In open quantum systems, environmental coupling turns deterministic Krylov phase-space trajectories into stochastic ones by adding diffusion, destroying the hyperbolic mechanism for exponential complexity growth beyond a controlled scale.
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Krylov complexity saturates in the full high-temperature Caldeira-Leggett system, reproduces dissipative features when decoherence is suppressed, shows oscillations when dissipation is suppressed, and remains insensitive to decoherence onset because the Krylov basis differs from the conventional one
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Stochastic Krylov Dynamics: Revisiting Operator Growth in Open Quantum Systems
In open quantum systems, environmental coupling turns deterministic Krylov phase-space trajectories into stochastic ones by adding diffusion, destroying the hyperbolic mechanism for exponential complexity growth beyond a controlled scale.
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Krylov Complexity for Open Quantum System: Dissipation and Decoherence
Krylov complexity saturates in the full high-temperature Caldeira-Leggett system, reproduces dissipative features when decoherence is suppressed, shows oscillations when dissipation is suppressed, and remains insensitive to decoherence onset because the Krylov basis differs from the conventional one