Applications of Lie systems in Quantum Mechanics and Control Theory

TL;DR

This paper explores how Lie systems can be applied to quantum physics and control theory, demonstrating unified approaches for classical and quantum models and illustrating control systems on Lie groups.

Contribution

It shows the application of Lie systems to both quantum and control problems, highlighting their utility in unifying classical and quantum models through geometric techniques.

Findings

Classical and quantum problems can be treated similarly using Lie group extensions.

Geometric techniques for Lie systems are effective in control theory.

Examples of control systems on Lie groups and homogeneous spaces are analyzed.

Abstract

Some simple examples from quantum physics and control theory are used to illustrate the application of the theory of Lie systems. We will show, in particular, that for certain physical models both of the corresponding classical and quantum problems can be treated in a similar way, may be up to the replacement of the involved Lie group by a central extension of it. The geometric techniques developed for dealing with Lie systems are also used in problems of control theory. Specifically, we will study some examples of control systems on Lie groups and homogeneous spaces.