CastroAlvaredo, O., Chen, Y., Doyon, B. & Hoogeveen, M. (2014). Thermodynamic Bethe ansatz for nonequilibrium steady states: exact energy current and fluctuations in integrable QFT. Journals of Statistical Mechanics [JSTAT], doi: 10.1088/17425468/2014/03/P03011

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Abstract
We evaluate the exact energy current and scaled cumulant generating function (related to the largedeviation function) in nonequilibrium steady states with energy flow, in any integrable model of relativistic quantum field theory (IQFT) with diagonal scattering. Our derivations are based on various recent results of Bernard and Doyon. The steady states are built by connecting homogeneously two infinite halves of the system thermalized at different temperatures Tl, Tr, and waiting for a long time. We evaluate the current J(Tl, Tr) using the exact QFT density matrix describing these nonequilibrium steady states and using Zamolodchikov's method of the thermodynamic Bethe ansatz (TBA). The scaled cumulant generating function is obtained from the extended fluctuation relations which hold in integrable models. We verify our formula in particular by showing that the conformal field theory (CFT) result is obtained in the hightemperature limit. We analyze numerically our nonequilibrium steadystate TBA equations for three models: the sinhGordon model, the roaming trajectories model, and the sineGordon model at a particular reflectionless point. Based on the numerics, we conjecture that an infinite family of nonequilibrium cfunctions, associated with the scaled cumulants, can be defined, which we interpret physically. We study the full scaled distribution function and find that it can be described by a set of independent Poisson processes. Finally, we show that the 'additivity' property of the current, which is known to hold in CFT and was proposed to hold more generally, does not hold in general IQFT—that is, J(Tl, Tr) is not of the form f(Tl) − f(Tr).
Item Type:  Article 

Uncontrolled Keywords:  Quantum transport, integrable quantum field theory, thermodynamic Bethe ansatz, large deviations in nonequilibrium systems 
Subjects:  Q Science > QA Mathematics 
Divisions:  School of Engineering & Mathematical Sciences > Department of Mathematical Science 
URI:  http://openaccess.city.ac.uk/id/eprint/3441 
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