Possibility of direct solution of the classical Liouville equation for inelastic molecular collisions; the reduced Liouville equation

Journal Article · Sun Jan 01 04:00:00 EST 1978 · J. Chem. Phys.; (United States)

DOI:https://doi.org/10.1063/1.435496· OSTI ID:5235548

Miller, W H; Skuse, B M

Starting with the ordinary classical Liouville equation for the time evolution of phase space distribution functions, total energy conservation is used to obtain a reduced Liouville equation which determines the steady-state (i.e., time independent) reduced distribution function on the ''energy shell'' in phase space. Boundary conditions which correspond to time-independent scattering theory are easily imposed, and one sees clearly how to extract the time-independent transition probability matrix for a given total energy; this is the classical analog of the time-independent on-shell S matrix of quantum scattering theory. The reduced Liouville equation is of a form that is amenable to direct numerical solution, and ways for approaching this are described. A particular approximate version of the reduced Liouville equation is seen to be equivalent to a recently proposed stochastic model.

• Research Organization: Department of Chemistry and Materials and Molecular Research Division of the Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720
• OSTI ID: 5235548
• Journal Information: J. Chem. Phys.; (United States), Journal Name: J. Chem. Phys.; (United States) Vol. 68:1; ISSN JCPSA
• Country of Publication: United States
• Language: English

Related Subjects

640304* -- Atomic
Molecular & Chemical Physics-- Collision Phenomena
74 ATOMIC AND MOLECULAR PHYSICS
BOLTZMANN-VLASOV EQUATION
COLLISIONS
DIFFERENTIAL EQUATIONS
DISTRIBUTION FUNCTIONS
EQUATIONS
INELASTIC SCATTERING
LIOUVILLE THEOREM
MATHEMATICAL SPACE
MECHANICS
MOLECULE COLLISIONS
PHASE SPACE
SCATTERING
SPACE
STATISTICAL MECHANICS