### Abstract

We present an extension of Nelson's stochastic quantum mechanics to finite temperature. Utilizing the formulation of Thermo Field Dynamics (TFD), we can show that Ito's stochastic equations for tilde and non-tilde particle positions reproduce the TFD-type Schrödinger equation which is equivalent to the Liouville-von Neumann equation. In our formalism, the drift terms in the Ito's stochastic equation have the temperature dependence and the thermal fluctuation is induced through the correlation of the non-tilde and tilde particles. We show that our formalism satisfies the position-momentum uncertainty relation at finite temperature.

Original language | English |
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Pages (from-to) | 3243-3249 |

Number of pages | 7 |

Journal | Physics Letters, Section A: General, Atomic and Solid State Physics |

Volume | 375 |

Issue number | 37 |

DOIs | |

Publication status | Published - 2011 Aug 29 |

### Fingerprint

### Keywords

- Nelson's stochastic mechanics
- Thermo field dynamics

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

**Extension of Nelson's stochastic quantization to finite temperature using thermo field dynamics.** / Kobayashi, K.; Yamanaka, Yoshiya.

Research output: Contribution to journal › Article

*Physics Letters, Section A: General, Atomic and Solid State Physics*, vol. 375, no. 37, pp. 3243-3249. https://doi.org/10.1016/j.physleta.2011.07.020

}

TY - JOUR

T1 - Extension of Nelson's stochastic quantization to finite temperature using thermo field dynamics

AU - Kobayashi, K.

AU - Yamanaka, Yoshiya

PY - 2011/8/29

Y1 - 2011/8/29

N2 - We present an extension of Nelson's stochastic quantum mechanics to finite temperature. Utilizing the formulation of Thermo Field Dynamics (TFD), we can show that Ito's stochastic equations for tilde and non-tilde particle positions reproduce the TFD-type Schrödinger equation which is equivalent to the Liouville-von Neumann equation. In our formalism, the drift terms in the Ito's stochastic equation have the temperature dependence and the thermal fluctuation is induced through the correlation of the non-tilde and tilde particles. We show that our formalism satisfies the position-momentum uncertainty relation at finite temperature.

AB - We present an extension of Nelson's stochastic quantum mechanics to finite temperature. Utilizing the formulation of Thermo Field Dynamics (TFD), we can show that Ito's stochastic equations for tilde and non-tilde particle positions reproduce the TFD-type Schrödinger equation which is equivalent to the Liouville-von Neumann equation. In our formalism, the drift terms in the Ito's stochastic equation have the temperature dependence and the thermal fluctuation is induced through the correlation of the non-tilde and tilde particles. We show that our formalism satisfies the position-momentum uncertainty relation at finite temperature.

KW - Nelson's stochastic mechanics

KW - Thermo field dynamics

UR - http://www.scopus.com/inward/record.url?scp=80051790165&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80051790165&partnerID=8YFLogxK

U2 - 10.1016/j.physleta.2011.07.020

DO - 10.1016/j.physleta.2011.07.020

M3 - Article

AN - SCOPUS:80051790165

VL - 375

SP - 3243

EP - 3249

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 37

ER -