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Discrete and continuous scale invariance in the quantum few-body problem

Grant number: 23/08600-9
Support Opportunities:Scholarships in Brazil - Post-Doctoral
Start date: October 01, 2023
End date: September 30, 2026
Field of knowledge:Physical Sciences and Mathematics - Physics - General Physics
Principal Investigator:Tobias Frederico
Grantee:Rafael Mendes Francisco
Host Institution: Divisão de Ciências Fundamentais (IEF). Instituto Tecnológico de Aeronáutica (ITA). Ministério da Defesa (Brasil). São José dos Campos , SP, Brazil
Associated research grant:17/05660-0 - Theoretical studies of the structure and reactions of exotic nuclei and many-body systems, AP.TEM

Abstract

Theoretically discovered in 1970, the Efimov effect is associated with the existence of a discrete scale symmetry in three-dimensional three-boson systems interacting with short-range interactionsin the limit of infinite scattering length. This discrete scale symmetry manifests itself through an infinite series of loosely bound states, geometrically separated, that condense at the continuum threshold. Cycles associated with these states have been observed in ultracold atomic gasesclose to Feshbach resonances. Besides that, theoretical evidences show that this phenomenon is more general and, in addition to the Efimov cycle, there are new interwoven cycles that are features of four or more particles, leading to the presence of new discrete-scale symmetries and few-body scales. We will investigate the consequences of new interwoven and separate cycles that lead to universal scaling laws (limit cycles) correlating different few-body observables. These scaling laws are present in reaction rates of atomic systems, in the structure of weakly bound molecules, as well as in ultracold magneto-optical traps close to the Feshbach resonances. Besides the investigations mentioned above, we intend to study systems of bosons in non-integer dimensions associated with the trap squeeze. In these systems, we will use the fact that decreasing the non-integer dimension leads to the transition from the discrete scale symmetry regime to the continuous one in order to investigate the "non-atomic" physics in few-atoms systems. By means of the Faddeev-Yakubovsky equations in the limit of a zero-range interaction, we will address mass imbalanced few-body systems, with up to four particles, in integer and non-integer dimensions. We will also study multi-body systems with extreme mass imbalance for heavy-light resonant s-wave interaction in harmonic traps with the aim to compare this approach with the non-integer dimension formulation.

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Scientific publications (4)
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
FREDERICO, T.; FRANCISCO, R. M.; ROSA, D. S.; KREIN, G.; YAMASHITA, M. T.. Discrete Scaling in Non-integer Dimensions. FEW-BODY SYSTEMS, v. 65, n. 2, p. 10-pg., . (17/05660-0, 23/08600-9, 19/07767-1, 23/02261-8, 18/25225-9)
ROSA, D. S.; FREDERICO, T.; FRANCISCO, R. M.; KREIN, G.; YAMASHITA, M. T.. Reliability of the Born-Oppenheimer Approximation in Noninteger Dimensions. FEW-BODY SYSTEMS, v. 65, n. 3, p. 11-pg., . (17/05660-0, 23/08600-9, 19/07767-1, 23/02261-8, 18/25225-9)
ROSA, D. S.; FRANCISCO, R. M.; FREDERICO, T.; KREIN, G.; YAMASHITA, M. T.. Confinement-induced unatomic trimer states. PHYSICAL REVIEW A, v. 110, n. 4, p. 9-pg., . (19/07767-1, 23/02261-8, 23/08600-9, 18/25225-9)
SANTOS, J. P.; MORAIS, R. H. M.; FRANCISCO, R. M.; ROSA, D. S.; NEPOMUCENO, E.. Magnetocaloric effect properties in the Ashkin-Teller model. Journal of Magnetism and Magnetic Materials, v. 607, p. 9-pg., . (23/02261-8, 23/08600-9)