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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 α -moments of the Husimi function and is known as the Rényi occupation of order α . 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 Rényi occupations with α > 1 are highly effective at revealing quantum scars. Furthermore, by analyzing the high moments ( α > 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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Periodic orbit scar in wavepacket propagation
This study analyzed the scar-like localization in the time-average of a time-evolving wavepacket on a desymmetrized stadium billiard. When a wavepacket is launched along the orbits, it emerges on classical unstable periodic orbits as a scar in stationary states. This localization along the periodic orbit is clarified through the semiclassical approximation. It essentially originates from the same mechanism of a scar in stationary states: piling up of the contribution from the classical actions of multiply repeated passes on a primitive periodic orbit. To achieve this, several states are required in the energy range determined by the initial wavepacket.
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- Award ID(s):
- 1800101
- PAR ID:
- 10314167
- Date Published:
- Journal Name:
- International Journal of Modern Physics C
- Volume:
- 30
- Issue:
- 04
- ISSN:
- 0129-1831
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1142/S0129183119500268
