Energy flow in quantum critical systems far from equilibrium

  • An Erratum to this article was published on 01 October 2015


Characterizing the behaviour of strongly coupled quantum systems out of equilibrium is a cardinal challenge for both theory and experiment. With diverse applications ranging from the dynamics of the quark–gluon plasma to transport in novel states of quantum matter, establishing universal results and organizing principles out of equilibrium is crucial. We present a universal description of energy transport between quantum critical heat baths in arbitrary dimension. The current-carrying non-equilibrium steady state (NESS) is a Lorentz-boosted thermal state. In the context of gauge/gravity duality this reveals an intimate correspondence between far-from-equilibrium transport and black hole uniqueness theorems. We provide analytical expressions for the energy current and the generating function of energy current fluctuations, together with predictions for experiment.

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Figure 1: Thermal transport set-up.
Figure 2: AdS/CFT correspondence.
Figure 3: Conformal hydrodynamics.

Change history

  • 03 September 2015

    In the print and PDF versions of this Article originally published the digital object identifier contained a typographical error and should have read 10.1038/nphys3320. This error has now been corrected in the online versions.


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We thank B. Benenowski, D. Bernard, P. Chesler, D. Haldane, C. Herzog, D. Marolf, B. Najian, C-A. Pillet, S. Sachdev and A. Starinets for helpful comments; we especially thank A. Green for suggesting the interpretation of TL, R in d = 1 as Doppler-shifted radiation. M.J.B. and K.S. thank the Kavli Royal Society Center Chicheley Hall and the Isaac Newton Institute, Cambridge for hospitality. M.J.B. and B.D. thank The Galileo Galilei Institute for Theoretical Physics. B.D. thanks Université Paris Diderot, where part of this work was done, for financial support through a visiting professorship. A.L. is supported by the Smith Family Science and Engineering Graduate Fellowship and thanks the Perimeter Institute for hospitality. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Economic Development & Innovation. This work was supported in part by a VICI grant of the Netherlands Organization for Scientific Research (NWO), by the Netherlands Organization for Scientific Research/Ministry of Science and Education (NWO/OCW) and by the Foundation for Research into Fundamental Matter (FOM).

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M.J.B. initiated and coordinated the project. B.D. led the field theory and fluctuation analysis. A.L. led the hydrodynamic analysis, and wrote and performed numerical simulations. K.S. led the gauge-gravity analysis. M.J.B. wrote the manuscript with input from all the authors.

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Correspondence to M. J. Bhaseen.

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Bhaseen, M., Doyon, B., Lucas, A. et al. Energy flow in quantum critical systems far from equilibrium. Nature Phys 11, 509–514 (2015).

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