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Thermodynamics of quantum dissipative many-body systems

A. Cuccoli·A. Fubini·V. Tognetti·R. Vaia
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Abstract

We consider quantum nonlinear many-body systems with dissipation described within the Caldeira-Leggett model, i.e., by a nonlocal action in the path integral for the density matrix. Approximate classical-like formulas for thermodynamic quantities are derived for the case of many degrees of freedom, with general kinetic and dissipative quadratic forms. The underlying scheme is the pure-quantum self-consistent harmonic approximation (PQSCHA), equivalent to the variational approach by the Feynman-Jensen inequality with a suitable quadratic nonlocal trial action. A low-coupling approximation permits to get manageable PQSCHA expressions for quantum thermal averages with a classical Boltzmann factor involving an effective potential and an inner Gaussian average that describes the fluctuations originating from the interplay of quanticity and dissipation. The application of the PQSCHA to a quantum phi4-chain with Drude-like dissipation shows nontrivial effects of dissipation, depending upon its strength and bandwidth.

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A. Cuccoli, A. Fubini, V. Tognetti, R. Vaia. 1999-05-26. Thermodynamics of quantum dissipative many-body systems. https://doi.org/10.1103/physreve.60.231

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