Premium
Analytical Results for the Boltzmann Equation
Author(s) -
Toepffer C.,
Cercignani C.
Publication year - 1997
Publication title -
contributions to plasma physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.531
H-Index - 47
eISSN - 1521-3986
pISSN - 0863-1042
DOI - 10.1002/ctpp.2150370217
Subject(s) - boltzmann equation , physics , diffusion equation , momentum (technical analysis) , domain (mathematical analysis) , distribution function , relaxation (psychology) , diffusion , function (biology) , boltzmann constant , constant (computer programming) , statistical physics , mathematical analysis , mathematics , quantum mechanics , programming language , computer science , economics , biology , service (business) , psychology , social psychology , economy , finance , evolutionary biology
The manifold of solutions of the Boltzmann equation in the relaxation time approximation for particles in a constant field is obtained in closed form. The Green's function for the infinite domain and the moments of the probability distribution are calculated explicitly. A generalized drift‐diffusion equation with local temperatures is obtained by matching moments. The Green's function for the finite domain is derived for vanishing equilibrium temperature β → ∞ in a ballistic regime of large momentum gain between collisions.