• Letter

Ubiquity of the quantum boomerang effect in Hermitian Anderson-localized systems

Flavio Noronha and Tommaso Macrì
Phys. Rev. B 106, L060301 – Published 8 August 2022
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Abstract

A particle with finite initial velocity in a disordered potential comes back and on average stops at the original location. This phenomenon, dubbed the “quantum boomerang effect” (QBE), has been recently observed in an experiment simulating the quantum kicked-rotor model [Sajjad et al., Phys. Rev. X 12, 011035 (2022)]. We provide analytical arguments that support the presence of the QBE in a wide class of disordered systems. Sufficient conditions to observe the real-space QBE are (a) Anderson localization, (b) the reality of the spectrum for the case of non-Hermitian systems, (c) the ensemble of disorder realizations {H} being invariant under the application of RT, and (d) the initial state being an eigenvector of RT, where R is a reflection xx and T is the time-reversal operator. The QBE can be observed in momentum space in systems with dynamical localization if conditions (c) and (d) are satisfied with respect to the operator T instead of RT. These conditions allow the observation of the QBE in time-reversal-symmetry-broken models, contrary to what was expected from previous analyses of the effect, and in a large class of non-Hermitian models. We provide examples of the QBE in lattice models with magnetic flux breaking time-reversal symmetry and in a model with an electric field. Whereas the QBE straightforwardly applies to noninteracting many-body systems, we argue that a real-space (momentum-space) QBE is absent in weakly interacting bosonic systems due to the breaking of reflection–time-reversal (time-reversal) symmetry.

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  • Received 18 April 2022
  • Revised 24 May 2022
  • Accepted 29 July 2022

DOI:https://doi.org/10.1103/PhysRevB.106.L060301

©2022 American Physical Society

Physics Subject Headings (PhySH)

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Flavio Noronha1 and Tommaso Macrì2,1

  • 1Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, Campus Universitário, Lagoa Nova, Natal-RN 59078-970, Brazil
  • 2ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA

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Issue

Vol. 106, Iss. 6 — 1 August 2022

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