The Gross-Pitaevskii Equation for Bose Particles in a Double Well Potential: Two Mode Models and Beyond

There have been many discussions of two-mode models for Bose condensates in a double well potential, but few cases in which parameters for these models have been calculated for realistic situations. Recent experiments lead us to use the Gross-Pitaevskii equation to obtain optimum two-mode parameters. We find that by using the lowest symmetric and antisymmetric wavefunctions, it is possible to derive equations for a more exact two-mode model that provides for a variable tunneling rate depending on the instantaneous values of the number of atoms and phase differences. Especially for larger values of the nonlinear interaction term and larger barrier heights, results from this model produce better agreement with numerical solutions of the time-dependent Gross-Pitaevskii equation in 1D and 3D, as compared with previous models with constant tunneling, and better agreement with experimental results for the tunneling oscillation frequency [Albiez et al., cond-mat/0411757]. We also show how this approach can be used to obtain modified equations for a second quantized version of the Bose double well problem.Comment: RevTeX, 14 pages, 14 figure

Isoscalar-isovector mass splittings in excited mesons

Mass splittings between the isovector and isoscalar members of meson nonets arise in part from hadronic loop diagrams which violate the Okubo-Zweig-Iizuka rule. Using a model for these loop processes which works qualitatively well in the established nonets, I tabulate predictions for the splittings and associated isoscalar mixing angles in the remaining nonets below about 2.5 GeV, and explain some of their systematic features. The results for excited vector mesons compare favorably with experiment.Comment: 8 RevTeX pages, including 1 LaTeX figure. CMU-HEP93-23/DOE-ER-40682-4

Why is the B -> eta' X decay width so large ?

New mechanism for the observed inclusive B -> \eta'X decay is suggested. We argue that the dominant contribution to this amplitude is due to the Cabbibo favored b -> \bar{c}cs process followed by the transition \bar{c}c -> \eta'. A large magnitude of the "intrinsic charm" component of \eta' is of critical importance in our approach. Our results are consistent with an unexpectedly large Br(B -> \eta'+X) \sim 10^{-3} recently announced by CLEO. We stress the uniqueness of this channel for 0^{-+} gluonia search.Comment: Comments on a mixing model for intrinsic charm and pre-asymptotic effects and some references are added. Latex, 9 page

Comment on Octet Baryon Magnetic Moments in the Chiral Quark Model with Configuration Mixing

The importance of exchange currents, and of conserving isotopic spin at both the quark and baryon levels in application of the chiral quark model to any calculation of baryon magnetic moments is emphasized.Comment: 5 pages, Latex fil

Final State Interactions and New Physics in B -> pi K Decays

Within the Standard Model, and if one assumes that soft rescattering effects are negligible, the CP asymmetry A^dir_CP (B^\pm -> \pi^\pm K) is predicted to be very small and the ratio R = BR(B_d -> \pi^\mp K^\pm)/BR(B^\pm -> \pi^\pm K) provides a bound on the angle \gamma of the unitarity triangle, sin^2 \gamma \leq R. We estimate the corrections from soft rescattering effects using an approach based on Regge phenomenology, and find effects of order 10% with large uncertainties. In particular, we conclude that A^dir_CP \sim 0.2 and sin^2 \gamma \sim 1.2 R could not be taken unambiguously to signal New Physics. Using SU(3) relations, we suggest experimental tests that could constrain the size of the soft rescattering effects thus reducing the related uncertainty. Finally, we study the effect of various models of New Physics on A^dir_CP and on R.Comment: 20 pages, RevTex, no figures; a few typos corrected, references added, brief additional discussion of uncertanties is adde

Beyond the relativistic mean-field approximation (II): configuration mixing of mean-field wave functions projected on angular momentum and particle number

