2023/12/09 by Eduard Ianovich, Ianovich, E. A.
Mathematics · Physics and Astronomy · #34E10 #47A75 #47B02 #47B07 #47B25 #47B28 #81Q10 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems #Quantum optics and atomic interactions #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2312.05646
openalex publication_date 2023/12/09 · openalex created_date 2023/12/13 · openalex updated_date 2026/07/28
In this work the general results about asymptotics of eigenvalues of unbounded operators are obtained. We consider here different cases of compact, relatively compact, selfadjoint or nonselfadjoint perturbations. In particular we prove a generalization of Janas-Naboko lemma about eigenvalues asymptotics of unbounded operators at compact perturbation. A generalization of our previous result about noncompact perturbation of oscillator spectrum is also given. As an example we consider two-photon quantum Rabi model. We obtain tree-term asymptotic formula for large eigenvalues of the energy operator of this model. The asymptotics of related to this model polynomials is found. We give also an original proof of the Perelomov factorization theorem for contraction operator of quantum optics.