Stochastic Krylov Dynamics: Revisiting Operator Growth in Open Quantum Systems

arXiv:2604.20619 · hep-th, cond-mat.stat-mech, quant-ph · Submitted 2026-04-22 · Read on arXiv

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

Submitted: 2026-04-22

Updated: 2026-04-22

Terminology

• Krylov Complexity — 24× in this paper · explained in 3 episodes
• Hilbert Space — 7× in this paper · explained in 2 episodes
• Lindblad Dynamics — 7× in this paper · explained in 2 episodes
• Effective Hamiltonian — 5× in this paper · explained in 2 episodes
• Phase Transitions — 5× in this paper · explained in 2 episodes
• Trace — 4× in this paper · explained in 2 episodes
• Chaotic Dynamics — 3× in this paper · explained in 2 episodes
• Stochastic Dynamics — 3× in this paper · explained in 2 episodes
• Conservation Laws — 2× in this paper · explained in 3 episodes
• Generalization — 2× in this paper · explained in 13 episodes
• Core — 1× in this paper · explained in 2 episodes
• Eigenstate Thermalization Hypothesis (ETH) — 1× in this paper · explained in 4 episodes
• Entanglement — 1× in this paper · explained in 3 episodes
• Fisher Information — 1× in this paper · explained in 3 episodes
• Hubbard Model — 1× in this paper · explained in 3 episodes
• Langevin Dynamics — 1× in this paper · explained in 2 episodes
• SYK Model — 1× in this paper · explained in 2 episodes
• Temporal Correlations — 1× in this paper · explained in 2 episodes
• Unified Framework — 1× in this paper · explained in 5 episodes
• Unitary Dynamics — 1× in this paper · explained in 2 episodes
• Universality Class — 1× in this paper · explained in 2 episodes

Sources

• Two-dimensional conformal field theory and the butterfly effect
• Black holes and the butterfly effect
• A bound on chaos
• A Universal Operator Growth Hypothesis
• Toda chain flow in Krylov space
• MMA Training: Direct Input Space Margin Maximization through Adversarial Training
• On The Evolution Of Operator Complexity Beyond Scrambling
• Operator complexity: a journey to the edge of Krylov space
• Krylov complexity from integrability to chaos
• Operator growth and Krylov Complexity in Bose-Hubbard Model
• Measurement-Induced Phase Transitions in the Dynamics of Entanglement
• Solution of a minimal model for many-body quantum chaos
• Dynamics of monitored SSH Model in Krylov Space: From Complexity to Quantum Fisher Information
• On Krylov complexity in open systems: an approach via bi-Lanczos algorithm
• A Schwinger-Keldysh Formulation of Semiclassical Operator Dynamics
• Krylov Complexity in Open Quantum Systems
• Spread complexity for measurement-induced non-unitary dynamics and Zeno effect
• The operator growth hypothesis in open quantum systems
• Operator dynamics in Lindbladian SYK: a Krylov complexity perspective
• Operator growth and spread complexity in open quantum systems

Related papers

• Entanglement Wedge Reconstruction Beyond the Large N Limit via the Twirled Petz Map
• Horizons and Soft Quantum Information
• Energy Transmission Across Holographic Conformal Interfaces in General Dimensions
• Why Cooper pairs live in AdS2: a spectral analysis of the Yukawa-SYK model
• The Schrodinger Equation as a Gauge Theory
• Inflation with vector fields revisited: non-Gaussianities