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Non-Equilibrium Steady States in Conformal Field Theory

Research output: Contribution to journalArticlepeer-review

Denis Bernard, Benjamin Doyon

Original languageEnglish
Pages (from-to)113-161
Number of pages49
JournalAnnales Henri Poincare
Issue number1
Early online date29 Jan 2014
Accepted/In press30 Nov 2013
E-pub ahead of print29 Jan 2014
PublishedJan 2015

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  • King's College London


We present a construction of non-equilibrium steady states in one-dimensional quantum critical systems carrying energy and charge fluxes. This construction is based on a scattering approach within a real-time hamiltonian reservoir formulation. Using conformal field theory techniques, we prove convergence towards steady states at large time. We discuss in which circumstances these states describe the universal non-equilibrium regime at low temperatures. We compute the exact large deviation functions for both energy and charge transfers, which encode for the quantum and statistical fluctuations of these transfers at large time. They are universal, depending only on fundamental constants ( {Mathematical expression}), on the central charge and on the external parameters such as the temperatures or the chemical potentials, and they satisfy fluctuation relations. A key point consists in relating the derivatives of these functions to the linear response functions but at complex shifted external parameters. 

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