## Abstract

We study the time evolution of the reduced density matrix of a system of spin-1/2 particles interacting with an environment of spin-1/2 particles. The initial state of the composite system is taken to be a product state of a pure state of the system and a pure state of the environment. The latter pure state is prepared such that it represents the environment at a given finite temperature in the canonical ensemble. The state of the composite system evolves according to the time-dependent Schrodinger equation, the interaction creating entanglement between the system and the environment. It is shown that independent of the strength of the interaction and the initial temperature of the environment, all the eigenvalues of the reduced density matrix converge to their stationary values, implying that also the entropy of the system relaxes to a stationary value. We demonstrate that the difference between the canonical density matrix and the reduced density matrix in the stationary state increases as the initial temperature of the environment decreases. As our numerical simulations are necessarily restricted to a modest number of spin-1/2 particles (

Original language | English |
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Article number | 124005 |

Pages (from-to) | 124005-1-124005-10 |

Number of pages | 10 |

Journal | Journal of the Physical Society of Japan |

Volume | 79 |

Issue number | 12 |

DOIs | |

Publication status | Published - Dec-2010 |

## Keywords

- quantum statistical mechanics
- canonical ensemble
- time-dependent Schrodinger equation
- thermalization
- decoherence
- DEPENDENT SCHRODINGER-EQUATION
- CANONICAL DISTRIBUTION
- STATISTICAL-MECHANICS
- QUANTUM-SYSTEMS
- HILBERT-SPACE
- ENVIRONMENTS
- DIFFUSION
- ELECTRONS