Evolution of the reduced density matrix: a generalized projection-operator approach

✍ Scribed by Irena Knezevic; David K. Ferry

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 57 KB
• Volume: 63
• Category: Article
• ISSN: 0167-9317
• DOI: 10.1016/s0167-9317(02)00610-x

✦ Synopsis

A convolutionless equation of motion for the reduced density matrix of a system coupled to its environment, where the system 1 environment is closed, may be obtained using a projection-operator technique. We show that, when both the system and the environment Hilbert spaces are finite-dimensional, it is possible to eliminate the need for the partial trace over the environment states by constructing a simple and transparent basis-induced isomorphism between the system Liouville space and the unit-eigenspace of a special projection operator. Consequently, an equation of motion for the reduced density matrix is derived by a mere basis transformation within the system 1 environment Hilbert space and the explicit dependence of the reduced density matrix on the matrix elements of the Hamiltonian is uncovered, in a form well suited for numerical calculation.