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arXiv · 2111.09891

Effective dimensions of infinite-dimensional Hilbert spaces: A phase-space approach

Saúl Pilatowsky-Cameo·David Villaseñor·Miguel A. Bastarrachea-Magnani·Sergio Lerma-Hernández·Jorge G. Hirsch
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Abstract

By employing Husimi quasiprobability distributions, we show that a bounded portion of an unbounded phase space induces a finite effective dimension in an infinite dimensional Hilbert space. We compare our general expressions with numerical results for the spin-boson Dicke model in the chaotic energy regime, restricting its unbounded four-dimensional phase space to a classically chaotic energy shell. This effective dimension can be employed to characterize quantum phenomena in infinite dimensional systems, such as localization and scarring.

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Saúl Pilatowsky-Cameo, David Villaseñor, Miguel A. Bastarrachea-Magnani, Sergio Lerma-Hernández, Jorge G. Hirsch. 2021-11-18. Effective dimensions of infinite-dimensional Hilbert spaces: A phase-space approach. https://doi.org/10.1103/physreve.105.064209

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