Quantum Systems Theory Viewed from Kossakowski-Lindblad Lie Semigroups — and Vice Versa

2017 ◽  
Vol 24 (04) ◽  
pp. 1740019 ◽  
Author(s):  
Thomas Schulte-Herbrüggen ◽  
Gunther Dirr ◽  
Robert Zeier
Keyword(s):  
Quantum Systems ◽  
Specific Form ◽  
Dissipative Systems ◽  
Lindblad Equation ◽  
Completely Positive ◽  
Systems And Control ◽  
Lie Semigroup ◽  
Lie Semigroups ◽  
Closed Systems ◽  
And Control

The solutions to the celebrated Kossakowski-Lindblad equation extended by coherent controls yield Markovian quantum maps. More precisely, the set of all its solutions forms a semigroup of completely positive trace-preserving maps taking the specific form of a Lie semigroup. Non-trivial symmetries of these semigroups are shown to preclude accessibility in Markovian dissipative systems. This is the open-system analogue to closed systems, where triviality of (quadratic) symmetries of the Hamiltonian part suffices to decide that the system is fully controllable. The findings are placed into a unifying Lie frame of quantum systems and control theory alongside with illustrating examples.

Systems and control in Scotland

2001 ◽  
Vol 2001 (1) ◽  
pp. 32-34 ◽  
Author(s):  
Clive Seager
Keyword(s):  
Systems And Control ◽  
And Control

scholarly journals Design and Research on Power Systems and Algorithms for Controlling Electric Underground Mining Machines Powered by Batteries

Energies ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 4060
Author(s):  
Artur Kozłowski ◽  
Łukasz Bołoz
Keyword(s):  
Power Systems ◽  
Power Supply ◽  
Internal Combustion Engines ◽  
Underground Mining ◽  
Test Stand ◽  
Research Network ◽  
Control Algorithms ◽  
Systems And Control ◽  
And Control ◽  
Supply Systems

This article discusses the work that resulted in the development of two battery-powered self-propelled electric mining machines intended for operation in the conditions of a Polish copper ore mine. Currently, the global mining industry is seeing a growing interest in battery-powered electric machines, which are replacing solutions powered by internal combustion engines. The cooperation of Mine Master, Łukasiewicz Research Network—Institute of Innovative Technologies EMAG and AGH University of Science and Technology allowed carrying out a number of works that resulted in the production of two completely new machines. In order to develop the requirements and assumptions for the designed battery-powered propulsion systems, underground tests of the existing combustion machines were carried out. Based on the results of these tests, power supply systems and control algorithms were developed and verified in a virtual environment. Next, a laboratory test stand for validating power supply systems and control algorithms was developed and constructed. The tests were aimed at checking all possible situations in which the battery gets discharged as a result of the machine’s ride or operation and when it is charged from the mine’s mains or with energy recovered during braking. Simulations of undesirable situations, such as fluctuations in the supply voltage or charging power limitation, were also carried out at the test stand. Positive test results were obtained. Finally, the power supply systems along with control algorithms were implemented and tested in the produced battery-powered machines during operational trials. The power systems and control algorithms are universal enough to be implemented in two different types of machines. Both machines were specially designed to substitute diesel machines in the conditions of a Polish ore mine. They are the lowest underground battery-powered drilling and bolting rigs with onboard chargers. The machines can also be charged by external fast battery chargers.

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 Introduction to Development of Centralized and Distributed Stochastic Approximation Algorithm with Expanding Truncations

Algorithms ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 174
Author(s):  
Wenxiao Zhao
Keyword(s):  
Approximation Algorithm ◽  
Stochastic Approximation ◽  
Probabilistic Method ◽  
Principal Component ◽  
Stochastic Approximation Algorithm ◽  
The Past ◽  
Systems And Control ◽  
Ode Method ◽  
Centralized Algorithm ◽  
And Control

The stochastic approximation algorithm (SAA), starting from the pioneer work by Robbins and Monro in 1950s, has been successfully applied in systems and control, statistics, machine learning, and so forth. In this paper, we will review the development of SAA in China, to be specific, the stochastic approximation algorithm with expanding truncations (SAAWET) developed by Han-Fu Chen and his colleagues during the past 35 years. We first review the historical development for the centralized algorithm including the probabilistic method (PM) and the ordinary differential equation (ODE) method for SAA and the trajectory-subsequence method for SAAWET. Then, we will give an application example of SAAWET to the recursive principal component analysis. We will also introduce the recent progress on SAAWET in a networked and distributed setting, named the distributed SAAWET (DSAAWET).

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