Supersymmetric Polytropic Gas Dynamics

We construct the N=1 supersymmetric extension of the polytropic gas dynamics. We give both the Lagrangian as well as the Hamiltonian description of this system. We construct the infinite set of "Eulerian'' conserved charges associated with this system and show that they are in involution, thereby proving complete integrability of this system. We construct the SUSY -B extension of this system as well and comment on the similarities and differences between this system and an earlier construction of the supersymmetric Chaplygin gas. We also derive the N=1 supersymmetric extension of the elastic medium equations, which, however, do not appear to be integrable.Comment: 15 page

Hall Conductance of a Two-Dimensional Electron Gas in Periodic Lattice with Triangular Antidots

The topic of this contribution is the investigation of quantum states and quantum Hall effect in electron gas subjected to a periodic potential of the lateral lattice. The potential is formed by triangular quantum antidos located on the sites of the square lattice. In a such system the inversion center and the four-fold rotation symmetry are absent. The topological invariants which characterize different magnetic subbands and their Hall conductances are calculated. It is shown that the details of the antidot geometry are crucial for the Hall conductance quantization rule. The critical values of lattice parameters defining the shape of triangular antidots at which the Hall conductance is changed drastically are determined. We demonstrate that the quantum states and Hall conductance quantization law for the triangular antidot lattice differ from the case of the square lattice with cylindrical antidots. As an example, the Hall conductances of magnetic subbands for different antidot geometries are calculated for the case when the number of magnetic flux quanta per unit cell is equal to three.Comment: 6 pages, 5 figure

An exact expression to calculate the derivatives of position-dependent observables in molecular simulations with flexible constraints

In this work, we introduce an algorithm to compute the derivatives of physical observables along the constrained subspace when flexible constraints are imposed on the system (i.e., constraints in which the hard coordinates are fixed to configuration-dependent values). The presented scheme is exact, it does not contain any tunable parameter, and it only requires the calculation and inversion of a sub-block of the Hessian matrix of second derivatives of the function through which the constraints are defined. We also present a practical application to the case in which the sought observables are the Euclidean coordinates of complex molecular systems, and the function whose minimization defines the constraints is the potential energy. Finally, and in order to validate the method, which, as far as we are aware, is the first of its kind in the literature, we compare it to the natural and straightforward finite-differences approach in three molecules of biological relevance: methanol, N-methyl-acetamide and a tri-glycine peptideComment: 13 pages, 8 figures, published versio

Quasi-classical approximation in vortex filament dynamics. Integrable systems, gradient catastrophe and flutter

Quasiclassical approximation in the intrinsic description of the vortex filament dynamics is discussed. Within this approximation the governing equations are given by elliptic system of quasi-linear PDEs of the first order. Dispersionless Da Rios system and dispersionless Hirota equation are among them. They describe motion of vortex filament with slow varying curvature and torsion without or with axial flow. Gradient catastrophe for governing equations is studied. It is shown that geometrically this catastrophe manifests as a fast oscillation of a filament curve around the rectifying plane which resembles the flutter of airfoils. Analytically it is the elliptic umbilic singularity in the terminology of the catastrophe theory. It is demonstrated that its double scaling regularization is governed by the Painleve' I equation.Comment: 25 pages, 5 figures, minor typos correcte

A search for the decay modes B+/- to h+/- tau l

We present a search for the lepton flavor violating decay modes B+/- to h+/- tau l (h= K,pi; l= e,mu) using the BaBar data sample, which corresponds to 472 million BBbar pairs. The search uses events where one B meson is fully reconstructed in one of several hadronic final states. Using the momenta of the reconstructed B, h, and l candidates, we are able to fully determine the tau four-momentum. The resulting tau candidate mass is our main discriminant against combinatorial background. We see no evidence for B+/- to h+/- tau l decays and set a 90% confidence level upper limit on each branching fraction at the level of a few times 10^-5.Comment: 15 pages, 7 figures, submitted to Phys. Rev.

