Energy spectra of small bosonic clusters having a large two-body scattering length

In this work we investigate small clusters of bosons using the hyperspherical harmonic basis. We consider systems with $A=2,3,4,5,6$ particles interacting through a soft inter-particle potential. In order to make contact with a real system, we use an attractive gaussian potential that reproduces the values of the dimer binding energy and the atom-atom scattering length obtained with one of the most widely used $^4$He-$^4$He interactions, the LM2M2 potential. The intensity of the potential is varied in order to explore the clusters' spectra in different regions with large positive and large negative values of the two-body scattering length. In addition, we include a repulsive three-body force to reproduce the trimer binding energy. With this model, consisting in the sum of a two- and three-body potential, we have calculated the spectrum of the four, five and six particle systems. In all the region explored, we have found that these systems present two bound states, one deep and one shallow close to the $A-1$ threshold. Some universal relations between the energy levels are extracted; in particular, we have estimated the universal ratios between thresholds of the three-, four-, and five-particle continuum using the two-body gaussia

The structure of the atomic helium trimers: Halos and Efimov states

The Faddeev equations for the atomic helium-trimer systems are solved numerically with high accuracy both for the most sophisticated realistic potentials available and for simple phenomenological potentials. An efficient numerical procedure is described. The large-distance asymptotic behavior, crucial for weakly bound three-body systems, is described almost analytically for arbitrary potentials. The Efimov effect is especially considered. The geometric structures of the bound states are quantitatively investigated. The accuracy of the schematic models and previous computations is comparable, i.e. within 20% for the spatially extended states and within 40% for the smaller ^4He-trimer ground state.Comment: 32 pages containing 7 figures and 6 table

Production of three-body Efimov molecules in an optical lattice

We study the possibility of associating meta-stable Efimov trimers from three free Bose atoms in a tight trap realised, for instance, via an optical lattice site or a microchip. The suggested scheme for the production of these molecules is based on magnetically tunable Feshbach resonances and takes advantage of the Efimov effect in three-body energy spectra. Our predictions on the energy levels and wave functions of three pairwise interacting 85Rb atoms rely upon exact solutions of the Faddeev equations and include the tightly confining potential of an isotropic harmonic atom trap. The magnetic field dependence of these energy levels indicates that it is the lowest energetic Efimov trimer state that can be associated in an adiabatic sweep of the field strength. We show that the binding energies and spatial extents of the trimer molecules produced are comparable, in their magnitudes, to those of the associated diatomic Feshbach molecule. The three-body molecular state follows Efimov's scenario when the pairwise attraction of the atoms is strengthened by tuning the magnetic field strength.Comment: 21 pages, 8 figures (final version

Rare decay pi0 -> e+e-: theory confronts KTeV data

Within the dispersive approach to the amplitude of the rare decay pi0 -> e+e- the nontrivial dynamics is contained only in the subtraction constant. We express this constant, in the leading order in (m_e/\Lambda)^2 perturbative series, in terms of the inverse moment of the pion transition form factor given in symmetric kinematics. By using the CELLO and CLEO data on the pion transition form factor given in asymmetric kinematics the lower bound on the decay branching ratio is found. The restrictions following from QCD allow us to make a quantitative prediction for the branching B(pi0 -> e+e-) =(6.2\pm 0.1)*10^{-8} which is 3\sigma below the recent KTeV measurement. We confirm our prediction by using the quark models and phenomenological approaches based on the vector meson dominance. The decays \eta -> l^+l^- are also discussed.Comment: 7 pages, 1 figur

A non-perturbative method of calculation of Green functions

A new method for non-perturbative calculation of Green functions in quantum mechanics and quantum field theory is proposed. The method is based on an approximation of Schwinger-Dyson equation for the generating functional by exactly soluble equation in functional derivatives. Equations of the leading approximation and the first step are solved for $\phi^4_d$-model. At $d=1$ (anharmonic oscillator) the ground state energy is calculated. The renormalization program is performed for the field theory at $d=2,3$. At $d=4$ the renormalization of the coupling involves a trivialization of the theory.Comment: 13 pages, Plain LaTex, no figures, some discussion of results for anharmonic oscillator and a number of references are added, final version published in Journal of Physics

Integrable magnetic geodesic flows on Lie groups

Right-invariant geodesic flows on manifolds of Lie groups associated with 2-cocycles of corresponding Lie algebras are discussed. Algebra of integrals of motion for magnetic geodesic flows is considered and necessary and sufficient condition of integrability in quadratures is formulated. Canonic forms for 2-cocycles of all 4-dimensional Lie algebras are given and integrable cases among them are separated.Comment: 16 page

Strong and radiative decays of the Ds0*(2317) meson in the DK-molecule picture

We consider a possible interpretation of the new charm-strange meson Ds0*(2317) as a hadronic molecule - a bound state of D and K mesons. Using an effective Lagrangian approach we calculate the strong Ds0* to Ds pi0 and radiative Ds0* to Ds* gamma decays. A new impact related to the DK molecular structure of the Ds0*(2317) meson is that the presence of u(d) quarks in the D and K mesons gives rise to a direct strong isospin-violating transition Ds0* to Ds pi0 in addition to the decay mechanism induced by eta-pi0 mixing considered previously. We show that the direct transition dominates over the eta-pi0 mixing transition in the Ds0* to Ds pi0 decay. Our results for the partial decay widths are consistent with previous calculations.Comment: 22 pages, 4 figures, accepted for publication in Phys. Rev.

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