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

K. Kobayashi, Y. 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

Keywords

  • Nelson's stochastic mechanics
  • Thermo field dynamics

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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