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Deutsche Physikalische Gessellschaft IOP Institute of Physics

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

Tomaž Prosen

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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 magnetic field.


PACS

05.30.Fk Fermion systems and electron gas

03.65.Fd Algebraic methods

75.10.Jm Quantized spin models

03.65.Yz Decoherence; open systems; quantum statistical methods

Subjects

Quantum gases, liquids and solids

Condensed matter: electrical, magnetic and optical

Quantum information and quantum mechanics

Statistical physics and nonlinear systems

Dates

Issue 4 (April 2008)

Received 7 January 2008

Published 15 April 2008



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