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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
|Authors (as Contributors):||Bermond Baptiste · David Carpentier|
|Date submitted:||2022-11-23 17:33|
|Submitted by:||Carpentier, David|
|Submitted to:||SciPost Physics|
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.
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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.