Master equations govern the time evolution of a quantum system interacting
with an environment, and may be written in a variety of forms. Markovian master
equations, in particular, can be cast in the well-known Lindblad form. Any
time-local master equation, Markovian or non-Markovian, may in fact also be
written in Lindblad-like form. A diagonalisation procedure results in a unique,
and in this sense canonical, representation of the equation. This
representation may be used to fully characterize the non-Markovianity of the
time evolution. Recently, several different measures of non-Markovianity have
been presented. Their common underlying definition of non-Markovianity is
whether negative decoherence rates may appear in the Lindblad-like form of the
master equation. We therefore propose to use the negative decoherence rates
themselves, as they appear in the unique canonical form of the master equation,
as a primary measure to more completely characterize non-Markovianity. The
advantages of this are especially apparent when many decoherence channels are
present.
Description
Canonical form of master equations and characterization of
non-Markovianity
%0 Generic
%1 Andersson2010
%A Andersson, Erika
%A Cresser, James D.
%A Hall, Michael J. W.
%D 2010
%K Lindblad Markov mastereq
%T Canonical form of master equations and characterization of
non-Markovianity
%U http://arxiv.org/abs/1009.0845
%X Master equations govern the time evolution of a quantum system interacting
with an environment, and may be written in a variety of forms. Markovian master
equations, in particular, can be cast in the well-known Lindblad form. Any
time-local master equation, Markovian or non-Markovian, may in fact also be
written in Lindblad-like form. A diagonalisation procedure results in a unique,
and in this sense canonical, representation of the equation. This
representation may be used to fully characterize the non-Markovianity of the
time evolution. Recently, several different measures of non-Markovianity have
been presented. Their common underlying definition of non-Markovianity is
whether negative decoherence rates may appear in the Lindblad-like form of the
master equation. We therefore propose to use the negative decoherence rates
themselves, as they appear in the unique canonical form of the master equation,
as a primary measure to more completely characterize non-Markovianity. The
advantages of this are especially apparent when many decoherence channels are
present.
@misc{Andersson2010,
abstract = { Master equations govern the time evolution of a quantum system interacting
with an environment, and may be written in a variety of forms. Markovian master
equations, in particular, can be cast in the well-known Lindblad form. Any
time-local master equation, Markovian or non-Markovian, may in fact also be
written in Lindblad-like form. A diagonalisation procedure results in a unique,
and in this sense canonical, representation of the equation. This
representation may be used to fully characterize the non-Markovianity of the
time evolution. Recently, several different measures of non-Markovianity have
been presented. Their common underlying definition of non-Markovianity is
whether negative decoherence rates may appear in the Lindblad-like form of the
master equation. We therefore propose to use the negative decoherence rates
themselves, as they appear in the unique canonical form of the master equation,
as a primary measure to more completely characterize non-Markovianity. The
advantages of this are especially apparent when many decoherence channels are
present.
},
added-at = {2010-09-09T22:10:21.000+0200},
author = {Andersson, Erika and Cresser, James D. and Hall, Michael J. W.},
biburl = {https://www.bibsonomy.org/bibtex/2eef4c952bb54f7754ede93982d914a27/noswpat},
description = {Canonical form of master equations and characterization of
non-Markovianity},
interhash = {27917df1210e3629a1c4fd09b1c48db2},
intrahash = {eef4c952bb54f7754ede93982d914a27},
keywords = {Lindblad Markov mastereq},
note = {cite arxiv:1009.0845
Comment: 5 pages},
timestamp = {2010-09-09T22:10:21.000+0200},
title = {Canonical form of master equations and characterization of
non-Markovianity},
url = {http://arxiv.org/abs/1009.0845},
year = 2010
}