Third quantization: a general method to solve master equations for quadratic open Fermi systems

Tomaž Prosen
2008 New Journal of Physics  
The Lindblad master equation for an arbitrary quadratic system of n fermions is solved explicitly in terms of diagonalization of a 4n x 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 and the calculation of asymptotic relaxation rates in the far from equilibrium problem of heat and spin transport in a nearest neighbor Heisenberg XY spin 1/2 chain in a transverse
more » ... a transverse magnetic field.
doi:10.1088/1367-2630/10/4/043026 fatcat:oh46n7wxozdr7foywg2jpnoa7y