The Universality and stability for a dilute Bose gas with a Feshbach resonance

We study the bosonic atoms with a wide Feshbach resonance at zero temperature in terms of the renormalization group. We indicate that this system will always collapse in the dilute limit. On the side with a positive scattering length, the atomic superfluid is an unstable local minimum in the dilute limit and it determines the thermodynamics of this system within its lifetime. We calculate the equilibrium properties at zero temperature in the unitary regime. They exhibit universal scaling forms in the dilute limit due to the presence of a nontrivial zero temperature, zero density fixed point. Moreover, we find that the T=0 thermodynamics of this system in the unitary limit is exactly identical to the one for an ideal Fermi gas.Comment: 6 pages, 4 figure

Enhanced Dimer Relaxation in an Atomic/Molecular BEC

We derive a universal formula for the rate constant \beta for relaxation of a shallow dimer into deeply-bound diatomic molecules in the case of atoms with a large scattering length a. We show that \beta is determined by a and by two 3-body parameters that also determine the binding energies and widths of Efimov states. The rate constant \beta scales like \hbar a/m near the resonance, but the coefficient is a periodic function of ln(a) that may have resonant enhancement at values of a that differ by multiples of 22.7.Comment: 5 pages, revtex4, 2 PS figures, title changed, final versio

Estiamte of the two-photon exchange effect on deuteron electromagnetic form factors

The corrections of two-photon exchange on deuteron electromagnetic form factors are estimated based on an effective Lagrangian approach. Numerical results for the form factors $G_{C,M,Q}$ of the deuteron with the corrections are compared to its empirical ones. Moreover, the two new form factors, due to the two-photon exchange, are analyzed. Possible way to test the two-photon exchange corrections to the deuteron form factors is discussed.Comment: 17 pages, 10 figure

The PCA-seq method applied to analyze of the dynamics of COVID-19 epidemic indicators

In time series analysis using the SSA method, a univariate series is converted into the multivariate one by shifts. The resulting trajectory matrix is subjected to principal component analysis (PCA). However, the principal components can also be computed using the PCA-Seq method if segments of the original series are selected as objects. The matrix of Euclidean distances between the objects can be obtained using any method, which offers additional opportunities for time series analysis compared to the conventional SSA. In this study, the PCA-Seq method was used to analyze the dynamics of COVID-19 epidemic indicators