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

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

URL: http://arxiv.org/abs/2111.09891v2
Date: Tue, 28 Jun 2022 20:13:03 GMT
Title: Effective dimensions of infinite-dimensional Hilbert spaces: A phase-space approach
Authors: Sa\'ul Pilatowsky-Cameo, David Villase\~nor, Miguel A. Bastarrachea-Magnani, Sergio Lerma-Hern\'andez, and Jorge G. Hirsch
Abstract summary: We show that a bounded portion of an unbounded phase space induces a finite effective dimension in an infinite dimensional Hilbert space. This effective dimension can be employed to characterize quantum phenomena in infinite dimensional systems, such as localization and scarring.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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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