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arXiv · 2602.00369

Dynamical witnesses and universal behavior across chaos and non-ergodicity in the tilted Bose-Hubbard model

Carlos Diaz-Mejia·Sergio Lerma-Hernandez·Jorge G. Hirsch
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Abstract

Quantum chaos in isolated quantum systems is intimately linked to thermalization and the rapid relaxation of observables. Although the spectral properties of the chaotic phase in the tilted Bose-Hubbard model have been well characterized, the corresponding dynamical signatures across the transition to regularity remain less explored . In this work, we investigate this transition by analyzing the time evolution of the survival probability, the single-site entanglement entropy, and the half-chain imbalance. Our results reveal a clear hierarchy in the sensitivity of these observables: the relaxation value of the entanglement entropy varies smoothly as a function of the Hamiltonian parameters across the chaos-regular transition, while the imbalance exhibits a more pronounced distinction. Most notably, the survival probability emerges as the most robust indicator of the transition between chaos and regularity. When appropriately scaled, all three observables converge onto a common behavior as a function of the Hamiltonian parameters for different numbers of sites and bosons,enabling a universal characterization of the transition between chaotic and regular dynamics.

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Carlos Diaz-Mejia, Sergio Lerma-Hernandez, Jorge G. Hirsch. 2026-01-30. Dynamical witnesses and universal behavior across chaos and non-ergodicity in the tilted Bose-Hubbard model. https://arxiv.org/abs/2602.00369

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