What is the Quantum Boltzmann equation and what does it describe? I think it describes the propagation of electrons and photons but I am not sure.
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5I've heard several things being called "quantum Boltzmann"? Do you mean the Fokker-Planck equation used in semiconductors? Do you mean one of the non-equilibrium evolution equations in non-equilibrium QFT? There will only be a good answer to this if you tell us where you encountered it, and what is done with it. – ACuriousMind Jul 28 '14 at 20:40
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Quite honestly, I am not sure. I am trying to find an equation that accurately characterizes the movement of electrons and photons and came across the term "quantum Boltzmann equation." But I didn't know that "quantum Boltzmann" referred to multiple different things, thanks for letting me know! – user56240 Jul 28 '14 at 21:03
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@ACuriousMind +1 for your comment. I checked on the web, and I found this reference: http://arxiv.org/abs/1011.3849 where it is stated that The equation for the time evolution of the distribution function of a quantum many-body system is variously called a quantum Boltzmann equation, a master equation (when the states are discrete), or a Fokker- Planck equation. Is that what you were referring to, user-xxx ? – FraSchelle Jul 30 '14 at 09:09
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@user56240 Also, when you will modify your question, think about adding the tag statistical mechanics, since your question is about that, too. Well, as far as I understood, it is not really about particle physics also... – FraSchelle Jul 30 '14 at 09:15
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Quantum Boltzmann/kinetic equation usually refers to the formalism pioneered by Kadanoff and Baym, which is a quasi-classical theory describing kinetic phenomena in metals - easier than the full Green's function approach, but more rigorous than the popular kinetic/Boltzmann equation treatment that is ubiquitous in many books on solid state physics.
Quantum field-theoretical methods in transport theory of metals by Rammer and Smith is probably the best place to start - the Bolttzmann equation is derived here coherently from the Green's function formalism, different levels of quantum corrections are calculated, and collision integrals for various types of scattering processes are treated in details.
For a more intuitive treatment see Quantum Kinetics in Transport and Optics of Semiconductors by Haug and Jauho.
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Another useful reference (but more for the foundations) is the review The Quantum linear Boltzmann equation but note the "linear" (i.e. no binary collisions, only collisions with a background). – Quillo Oct 03 '23 at 08:57