TY - JOUR

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

AU - Kobayashi, K.

AU - Yamanaka, Y.

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

SN - 0375-9601

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

IS - 37

ER -