Variational procedure for time-dependent processes.
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 Navier-Stokes equations of hydrodynamics, transport theory, etc. It recaptures the least dissipation function condition of Rayleigh-Onsager and in practical applications is flexible. The variational proposal is tested on a two-level system interacting that is subject, in one instance, to an interaction with a single oscillator and, in another, that evolves in a dissipative mode.
Department of Physics and Applied Mathematics, Soreq NRC, Yavne 81800, Israel. englman@vms.huji.ac.il
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Englman
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Yahalom
D007700:Kinetics; D015233:Models, Statistical; D009991:Oscillometry; D010825:Physics / Q000379:methods*; D013598:Systems Theory; D013997:Time Factors; D014867:Water / Q000737:chemistry
D014867:Water