Quantum origin of Ohm’s reciprocity relation and its violation: conductivity as inverse resistivity

Frangi, Giorgio (author), Grozdanov, Sašo (author)

Conventional wisdom teaches us that the electrical conductivity in a material is the inverse of its resistivity. In this work, we show that, when both of these transport coefficients are defined in linear response through the Kubo formulas as two-point correlators of conserved currents in quantum field theory, this Ohm’s reciprocity relation is generically violated in theories with dynamical electromagnetism. We then elucidate how in certain special limits (e.g., in the dc limit in the presence of thermal effects, in certain 2+1⁢d conformal theories, and in holographic supersymmetric theories) the reciprocity relation is reinstated as an emergent property of conductive and resistive transport. We also show that if the response of a material is measured with respect to the total electric field that includes quantum corrections, then the reciprocity relation is satisfied by definition. However, in that case, the transport coefficients are given by the photon vacuum polarization and not the correlators of conserved currents that dominate the hydrodynamic macroscopic late-time transport.

• Language: English
• Keywords: electrical conductivity, electrical resistivity, quantum physics, field theory
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2025
• Number of pages: Str. 056010-1-056010-8
• Numbering: Vol. 111, iss. 5
• PID: 20.500.12556/RUL-167793
• UDC: 53
• ISSN on article: 2470-0010
• DOI: 10.1103/PhysRevD.111.056010
• COBISS.SI-ID: 228678403
• Publication date in RUL: 12.03.2025

Record is a part of a journal

• Title: Physical review
• Shortened title: Phys. rev., D
• Publisher: American Physical Society
• ISSN: 2470-0010
• COBISS.SI-ID: 29757223

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: električna prevodnost, električna upornost, kvantna fizika, teorija polja

Projects

• Funder: UKRI - UK Research and Innovation
• Project number: ST/T00388X/1
• Name: From quantum chaos to collective transport in plasmas

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: N1-0245-2023
• Name: Kvantni kaos v relativističnih plazmah