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arXiv · 0801.1257

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

Tomaz Prosen
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Abstract

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 magnetic field.

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Tomaz Prosen. 2008-12-04. Third quantization: a general method to solve master equations for quadratic open Fermi systems. https://doi.org/10.1088/1367-2630%2F10%2F4%2F043026

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