Robust quantification of spectral transitions in perturbed quantum systems
Fuente:
arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915473894932480 |
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| author | Szabó, Zsolt Gehr, Stefan Facchi, Paolo Yuasa, Kazuya Burgarth, Daniel Lonigro, Davide |
| author_facet | Szabó, Zsolt Gehr, Stefan Facchi, Paolo Yuasa, Kazuya Burgarth, Daniel Lonigro, Davide |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_19904 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Robust quantification of spectral transitions in perturbed quantum systems Szabó, Zsolt Gehr, Stefan Facchi, Paolo Yuasa, Kazuya Burgarth, Daniel Lonigro, Davide Quantum Physics Mathematical Physics 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. |
| title | Robust quantification of spectral transitions in perturbed quantum systems |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2505.19904 |