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

Irena Knezevic, David K. Ferry

Research output: Contribution to journalArticle


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 languageEnglish (US)
Pages (from-to)105-108
Number of pages4
JournalMicroelectronic Engineering
Issue number1-3
StatePublished - Aug 1 2002



  • 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

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