Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-26T03:56:20.018Z Has data issue: false hasContentIssue false
  • English
  • Français

Electromagnetic responses of relativistic electrons

Published online by Cambridge University Press:  15 February 2018

C. A. A. de Carvalho  and
D. M. Reis
C. A. A. de Carvalho*
Affiliation:
Diretoria-Geral de Desenvolvimento Nuclear e Tecnológico da Marinha – DGDNTM, Rua da Ponte, Ed. 23 do AMRJ, Rio de Janeiro – RJ, 20091-000, Brazil Instituto de Física, Universidade Federal do Rio de Janeiro – UFRJ, Caixa Postal 68528, Rio de Janeiro – RJ, 21945-972, Brazil
D. M. Reis
Affiliation:
Centro Brasileiro de Pesquisas Físicas – CBPF, Rua Dr. Xavier Sigaud 150, Rio de Janeiro – RJ, 22290-180, Brazil
*
†Email address for correspondence: carlos.aragao51@gmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

We compute the real and imaginary parts of the electric permittivities and magnetic permeabilities of relativistic electrons from quantum electrodynamics at finite temperatures and densities, for weak fields, neglecting electron–electron interactions. For non-zero temperatures, electromagnetic responses are reduced to one-dimensional integrals computed numerically. For zero temperature, we find analytic expressions for both their real/dispersive and imaginary/absorptive parts. As an application of our results, we obtain the dispersion relation for longitudinal electric plasmons. Present calculations support our recent claim that, at low frequencies and long wavelengths, the system will exhibit simultaneously negative electric and magnetic responses.

Keywords

astrophysical plasmasplasma propertiesquantum plasma
Type
Research Article
Information
Journal of Plasma Physics , Volume 84 , Issue 1 , February 2018 , 905840112
Copyright
© Cambridge University Press 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abrikosov, A. A., Gorkov, L. P. & Dzyaloshinski, I. E. 1975 Methods of Quantum Field Theory in Statistical Physics. Dover.Google Scholar
Ahmed, K. & Masood, S. 1991 Vacuum polarization at finite temperature and density in qed. Ann. Phys. 207 (2), 460–473.Google Scholar
Akhiezer, I. A. & Peletminskii, S. V. 1960 Use of the methods of quantum field theory for the investigation of the thermodynamical properties of a gas of electrons and photons. Zh. Eksp. Teor. Fiz. 11, 1316–1322.Google Scholar
Ashcroft, N. W. & Mermin, N. D. 2005 Solid State Physics. Holt, Rinehart and Winston.Google Scholar
Barbaro, M. B., Cenni, R. & Quaglia, M. R. 2005 The generalised relativistic lindhard functions. Eur. Phys. J. A 25 (2), 299–318.CrossRefGoogle Scholar
Barton, G. 1990 On the finite-temperature quantum electrodynamics of free electrons and photons. Ann. Phys. 200 (2), 271–303.Google Scholar
Berry, M. V. 2005 The optical singularities of bianisotropic crystals. Proc. R. Soc. Lond. A 461, 2071–2098.Google Scholar
de Carvalho, C. A. A. 2016 Relativistic electron gas: a candidate for nature’s left-handed materials. Phys. Rev. D 93 (10), 105005.CrossRefGoogle Scholar
Donoghue, J. F., Holstein, B. R. & Robinett, R. W. 1985 Quantum electrodynamics at finite temperature. Ann. Phys. 164 (2), 233–276.Google Scholar
Eliasson, B. & Shukla, P. K. 2011 Relativistic laser-plasma interactions in the quantum regime. Phys. Rev. E 83 (4), 046407.Google Scholar
Fetter, A. L. & Walecka, J. D. 2012 Quantum Theory of Many-particle Systems. Courier Corporation.Google Scholar
Gu, X.-Q., Wang, S.-Y. & Yin, W.-Y. 2014 Optical responses of planar composites consisting of monolayer graphene sheets and axially helicoidal (bi) anisotropic films. Opt. Commun. 313, 9–14.Google Scholar
Itzykson, C. & Zuber, J.-B. 2006 Quantum Field Theory. Courier Corporation.Google Scholar
Jancovici, B. 1962 On the relativistic degenerate electron gas. Il Nuovo Cimento 25 (2), 428–455.Google Scholar
Kapusta, J. I. & Gale, C. 2006 Finite-temperature Field Theory: Principles and Applications. Cambridge University Press.Google Scholar
Le Bellac, M. 2000 Thermal Field Theory. Cambridge University Press.Google Scholar
Lindhard, J. 1954 On the properties of a gas of charged particles. Kgl. Danske Videnskab. Selskab Mat.-Fys. Medd. 28, 1–57.Google Scholar
Masood, S. & Saleem, I. 2016 Propagation of electromagnetic waves in extremely dense media. Intl J. Mod. Phys. A 1750081.Google Scholar
McOrist, J., Melrose, D. B. & Weise, J. I. 2007 Dispersion in a relativistic degenerate electron gas. J. Plasma Phys. 73 (4), 495–513.Google Scholar
Melrose, D. B. & Hayes, L. M. 1984 Dispersion in a relativistic quantum electron gas. II. Thermal distributions. Austral. J. Phys. 37 (6), 639–650.Google Scholar
Pendry, J. B. 2003 Focus issue: negative refraction and metamaterials. Optics Express 11 (7), 639–639.Google Scholar
Pérez Rojas, H. & Shabad, A. E. 1982 Absorption and dispersion of electromagnetic eigenwaves of electron-positron plasma in a strong magnetic field. Ann. Phys. 138 (1), 1–35.CrossRefGoogle Scholar
Pulsifer, P. & Kalman, G. 1992 Pair-creation collective modes in an electron gas. Phys. Rev. A 45 (8), 5820–5829.Google Scholar
Reis, D. M., Reyes-Gómez, E.-O. L. E. & de Carvalho, C. A. A.2017 Electromagnetic propagation in a relativistic electron gas at finite temperatures. Ann. Phys. arXiv:1711.07818.Google Scholar
Reyes-Gómez, E., Oliveira, L. E. & de Carvalho, C. A. A. 2016 The electromagnetic response of a relativistic fermi gas at finite temperatures: applications to condensed-matter systems. Europhys. Lett. 114 (1), 17009.Google Scholar
Sturm, K. 1982 Electron energy loss in simple metals and semiconductors. Adv. Phys. 31 (1), 1–64.Google Scholar
Sturm, K. & Oliveira, L. E. 1980 High-frequency dielectric properties of covalent semiconductors within the nearly-free-electron approximation. I. The one-plasmon-band model. Phys. Rev. B 22 (12), 6268.CrossRefGoogle Scholar
Sturm, K. & Oliveira, L. E. 1981 Wave-vector-dependent plasmon linewidth in the alkali metals. Phys. Rev. B 24 (6), 3054.Google Scholar
Tsai, W.-Y. & Erber, T. 1974 Photon pair creation in intense magnetic fields. Phys. Rev. D 10 (2), 492.Google Scholar
Veselago, V. G. 1968 The electrodynamics of substances with simultaneously negative values of and $\unicode[STIX]{x1D707}$ . Sov. Phys. Uspekhi 10 (4), 509.Google Scholar
Weldon, H. A. 1982 Covariant calculations at finite temperature: the relativistic plasma. Phys. Rev. D 26 (6), 1394.Google Scholar