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

@article{Prosen2008ThirdQA, title={Third quantization: a general method to solve master equations for quadratic open Fermi systems}, author={Toma{\vz} Prosen}, journal={New Journal of Physics}, year={2008}, volume={10}, pages={043026} }

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…

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