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TUE: Tuesday Contributed Sessions
TUE 10: Foundational / Mathematical Aspects – Rigorous Results
TUE 10.4: Vortrag
Dienstag, 9. September 2025, 15:00–15:15, ZHG103
Robust quantification of spectral transitions in perturbed quantum systems — Zsolt Szabó1,2, Stefan Gehr3, Paolo Facchi4,5, Kazuya Yuasa6, Daniel Burgarth3, and •Davide Lonigro3 — 1School of Mathematical and Physical Sciences, Macquarie University, NSW 2109, Australia — 2ARC Centre of Excellence for Engineered Quantum Systems, Macquarie University, NSW 2109, Australia — 3Department Physik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstraße 7, 91058 Erlangen, Germany — 4Dipartimento di Fisica, Università di Bari, I-70126 Bari, Italy — 5INFN, Sezione di Bari, I-70126 Bari, Italy — 6Department of Physics, Waseda University, Tokyo 169-8555, Japan
A quantum system subject to an external perturbation can experience leakage between uncoupled regions of its energy spectrum separated by a gap. To quantify this phenomenon, we present two complementary results. First, we establish time-independent bounds on the distances between the true dynamics and the dynamics generated by block-diagonal effective evolutions constructed via the Schrieffer-Wolff and Bloch methods. Second, we prove that, under the right conditions, this leakage remains small eternally. That is, we derive a time-independent bound on the leakage itself, expressed in terms of the spectral gap of the unperturbed Hamiltonian and the norm of the perturbation, ensuring its validity for arbitrarily large times. Our approach only requires the existence of a finite spectral gap, thus accommodating continuous and unbounded spectra.
Based on arXiv:2505.19904.
Keywords: Spectral transitions; Perturbed quantum systems; Spectral gap; Effective quantum evolution