Quantum integrability in systems with finite number of levels

Abstract

We consider the problem of defining quantum integrability in systems with finite number of energy levels starting from commuting matrices and construct new general classes of such matrix models with a given number of commuting partners. We argue that if the matrices depend on a (real) parameter, one can define quantum integrability from this feature alone, leading to specific results such as exact solvability, Poissonian energy level statistics and to level crossings.

10 pages, 1 figure, journal version, new material added

References in corpus (2)

• The Link between Integrability, Level Crossings, and Exact Solution in Quantum Models
• Classification of Parameter-Dependent Quantum Integrable Models, Their Parameterization, Exact Solution, and Other Properties

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