Anomalous Luttinger equivalence between temperature and curved spacetime: From black holes to thermal quenches
David Carpentier (Laboratoire de Physique, ENS Lyon)
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In condensed matter, thermal response theory relies on a deep connection
between gravitational fields and thermal transport, established in 1964 by Luttinger, building on earlier ideas of Tolman and Ehrenfest. Does this connection extend beyond pure technical considerations ? In this work, we revisit the celebrated Tolman-Ehrenfest and Luttinger relations and show how to incorporate anomalous quantum fluctuations that become paramount in a strongly curved spacetime. Our extended correspondence between temperature variations and curvature of spacetime incorporates new quantum energy scales associated with these fluctuations, captured by the so-called gravitational anomalies of quantum field theories.
On one hand we point out that such anomalous fluctuations naturally occur in the quantum atmosphere of a black hole. On the other hand, our extended correspondance implies that analogous fluctuations are also observable in thermal conductors in the flat-space time of a laboratory, provided that the 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.