Quantum corrections to the ground state energy of a trapped Bose-Einstein condensate: A diffusion Monte Carlo calculation

The diffusion Monte Carlo method is applied to describe a trapped atomic Bose-Einstein condensate at zero temperature, fully quantum mechanically and nonperturbatively. For low densities, $n(0)a^3 \le 2 \cdot 10^{-3}$ [n(0): peak density, a: s-wave scattering length], our calculations confirm that the exact ground state energy for a sum of two-body interactions depends on only the atomic physics parameter a, and no other details of the two-body model potential. Corrections to the mean-field Gross-Pitaevskii energy range from being essentially negligible to about 20% for N=2-50 particles in the trap with positive s-wave scattering length a=100-10000 a.u.. Our numerical calculations confirm that inclusion of an additional effective potential term in the mean-field equation, which accounts for quantum fluctuations [see e.g. E. Braaten and A. Nieto, Phys. Rev. B 56}, 14745 (1997)], leads to a greatly improved description of trapped Bose gases.Comment: 7 pages, 4 figure

The theta^+ baryon in soliton models: large Nc QCD and the validity of rigid-rotor quantization

A light collective theta+ baryon state (with strangeness +1) was predicted via rigid-rotor collective quantization of SU(3) chiral soliton models. This paper explores the validity of this treatment. A number of rather general analyses suggest that predictions of exotic baryon properties based on this approximation do not follow from large Nc QCD. These include an analysis of the baryon's width, a comparison of the predictions with general large Nc consistency conditions of the Gervais-Sakita-Dashen-Manohar type; an application of the technique to QCD in the limit where the quarks are heavy; a comparison of this method with the vibration approach of Callan and Klebanov; and the 1/Nc scaling of the excitation energy. It is suggested that the origin of the problem lies in an implicit assumption in the that the collective motion is orthogonal to vibrational motion. While true for non-exotic motion, the Wess-Zumino term induces mixing at leading order between collective and vibrational motion with exotic quantum numbers. This suggests that successful phenomenological predictions of theta+ properties based on rigid-rotor quantization were accidental.Comment: 19 pages; A shorter more readable versio

Signals of Disoriented Chiral Condensate

If a disoriented chiral condensate is created over an extended space-time region following a rapid cooling in hadronic or nuclear collisions, the misalignment of the condensate with the electroweak symmetry breaking can generate observable effects in the processes which involve both strong and electromagnetic interactions. We point out the relevance of the dilepton decay of light vector mesons as a signal for formation of the disoriented condensate. We predict that the decay \rho^0 to dileptons will be suppressed and/or the \rho resonance peak widens, while the decay \omega to dileptons will not be affected by the condensate.Comment: 13 pages in LaTeX, UCB-PTH-94/05, LBL-3533

Pedestrian Solution of the Two-Dimensional Ising Model

The partition function of the two-dimensional Ising model with zero magnetic field on a square lattice with m x n sites wrapped on a torus is computed within the transfer matrix formalism in an explicit step-by-step approach inspired by Kaufman's work. However, working with two commuting representations of the complex rotation group SO(2n,C) helps us avoid a number of unnecessary complications. We find all eigenvalues of the transfer matrix and therefore the partition function in a straightforward way.Comment: 10 pages, 2 figures; eqs. (101) and (102) corrected, files for fig. 2 fixed, minor beautification

Distribution and density of the partition function zeros for the diamond-decorated Ising model

Exact renormalization map of temperature between two successive decorated lattices is given, and the distribution of the partition function zeros in the complex temperature plane is obtained for any decoration-level. The rule governing the variation of the distribution pattern as the decoration-level changes is given. The densities of the zeros for the first two decoration-levels are calculated explicitly, and the qualitative features about the densities of higher decoration-levels are given by conjecture. The Julia set associated with the renormalization map is contained in the distribution of the zeros in the limit of infinite decoration level, and the formation of the Julia set in the course of increasing the decoration-level is given in terms of the variations of the zero density.Comment: 8 pages,8figure

