scholarly journals A hybrid stochastic hierarchy equations of motion approach to treat the low temperature dynamics of non-Markovian open quantum systems

2013 ◽  
Vol 139 (13) ◽  
pp. 134106 ◽  
Author(s):  
Jeremy M. Moix ◽  
Jianshu Cao
Keyword(s):  
Low Temperature ◽  
Open Quantum Systems ◽  
Equations Of Motion ◽  
Quantum Systems ◽  
Open Quantum ◽  
Temperature Dynamics ◽  
Hierarchy Equations

scholarly journals QuantumCumulants.jl: A Julia framework for generalized mean-field equations in open quantum systems

Quantum ◽  
2022 ◽  
Vol 6 ◽  
pp. 617
Author(s):  
David Plankensteiner ◽  
Christoph Hotter ◽  
Helmut Ritsch
Keyword(s):  
Open Quantum Systems ◽  
Equations Of Motion ◽  
Mean Field ◽  
Quantum Systems ◽  
Cumulant Expansion ◽  
Field Equations ◽  
Expectation Values ◽  
Closed Set ◽  
Open Quantum ◽  
Mean Field Equations

A full quantum mechanical treatment of open quantum systems via a Master equation is often limited by the size of the underlying Hilbert space. As an alternative, the dynamics can also be formulated in terms of systems of coupled differential equations for operators in the Heisenberg picture. This typically leads to an infinite hierarchy of equations for products of operators. A well-established approach to truncate this infinite set at the level of expectation values is to neglect quantum correlations of high order. This is systematically realized with a so-called cumulant expansion, which decomposes expectation values of operator products into products of a given lower order, leading to a closed set of equations. Here we present an open-source framework that fully automizes this approach: first, the equations of motion of operators up to a desired order are derived symbolically using predefined canonical commutation relations. Next, the resulting equations for the expectation values are expanded employing the cumulant expansion approach, where moments up to a chosen order specified by the user are included. Finally, a numerical solution can be directly obtained from the symbolic equations. After reviewing the theory we present the framework and showcase its usefulness in a few example problems.

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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