Classical and Quantum Integrability: A Formulation That Admits Quantum Chaos

Authors

Paul Bracken, The University of Texas Rio Grande ValleyFollow

Document Type

Book

Publication Date

11-17-2020

Abstract

The concept of integrability of a quantum system is developed and studied. By formulating the concepts of quantum degree of freedom and quantum phase space, a realization of the dynamics is achieved. For a quantum system with a dynamical group G in one of its unitary irreducible representative carrier spaces, the quantum phase space is a finite topological space. It is isomorphic to a coset space G=R by means of the unitary exponential mapping, where R is the maximal stability subgroup of a fixed state in the carrier space. This approach has the distinct advantage of exhibiting consistency between classical and quantum integrability. The formalism will be illustrated by studying several quantum systems in detail after this development.

Comments

© 2020 The Author(s). Licensee IntechOpen.

Recommended Citation

Paul Bracken (November 17th 2020). Classical and Quantum Integrability: A Formulation That Admits Quantum Chaos, A Collection of Papers on Chaos Theory and Its Applications, Paul Bracken and Dimo I. Uzunov, IntechOpen, DOI: 10.5772/intechopen.94491. Available from: https://www.intechopen.com/chapters/74091

Creative Commons License

This work is licensed under a Creative Commons Attribution 3.0 License.

Publication Title

A Collection of Papers on Chaos Theory and Its Applications

DOI

10.5772/intechopen.94491