### Abstract

Lingua originale | English |
---|---|

pagine (da-a) | 518- |

Numero di pagine | 28 |

Rivista | Symmetry |

Volume | 10 |

Stato di pubblicazione | Published - 2018 |

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### All Science Journal Classification (ASJC) codes

- Computer Science (miscellaneous)
- Chemistry (miscellaneous)
- Mathematics(all)
- Physics and Astronomy (miscellaneous)

### Cita questo

*Symmetry*,

*10*, 518-.

**Quasi-Lie brackets and the breaking of time-translation symmetry for quantum systems embedded in classical baths.** / Grimaudo, Roberto; Messina, Antonino; Sergi, Alessandro; Grimaudo, Roberto; Messina, Antonino; Hanna, Gabriel.

Risultato della ricerca: Article

*Symmetry*, vol. 10, pagg. 518-.

}

TY - JOUR

T1 - Quasi-Lie brackets and the breaking of time-translation symmetry for quantum systems embedded in classical baths

AU - Grimaudo, Roberto

AU - Messina, Antonino

AU - Sergi, Alessandro

AU - Grimaudo, Roberto

AU - Messina, Antonino

AU - Hanna, Gabriel

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

KW - Breaking of time-translation symmetry

KW - Chemistry (miscellaneous)

KW - Classical spin dynamics

KW - Computer Science (miscellaneous)

KW - Hybrid quantum-classical systems

KW - Langevin dynamics

KW - Mathematics (all)

KW - Nosé-Hoover dynamics

KW - Physics and Astronomy (miscellaneous)

KW - Quantum-classical Liouville equation

KW - Quasi-lie brackets

UR - http://hdl.handle.net/10447/328093

UR - https://www.mdpi.com/2073-8994/10/10/518/pdf

M3 - Article

VL - 10

SP - 518-

JO - Symmetry

JF - Symmetry

SN - 2073-8994

ER -