arXiv subjects

Gastón F. Scialchi

Publications and source records attributed to Gastón F. Scialchi.

4 recordsLinked to original sources

arXiv2026

Classical chaotic signatures in Krylov space

In recent years, Krylov space approaches have emerged as a useful framework for characterizing dynamical chaos in a wide variety of physical systems. However, the connection between Krylov dynamics and the established structures of classical chaos remains largely unexplored. Classical chaos is characterized by exponential stretching and mixing. For quantum maps with a classical limit, we show that these two signatures are encoded in different structures within Krylov space: stretching is encoded in the geometry of the Krylov operators as determined by the Lyapunov exponent, while mixing manifests itself as an exponential decay of the Arnoldi sequences in agreement with the Ruelle-Pollicott resonances.

quant-ph↗

arXiv2026

Quantum-to-classical correspondence in Krylov complexity

We study quantum-to-classical correspondence of the Krylov space for evolutions driven by unitary maps with a classical limit. This entails a proper definition of corresponding quantum and classical operators, inner products and initial states. We prove that with these definitions the purely classical Krylov space is indeed obtained as the asymptotic $\hbar\to 0$ expansion of the quantum Krylov space, and provide several examples of such correspondence. We use these examples to analyze some general aspects about the evolution of the Krylov complexity as they relate to the phase-space representation for the Krylov states. Additionally, we discuss alternative definitions to obtain the correspondence and why they fail. This paper constitutes a first step in understanding complexity and ergodicity of unitary evolution through the Krylov perspective as they relate to classical dynamical notions.

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arXiv2025

Exploring quantum ergodicity of unitary evolution through the Krylov approach

In recent years, there has been growing interest in characterizing the complexity of quantum evolutions of interacting many-body systems. When a time-independent Hamiltonian governs the dynamics, Krylov complexity has emerged as a powerful tool. For unitary evolutions like kicked systems or Trotterized dynamics, a similar formulation based on the Arnoldi approach has been proposed yielding a new notion of quantum ergodicity [P. Suchsland, R. Moessner, and P. W. Claeys, Phys. Rev. B 111, 014309 (2025)]. In this work, we show that this formulation is robust for observing the transition from integrability to chaos in both autonomous and kicked systems. Examples from random matrix theory and spin chains are shown in this paper.

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arXiv2023

Integrability to chaos transition through Krylov approach for state evolution

The complexity of quantum evolutions can be understood by examining their dispersion in a chosen basis. Recent research has stressed the fact that the Krylov basis is particularly adept at minimizing this dispersion [V. Balasubramanian et al, Physical Review D 106, 046007 (2022)]. This property assigns a central role to the Krylov basis in the investigation of quantum chaos. Here, we delve into the transition from integrability to chaos using the Krylov approach, employing an Ising spin chain and a banded random matrix model as our testing models. Our findings indicate that both the saturation of Krylov complexity and the dispersion of the Lanczos coefficients can exhibit a significant dependence on the initial condition. However, both quantities can gauge dynamical quantum chaos with a proper choice of the initial state.

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