1302.5398 (Ignacio Gomez et al.)

A Quantum Version of The Spectral Decomposition Theorem of Dynamical
Systems, Quantum Chaos Hierarchy: Ergodic, Mixing and Exact    [PDF]

Ignacio Gomez, Mario Castagnino

In this paper we study the Spectral Decomposition Theorem [5] and translate it to the quantum language through the Wigner Transform. We obtain a Quantum Version of The Spectral Decomposition Theorem that allows us to three things: First, to rank the levels of the Quantum Ergodic Hierarchy [1]. Second, to analyze the classical limit in quantum ergodic systems and quantum mixing systems. And third, and maybe the most important feature, to find a relevant and simple connection between the first three levels of the Quantum Ergodic Hierarchy (ergodic, exact and mixing) and the type of spectrum of the quantum systems in the classical limit.

View original: http://arxiv.org/abs/1302.5398