Large Deviations and Fluctuation Theorem for the Quantum Heat Current in the Spin-Boson Model

Erik E. Aurell (1) , Brecht Donvil (2) , Kirone Mallick (3)

1 KTH - Royal Institute of Technology [Stockholm]
2 Department of Mathematics and Statistics [Helsinki]
3 IPHT - Institut de Physique Théorique - UMR CNRS 3681

We study the heat current flowing between two baths consisting of harmonic oscillators interacting with a qubit through a spin-boson coupling. An explicit expression for the generating function of the total heat flowing between the right and left baths is derived by evaluating the corresponding Feynman-Vernon path integral by performing the non-interacting blip approximation (NIBA). We recover the known expression, obtained by using the polaron transform. This generating function satisfies the Gallavotti-Cohen fluctuation theorem, both before and after performing the NIBA. We also verify that the heat conductance is proportional to the variance of the heat current, retrieving the well known fluctuation dissipation relation. Finally, we present numerical results for the heat current.

Domains: Statistical Mechanics [cond-mat.stat-mech]

Erik E. Aurell, Brecht Donvil, Kirone Mallick. Large Deviations and Fluctuation Theorem for the Quantum Heat Current in the Spin-Boson Model. Physical Review E , 2020, 101 (5), pp.052116. ⟨10.1103/PhysRevE.101.052116⟩. ⟨cea-02923402⟩