Talk:Lindblad equation
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Might be nice to add some discussion comparing with Fermi's golden rule -- Jheald 18:08, 10 November 2005 (UTC)
Might be nice to add something about Lindblad himself. Or maybe create a page about him? --Tiglet 15:08, 13 July 2006 (UTC)
[edit] Most General Master Equation?
Finite temperature dissipative environments, and environments in general are non-Markovian. I was under the impression that the Linbald Equation is Markovian only. Which for dissipative environments often means high temperature only. CHF
Additionally there are open systems that simply do not have master equations for their reduced density matrix. CHF
-- A Master equation, by definition is Markovian. If the bath correlation functions do not decay to zero fast enough (regardless of Temperature) a master equation is indeed inappropriate. People do use master equations that are not of Linblad form (i.e. Redfield equation) but these are not "allowed by quantum mechanics", as they don't preserve the positivity of the density matrix (or at least are not completely positive.)
Cederal 12:58, 1 April 2007 (UTC)
If the master equation contains coefficients that involve integrals over the history of the system, then the master equation is still Markovian? And there are master equations that are allowed by quatum mechanics but not of the Lindblad form. For instance, the convolutionless master equation of Strunz and Yu arXiv:quant-ph/0312103. A more well known, but less general example would be the HPZ (Hu Paz Zhang) master equation for quantum brownian motion, phys rev D 45, 2843 (1992). Neither of these are in Lindblad form but they are both valid master equations for reduced density matrices. CHF
No, a Master equation that contains the history of the system is certainly not Markovian. I stand corrected as to the definition of the Master equation (the title of the cited article contains the phrase "...Non Markovian Master equations..."). The Lindblad form describes the most general Markovian Master equation that preserves complete positivity and the trace of the density matrix for any positive initial density matrix. There are however other Markovian Master equations that are 'allowed by quantum mechanics', but only for some initial conditions (i.e. the Redfield equation).
Cederal 12:32, 17 April 2007 (UTC)
