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.
|ジャーナル||Physics Letters, Section A: General, Atomic and Solid State Physics|
|出版物ステータス||Published - 2011 8 29|
ASJC Scopus subject areas
- Physics and Astronomy(all)