2023/09/17 by Wei Fan, Fan, Wei, H. W. Zhang +2 · 1 citation
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Physics (quant-ph) #Spectroscopy and Quantum Chemical Studies #Strong Light-Matter Interactions
paper · pdf · doi:10.48550/arxiv.2309.09269
openalex publication_date 2023/09/17 · openalex created_date 2023/09/20 · openalex updated_date 2026/07/28
We study the effect of anharmonicity in quantum anharmonic oscillators, by computing the energy gap between the ground and the 1st excited state using the numerical bootstrap method. Based on perturbative formulae of limiting coupling regimes, we propose a qualitative formula of the energy gap across all coupling values. Except detailed numerical parameter values, the proposed formula has the same functional form as the formula of ground state level splitting of double-well potentials, proposed recently in arXiv:2308.11516. This unifies the effects of anharmonicity in both the anharmonic oscillators and the double-well potentials, although the underlying physical process of them are completely different. We give an explanation of this connection of their anharmonicity from the viewpoint of quantum phase transitions. This connection is justified up to the octic anharmonicities by the numerical bootstrap.