Condensates of Strongly-interacting Atoms and Dynamically Generated Dimers

In a system of atoms with large positive scattering length, weakly-bound diatomic molecules (dimers) are generated dynamically by the strong interactions between the atoms. If the atoms are modeled by a quantum field theory with an atom field only, condensates of dimers cannot be described by the mean-field approximation because there is no field associated with the dimers. We develop a method for describing dimer condensates in such a model based on the one-particle-irreducible (1PI) effective action. We construct an equivalent 1PI effective action that depends not only on the classical atom field but also on a classical dimer field. The method is illustrated by applying it to the many-body behavior of bosonic atoms with large scattering length at zero temperature using an approximation in which the 2-atom amplitude is treated exactly but irreducible $N$-atom amplitudes for $N \ge 3$ are neglected. The two 1PI effective actions give identical results for the atom superfluid phase, but the one with a classical dimer field is much more convenient for describing the dimer superfluid phase. The results are also compared with previous work on the Bose gas near a Feshbach resonance.Comment: 10 figure

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 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

Ds0*(2317) and Ds1(2460) mesons in two-body B-meson decays

We analyze the branching ratios of B to D(*) + Ds0*(Ds1) decays using the factorization hypothesis. The B to D(*) transition form factors are taken from a model-independent analysis done by Caprini, Lellouch and Neubert based on heavy quark spin symmetry and dispersive constraints, including short-distance and power corrections. The leptonic decay constants fDs0* and fDs1 are calculated assuming a molecular structure for the Ds0* and Ds1 mesons. The calculated branching ratios of B-meson two-body decays are compared with experimental data and other theoretical results.Comment: 12 pages, 2 figure

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

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

The maximum depth of shower with E sub 0 larger than 10(17) eV on average characteristics of EAS different components

The extensive air shower (EAS) development model independent method of the determination of a maximum depth of shower (X sub m) is considered. X sub m values obtained on various EAS parameters are in a good agreement

Estimation of composition of cosmic rays with E sub zero approximately equals 10(17) - 10(18) eV

Fluctuations of the shower maximum depth obtained from analysis of electron and muon fluctuations and the extensive air showers (EAS) Cerenkov light on the Yakutsk array data and data of other arrays are considered. On the basis of these the estimation of composition of primaries with E sub 0 = 5.10 to the 17th power eV is received. Estimation of gamma-quanta flux with E sub 0 10 to the 17th power eV is given on the poor-muon showers

Exact relations for quantum-mechanical few-body and many-body problems with short-range interactions in two and three dimensions

We derive relations between various observables for N particles with zero-range or short-range interactions, in continuous space or on a lattice, in two or three dimensions, in an arbitrary external potential. Some of our results generalise known relations between large-momentum behavior of the momentum distribution, short-distance behavior of the pair correlation function and of the one-body density matrix, derivative of the energy with respect to the scattering length or to time, and the norm of the regular part of the wavefunction; in the case of finite-range interactions, the interaction energy is also related to dE/da. The expression relating the energy to a functional of the momentum distribution is also generalised, and is found to break down for Efimov states with zero-range interactions, due to a subleading oscillating tail in the momentum distribution. We also obtain new expressions for the derivative of the energy of a universal state with respect to the effective range, the derivative of the energy of an efimovian state with respect to the three-body parameter, and the second order derivative of the energy with respect to the inverse (or the logarithm in the two-dimensional case) of the scattering length. The latter is negative at fixed entropy. We use exact relations to compute corrections to exactly solvable three-body problems and find agreement with available numerics. For the unitary gas, we compare exact relations to existing fixed-node Monte-Carlo data, and we test, with existing Quantum Monte Carlo results on different finite range models, our prediction that the leading deviation of the critical temperature from its zero range value is linear in the interaction effective range r_e with a model independent numerical coefficient.Comment: 51 pages, 5 figures. Split into three articles: Phys. Rev. A 83, 063614 (2011) [arXiv:1103.5157]; Phys. Rev. A 86, 013626 (2012) [arXiv:1204.3204]; Phys. Rev. A 86, 053633 (2012) [ arXiv:1210.1784

A semiclassical analysis of the Efimov energy spectrum in the unitary limit

We demonstrate that the (s-wave) geometric spectrum of the Efimov energy levels in the unitary limit is generated by the radial motion of a primitive periodic orbit (and its harmonics) of the corresponding classical system. The action of the primitive orbit depends logarithmically on the energy. It is shown to be consistent with an inverse-squared radial potential with a lower cut-off radius. The lowest-order WKB quantization, including the Langer correction, is shown to reproduce the geometric scaling of the energy spectrum. The (WKB) mean-squared radii of the Efimov states scale geometrically like the inverse of their energies. The WKB wavefunctions, regularized near the classical turning point by Langer's generalized connection formula, are practically indistinguishable from the exact wave functions even for the lowest ($n=0$) state, apart from a tiny shift of its zeros that remains constant for large $n$.Comment: LaTeX (revtex 4), 18pp., 4 Figs., already published in Phys. Rev. A but here a note with a new referece is added on p. 1