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

Pilatowsky-Cameo, Saúl; Villaseñor, David; Bastarrachea-Magnani, Miguel A; Lerma-Hernández, Sergio; Hirsch, Jorge G · Phys Rev E · 2022

basic_science · Level V

Where this comes from

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.