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.
|Number of pages||7|
|Journal||Physics Letters, Section A: General, Atomic and Solid State Physics|
|Publication status||Published - 2011 Aug 29|
- Nelson's stochastic mechanics
- Thermo field dynamics
ASJC Scopus subject areas
- Physics and Astronomy(all)