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

doi:10.22331/q-2022-02-08-644

Identification of quantum scars via phase-space localization measures

Saúl Pilatowsky-Cameo^1,2, David Villaseñor¹, Miguel A. Bastarrachea-Magnani³, Sergio Lerma-Hernández⁴, Lea F. Santos⁵, and Jorge G. Hirsch¹

¹Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apdo. Postal 70-543, C.P. 04510 CDMX, Mexico
²Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
³Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, San Rafael Atlixco 186, C.P. 09340 CDMX, Mexico
⁴Facultad de Física, Universidad Veracruzana, Circuito Aguirre Beltrán s/n, C.P. 91000 Xalapa, Veracruz, Mexico
⁵Department of Physics, Yeshiva University, New York, New York 10016, USA

Published:	2022-02-08, volume 6, page 644
Eprint:	arXiv:2107.06894v2
Doi:	https://doi.org/10.22331/q-2022-02-08-644
Citation:	Quantum 6, 644 (2022).

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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 Rényi 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 Rényi occupations with $\alpha \gt 1$ are highly effective at revealing quantum scars. Furthermore, by analyzing the high moments ($\alpha \gt 1$) 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.

► BibTeX data

@article{PilatowskyCameo2022identificationof,
  doi = {10.22331/q-2022-02-08-644},
  url = {https://doi.org/10.22331/q-2022-02-08-644},
  title = {Identification of quantum scars via phase-space localization measures},
  author = {Pilatowsky-Cameo, Sa{\'{u}}l and Villase{\~{n}}or, David and Bastarrachea-Magnani, Miguel A. and Lerma-Hern{\'{a}}ndez, Sergio and F. Santos, Lea and Hirsch, Jorge G.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {6},
  pages = {644},
  month = feb,
  year = {2022}
}

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