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Quasi-Lie Brackets and the Breaking of Time-Translation Symmetry for Quantum Systems Embedded in Classical Baths

2018; Multidisciplinary Digital Publishing Institute; Volume: 10; Issue: 10 Linguagem: Inglês

10.3390/sym10100518

2073-8994

Alessandro Sergi, Gabriel Hanna, Roberto Grimaudo, A. Messina,

Quantum chaos and dynamical systems

Many open quantum systems encountered in both natural and synthetic situations are embedded in classical-like baths. Often, the bath degrees of freedom may be represented in terms of canonically conjugate coordinates, but in some cases they may require a non-canonical or non-Hamiltonian representation. Herein, we review an approach to the dynamics and statistical mechanics of quantum subsystems embedded in either non-canonical or non-Hamiltonian classical-like baths which is based on operator-valued quasi-probability functions. These functions typically evolve through the action of quasi-Lie brackets and their associated Quantum-Classical Liouville Equations.