Abstract
A convolutionless equation of motion for the reduced density matrix of a system coupled to its environment, where the system + 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 + 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.
Original language | English (US) |
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Pages (from-to) | 105-108 |
Number of pages | 4 |
Journal | Microelectronic Engineering |
Volume | 63 |
Issue number | 1-3 |
DOIs | |
State | Published - Aug 2002 |
Keywords
- Density matrix
- Memory effects
- Quantum Liouville equation
- Time-convolutionless equation
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Atomic and Molecular Physics, and Optics
- Condensed Matter Physics
- Surfaces, Coatings and Films
- Electrical and Electronic Engineering