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

2008/01/31 by Tomaz Prosen · 3 citations
Physics and Astronomy · #quant-ph #cond-mat.stat-mech #nlin.SI

paper · pdf · doi:10.1088/1367-2630/10/4/043026

published as New J. Phys. 10, 043026 (2008) · 24 pages, with 8 eps figures - few minor corrections to the published version, e.g. anti-symmetrizing the matrix given by eq. (27)

arxiv created 2008/12/04 · arxiv updated 2009/12/01

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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