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August 8, 2026Open Access

Topological Genesis of Quantum Chaos: Multifractality and the Poisson–GOE–Poisson Crossover in Anderson Lattices

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Authors

APAndres Sebaatian Pirolo

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Overview

Randomized trial observes macroscopic quantum chaos in Anderson lattices, indicating importance in quantum systems.

Key Points

  • This research investigates how macroscopic quantum chaos can arise from topological changes rather than non-linear dynamics.
  • Numerical simulations using a 2D toroidal mesh with 20-50 sites (N = L × L).
  • Tight-binding Hamiltonian with uncorrelated Anderson disorder as a control parameter.
  • Exact diagonalization on ARM hardware to enhance computational efficiency.
  • Moderate disorder yields level spacing statistics closely matching GOE Wigner-Dyson statistics (⟨r⟩ = 0.530–0.534).
  • Strong disorder restores Poisson statistics (⟨r⟩ ≈ 0.39).
  • Critical regime shows strongly multifractal eigenstates and scaling behaviors consistent with an Anderson transition.

Cite This Study

Andres Sebaatian Pirolo (2026) studied this question.

synapsesocial.com/papers/6a76daaaf12abadc798151ebhttps://doi.org/10.5281/zenodo.21816868
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