Discrete Scaling in Non-integer Dimensions

IF 1.7 4区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Few-Body Systems Pub Date : 2024-03-19 DOI:10.1007/s00601-024-01895-4

引用次数: 0

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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非整数维离散缩放

摘要我们探讨了两个重玻色子杂质浸入轻玻色子系统的离散尺度对称体系中有限双体能量的影响。通过非整数维（D）的玻恩-奥本海默近似，我们讨论了重粒子薛定谔方程的有效势。我们研究了有效势中的双体能量如何改变轻粒子波函数以及连续埃菲莫夫态之间的比率。我们提出了与三体和四体系统连续级能之间的相关性有关的极限循环。我们的研究通过考虑一个由 N-玻色子组成的系统，即两个与 N-2 锂原子相互作用的铷原子（\(^7\) Li \(_{N-2}{-}^{87}\) Rb \(_2\)）来举例说明，它们代表了当前实验关注的化合物。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Few-Body Systems 物理-物理：综合

CiteScore

2.90

自引率

18.80%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal Few-Body Systems presents original research work – experimental, theoretical and computational – investigating the behavior of any classical or quantum system consisting of a small number of well-defined constituent structures. The focus is on the research methods, properties, and results characteristic of few-body systems. Examples of few-body systems range from few-quark states, light nuclear and hadronic systems; few-electron atomic systems and small molecules; and specific systems in condensed matter and surface physics (such as quantum dots and highly correlated trapped systems), up to and including large-scale celestial structures. Systems for which an equivalent one-body description is available or can be designed, and large systems for which specific many-body methods are needed are outside the scope of the journal. The journal is devoted to the publication of all aspects of few-body systems research and applications. While concentrating on few-body systems well-suited to rigorous solutions, the journal also encourages interdisciplinary contributions that foster common approaches and insights, introduce and benchmark the use of novel tools (e.g. machine learning) and develop relevant applications (e.g. few-body aspects in quantum technologies).