article
Justifying Kubo’s formula for gapped systems at zero temperature: A brief review and some new results
published
yes
Sven Joscha
Henheik
author 31d731d7-d235-11ea-ad11-b50331c8d7fb0000-0003-1106-327X
Stefan
Teufel
author
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.
World Scientific Publishing2021
eng
Mathematical PhysicsStatistical and Nonlinear Physics
Reviews in Mathematical Physics
0129-055X
1793-6659
2002.0866910.1142/s0129055x20600041
3301
yes
S. J. Henheik and S. Teufel, “Justifying Kubo’s formula for gapped systems at zero temperature: A brief review and some new results,” <i>Reviews in Mathematical Physics</i>, vol. 33, no. 01. World Scientific Publishing, 2021.
Henheik, Sven Joscha, and Stefan Teufel. “Justifying Kubo’s Formula for Gapped Systems at Zero Temperature: A Brief Review and Some New Results.” <i>Reviews in Mathematical Physics</i>, vol. 33, no. 01, 2060004, World Scientific Publishing, 2021, doi:<a href="https://doi.org/10.1142/s0129055x20600041">10.1142/s0129055x20600041</a>.
Henheik SJ, Teufel S. Justifying Kubo’s formula for gapped systems at zero temperature: A brief review and some new results. <i>Reviews in Mathematical Physics</i>. 2021;33(01). doi:<a href="https://doi.org/10.1142/s0129055x20600041">10.1142/s0129055x20600041</a>
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.
S.J. Henheik, S. Teufel, Reviews in Mathematical Physics 33 (2021).
Henheik, Sven Joscha, and Stefan Teufel. “Justifying Kubo’s Formula for Gapped Systems at Zero Temperature: A Brief Review and Some New Results.” <i>Reviews in Mathematical Physics</i>. World Scientific Publishing, 2021. <a href="https://doi.org/10.1142/s0129055x20600041">https://doi.org/10.1142/s0129055x20600041</a>.
Henheik, S. J., & Teufel, S. (2021). Justifying Kubo’s formula for gapped systems at zero temperature: A brief review and some new results. <i>Reviews in Mathematical Physics</i>. World Scientific Publishing. <a href="https://doi.org/10.1142/s0129055x20600041">https://doi.org/10.1142/s0129055x20600041</a>
92852021-03-26T11:29:46Z2023-02-23T13:53:59Z