Justifying Kubo’s formula for gapped systems at zero temperature: A brief review and some new results

Henheik SJ, Teufel S. 2021. Justifying Kubo’s formula for gapped systems at zero temperature: A brief review and some new results. Reviews in Mathematical Physics. 33(01), 2060004.


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Abstract
We first review the problem of a rigorous justification of Kubo’s formula for transport coefficients in gapped extended Hamiltonian quantum systems at zero temperature. In particular, the theoretical understanding of the quantum Hall effect rests on the validity of Kubo’s formula for such systems, a connection that we review briefly as well. We then highlight an approach to linear response theory based on non-equilibrium almost-stationary states (NEASS) and on a corresponding adiabatic theorem for such systems that was recently proposed and worked out by one of us in [51] for interacting fermionic systems on finite lattices. In the second part of our paper, we show how to lift the results of [51] to infinite systems by taking a thermodynamic limit.
Publishing Year
Date Published
2021-02-01
Journal Title
Reviews in Mathematical Physics
Volume
33
Issue
01
Article Number
2060004
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Henheik SJ, Teufel S. Justifying Kubo’s formula for gapped systems at zero temperature: A brief review and some new results. Reviews in Mathematical Physics. 2021;33(01). doi:10.1142/s0129055x20600041
Henheik, S. J., & Teufel, S. (2021). Justifying Kubo’s formula for gapped systems at zero temperature: A brief review and some new results. Reviews in Mathematical Physics. World Scientific Publishing. https://doi.org/10.1142/s0129055x20600041
Henheik, Sven Joscha, and Stefan Teufel. “Justifying Kubo’s Formula for Gapped Systems at Zero Temperature: A Brief Review and Some New Results.” Reviews in Mathematical Physics. World Scientific Publishing, 2021. https://doi.org/10.1142/s0129055x20600041.
S. J. Henheik and S. Teufel, “Justifying Kubo’s formula for gapped systems at zero temperature: A brief review and some new results,” Reviews in Mathematical Physics, vol. 33, no. 01. World Scientific Publishing, 2021.
Henheik SJ, Teufel S. 2021. Justifying Kubo’s formula for gapped systems at zero temperature: A brief review and some new results. Reviews in Mathematical Physics. 33(01), 2060004.
Henheik, Sven Joscha, and Stefan Teufel. “Justifying Kubo’s Formula for Gapped Systems at Zero Temperature: A Brief Review and Some New Results.” Reviews in Mathematical Physics, vol. 33, no. 01, 2060004, World Scientific Publishing, 2021, doi:10.1142/s0129055x20600041.
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