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Discrete Scaling in Non-integer Dimensions

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Abstract

We explore the effect of a finite two-body energy in the discrete scale symmetry regime of two heavy bosonic impurities immersed in a light bosonic system. By means of the Born–Oppenheimer approximation in non-integer dimensions (D), we discuss the effective potential of the heavy-particles Schrodinger equation. We study how including the two-body energy in the effective potential changes the light-particles wave function and the ratio between successive Efimov states. We present the limit cycles associated with correlation between the energy of successive levels for the three and four-body systems. Our study is exemplified by considering a system composed of N-bosons, namely two Rubidium atoms interacting with N-2 Lithium ones (\(^7\)Li\(_{N-2}{-}^{87}\)Rb\(_2\)), which represent compounds of current experimental interest.

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Acknowledgements

This work was partially supported by Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) [Grant Nos. 2017/05660-0 and 2019/07767-1 (T.F.), 2023/08600-9 (R.M.F.), 2023/02261-8 (D.S.R.) and 2018/25225-9 (G.K.)] and Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) [Grant Nos. 306834/2022-7 (T.F.), 302105/2022-0 (M.T.Y.), and 309262/2019-4 (G.K.)].

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  1. T. Frederico, R. M. Francisco, D. S. Rosa, G. Krein and M. T. Yamashita have contributed equally to this work.

Authors and Affiliations

  1. DCTA, Instituto Tecnológico de Aeronáutica, Pr. Mal. Eduardo Gomes, São José dos Campos, SP, 12228-900, Brazil

    T. Frederico, R. M. Francisco & D. S. Rosa

  2. Instituto de Física Teórica, Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz, 271-Bloco II, São Paulo, SP, 01140-070, Brazil

    G. Krein & M. T. Yamashita

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Frederico, T., Francisco, R.M., Rosa, D.S. et al. Discrete Scaling in Non-integer Dimensions. Few-Body Syst 65, 28 (2024). https://doi.org/10.1007/s00601-024-01895-4

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