Variational procedure for timedependent processes
Abstract
A simple variational Lagrangian is proposed for the time development of an arbitrary density matrix, employing the “factorization” of the density. Only the “kinetic energy” appears in the Lagrangian. The formalism applies to pure and mixed state cases, the NavierStokes equations of hydrodynamics, transport theory, etc. It recaptures the least dissipation function condition of RayleighOnsager and in practical applications is flexible. The variational proposal is tested on a twolevel system interacting that is subject, in one instance, to an interaction with a single oscillator and, in another, that evolves in a dissipative mode.
 Publication:

Physical Review E
 Pub Date:
 February 2004
 DOI:
 10.1103/PhysRevE.69.026120
 arXiv:
 arXiv:physics/0406123
 Bibcode:
 2004PhRvE..69b6120E
 Keywords:

 02.50.r;
 82.20.w;
 05.70.Ln;
 Probability theory stochastic processes and statistics;
 Chemical kinetics and dynamics;
 Nonequilibrium and irreversible thermodynamics;
 Fluid Dynamics;
 General Physics
 EPrint:
 25 pages, 4 figures