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Full-Text Articles in Physical Sciences and Mathematics
Classical And Quantum Integrability: A Formulation That Admits Quantum Chaos, Paul Bracken
Classical And Quantum Integrability: A Formulation That Admits Quantum Chaos, Paul Bracken
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
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 …
Complete Integrability And Discretization Of Euler Top And Manakov Top, Austin Marstaller
Complete Integrability And Discretization Of Euler Top And Manakov Top, Austin Marstaller
Theses and Dissertations
The Euler top is a completely integrable system with physical system implications and the Manakov top is its four-dimensional extension. We are concerned about their complete integrability and the preservation of this property under a specific discretization known as the Hirota-Kimura Discretization. Surprisingly, it is not guaranteed that under any discretization the conserved quantities are preserved and therefore they must be discovered. In this work we construct the Poisson bracket and Lax pair for each system and provide the Lie algebra background needed to do such such constructions.