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arXiv:quant-ph/9810011 · Journal of Physics A Mathematical and General

Quantum phase space distributions in thermofield dynamics

S. Chaturvedi, Venkatraman Srinivasan, G. S. Agarwal

Published Jan 1, 1999• 34 citations
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Abstract

It is shown that the quantum phase space distributions corresponding to a density operator can be expressed, in thermofield dynamics, as overlaps between the state and `thermal' coherent states. The usefulness of this approach is brought out in the context of a master equation describing a nonlinear oscillator for which exact expressions for the quantum phase distributions for an arbitrary initial condition are derived.

DOI
10.1088/0305-4470/32/10/009

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It is shown that the quantum phase space distributions corresponding to a density operator can be expressed, in thermofield dynamics, as overlaps between the state and `thermal' coherent states. The usefulness of this approach is brought out in the context of a master equation describing a nonlinear oscillator for which exact expressions for the quantum phase distributions for an arbitrary initial condition are derived.
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We investigate the dynamics of a driven quantum field coupled to a finite-temperature reservoir. The corresponding master equation is solved using superoperator techniques, yielding an analytical expression for the density operator. To obtain a compact and physically transparent description of the dynamics, we adopt a phase-space representation based on the Husimi Q-function. For an initially coherent state, we derive a closed-form Gaussian expression for the Husimi Q-function whose stationary limit corresponds to a displaced thermal state. This approach also enables an analytical study of quantum-interference dynamics for an initial superposition of coherent states. Furthermore, we derive the corresponding Fokker–Planck equation for the Husimi Q-function and obtain closed-form expressions for relevant statistical quantities, including the mean photon number, the photon-number standard deviation, and the Mandel parameter. We also investigate the Wehrl and linear entropies, which quantify the loss of phase-space information and purity induced by the thermal environment. The framework provides a complete analytical characterization of the phase-space dynamics, photon statistics, and entropic properties of driven–dissipative quantum fields while avoiding the explicit manipulation of the density operator.
We derive <η| representation of density matrices ρ for radiation fields, where <η| is the newly established coherent thermal state [H.-Y. Fan and Y. Fan, Phys. Lett.A246, 242 (1998)] in thermal field dynamics. We then apply <η|ρ> to calculate thermal averages and develop the theory for the quantum phase space distributions. We also study the quantum master equations in the <η| representation and find it has similar evolving property to the coherent representation of a pure state.