Quasi-Lie Brackets and the Breaking of Time-Translation Symmetry for Quantum Systems Embedded in Classical Baths
Abstract
:1. Introduction
2. Quasi-Lie Brackets and Hybrid Quantum-Classical Systems
2.1. Derivation of the QCLE through a Partial Wigner Transform
2.2. Integration Algorithm
3. Classical Spin Baths
4. Stochastic Classical Baths
5. Non-Hamiltonian Dynamics in Thermal Baths
Nosé–Hoover Chain Thermal Baths
6. Conclusions and Perspectives
Author Contributions
Funding
Conflicts of Interest
Abbreviations
DOF | Degrees of Freedom |
QCLE | Quantum-Classical Liouville Equation |
QLE | Quantum Liouville Equation |
SSTP | Sequential Short-Time Propagation |
Appendix A. Representation in the Adiabatic Basis
Appendix B. The Nosè–Hoover Thermostat
Appendix C. Stationary Operator-Valued Nosé Quasi-Probability Function
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Sergi, A.; Hanna, G.; Grimaudo, R.; Messina, A. Quasi-Lie Brackets and the Breaking of Time-Translation Symmetry for Quantum Systems Embedded in Classical Baths. Symmetry 2018, 10, 518. https://0-doi-org.brum.beds.ac.uk/10.3390/sym10100518
Sergi A, Hanna G, Grimaudo R, Messina A. Quasi-Lie Brackets and the Breaking of Time-Translation Symmetry for Quantum Systems Embedded in Classical Baths. Symmetry. 2018; 10(10):518. https://0-doi-org.brum.beds.ac.uk/10.3390/sym10100518
Chicago/Turabian StyleSergi, Alessandro, Gabriel Hanna, Roberto Grimaudo, and Antonino Messina. 2018. "Quasi-Lie Brackets and the Breaking of Time-Translation Symmetry for Quantum Systems Embedded in Classical Baths" Symmetry 10, no. 10: 518. https://0-doi-org.brum.beds.ac.uk/10.3390/sym10100518