Nonequilibrium steady-state Kubo formula: Equality of transport coefficients

Marko Žnidarič
Phys. Rev. B 99, 035143 – Published 22 January 2019

Abstract

We address the question of whether transport coefficients obtained from a unitary closed system setting, i.e., the standard equilibrium Green-Kubo formula, are the same as the ones obtained from a weakly driven nonequilibrium steady-state calculation. We first derive a nonequilibrium Kubo-like expression for the steady-state diffusion constant expressed as a time integral of either a current or a conserved density nonequilibrium correlation function. This expression has certain advantages over the equilibrium Green-Kubo formula, but it is not clear if it gives the same value of the diffusion constant. We then rigorously show that if the unitary dynamics is diffusive, the nonequilibrium formula indeed gives exactly the same transport coefficient. The form of finite-size correction is also predicted. Theoretical results are verified by an explicit calculation of the diffusion constant in several interacting many-body models.

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  • Received 6 July 2018
  • Revised 12 October 2018

DOI:https://doi.org/10.1103/PhysRevB.99.035143

©2019 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Marko Žnidarič

  • Physics Department, Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana, Slovenia and Adbus Salam ICTP, Strada Costiera 11, 34151 Trieste, Italy

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Vol. 99, Iss. 3 — 15 January 2019

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