Extension of Nelson's Stochastic Quantization to Thermal Situation in Thermo Field Dynamics

Details Extension of Nelson's Stochastic Quantization to Thermal Situation in Thermo Field Dynamics Extension of Nelson's Stochastic Quantization to Thermal Situation in Thermo Field Dynamics

2010-07-21

arxiv.org/abs/1007.3603v1

Physics

Quantum Physics

15 page, 2 figures

Scientific paper

We present an extension of Nelson's stochastic quantum mechanics to thermal situation. Utilizing the formulation of Thermo Field Dynamics (TFD) with doubled degree of freedom (non-tilde and tilde), we set up the stochastic equations and Nelson-Newton equations for tilde and non-tilde particles which reproduce the TFD-type Schr\"odinger equation, equivalent to the Liouville-von Neumann equation. In our formalism, the drift terms of the stochastic equations have the temperature dependence and the thermal fluctuation is induced through the quantum correlations of the non-tilde and tilde particles. As an example of application of our formalism, the position-momentum uncertainty relation at finite temperature is visualized.

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