Robust quantification of spectral transitions in perturbed quantum systems

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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Publication Details

Journal
Physical review. A/Physical review, A
Published
2025-09-02
DOI
https://doi.org/10.1103/j44p-13j7
Primary Topic
Quantum chaos and dynamical systems
Type
article
Field-Weighted Citation Impact
0.00

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article

Robust quantification of spectral transitions in perturbed quantum systems

Daniel Burgarth, Paolo Facchi, Davide Lonigro, Kazuya Yuasa et al.
Physical review. A/Physical review, A
Quantum chaos and dynamical systems
article

Robust quantification of spectral transitions in perturbed quantum systems

Daniel Burgarth, Paolo Facchi, Davide Lonigro, Kazuya Yuasa, Zsolt Szabó, Stefan Gehr
article en

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.

Physical review. A/Physical review, AVol. 112(3)
Waseda University (JP), Friedrich-Alexander-Universität Erlangen-Nürnberg (DE), Istituto Nazionale di Fisica Nucleare, Sezione di Bari (IT), ARC Centre of Excellence for Engineered Quantum Systems (AU), University of Bari Aldo Moro (IT), Macquarie University (AU)
Istituto Nazionale di Alta Matematica "Francesco Severi", Dipartimenti di Eccellenza, Friedrich-Alexander-Universität Erlangen-Nürnberg, Ministry of Education, Culture, Sports, Science and Technology, Gruppo Nazionale per la Fisica Matematica, Japan Society for the Promotion of Science
Openalex Percentile: Top 82%
Quantum chaos and dynamical systems
DOIOpen Access PDFOpenAlex
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