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Quantum Physics
Title: Identification of quantum scars via phase-space localization measures
(Submitted on 14 Jul 2021 (v1), last revised 3 Feb 2022 (this version, v2))
Abstract: There is no unique way to quantify the degree of delocalization of quantum states in unbounded continuous spaces. In this work, we explore a recently introduced localization measure that quantifies the portion of the classical phase space occupied by a quantum state. The measure is based on the $\alpha$-moments of the Husimi function and is known as the R\'enyi occupation of order $\alpha$. With this quantity and random pure states, we find a general expression to identify states that are maximally delocalized in phase space. Using this expression and the Dicke model, which is an interacting spin-boson model with an unbounded four-dimensional phase space, we show that the R\'enyi occupations with $\alpha>1$ are highly effective at revealing quantum scars. Furthermore, by analyzing the high moments ($\alpha>1$) of the Husimi function, we are able to identify qualitatively and quantitatively the unstable periodic orbits that scar some of the eigenstates of the model.
Submission history
From: Saúl Pilatowsky-Cameo [view email][v1] Wed, 14 Jul 2021 18:00:00 GMT (5304kb,D)
[v2] Thu, 3 Feb 2022 18:31:18 GMT (5318kb,D)
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