Effective dimensions of infinite-dimensional Hilbert spaces: A phase-space approach.
basic_science · Level V
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- Record sourced from PubMed, PMID 35854500.
- Also identified by DOI 10.1103/PhysRevE.105.064209.
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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.