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
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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 -