| Popis: |
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. |
