Boltzmann Transport Equation


by go quantum!
Tags: boltzmann, equation, transport
go quantum!
go quantum! is offline
#1
May19-11, 06:21 AM
P: 54
Hello. Do you know any textbook about Statistical Mechanics that discusses Boltzmann Transport Equation? It is not discussed in the textbooks that I know.

Thank you.
Phys.Org News Partner Physics news on Phys.org
Information storage for the next generation of plastic computers
Scientists capture ultrafast snapshots of light-driven superconductivity
Progress in the fight against quantum dissipation
Andy Resnick
Andy Resnick is offline
#2
May19-11, 09:08 AM
Sci Advisor
P: 5,468
http://en.wikipedia.org/wiki/Boltzmann_equation

It looks like a specific case of the Reynolds transport equation, but it also appears related to "detailed balance", the Langevin model, the Smoluchowski equation, the Fokker-Planck equation...

The context seems to be kinetic theory and correlation functions- I found brief discussions in Boon and Yip's "Molecular Hydrodynamics", and additional material in Chaikin and Lubensky's "Principles of Condensed Matter Physics" and Brenner and Edwards "Macrotransport Processes".
dextercioby
dextercioby is offline
#3
May19-11, 09:14 AM
Sci Advisor
HW Helper
P: 11,863
Landau & Lifschitz' <Physical Kinetics> and R. Balescu's <Nonequilibrium Statistical Mechanics> are sources on this issue. Of course, basically any textbook on nonequlibrium statistical mechanics discusses the BBGKY hierarchy and Boltzmann's equation.

vanhees71
vanhees71 is offline
#4
May19-11, 02:17 PM
Sci Advisor
Thanks
P: 2,132

Boltzmann Transport Equation


One of the best books on the subject is

L. Kadanoff, G. Baym, Quantum Statistical Mechanics

An original paper, which however has textbook quality and uses the Schwinger-Keldysh real-time contour formulation of non-relativistic off-equilibrium quantum field theory is the publication of Pawel Danielevic's PhD-Thesis:

Danielewicz, P.: Quantum Theory of Nonequilibrium Processes. 1, Ann. Phys. 152, 239, 1984

For the relativistic case and with extensions to off-shell transport, see the lecture notes by Wolfgang Cassing

Cassing, W.: From Kadanoff-Baym dynamics to off-shell parton transport, Eur. Phys. J. ST 168, 387, 2009

For a more general approach also for the relativistic case:

S. R. de Groot, W. A. van Leeuwen, Ch. G. van Weert, Relativistic kinetic theory


Register to reply

Related Discussions
scattering in Boltzmann transport equation Atomic, Solid State, Comp. Physics 0
the boltzmann transport equation double integral High Energy, Nuclear, Particle Physics 1
Boltzmann-Charge transport for Traveling-wave Classical Physics 0
Know of an open source Boltzmann solver for photon transport? Nuclear Engineering 1
Boltzmann transport equation General Physics 6