Third quantization: a general method to solve master equations for quadratic open Fermi systems
Quantum Physics
2009-11-13 v3 Statistical Mechanics
Exactly Solvable and Integrable Systems
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.
Cite
@article{arxiv.0801.1257,
title = {Third quantization: a general method to solve master equations for quadratic open Fermi systems},
author = {Tomaz Prosen},
journal= {arXiv preprint arXiv:0801.1257},
year = {2009}
}
Comments
24 pages, with 8 eps figures - few minor corrections to the published version, e.g. anti-symmetrizing the matrix given by eq. (27)