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

K. Kobayashi, Yoshiya Yamanaka

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    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 languageEnglish
    Pages (from-to)3243-3249
    Number of pages7
    JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
    Volume375
    Issue number37
    DOIs
    Publication statusPublished - 2011 Aug 29

    Fingerprint

    formalism
    temperature
    quantum mechanics
    momentum
    formulations
    temperature dependence

    Keywords

    • Nelson's stochastic mechanics
    • Thermo field dynamics

    ASJC Scopus subject areas

    • Physics and Astronomy(all)

    Cite this

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    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 Schr{\"o}dinger 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.",
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    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.

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    KW - Thermo field dynamics

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