Talk:Lindbladian

Might be nice to add some discussion comparing with Fermi's golden rule -- Jheald 18:08, 10 November 2005 (UTC)

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Might be nice to add something about Lindblad himself. Or maybe create a page about him? --Tiglet 15:08, 13 July 2006 (UTC)

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

== Scaling factor for "h" matrix The master equation has been modified by reordering the terms so that the general expression and L(C) are compatible, and more importantly, "h" was rescaled by a factor of 1/2 (so we have A{\rho}A^\dagger - (1/2) (....) and not 2A{\rho}A^\dagger - (...)). This results in dissipation proportional to exp(-t/h) when applied to simple test case, such as a qubit coupled with a dissipation operator of "a" to the environment. If you keep the factor of 2 in the M.E., it finds its way into the exponent, which is not what one would expect. — Preceding unsigned comment added by Shai mach (talk • contribs) 16:52, 19 September 2012 (UTC)

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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)

Restrictions on Lindblad operators

The Lindblad eq. is the most general form time evolution for a density matrix meeting certain conditions (markovian, trace preserving, etc). In order to meet these conditions, what are the restrictions on the Lindblad operators? I think they have to be positive, but I also think there might be some sort of norm requirement. Anyone have a source? Njerseyguy (talk) 20:10, 10 December 2009 (UTC)

Nevermind, I figured it out and added to the article. Njerseyguy (talk) 21:14, 10 December 2009 (UTC)

The article says the h coefficients have to be positive. However, in the example the h coefficients are negative. Is there a mistake here or am I just missing something? (Syberspot (talk) 15:48, 13 November 2013 (UTC))

Derivation and limitations of the Lindblad equation

The current version of the article lacks the derivation of the Lindblad equation from other master equations (for example from a Redfield-like equation) and lacks any discussion of the defects of the Lindblad equation (resulting in unphysical behavior) and of the modifications done by Lindblad to correct those deficiencies.

I will write such a material in brief. What do you prefer one or two new sections? JuanR (talk) 12:20, 4 February 2011 (UTC)

Scaling factor for "h" matrix

The master equation has been modified by reordering the terms so that the general expression and L(C) are compatible, and more importantly, "h" was rescaled by a factor of 1/2 (so we have A{\rho}A^\dagger - (1/2) (....) and not 2A{\rho}A^\dagger - (...)). This results in dissipation proportional to exp(-t/h) when applied to simple test case, such as a qubit coupled with a dissipation operator of "a" to the environment. If you keep the factor of 2 in the M.E., it finds its way into the exponent, which is not what one would expect. Also, this is now compatible with the derivation in the "diagonalization" section — Preceding unsigned comment added by Shai mach (talk • contribs) 16:54, 19 September 2012 (UTC)

In the opening paragraph: Lindblad is "more general" than Schrödinger equation - questionable.

I am not an expert so I will not edit the article myself, but the assertion that the Lindblad equation is a generalization of the Schrödinger equation seems more false than true, given that it is derived from the Schrödinger equation on a joint system. For someone looking for an overview of the subject, the opening paragraph in its current form could be somewhat misleading. — Preceding unsigned comment added by Doublefelix921 (talk • contribs) 17:15, 7 June 2017 (UTC)

This may be confusing, and I agree that the wording here needs to be changed, but what you suggest is not quite the case. Take a more particular case of the Linddblad equation when no outside environment is acting on the system: the Von Neumann equation. You can in a sense "derive" the Von Neuman equation from the Schrodinger equation, but you can just as easily "derive" the Schrodinger equation from the Von Neumann equation, it all depends on wheither you take the density matrix or the wavefunction to be more fundamental, which is entirely subjective.

What is meant by generalization is not based on a direction of derivation, but which equation takes into account the most number of situations. In this way, Newton's equation of motion is more general than the equation for the trajectory of a cannon ball, which can be further generalized taking into account relativistic effects etc. Pjbeierle (talk) 10:25, 19 July 2018 (UTC)