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

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.