The Second Order Upper Bound for the Ground Energy of a Bose Gas

Consider $N$ bosons in a finite box $\Lambda= [0,L]^3\subset \mathbf R^3$ interacting via a two-body smooth repulsive short range potential. We construct a variational state which gives the following upper bound on the ground state energy per particle $$\bar\lim_{\rho\to0} \bar \lim_{L \to \infty, N/L^3 \to \rho} (\frac{e_0(\rho)- 4 \pi a \rho}{(4 \pi a)^{5/2}(\rho)^{3/2}})\leq \frac{16}{15\pi^2},$$ where $a$ is the scattering length of the potential. Previously, an upper bound of the form $C 16/15\pi^2$ for some constant $C > 1$ was obtained in \cite{ESY}. Our result proves the upper bound of the the prediction by Lee-Yang \cite{LYang} and Lee-Huang-Yang \cite{LHY}.Comment: 62 pages, no figure

Self-Trapping, Quantum Tunneling and Decay Rates for a Bose Gas with Attractive Nonlocal Interaction

We study the Bose-Einstein condensation for a cloud of $^7$Li atoms with attractive nonlocal (finite-range) interaction in a harmonic trap. In addition to the low-density metastable branch, that is present also in the case of local interaction, a new stable branch appears at higher densities. For a large number of atoms, the size of the cloud in the stable high-density branch is independent of the trap size and the atoms are in a macroscopic quantum self-trapped configuration. We analyze the macroscopic quantum tunneling between the low-density metastable branch and the high-density one by using the istanton technique. Moreover we consider the decay rate of the Bose condensate due to inelastic two- and three-body collisions.Comment: 5 pages, 4 figures, submitted to Phys. Rev.

Supersymmetric CP Violation in B→Xsl+l−B \to X_s l^+ l^- in Minimal Supergravity Model

Direct CP asymmetries and the CP violating normal polarization of lepton in inclusive decay B \to X_s l^+ l^- are investigated in minimal supergravity model with CP violating phases. The contributions coming from exchanging neutral Higgs bosons are included. It is shown that the direct CP violation in branching ratio, A_{CP}^1, is of {\cal{O}}(10^{-3}) for l=e, \mu, \tau. The CP violating normal polarization for l=\mu can reach 0.5 percent when tan\beta is large (say, 36). For l=\tau and in the case of large \tan\beta, the direct CP violation in backward-forward asymmetry, A_{CP}^2, can reach one percent, the normal polarization of \tau can be as large as a few percent, and both are sensitive to the two CP violating phases, \phi_\mu and \phi_{A_0}, and consequently it could be possible to observe them (in particular, the normal polarization of \tau) in the future B factories.Comment: 14 pages, latex, 5 figure

Quantum Corrections to Dilute Bose Liquids

It was recently shown (A. Bulgac. Phys. Rev. Lett. {\bf 89}, 050402 (2002)) that an entirely new class of quantum liquids with widely tunable properties could be manufactured from bosons (boselets), fermions (fermilets) and their mixtures (ferbolets) by controlling their interaction properties by the means of a Feshbach resonance. We extend the previous mean--field analysis of these quantum liquids by computing the lowest order quantum corrections to the ground state energy and the depletion of the Bose--Einstein condensate and by estimating higher order corrections as well. We show that the quantum corrections are relatively small and controlled by the diluteness parameter $\sqrt{n|a|^3} \ll 1$, even though strictly speaking in this case there is no low density expansion.Comment: final published version, typos corrected, updated references and added one referenc

A Naturally Narrow Positive Parity Theta^+

We present a consistent color-flavor-spin-orbital wave function for a positive parity Theta^+ that naturally explains the observed narrowness of the state. The wave function is totally symmetric in its flavor-spin part and totally antisymmetric in its color-orbital part. If flavor-spin interactions dominate, this wave function renders the positive parity Theta^+ lighter than its negative parity counterpart. We consider decays of the Theta^+ and compute the overlap of this state with the kinematically allowed final states. Our results are numerically small. We note that dynamical correlations between quarks are not necessary to obtain narrow pentaquark widths.Comment: 10 pages, 1 figure, Revtex4, two-column format, version to be published in Phys. Rev. D, includes numerical estimates of decay width