented in the form of the Chowla-Selberg expansion of the Epstein zeta function. Various resummations of this expansion are considered. The general procedure developed is then applied to two models: massless particles in a box both at zero and nonzero chemical potential, and electrons in a thin metal film. Rapidly convergent expansions of the partition function and average particle number are obtained for these models. In particular, the oscillations of the chemical potential of conduction electrons in graphene and a thin metal film due to a variation of size of the crystal are described.

KW - Casimir effect

KW - Chemical potential oscillations

KW - Chowla-Selberg expansion

KW - High-temperature expansion

UR - http://www.scopus.com/inward/record.url?scp=80052907973&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80052907973&partnerID=8YFLogxK

U2 - 10.1016/j.aop.2011.07.004

DO - 10.1016/j.aop.2011.07.004

M3 - Article

AN - SCOPUS:80052907973

VL - 326

SP - 2658

EP - 2693

JO - Annals of Physics

JF - Annals of Physics

SN - 0003-4916

IS - 10

ER -