Identification of quantum scars via phase-space localization measures

• URL: http://arxiv.org/abs/2107.06894v2
• Date: Thu, 3 Feb 2022 18:31:18 GMT
• Title: Identification of quantum scars via phase-space localization measures
• Authors: Sa\'ul Pilatowsky-Cameo, David Villase\~nor, Miguel A. Bastarrachea-Magnani, Sergio Lerma-Hern\'andez, Lea F. Santos, and Jorge G. Hirsch
• Abstract summary: Measure is based on the $alpha$-moments of the Husimi function and is known as the R'enyi occupation of order $alpha$. We show that the R'enyi occupations with $alpha>1$ are highly effective at revealing quantum scars.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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