### Abstract

We consider a quantum particle in thermal equilibrium with any quantum system in a finite volume under some conditions. For the Heisenberg operator of the momentum operator of the quantum particle, we show that, on a partial *-algebra, the Heisenberg operator satisfies a quantum Langevin equation, which is similar to the work of Ford et al. [G. W. Ford, J. T. Lewis, and R. F. O'Connell, Phys. Rev. A 37, 4419 (1988)]. Through the Langevin equation, we show general and mathematical properties between the canonical correlation and the independent-oscillator model.

Original language | English |
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Pages (from-to) | 121-146 |

Number of pages | 26 |

Journal | Journal of Mathematical Physics |

Volume | 37 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 1996 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

**General properties between the canonical correlation and the independent-oscillator model on a partial *-algebra.** / Hirokawa, Masao.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - General properties between the canonical correlation and the independent-oscillator model on a partial *-algebra

AU - Hirokawa, Masao

PY - 1996/1/1

Y1 - 1996/1/1

N2 - We consider a quantum particle in thermal equilibrium with any quantum system in a finite volume under some conditions. For the Heisenberg operator of the momentum operator of the quantum particle, we show that, on a partial *-algebra, the Heisenberg operator satisfies a quantum Langevin equation, which is similar to the work of Ford et al. [G. W. Ford, J. T. Lewis, and R. F. O'Connell, Phys. Rev. A 37, 4419 (1988)]. Through the Langevin equation, we show general and mathematical properties between the canonical correlation and the independent-oscillator model.

AB - We consider a quantum particle in thermal equilibrium with any quantum system in a finite volume under some conditions. For the Heisenberg operator of the momentum operator of the quantum particle, we show that, on a partial *-algebra, the Heisenberg operator satisfies a quantum Langevin equation, which is similar to the work of Ford et al. [G. W. Ford, J. T. Lewis, and R. F. O'Connell, Phys. Rev. A 37, 4419 (1988)]. Through the Langevin equation, we show general and mathematical properties between the canonical correlation and the independent-oscillator model.

UR - http://www.scopus.com/inward/record.url?scp=0030553166&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030553166&partnerID=8YFLogxK

U2 - 10.1063/1.531379

DO - 10.1063/1.531379

M3 - Article

AN - SCOPUS:0030553166

VL - 37

SP - 121

EP - 146

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 1

ER -