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arXiv · 2107.06894

Identification of quantum scars via phase-space localization measures

Saúl Pilatowsky-Cameo·David Villaseñor·Miguel A. Bastarrachea-Magnani·Sergio Lerma-Hernández·Lea F. Santos·Jorge G. Hirsch
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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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Saúl Pilatowsky-Cameo, David Villaseñor, Miguel A. Bastarrachea-Magnani, Sergio Lerma-Hernández, Lea F. Santos, Jorge G. Hirsch. 2021-07-14. Identification of quantum scars via phase-space localization measures. https://doi.org/10.22331/q-2022-02-08-644

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