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
Summary
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.
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.
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