scholarly journals Reduced Operator Approximation for Modelling Open Quantum Systems

2015 ◽  
Vol 22 (02) ◽  
pp. 1550008
Author(s):  
A. Werpachowska
Keyword(s):  
Quantum Dynamics ◽  
Quantum Coherence ◽  
Degrees Of Freedom ◽  
Open Quantum Systems ◽  
Interaction Strength ◽  
Quantum Systems ◽  
Computationally Efficient ◽  
Memory Length ◽  
Open Quantum ◽  
Operator Approximation

We present the reduced operator approximation: a simple, physically transparent and computationally efficient method of modelling open quantum systems. It employs the Heisenberg picture of the quantum dynamics, which allows us to focus on the system degrees of freedom in a natural and easy way. We describe different variants of the method, low- and high-order in the system–bath interaction operators, defining them for either general quantum harmonic oscillator baths or specialising them for independent baths with Lorentzian spectral densities. Its wide applicability is demonstrated on the examples of systems coupled to different baths (with varying system–bath interaction strength and bath memory length), and compared with the exact pseudomode and the popular quantum state diffusion approach. The method captures the decoherence of the system interacting with the bath, while conserving the total energy. Our results suggest that quantum coherence effects persist in open quantum systems for much longer times than previously thought.

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 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.

scholarly journals Accurate Truncations of Chain Mapping Models for Open Quantum Systems

Nanomaterials ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 2104
Author(s):  
Mónica Sánchez-Barquilla ◽  
Johannes Feist
Keyword(s):  
Degrees Of Freedom ◽  
Nearest Neighbor ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Open Quantum ◽  
Research Fields ◽  
A Chain ◽  
Chain Lengths ◽  
Mapping Models ◽  
Nearest Neighbor Coupling

The dynamics of open quantum systems are of great interest in many research fields, such as for the interaction of a quantum emitter with the electromagnetic modes of a nanophotonic structure. A powerful approach for treating such setups in the non-Markovian limit is given by the chain mapping where an arbitrary environment can be transformed to a chain of modes with only nearest-neighbor coupling. However, when long propagation times are desired, the required long chain lengths limit the utility of this approach. We study various approaches for truncating the chains at manageable lengths while still preserving an accurate description of the dynamics. We achieve this by introducing losses to the chain modes in such a way that the effective environment acting on the system remains unchanged, using a number of different strategies. Furthermore, we demonstrate that extending the chain mapping to allow next-nearest neighbor coupling permits the reproduction of an arbitrary environment, and adding longer-range interactions does not further increase the effective number of degrees of freedom in the environment.

scholarly journals On Time-Local Generators of Quantum Evolution

2014 ◽  
Vol 21 (01n02) ◽  
pp. 1440004 ◽  
Author(s):  
Dariusz Chruściński
Keyword(s):  
Quantum Dynamics ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Master Equations ◽  
Quantum Evolution ◽  
Completely Positive ◽  
Open Quantum ◽  
The Family

We present a basic introduction to the dynamics of open quantum systems based on local-in-time master equations. We characterize the properties of time-local generators giving rise to legitimate completely positive trace preserving quantum evolutions. The analysis of Markovian and non-Markovian quantum dynamics is presented as well. The whole discussion is illustrated by the family of many instructive examples.

scholarly journals Quantum Maps with Memory from Generalized Lindblad Equation

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 544
Author(s):  
Vasily E. Tarasov
Keyword(s):  
Discrete Time ◽  
Power Law ◽  
Quantum Dynamics ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Periodic Sequence ◽  
Lindblad Equation ◽  
Open Quantum ◽  
Systems With Memory ◽  
With Memory

In this paper, we proposed the exactly solvable model of non-Markovian dynamics of open quantum systems. This model describes open quantum systems with memory and periodic sequence of kicks by environment. To describe these systems, the Lindblad equation for quantum observable is generalized by taking into account power-law fading memory. Dynamics of open quantum systems with power-law memory are considered. The proposed generalized Lindblad equations describe non-Markovian quantum dynamics. The quantum dynamics with power-law memory are described by using integrations and differentiation of non-integer orders, as well as fractional calculus. An example of a quantum oscillator with linear friction and power-law memory is considered. In this paper, discrete-time quantum maps with memory, which are derived from generalized Lindblad equations without any approximations, are suggested. These maps exactly correspond to the generalized Lindblad equations, which are fractional differential equations with the Caputo derivatives of non-integer orders and periodic sequence of kicks that are represented by the Dirac delta-functions. The solution of these equations for coordinates and momenta are derived. The solutions of the generalized Lindblad equations for coordinate and momentum operators are obtained for open quantum systems with memory and kicks. Using these solutions, linear and nonlinear quantum discrete-time maps are derived.

scholarly journals Advances in Sequential Measurement and Control of Open Quantum Systems

Proceedings ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 11 ◽  
Author(s):  
Stefano Gherardini ◽  
Andrea Smirne ◽  
Matthias M. Müller ◽  
Filippo Caruso
Keyword(s):  
Quantum System ◽  
Quantum Dynamics ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Noise Sources ◽  
Open Quantum ◽  
Quantum Science ◽  
And Control ◽  
Measurement And Control ◽  
Sequential Measurements

Novel concepts, perspectives and challenges in measuring and controlling an open quantum system via sequential schemes are shown. We discuss how similar protocols, relying both on repeated quantum measurements and dynamical decoupling control pulses, can allow to: (i) Confine and protect quantum dynamics from decoherence in accordance with the Zeno physics. (ii) Analytically predict the probability that a quantum system is transferred into a target quantum state by means of stochastic sequential measurements. (iii) Optimally reconstruct the spectral density of environmental noise sources by orthogonalizing in the frequency domain the filter functions driving the designed quantum-sensor. The achievement of these tasks will enhance our capability to observe and manipulate open quantum systems, thus bringing advances to quantum science and technologies.

scholarly journals OPEN QUANTUM DYNAMICS: COMPLETE POSITIVITY AND ENTANGLEMENT

2005 ◽  
Vol 19 (19) ◽  
pp. 3063-3139 ◽  
Author(s):  
FABIO BENATTI ◽  
ROBERTO FLOREANINI
Keyword(s):  
Quantum Entanglement ◽  
Quantum Dynamics ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Complete Positivity ◽  
Information Communication ◽  
Open Quantum ◽  
Statistical Correlations ◽  
Quantum Open System ◽  
Algebraic Constraint

We review the standard treatment of open quantum systems in relation to quantum entanglement, analyzing, in particular, the behavior of bipartite systems immersed in the same environment. We first focus upon the notion of complete positivity, a physically motivated algebraic constraint on the quantum dynamics, in relation to quantum entanglement, i.e. the existence of statistical correlations which can not be accounted for by classical probability. We then study the entanglement power of heat baths versus their decohering properties, a topic of increasing importance in the framework of the fast developing fields of quantum information, communication and computation. The presentation is self contained and, through several examples, it offers a detailed survey of the physics and of the most relevant and used techniques relative to both quantum open system dynamics and quantum entanglement.

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