𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Variation principle for the time dependence of density operators and its relation to linear decoupling procedures for propagators

✍ Scribed by Esper Dalgaard

Publisher
John Wiley and Sons
Year
1980
Tongue
English
Weight
500 KB
Volume
17
Category
Article
ISSN
0020-7608

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

A modified form of Frenkel's time‐dependent variation principle, suggested by McLachlan for state vectors, is employed to discuss the optimal time evolution of a density operator ρ(t). An ansatz is made for this operator such that i(__d__ρ/dt) = [S, ρ], where S(t) is a linear combination of operators belonging to a particular manifold of “basis operators.” The expansion coefficients are required to minimize the error Tr{[S – H, ρ]† [S – H, ρ]}. Linear response functions corresponding to the variationally determined density operator are compared to those derived by means of linear decoupling procedures for propagators based on the same operator manifold. The two approximation schemes are not equivalent, in general, and several consistency requirements must be fulfilled before it can be ascertained that a given linear decoupling procedure corresponds to an optimal time development of the density operator in the sense of McLachlan. Finally, the general applicability of the suggested variation principle is discussed.

📜 SIMILAR VOLUMES

Time-dependent variational principle for
Time-dependent variational principle for nonlinear Hamiltonians and its application to molecules in the liquid phase
✍ R. Cammi; J. Tomasi 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 784 KB

The formulation of the time-dependent Frenkel variational principle for Hamiltonians containing a term depending on the wave function is here considered. Starting from the basic principles, it is shown that it requires the introduction of a related functional, 3', which, for the systems we are consi

The method of weighted residuals and its
The method of weighted residuals and its relation to certain variational principles for the analysis of transport processes
✍ B.A. Finlayson; L.E. Scriven 📂 Article 📅 1965 🏛 Elsevier Science 🌐 English ⚖ 913 KB

The approximation scheme entitled method of weighted residuals is extended to systems of differential equations and vector differential equations. The variational principles proposed by ROSEN, CHAMBERS and BIOT for unsteady-state heat transport are all shown to he applications of the method of weigh

Time-dependent density operator in the r
Time-dependent density operator in the random impulse approximation: I. Connections with the “generalized sudden approximation” for photoionization and electron impact ionization; and II. Relevance to reduced density operators, particle–hole matrices, and propagators for the initial state
✍ Everett G. Larson 📂 Article 📅 1983 🏛 John Wiley and Sons 🌐 English ⚖ 803 KB

## Abstract A density operator analysis is made of the particle‐ejection (e.g., photoionization) problem in the “generalized sudden approximation” for the case in which the ejected particle is detected but its dynamical properties are not observed. It is shown that the resultant statistical density