### 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 1 2002 |

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### 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

### Cite this

*Microelectronic Engineering*,

*63*(1-3), 105-108. https://doi.org/10.1016/S0167-9317(02)00610-X