The framework of relativistic self-consistent mean-field models is extended to include correlations related to the restoration of broken symmetries and to fluctuations of collective variables. The generator coordinate method is used to perform configuration mixing of angular-momentum and particle-number projected relativistic wave functions. The geometry is restricted to axially symmetric shapes, and the intrinsic wave functions are generated from the solutions of the relativistic mean-field + Lipkin-Nogami BCS equations, with a constraint on the mass quadrupole moment. The model employs a relativistic point-coupling (contact) nucleon-nucleon effective interaction in the particle-hole channel, and a density-independent $\delta$-interaction in the pairing channel. Illustrative calculations are performed for $^{24}$Mg, $^{32}$S and $^{36}$Ar, and compared with results obtained employing the model developed in the first part of this work, i.e. without particle-number projection, as well as with the corresponding non-relativistic models based on Skyrme and Gogny effective interactions.Comment: 37 pages, 10 figures, submitted to Physical Review

On the feasibility of a nuclear exciton laser

Nuclear excitons known from M\"ossbauer spectroscopy describe coherent excitations of a large number of nuclei -- analogous to Dicke states (or Dicke super-radiance) in quantum optics. In this paper, we study the possibility of constructing a laser based on these coherent excitations. In contrast to the free electron laser (in its usual design), such a device would be based on stimulated emission and thus might offer certain advantages, e.g., regarding energy-momentum accuracy. Unfortunately, inserting realistic parameters, the window of operability is probably not open (yet) to present-day technology -- but our design should be feasible in the UV regime, for example.Comment: 7 pages RevTeX, 4 figure

Diquarks and Exotic Spectroscopy

We propose that the recently discovered \Theta baryon is a bound state of four quarks and an antiquark, containing two highly correlated ud-pairs. If so, the \Theta baryon has positive parity, and it lies in an near-ideally mixed SU(3)_{f} \mathbf{\bar{10}}_{f} oplus \mathbf{8}_{f}. The Roper resonance and the P_{11}(1710) fit naturally into this classification. We predict an isospin 3/2 multiplet of \Xi's (S=-2) with J^{\Pi}=\half^{+} around 1750 MeV. A search for manifestly exotic \Xi^{+} and \Xi^{--} in this mass range could provide a sharp test of our proposal. We predict that charm and bottom analogues of the \Theta baryon are stable against strong decays.Comment: 5 pages, 2 figures, revtex 4, minor corrections and revisions for journal publicatio

Broken SU(3) Symmetry in Two-Body B Decays

The decays of $B$ mesons to two-body hadronic final states are analyzed within the context of broken flavor SU(3) symmetry, extending a previous analysis involving pairs of light pseudoscalars to decays involving one or two charmed quarks in the final state. A systematic program is described for learning information {}from decay rates regarding (i) SU(3)-violating contributions, (ii) the magnitude of exchange and annihilation diagrams (effects involving the spectator quark), and (iii) strong final-state interactions. The implication of SU(3)-breaking effects for the extraction of weak phases is also examined. The present status of data on these questions is reviewed and suggestions for further experimental study are made.Comment: 38 pages, 8 figures, LaTeX file. The full postscript manuscript is available by anon ftp at ftp://lpsvsh.lps.umontreal.ca/theorie/hep-ph/SU3break.ps (a VAX so use the format theorie.hep-ph if you change by more than one directory at a time

On the equivalence of pairing correlations and intrinsic vortical currents in rotating nuclei

The present paper establishes a link between pairing correlations in rotating nuclei and collective vortical modes in the intrinsic frame. We show that the latter can be embodied by a simple S-type coupling a la Chandrasekhar between rotational and intrinsic vortical collective modes. This results from a comparison between the solutions of microscopic calculations within the HFB and the HF Routhian formalisms. The HF Routhian solutions are constrained to have the same Kelvin circulation expectation value as the HFB ones. It is shown in several mass regions, pairing regimes, and for various spin values that this procedure yields moments of inertia, angular velocities, and current distributions which are very similar within both formalisms. We finally present perspectives for further studies.Comment: 8 pages, 4 figures, submitted to Phys. Rev.