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One-dimensional Lévy quasicrystal.

Pallabi Chatterjee1, Ranjan Modak1

  • 1Department of Physics, Indian Institute of Technology Tirupati, Tirupati 517619, India.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|September 14, 2023
PubMed
Summary
This summary is machine-generated.

This study introduces Lévy quasicrystals, a model for space-fractional quantum mechanics, exhibiting a delocalization-localization transition. This offers a new platform for testing quantum mechanics models in optical experiments.

Keywords:
Anderson localizationLévymobility edgepower-law hoppingquasicrystalquasiperiodic potentialspace fractional quantum mechanics

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Area of Science:

  • Quantum Mechanics
  • Condensed Matter Physics
  • Mathematical Physics

Background:

  • Space-fractional quantum mechanics (SFQM) generalizes standard quantum mechanics by incorporating Lévy flights into Feynman path integrals.
  • The Aubry-André (AA) model describes localization-delocalization transitions in one dimension.

Purpose of the Study:

  • Introduce Lévy quasicrystals by discretizing the space-fractional Schrödinger equation.
  • Investigate the localization-delocalization transition in this new model.
  • Explore potential experimental realizations in optical systems.

Main Methods:

  • Discretization of the space-fractional Schrödinger equation using Grünwald-Letnikov derivatives.
  • Inclusion of an on-site quasiperiodic potential.
  • Analysis of the resulting Hamiltonian and its properties.

Main Results:

  • The Lévy quasicrystal model exhibits similarities to the AA model with power-law hopping.
  • A tunable delocalization-localization transition is observed by varying the quasiperiodic potential strength.
  • Coexistence of localized and delocalized states separated by a mobility edge.

Conclusions:

  • Lévy quasicrystals provide a novel framework for studying phenomena in SFQM.
  • The model serves as a potential experimental platform for testing AA models with power-law hopping in optical experiments.