Thermodynamics of quantum dissipative many-body systems

We consider quantum nonlinear many-body systems with dissipation described within the Caldeira-Leggett model, i.e., by a nonlocal action in the path i ntegral for the density matrix. Approximate classical-like formulas for the rmodynamic 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), equiv alent to the variational approach by the Feynman-Jensen inequality with a s uitable quadratic nonlocal trial action. A tow-coupling approximation permi ts us to get manageable PQSCHA expressions for quantum thermal averages wit h a classical Boltzmann factor involving an effective potential and an inne r Gaussian average that describes the fluctuations originating from the int erplay of quanticity and dissipation. The application of the PQSCHA to a qu antum phi(4) chain with Drude-like dissipation shows nontrivial effects of dissipation, depending upon its strength and bandwidth. [S1063-651X(99)0870 7-3].