Quasi-Lie Brackets and the Breaking of Time-Translation Symmetry for Quantum Systems Embedded in Classical Baths
| Autor: | Antonino Messina, Gabriel Hanna, Roberto Grimaudo, Alessandro Sergi |
|---|---|
| Přispěvatelé: | Sergi, Alessandro, Hanna, Gabriel, Grimaudo, Roberto, Messina, Antonino |
| Rok vydání: | 2018 |
| Předmět: |
Hybrid quantum-classical system
Breaking of time-translation symmetry Classical spin dynamics Hybrid quantum-classical systems Langevin dynamics Nosé-Hoover dynamics Quantum-classical Liouville equation Quasi-lie brackets Computer Science (miscellaneous) Chemistry (miscellaneous) Mathematics (all) Physics and Astronomy (miscellaneous) General Mathematics Degrees of freedom (physics and chemistry) FOS: Physical sciences Nosé-Hoover dynamic 02 engineering and technology Quasi-lie bracket 01 natural sciences breaking of time-translation symmetry symbols.namesake Langevin dynamic Classical spin dynamic 0103 physical sciences 010306 general physics quantum-classical Liouville equation Physics Quantum Physics quasi-lie brackets lcsh:Mathematics Observable Statistical mechanics classical spin dynamics lcsh:QA1-939 021001 nanoscience & nanotechnology Action (physics) Nosé–Hoover dynamics Classical mechanics Geometric phase Phase space symbols hybrid quantum-classical systems Noether's theorem 0210 nano-technology Quantum Physics (quant-ph) |
| Zdroj: | Symmetry, Vol 10, Iss 10, p 518 (2018) |
| DOI: | 10.48550/arxiv.1810.07095 |
| Popis: | 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, or through quasi-Lie brackets augmented by dissipative terms. Quasi-Lie brackets possess the unique feature that, while conserving the energy (which the Noether theorem links to time-translation symmetry), they violate the time-translation symmetry of their algebra. This fact can be heuristically understood in terms of the dynamics of the open quantum subsystem. We then describe an example in which a quantum subsystem is embedded in a bath of classical spins, which are described by non-canonical coordinates. In this case, it has been shown that an off-diagonal open-bath geometric phase enters into the propagation of the quantum-classical dynamics. Next, we discuss how non-Hamiltonian dynamics may be employed to generate the constant-temperature evolution of phase space degrees of freedom coupled to the quantum subsystem. Constant-temperature dynamics may be generated by either a classical Langevin stochastic process or a Nosé–Hoover deterministic thermostat. These two approaches are not equivalent but have different advantages and drawbacks. In all cases, the calculation of the operator-valued quasi-probability function allows one to compute time-dependent statistical averages of observables. This may be accomplished in practice using a hybrid Molecular Dynamics/Monte Carlo algorithms, which we outline herein. |
| Databáze: | OpenAIRE |
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