New J. Phys. 10 (April 2008) 043026 (23pp) doi: 10.1088/1367-2630/10/4/043026
Third quantization: a general method to solve master equations for quadratic open Fermi systems
Tomaž Prosen
Department of Physics, FMF, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia
E-mail: tomaz.prosen@fmf.uni-lj.siAbstract.
The Lindblad master equation for an arbitrary quadratic system of n fermions is solved explicitly in terms of diagonalization of a 4n×4n matrix, provided that all Lindblad bath operators are linear in the fermionic variables. The method is applied to the explicit construction of non-equilibrium steady states (NESS) and the calculation of asymptotic relaxation rates in the far from equilibrium problem of heat and spin transport in a nearest neighbour Heisenberg XY spin-1/2 chain in a transverse magnetic field.
Received 7 January 2008
Published 15 April 2008
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