Relativistic covariance of Ohm's law
- Author(s)
- R. Starke, G. A. H. Schober
- Abstract
The derivation of Lorentz-covariant generalizations of Ohm's law has been a long-term issue in theoretical physics with deep implications for the study of relativistic effects in optical and atomic physics. In this article, we propose an alternative route to this problem, which is motivated by the tremendous progress in first-principles materials physics in general and ab initio electronic structure theory in particular. We start from the most general, Lorentz-covariant first-order response law, which is written in terms of the fundamental response tensor μ relating induced four-currents to external four-potentials. By showing the equivalence of this description to Ohm's law, we prove the validity of Ohm's law in every inertial frame. We further use the universal relation between μ and the microscopic conductivity tensor σk to derive a fully relativistic transformation law for the latter, which includes all effects of anisotropy and relativistic retardation. In the special case of a constant, scalar conductivity, this transformation law can be used to rederive a standard textbook generalization of Ohm's law.
- Organisation(s)
- Computational Materials Physics
- External organisation(s)
- Technische Universität Bergakademie Freiberg, Scientific Software Center
- Journal
- International Journal of Modern Physics D
- Volume
- 25
- No. of pages
- 12
- ISSN
- 0218-2718
- DOI
- https://doi.org/10.1142/S0218271816400101
- Publication date
- 10-2016
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 103025 Quantum mechanics, 103036 Theoretical physics, 103015 Condensed matter, 103009 Solid state physics
- Keywords
- ASJC Scopus subject areas
- Astronomy and Astrophysics, Mathematical Physics, Space and Planetary Science
- Portal url
- https://ucris.univie.ac.at/portal/en/publications/relativistic-covariance-of-ohms-law(a7b4d6e4-a7c2-4895-8334-24a051aff818).html