Identification of quantum scars via phase-space localization measures

There is no unique way to quantify the de-gree of delocalization of quantum states in un-bounded continuous spaces. In this work, we explore a recently introduced localization mea -sure that quantifies the portion of the classi-cal phase space occupied by a quantum state. The measure is based on the alpha-moments of the Husimi function and is known as the Renyi oc-cupation of order alpha. With this quantity and random pure states, we find a general expres-sion to identify states that are maximally de-localized in phase space. Using this expres-sion and the Dicke model, which is an inter -acting spin-boson model with an unbounded four-dimensional phase space, we show that the Renyi occupations with alpha > 1 are highly effective at revealing quantum scars. Further-more, by analyzing the high moments (alpha > 1) of the Husimi function, we are able to iden-tify qualitatively and quantitatively the unsta-ble periodic orbits that scar some of the eigen-states of the model.