Eur. Phys. J. B 42, 555-559 (2004)
https://doi.org/10.1140/epjb/e2005-00014-x

Heat conductivity in small quantum systems: Kubo formula in Liouville space

¹ Institute of Theoretical Physics I, University of Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany
² Physics Department, University of Osnabrück, Barbarastr. 7, 49069 Osnabrück, Germany

Corresponding author: ^a mathias@theo1.physik.uni-stuttgart.de

Received: 15 September 2004
Published online: 18 January 2005

Abstract

We consider chains consisting of several identical subsystems weakly coupled by various types of next neighbor interactions. At both ends the chain is coupled to a respective heat bath with different temperature modeled by a Lindblad formalism. The temperature gradient introduced by this environment is then treated as an external perturbation. We propose a method to evaluate the heat current and the local temperature profile of the resulting stationary state as well as the heat conductivity in such systems. This method is similar to Kubo techniques used e.g. for electrical transport but extended here to the Liouville space.