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Anomalous Luttinger equivalence between temperature and curved spacetime: From black holes to thermal quenches

by Baptiste Bermond, Maxim Chernodub, Adolfo G. Grushin and David Carpentier

Submission summary

Authors (as Contributors): Bermond Baptiste · David Carpentier
Submission information
Preprint link: scipost_202211_00043v1
Date submitted: 2022-11-23 17:33
Submitted by: Carpentier, David
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
Approach: Theoretical


Building on the idea of Tolman and Ehrenfest that heat has weight, Luttinger established a deep connection between gravitational fields and thermal transport. However, this relation does not include anomalous quantum fluctuations that become paramount in strongly curved spacetime. In this work, we revisit the celebrated Tolman-Ehrenfest and Luttinger relations and show how to incorporate the quantum energy scales associated with these fluctuations, captured by gravitational anomalies of quantum field theories. We point out that such anomalous fluctuations naturally occur in the quantum atmosphere of a black hole. Our results reveal that analogous fluctuations are also observable in thermal conductors in flat-space time provided local temperature varies strongly. As a consequence, we establish that the gravitational anomalies manifest themselves naturally in non-linear thermal response of a quantum wire. In addition, we propose a systematic way to identify thermal analogues of black hole's anomalous quantum fluctuations associated to gravitational anomalies. We identify their signatures in propagating energy waves following a thermal quench, as well as in the energy density of heating Floquet states induced by repeated thermal quenches.

Current status:
In refereeing

Submission & Refereeing History

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Submission scipost_202211_00043v1 on 23 November 2022

Reports on this Submission

Anonymous Report 1 on 2023-1-25 (Invited Report)


The manuscript discusses corrections to Luttinger relations due to quantum anomalies. It is clearly written, and the computations are easy to follow. In my opinion the only aspect of the manuscript that needs to be expanded is the discussion that the particles transport ballistically, and the two species don’t thermalize. This assumption for thermal systems seems to be very strong and in general valid for temperatures close to zero. Therefore, I would expect that it breaks down quite quickly as the temperature rises. However, I have not seen any discussion of the applicability of the formulas presented in the paper. Moreover, the validity of the corrections derived in this work requires that different species of fermions are kept at different temperatures. Again, no discussion of how close to realistic systems is this requirement, is included. I do not expect these relations to hold near black holes.

  • validity: ok
  • significance: ok
  • originality: good
  • clarity: top
  • formatting: excellent
  • grammar: excellent

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