Robust quantification of spectral transitions in perturbed quantum systems

• URL: http://arxiv.org/abs/2505.19904v1
• Date: Mon, 26 May 2025 12:33:07 GMT
• Title: Robust quantification of spectral transitions in perturbed quantum systems
• Authors: Zsolt Szabó, Stefan Gehr, Paolo Facchi, Kazuya Yuasa, Daniel Burgarth, Davide Lonigro,
• Abstract summary: A quantum system can experience leakage between uncoupled regions of its energy spectrum separated by a gap.<n>We establish time-independent bounds on the distances between the true dynamics and the dynamics generated by block-diagonal effective evolutions.<n>We prove that, under the right conditions, this leakage remains small eternally.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 a finite spectral gap, thus accommodating continuous and unbounded spectra. Finally, we apply our bounds to specific systems of practical interest.

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