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Operator growth and Krylov construction in dissipative open quantum systems

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arxiv 2207.05347 v3 pith:FVKECOTM submitted 2022-07-12 quant-ph cond-mat.stat-mechcond-mat.str-elhep-th

classification quant-phcond-mat.stat-mechcond-mat.str-elhep-th
keywords arnoldicoefficientsconstructiondissipativegrowthiterationlanczosopen
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Inspired by the universal operator growth hypothesis, we extend the formalism of Krylov construction in dissipative open quantum systems connected to a Markovian bath. Our construction is based upon the modification of the Liouvillian superoperator by the appropriate Lindbladian, thereby following the vectorized Lanczos algorithm and the Arnoldi iteration. This is well justified due to the incorporation of non-Hermitian effects due to the environment. We study the growth of Lanczos coefficients in the transverse field Ising model (integrable and chaotic limits) for boundary amplitude damping and bulk dephasing. Although the direct implementation of the Lanczos algorithm fails to give physically meaningful results, the Arnoldi iteration retains the generic nature of the integrability and chaos as well as the signature of non-Hermiticity through separate sets of coefficients (Arnoldi coefficients) even after including the dissipative environment. Our results suggest that the Arnoldi iteration is meaningful and more appropriate in dealing with open systems.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The Geometry of Quantum Complexity in Open Systems

    quant-ph 2026-07 conditional novelty 7.0 of 10

    Open-system quantum complexity is governed by a sub-Finslerian geometry whose curvature depends on the cost penalties for unitary and dissipative controls.

  2. Scrambling Enabled Entropy Accumulation in Open Quantum Systems

    quant-ph 2025-02 conditional novelty 6.0 of 10

    A weak probe coupled to an open quantum system accumulates a finite Rényi entropy increase only when the system is in the scrambling phase, vanishing in the dissipative phase as the probe coupling goes to zero.

  3. Two-dimensional Toda--Arnoldi correspondence: Holomorphic Krylov geometry and counterdiabatic transport

    quant-ph 2026-08 conditional novelty 5.0 of 10

    For non-Hermitian Hamiltonians, the Arnoldi diagonal and subdiagonal coefficients are the Flaschka variables of the finite two-dimensional Toda lattice, and their squares give both the Fubini-Study metric and the Berr...

  4. Dynamics of monitored SSH Model in Krylov Space: From Complexity to Quantum Fisher Information

    quant-ph 2025-02 conditional novelty 5.0 of 10

    Time-averaged quantum Fisher information in Krylov space changes slope at the PT transition (gamma=1) and saturates near the entanglement transition (gamma=2) in the monitored SSH model, suggesting it as a probe of both.

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