Krylov winding emerges as a generic feature of quantum chaotic systems from the universal operator growth bound, producing size winding when a low-rank Krylov-to-size mapping exists and the chaos bound saturates.
Krylov complexity from inte- grability to chaos,
5 Pith papers cite this work, alongside 146 external citations. Polarity classification is still indexing.
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The paper establishes a Lie-algebraic framework for exact Krylov dynamics in time-dependent quantum systems and introduces a quantum speed limit for complexity growth that retains its time-independent form but saturates only when the Hamiltonian commutes with itself at different times.
Krylov complexity grows quadratically in pure Lifshitz backgrounds and its late-time exponent is controlled by the hyperscaling violation parameter, with a special oscillatory regime.
Krylov complexity is a canonical, parameter-independent measure of operator spreading that probes chaotic dynamics to late times and admits a geometric interpretation in holographic duals.
Krylov subspace methods efficiently describe quantum evolution, operator growth, and chaos in many-body systems, with metrics like Krylov complexity and applications in open systems, QFT, and quantum computing.
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Krylov Winding and Emergent Coherence in Operator Growth Dynamics
Krylov winding emerges as a generic feature of quantum chaotic systems from the universal operator growth bound, producing size winding when a low-rank Krylov-to-size mapping exists and the chaos bound saturates.
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Krylov Dynamics and Operator Growth in Time-Dependent Systems via Lie Algebras
The paper establishes a Lie-algebraic framework for exact Krylov dynamics in time-dependent quantum systems and introduces a quantum speed limit for complexity growth that retains its time-independent form but saturates only when the Hamiltonian commutes with itself at different times.
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Holographic Krylov Complexity with Lifshitz Scaling and Hyperscaling Violation
Krylov complexity grows quadratically in pure Lifshitz backgrounds and its late-time exponent is controlled by the hyperscaling violation parameter, with a special oscillatory regime.
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Krylov Complexity
Krylov complexity is a canonical, parameter-independent measure of operator spreading that probes chaotic dynamics to late times and admits a geometric interpretation in holographic duals.
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Quantum Dynamics in Krylov Space: Methods and Applications
Krylov subspace methods efficiently describe quantum evolution, operator growth, and chaos in many-body systems, with metrics like Krylov complexity and applications in open systems, QFT, and quantum computing.