Quantum Chaos Diagnostics for non-Hermitian Systems from Bi-Lanczos Krylov Dynamics

arXiv:2508.13956 · hep-th, cond-mat.stat-mech, nlin.CD, quant-ph · Submitted 2025-08-19 · Read on arXiv

hep-th, cond-mat.stat-mech, nlin.CD, quant-ph

Submitted: 2025-08-19

Updated: 2026-09-16

Terminology

• Krylov Complexity — 23× in this paper · explained in 3 episodes
• Robustness — 7× in this paper · explained in 5 episodes
• SYK Model — 5× in this paper · explained in 2 episodes
• Hermitian Sachdev-Ye-Kitaev — 3× in this paper
• Verification — 3× in this paper · explained in 2 episodes
• Anisotropy — 2× in this paper · explained in 3 episodes
• Asia Pacific Center for Theoretical Physics — 2× in this paper
• Hilbert Space — 2× in this paper · explained in 2 episodes
• Benchmark — 1× in this paper · explained in 2 episodes
• Chaotic Dynamics — 1× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Cooperation — 1× in this paper · explained in 2 episodes
• Effective Hamiltonian — 1× in this paper · explained in 2 episodes
• Entanglement — 1× in this paper · explained in 4 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Fisher Information — 1× in this paper · explained in 3 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Non-Hermitian Phase Transition — 1× in this paper · explained in 2 episodes
• Phase Transitions — 1× in this paper · explained in 2 episodes
• Quantum Zeno Effect — 1× in this paper · explained in 2 episodes
• Random Matrix Theory (RMT) — 1× in this paper · explained in 3 episodes
• Universality Class — 1× in this paper · explained in 2 episodes

Sources

• A Universal Operator Growth Hypothesis
• Quantum chaos and the complexity of spread of states
• Krylov complexity of density matrix operators
• Quantum Dynamics in Krylov Space: Methods and Applications
• Krylov Complexity
• Operator growth in 2d CFT
• Universal chaotic dynamics from Krylov space
• Integrability to chaos transition through Krylov approach for state evolution
• Spread and Spectral Complexity in Quantum Spin Chains: from Integrability to Chaos
• Krylov complexity as an order parameter for quantum chaotic-integrable transitions
• Krylov Complexity in Mixed Phase Space
• Non-Hermitian Physics
• Quantum state tomography across the exceptional point in a single dissipative qubit
• Symmetry Classification and Universality in Non-Hermitian Many-Body Quantum Chaos by the Sachdev-Ye-Kitaev Model
• Correspondence principle, dissipation, and Ginibre ensemble
• Transient and steady-state chaos in dissipative quantum systems
• Quantum and Semi-Classical Signatures of Dissipative Chaos in the Steady State
• Singular-Value Statistics of Non-Hermitian Random Matrices and Open Quantum Systems
• Krylov space approach to Singular Value Decomposition in non-Hermitian systems
• Singular Value Decomposition and Its Blind Spot for Quantum Chaos in Non-Hermitian Sachdev-Ye-Kitaev Models

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