Effective dimensions of infinite-dimensional Hilbert spaces: A phase-space approach
arXiv:2111.09891 · doi:10.1103/PhysRevE.105.064209
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.
arXiv comment12 pages, 4 figures. (As published)
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