| name | quantum-chaos-diagnostics-topological-control |
| description | Topological control framework for quantum chaos diagnostics using OTOCs, spectral statistics, and information scrambling. Bridges network topology with information-theoretic, operator, and spectral diagnostics for quantum many-body systems. |
| trigger | quantum chaos, OTOC, information scrambling, spectral statistics, integrability breaking, Lyapunov exponent, Krylov complexity, Ising model |
| category | ai_collection/collection/skills |
Topological Control of Quantum Chaos Diagnostics
Overview
Unified framework bridging network topology with information-theoretic, operator, and spectral diagnostics for quantum many-body systems.
Key Components
1. Information Scrambling Quantification
- Bipartite Mutual Information: Track information propagation between subsystems
- Tripartite Information: Large negative values signal deep information scrambling
- OTOCs: Exponential early-time growth yields quantum Lyapunov exponents
2. Spectral Diagnostics
- Level Spacing Statistics: Poissonian → Wigner-Dyson transition marks integrability breaking
- Spectral Form Factor (SFF): Slope-dip-ramp-plateau structure
- Thouless Time: Reduced time correlates with accelerated scrambling
- Heisenberg Time: Extractable from SFF plateau
3. Operator Growth
- Krylov Complexity: Rapid operator growth in chaotic phase
- Synchronizes with OTOC and mutual information dynamics
4. Topology Effects
- Long-range couplings: Accelerate quantum information propagation
- Heterogeneous degree distributions: Enhance scrambling speed
- Network topologies studied: Path, Erdős-Rényi, Watts-Strogatz
Implementation
- Model spins as vertices, interactions via adjacency matrices
- Tune non-local coupling and field heterogeneity for integrability breaking
- Compute OTOCs for Lyapunov exponent estimation
- Extract SFF for Thouless/Heisenberg times
- Calculate Krylov complexity for operator growth tracking
Activation Keywords
quantum chaos, OTOC, information scrambling, spectral statistics, integrability breaking, Lyapunov exponent, Krylov complexity, Thouless time, spectral form factor
Source
arXiv: 2607.02463 (2026-07-02)
