scholarly journals Exact description of coalescing eigenstates in open quantum systems in terms of microscopic Hamiltonian dynamics

2017 ◽  
Vol 58 (9) ◽  
pp. 092101 ◽  
Author(s):  
Kazuki Kanki ◽  
Savannah Garmon ◽  
Satoshi Tanaka ◽  
Tomio Petrosky
Keyword(s):  
Open Quantum Systems ◽  
Hamiltonian Dynamics ◽  
Quantum Systems ◽  
Open Quantum ◽  
Exact Description

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

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 518 ◽  
Author(s):  
Alessandro Sergi ◽  
Gabriel Hanna ◽  
Roberto Grimaudo ◽  
Antonino Messina
Keyword(s):  
Constant Temperature ◽  
Degrees Of Freedom ◽  
Open Quantum Systems ◽  
Hamiltonian Dynamics ◽  
Quantum Systems ◽  
Classical Dynamics ◽  
Open Quantum ◽  
Time Translation ◽  
Translation Symmetry ◽  
Lie Brackets

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.

Relaxation of interacting open quantum systems

2018 ◽  
Vol 189 (05) ◽  
Author(s):  
Vladislav Yu. Shishkov ◽  
Evgenii S. Andrianov ◽  
Aleksandr A. Pukhov ◽  
Aleksei P. Vinogradov ◽  
A.A. Lisyansky
Keyword(s):  
Open Quantum Systems ◽  
Quantum Systems ◽  
Open Quantum

scholarly journals Hamiltonian assignment for open quantum systems

2020 ◽  
Vol 2 (3) ◽  
Author(s):  
Eugene F. Dumitrescu ◽  
Pavel Lougovski
Keyword(s):  
Open Quantum Systems ◽  
Quantum Systems ◽  
Open Quantum

scholarly journals Perturbation Analysis of Quantum Reset Models

2021 ◽  
Vol 183 (1) ◽  
Author(s):  
Géraldine Haack ◽  
Alain Joye
Keyword(s):  
Steady State ◽  
Perturbation Analysis ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Markov Semigroup ◽  
Coupling Constant ◽  
Coupling Term ◽  
Open Quantum ◽  
Effective Dynamics ◽  
A Chain

AbstractThis paper is devoted to the analysis of Lindblad operators of Quantum Reset Models, describing the effective dynamics of tri-partite quantum systems subject to stochastic resets. We consider a chain of three independent subsystems, coupled by a Hamiltonian term. The two subsystems at each end of the chain are driven, independently from each other, by a reset Lindbladian, while the center system is driven by a Hamiltonian. Under generic assumptions on the coupling term, we prove the existence of a unique steady state for the perturbed reset Lindbladian, analytic in the coupling constant. We further analyze the large times dynamics of the corresponding CPTP Markov semigroup that describes the approach to the steady state. We illustrate these results with concrete examples corresponding to realistic open quantum systems.

scholarly journals Matrix Product State Simulations of Non-Equilibrium Steady States and Transient Heat Flows in the Two-Bath Spin-Boson Model at Finite Temperatures

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 77
Author(s):  
Angus J. Dunnett ◽  
Alex W. Chin
Keyword(s):  
Finite Temperature ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Steady States ◽  
Matrix Product ◽  
Open Quantum ◽  
Matrix Product State ◽  
Wide Range ◽  
Boson Model ◽  
Non Equilibrium

Simulating the non-perturbative and non-Markovian dynamics of open quantum systems is a very challenging many body problem, due to the need to evolve both the system and its environments on an equal footing. Tensor network and matrix product states (MPS) have emerged as powerful tools for open system models, but the numerical resources required to treat finite-temperature environments grow extremely rapidly and limit their applications. In this study we use time-dependent variational evolution of MPS to explore the striking theory of Tamascelli et al. (Phys. Rev. Lett. 2019, 123, 090402.) that shows how finite-temperature open dynamics can be obtained from zero temperature, i.e., pure wave function, simulations. Using this approach, we produce a benchmark dataset for the dynamics of the Ohmic spin-boson model across a wide range of coupling strengths and temperatures, and also present a detailed analysis of the numerical costs of simulating non-equilibrium steady states, such as those emerging from the non-perturbative coupling of a qubit to baths at different temperatures. Despite ever-growing resource requirements, we find that converged non-perturbative results can be obtained, and we discuss a number of recent ideas and numerical techniques that should allow wide application of MPS to complex open quantum systems.

scholarly journals Memory Effects in Quantum Dynamics Modelled by Quantum Renewal Processes

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 905
Author(s):  
Nina Megier ◽  
Manuel Ponzi ◽  
Andrea Smirne ◽  
Bassano Vacchini
Keyword(s):  
Quantum Dynamics ◽  
Open Quantum System ◽  
Open Quantum Systems ◽  
Phenomenological Approach ◽  
Quantum Systems ◽  
Renewal Processes ◽  
Continuous Part ◽  
Trace Distance ◽  
Open Quantum ◽  
And Control

Simple, controllable models play an important role in learning how to manipulate and control quantum resources. We focus here on quantum non-Markovianity and model the evolution of open quantum systems by quantum renewal processes. This class of quantum dynamics provides us with a phenomenological approach to characterise dynamics with a variety of non-Markovian behaviours, here described in terms of the trace distance between two reduced states. By adopting a trajectory picture for the open quantum system evolution, we analyse how non-Markovianity is influenced by the constituents defining the quantum renewal process, namely the time-continuous part of the dynamics, the type of jumps and the waiting time distributions. We focus not only on the mere value of the non-Markovianity measure, but also on how different features of the trace distance evolution are altered, including times and number of revivals.

scholarly journals An exponential quantum projection filter for open quantum systems

Automatica ◽  
2019 ◽  
Vol 99 ◽  
pp. 59-68 ◽  
Author(s):  
Qing Gao ◽  
Guofeng Zhang ◽  
Ian R. Petersen
Keyword(s):  
Open Quantum Systems ◽  
Quantum Systems ◽  
Open Quantum
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