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Rendiconti Lincei - Matematica e Applicazioni


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Volume 19, Issue 4, 2008, pp. 325–334
DOI: 10.4171/RLM/528

Published online: 2008-12-31

On the notion of ergodicity for finite quantum systems

Mirko Degli Espositi[1], Sandro Graffi[2] and Stefano Isola[3]

(1) Università di Bologna, Italy
(2) Università di Bologna, Italy
(3) Università di Camerino, Italy

We show that the orginal definition of ergodicity of Boltzmann can be directly applied to finite quantum systems, such as those arising from the quantization of classical systems on a compact phase space. It yields a notion of quantum ergodicity strictly stronger than the Von Neumann one. As an example, we remark that the quantized hyperbolic symplectomorphisms (a particular case is the quantized Arnold cat) are ergodic in this sense.

Keywords: Quantum ergodicity, Boltzmann ergodicity, quantized toral automorphisms

Degli Espositi Mirko, Graffi Sandro, Isola Stefano: On the notion of ergodicity for finite quantum systems. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 19 (2008), 325-334. doi: 10.4171/RLM/528