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arXiv · 2503.15572

Universal spectral bounds for the quantum Rabi model: Reformulating Braak's conjecture

Alfonso Lanuza
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Abstract

The quantum Rabi model is a paradigmatic example of a minimal yet nontrivial light-matter interaction, whose spectrum is transcendental yet exhibits a number of regularities. Braak observed that the eigenvalues bunch or anti-bunch following strict rules, leading to a conjecture that links integrability in quantum systems and residual order in their spectra. Understanding this structure is crucial for distinguishing deterministic quantum dynamics from chaotic behavior. Here, we present violations of Braak's conjecture and reformulate it through a set of eigenvalue inequalities that conjecturally hold across all parameter regimes. We prove these bounds in the low splitting regime, we characterize the strongly-coupled widely-split limit, and provide universal upper bounds on the entire spectrum. Our results uncover additional layers of spectral organization in the quantum Rabi model and expand the analytic toolkit for strongly coupled quantum systems.

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Alfonso Lanuza. 2025-03-19. Universal spectral bounds for the quantum Rabi model: Reformulating Braak's conjecture. https://arxiv.org/abs/2503.15572

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