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This research advances the theoretical understanding of quantum optics by proving the Braak conjecture for perturbative models of the Rabi system and analyzing spectral asymptotics in generalized N-level atom configurations. The work provides rigorous mathematical expansions for eigenvalues within this specific class of non-integrable Hamiltonian systems, contributing directly to foundational developments in Quantum Computing physics rather than consumer applications or general software events.

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Perturbation Theory and the Quantum Rabi-model

arXiv21 iulie 20261 min de cititArticolul și perspectiva sunt în engleză.

arXiv:2601.17924v3 Announce Type: replace Abstract: In the first part of the paper we study a perturbative model of the Rabi system of Quantum Optics. We are therefore able to describe, through Rellich's theory, an analytic expansion of finite families of eigenvalues, of arbitrary fixed length. In particular, we prove that for finite families of eigenvalues the Braak conjecture holds. In the second part we study the asymptotics of the Weyl spectral counting function of a class of systems that generalize the Quantum Rabi Model to an $N$-level atom ($N\geq3$) with $N-1$ cavity modes of the electromagnetic field.

Abstract:In the first part of the paper we study a perturbative model of the Rabi system of Quantum Optics. We are therefore able to describe, through Rellich's theory, an analytic expansion of finite families of eigenvalues, of arbitrary fixed length. In particular, we prove that for finite families of eigenvalues the Braak conjecture holds. In the second part we study the asymptotics of the Weyl spectral counting function of a class of systems that generalize the Quantum Rabi Model to an $N$-level atom ($N\geq3$) with $N-1$ cavity modes of the electromagnetic field.

Quantum Physics (quant-ph); Analysis of PDEs (math.AP); Spectral Theory (math.SP)

arXiv:2601.17924 [quant-ph]

(or arXiv:2601.17924v3 [quant-ph] for this version)

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