Topological Genesis of Quantum Chaos

Macroscopic Quantum Chaos from Topological Degradation We present numerical evidence that macroscopic quantum chaos can emerge without nonlinear dynamics in the evolution equation. Instead, it arises as a continuous phase transition driven solely by the topological degradation of the underlying spatial substrate. ◆ Key Features • 2D toroidal mesh: N = L × L sites (L = 20–50). • Tight-binding Hamiltonian with uncorrelated Anderson disorder (W as the primary control parameter). • Independent 10% bond-percolation channel confirming that the observed behavior is a generic consequence of connectivity loss. • Exact diagonalization on mobile ARM (Snapdragon 8 Gen 2) hardware without spectral unfolding: ~25–75 s per 50-realization ensemble, achieving ~25× speedup over conventional HPC workflows. ◆ Main Results • Perfect torus exhibits symmetry-induced spectral degeneracy, numerically close to Poisson statistics. • Moderate disorder (W ≈ 1–4) yields ⟨r⟩ = 0.530–0.534, matching GOE Wigner–Dyson statistics. • Strong disorder (W ≳ 8) restores genuine Poisson statistics (⟨r⟩ ≈ 0.39). • Critical regime (W ≈ 4–6): strongly multifractal eigenstates, monotonic decay of generalized dimensions Dq, and f(α) peaking near α ≈ 2.2–2.3. • Finite-size scaling confirms Anderson-transition-like criticality. ◆ Implications These results show that Wigner–Dyson level repulsion and algorithmic chaos are thermodynamic consequences of spatial frustration. The critical threshold (W ≈ 4–6) defines a quantitative failure boundary for distributed tensor-processing interconnects, while the unfolding-free methodology enables rapid, on-device spectral diagnostics for next-generation fault-tolerant AI accelerators.