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 Description of Quantum Dynamics of Open Systems Based on Collision-Like Models

2005 ◽  
Vol 12 (01) ◽  
pp. 81-91 ◽  
Author(s):  
Mário Ziman ◽  
Peter Štelmachovič ◽  
Vladimír Bužek
Keyword(s):  
Quantum System ◽  
Quantum Dynamics ◽  
Open Systems ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Master Equations ◽  
Discrete Dynamics ◽  
Completely Positive ◽  
Semigroup Property ◽  
System A

Master equations in the Lindblad form describe evolution of open quantum systems that are completely positive and simultaneously have a semigroup property. We analyze the possibility to derive this type of master equations from an intrinsically discrete dynamics that is modelled as a sequence of collisions between a given quantum system (a qubit) with particles that form the environment. In order to illustrate our approach we analyze in detail how the process of an exponential decay and the process of decoherence can be derived from a collision-like model in which particular collisions are described by SWAP and controlled-NOT interactions, respectively.

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 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 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 On non-Markovian Time Evolution in Open Quantum Systems

2007 ◽  
Vol 14 (03) ◽  
pp. 265-274 ◽  
Author(s):  
Andrzej Kossakowski ◽  
Rolando Rebolledo
Keyword(s):  
Time Evolution ◽  
Open System ◽  
Open Quantum Systems ◽  
Vacuum State ◽  
Quantum Systems ◽  
Initial State ◽  
Completely Positive ◽  
Open Quantum

Non-Markovian reduced dynamics of an open system is investigated. In the case when the initial state of the reservoir is the vacuum state, an approximation is introduced which makes it possible to construct a reduced dynamics which is completely positive.

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.

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