The Renormalization Group Limit Cycle for the 1/r^2 Potential

Previous work has shown that if an attractive 1/r^2 potential is regularized at short distances by a spherical square-well potential, renormalization allows multiple solutions for the depth of the square well. The depth can be chosen to be a continuous function of the short-distance cutoff R, but it can also be a log-periodic function of R with finite discontinuities, corresponding to a renormalization group (RG) limit cycle. We consider the regularization with a delta-shell potential. In this case, the coupling constant is uniquely determined to be a log-periodic function of R with infinite discontinuities, and an RG limit cycle is unavoidable. In general, a regularization with an RG limit cycle is selected as the correct renormalization of the 1/r^2 potential by the conditions that the cutoff radius R can be made arbitrarily small and that physical observables are reproduced accurately at all energies much less than hbar^2/mR^2.Comment: 11 pages, 4 figure

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

Atom-Dimer Scattering in a Three-Component Fermi Gas

Ultracold gases of three distinguishable particles with large scattering lengths are expected to show rich few-body physics related to the Efimov effect. We have created three different mixtures of ultracold 6Li atoms and weakly bound 6Li2 dimers consisting of atoms in three different hyperfine states and studied their inelastic decay via atom-dimer collisions. We have found resonant enhancement of the decay due to the crossing of Efimov-like trimer states with the atom-dimer continuum in one mixture as well as minima of the decay in another mixture, which we interpret as a suppression of exchange reactions of the type |12>+|3> -> |23>+|1>. Such a suppression is caused by interference between different decay paths and demonstrates the possiblity to use Efimov physics to control the rate constants for molecular exchange reactions in the ultracold regime.Comment: 5 pages, 3 figure

Non-commutative low dimension spaces and superspaces associated with contracted quantum groups and supergroups

Quantum planes which correspond to all one parameter solutions of QYBE for the two-dimensional case of GL-groups are summarized and their geometrical interpretations are given. It is shown that the quantum dual plane is associated with an exotic solution of QYBE and the well-known quantum $h$-plane may be regarded as the quantum analog of the flag (or fiber) plane. Contractions of the quantum supergroup $GL_q(1|2)$ and corresponding quantum superspace $C_q(1|2)$ are considered in Cartesian basis. The contracted quantum superspace $C_h(1|2;\iota)$ is interpreted as the non-commutative analog of the superspace with the fiber odd part.Comment: Talk given at the XIII Int. Coll. on Integrable Systems and Quantum Groups, June 17-19, 2004, Prague, Czech Republic. Submitted in Czech. J. of Physic

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.

Gap-Townes solitons and localized excitations in low dimensional Bose Einstein condensates in optical lattices

We discuss localized ground states of Bose-Einstein condensates in optical lattices with attractive and repulsive three-body interactions in the framework of a quintic nonlinear Schr\"odinger equation which extends the Gross-Pitaevskii equation to the one dimensional case. We use both a variational method and a self-consistent approach to show the existence of unstable localized excitations which are similar to Townes solitons of the cubic nonlinear Schr\"odinger equation in two dimensions. These solutions are shown to be located in the forbidden zones of the band structure, very close to the band edges, separating decaying states from stable localized ones (gap-solitons) fully characterizing their delocalizing transition. In this context usual gap solitons appear as a mechanism for arresting collapse in low dimensional BEC in optical lattices with attractive real three-body interaction. The influence of the imaginary part of the three-body interaction, leading to dissipative effects on gap solitons and the effect of atoms feeding from the thermal cloud are also discussed. These results may be of interest for both BEC in atomic chip and Tonks-Girardeau gas in optical lattices

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

Light baryon magnetic moments and N -> Delta gamma transition in a Lorentz covariant chiral quark approach

We calculate magnetic moments of light baryons and N -> Delta gamma transition characteristics using a manifestly Lorentz covariant chiral quark approach for the study of baryons as bound states of constituent quarks dressed by a cloud of pseudoscalar mesons.Comment: 29 pages, 10 figures, accepted for publication in Phys. Rev.