Universal Loss Dynamics in a Unitary Bose Gas

The low temperature unitary Bose gas is a fundamental paradigm in few-body and many-body physics, attracting wide theoretical and experimental interest. Here we first present a theoretical model that describes the dynamic competition between two-body evaporation and three-body re-combination in a harmonically trapped unitary atomic gas above the condensation temperature. We identify a universal magic trap depth where, within some parameter range, evaporative cooling is balanced by recombination heating and the gas temperature stays constant. Our model is developed for the usual three-dimensional evaporation regime as well as the 2D evaporation case. Experiments performed with unitary 133 Cs and 7 Li atoms fully support our predictions and enable quantitative measurements of the 3-body recombination rate in the low temperature domain. In particular, we measure for the first time the Efimov inelasticity parameter $\eta$ * = 0.098(7) for the 47.8-G d-wave Feshbach resonance in 133 Cs. Combined 133 Cs and 7 Li experimental data allow investigations of loss dynamics over two orders of magnitude in temperature and four orders of magnitude in three-body loss. We confirm the 1/T 2 temperature universality law up to the constant $\eta$ *

Genes and Pathways Associated with Skeletal Sagittal Malocclusions: A Systematic Review

Skeletal class II and III malocclusions are craniofacial disorders that negatively impact people’s quality of life worldwide. Unfortunately, the growth patterns of skeletal malocclusions and their clinical correction prognoses are difficult to predict largely due to lack of knowledge of their precise etiology. Inspired by the strong inheritance pattern of a specific type of skeletal malocclusion, previous genome-wide association studies (GWAS) were reanalyzed, resulting in the identification of 19 skeletal class II malocclusion-associated and 53 skeletal class III malocclusion-associated genes. Functional enrichment of these genes created a signal pathway atlas in which most of the genes were associated with bone and cartilage growth and development, as expected, while some were characterized by functions related to skeletal muscle maturation and construction. Interestingly, several genes and enriched pathways are involved in both skeletal class II and III malocclusions, indicating the key regulatory effects of these genes and pathways in craniofacial development. There is no doubt that further investigation is necessary to validate these recognized genes’ and pathways’ specific function(s) related to maxillary and mandibular development. In summary, this systematic review provides initial insight on developing novel gene-based treatment strategies for skeletal malocclusions and paves the path for precision medicine where dental care providers can make an accurate prediction of the craniofacial growth of an individual patient based on his/her genetic profile. © 2021 by the authors. Licensee MDPI, Basel, Switzerland

Polynomial Growth Harmonic Functions on Finitely Generated Abelian Groups

In the present paper, we develop geometric analytic techniques on Cayley graphs of finitely generated abelian groups to study the polynomial growth harmonic functions. We develop a geometric analytic proof of the classical Heilbronn theorem and the recent Nayar theorem on polynomial growth harmonic functions on lattices \mathds{Z}^n that does not use a representation formula for harmonic functions. We also calculate the precise dimension of the space of polynomial growth harmonic functions on finitely generated abelian groups. While the Cayley graph not only depends on the abelian group, but also on the choice of a generating set, we find that this dimension depends only on the group itself.Comment: 15 pages, to appear in Ann. Global Anal. Geo

Extracting density-density correlations from in situ images of atomic quantum gases

We present a complete recipe to extract the density-density correlations and the static structure factor of a two-dimensional (2D) atomic quantum gas from in situ imaging. Using images of non-interacting thermal gases, we characterize and remove the systematic contributions of imaging aberrations to the measured density-density correlations of atomic samples. We determine the static structure factor and report results on weakly interacting 2D Bose gases, as well as strongly interacting gases in a 2D optical lattice. In the strongly interacting regime, we observe a strong suppression of the static structure factor at long wavelengths.Comment: 15 pages, 5 figure