Coexistence of Anderson Localization and Quantum Scarring in Two Dimensions
arXiv:2512.20788 · doi:10.1103/hy7f-8fbn
Abstract
We investigate finite two-dimensional disordered systems with periodic confinement. At low energies, eigenstates exhibit strong Anderson localization, while at higher energies a subset of states exhibits variational scarring with anisotropic intensity patterns that deviate from random-wave expectations. Scaling theory predicts that in two dimensions all eigenstates localize in the large-system-size limit, yet the energy-dependent localization length and finite-size effects allow these regimes to coexist. We demonstrate that this coexistence produces distinct, robust signatures in both spatial intensity patterns and spectral statistics that are directly observable in mesoscopic electronic, photonic, and cold-atom systems.
arXiv comment8 pages, 4 figures + supplementary material
References in corpus (33)
- Random Matrix Theories in Quantum Physics: Common Concepts
- Many-body localization, thermalization, and entanglement
- Anderson localization of a non-interacting Bose-Einstein condensate
- Direct observation of Anderson localization of matter-waves in a controlled disorder
- The distribution of the ratio of consecutive level spacings in random matrix ensembles
- Ray and wave chaos in asymmetric resonant optical cavities
- Coherent Branched Flow in a Two-Dimensional Electron Gas
- Non-ergodic phases in strongly disordered random regular graphs
- Light transport and localization in two-dimensional correlated disorder
- Multifractality meets entanglement: relation for non-ergodic extended states
- First Experimental Observation of Superscars in a Pseudointegrable Barrier Billiard
- How Chaotic is the Stadium Billiard? A Semiclassical Analysis
- Quantum Lissajous Scars
- Branched Flow
- Controllable quantum scars in semiconductor quantum dots
- Direct Visualization of Relativistic Quantum Scars
- Normal and Anomalous Diffusion in Soft Lorentz Gases
- Ground-state energy and spin in disordered quantum dots
- Polyatomic trilobite Rydberg molecules in a dense random gas
- Classical dynamical localization
- Density functional theory of spin-polarized disordered quantum dots
- Effects of scarring on quantum chaos in disordered quantum wells
- Two-dimensional Bloch electrons in perpendicular magnetic fields: an exact calculation of the Hofstadter butterfly spectrum
- Imaginary time propagation code for large-scale two-dimensional eigenvalue problems in magnetic fields
- Chaos-Assisted Dynamical Tunneling in Flat Band Superwires
- Formation, prevalence, and stability of bouncing-ball quantum scars
- Characterization of hybrid quantum eigenstates in systems with mixed classical phasespace
- Variational Scarring in Graphene Quantum Dots
- Emergent multifractality in power-law decaying eigenstates
- Level statistics and Anderson delocalization in two-dimensional granular materials
- Variational Scarring in Open Two-Dimensional Quantum Dots
- Experimental phase-space-based optical amplification of scar modes
- Anomalous Diffusion in the Square Soft Lorentz Gas