A HILBERT SPACE DERIVATION OF THE CLASSICAL GENERALIZED MASTER EQUATION,

Abstract

The ket-vector notation of Dirac is used to formulate the classical Liouville equation in a Hilbert space of functions spanned by the eigenkets of the Liouville operator. The formalism applies to finite as well as infinte systems. The solutions of the inhomogeneous Liouville equation is considered where the inhomogeneity is taken as the perturbation. The Hilbert space formalism allows the introduction of projection operators, and the derivation of the generalized master equations without perturbation theory. In the weak coupling limit this is shown to reduce to the Brout-Prigogine equation. A thermodynamic interpretation is given to spacially inhomogeneous terms in the equation. (Author)

Document Details

Document Type
Technical Report
Publication Date
Mar 29, 1967
Accession Number
AD0651428

Entities

People

  • B. Leaf
  • W. C. Schieve

Organizations

  • Naval Radiological Defense Laboratory

Tags

DTIC Thesaurus Topics

  • Couplings
  • Equations
  • Hilbert Space
  • Liouville Equation
  • Mathematical Analysis
  • Mathematics
  • Notation
  • Perturbation Theory
  • Perturbations

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis

Technology Areas

  • Space