Geodesic motion in the neighbourhood of submanifolds embedded in warped product spaces

We study the classical geodesic motions of nonzero rest mass test particles and photons in (3+1+n)- dimensional warped product spaces. An important feature of these spaces is that they allow a natural decoupling between the motions in the (3+1)-dimensional spacetime and those in the extra n dimensions. Using this decoupling and employing phase space analysis we investigate the conditions for confinement of particles and photons to the (3+1)- spacetime submanifold. In addition to providing information regarding the motion of photons, we also show that these motions are not constrained by the value of the extrinsic curvature. We obtain the general conditions for the confinement of geodesics in the case of pseudo-Riemannian manifolds as well as establishing the conditions for the stability of such confinement. These results also generalise a recent result of the authors concerning the embeddings of hypersurfaces with codimension one.Comment: 8 pages, 1 figure. To appear in General Relativity and Gravitation as a contributed paper to Mashhoon Festschrif

Observation and study of baryonic B decays: B -> D(*) p pbar, D(*) p pbar pi, and D(*) p pbar pi pi

We present a study of ten B-meson decays to a D(*), a proton-antiproton pair, and a system of up to two pions using BaBar's data set of 455x10^6 BBbar pairs. Four of the modes (B0bar -> D0 p anti-p, B0bar -> D*0 p anti-p, B0bar -> D+ p anti-p pi-, B0bar -> D*+ p anti-p pi-) are studied with improved statistics compared to previous measurements; six of the modes (B- -> D0 p anti-p pi-, B- -> D*0 p anti-p pi-, B0bar -> D0 p anti-p pi- pi+, B0bar -> D*0 p anti-p pi- pi+, B- -> D+ p anti-p pi- pi-, B- -> D*+ p anti-p pi- pi-) are first observations. The branching fractions for 3- and 5-body decays are suppressed compared to 4-body decays. Kinematic distributions for 3-body decays show non-overlapping threshold enhancements in m(p anti-p) and m(D(*)0 p) in the Dalitz plots. For 4-body decays, m(p pi-) mass projections show a narrow peak with mass and full width of (1497.4 +- 3.0 +- 0.9) MeV/c2, and (47 +- 12 +- 4) MeV/c2, respectively, where the first (second) errors are statistical (systematic). For 5-body decays, mass projections are similar to phase space expectations. All results are preliminary.Comment: 28 pages, 90 postscript figures, submitted to LP0

Study of Upsilon(3S,2S) -> eta Upsilon(1S) and Upsilon(3S,2S) -> pi+pi- Upsilon(1S) hadronic trasitions

We study the Upsilon(3S,2S)->eta Upsilon(1S) and Upsilon(3S,2S)->pi+pi- Upsilon(1S) transitions with 122 million Upsilon(3S) and 100 million Upsilon(2S) mesons collected by the BaBar detector at the PEP-II asymmetric energy e+e- collider. We measure B[Upsilon(2S)->eta Upsilon(1S)]=(2.39+/-0.31(stat.)+/-0.14(syst.))10^-4 and Gamma[Upsilon(2S)->eta Upsilon(1S)]/Gamma[Upsilon(2S)-> pi+pi- Upsilon(1S)]=(1.35+/-0.17(stat.)+/-0.08(syst.))10^-3. We find no evidence for Upsilon(3S)->eta Upsilon(1S) and obtain B[Upsilon(3S)->eta Upsilon(1S)]<1.0 10^-4 and Gamma[Upsilon(3S)->eta Upsilon(1S)]/Gamma[Upsilon(3S)->pi+pi- Upsilon(1S)]<2.3 10^-3 as upper limits at the 90% confidence level. We also provide improved measurements of the Upsilon(2S) - Upsilon(1S) and Upsilon(3S) - Upsilon(1S) mass differences, 562.170+/-0.007(stat.)+/-0.088(syst.) MeV/c^2 and 893.813+/-0.015(stat.)+/-0.107(syst.) MeV/c^2 respectively.Comment: 8 pages, 16 encapsulated postscript figures, submitted to Phys.Rev.

Evidence for the h_b(1P) meson in the decay Upsilon(3S) --> pi0 h_b(1P)

Using a sample of 122 million Upsilon(3S) events recorded with the BaBar detector at the PEP-II asymmetric-energy e+e- collider at SLAC, we search for the $h_b(1P)$ spin-singlet partner of the P-wave chi_{bJ}(1P) states in the sequential decay Upsilon(3S) --> pi0 h_b(1P), h_b(1P) --> gamma eta_b(1S). We observe an excess of events above background in the distribution of the recoil mass against the pi0 at mass 9902 +/- 4(stat.) +/- 2(syst.) MeV/c^2. The width of the observed signal is consistent with experimental resolution, and its significance is 3.1sigma, including systematic uncertainties. We obtain the value (4.3 +/- 1.1(stat.) +/- 0.9(syst.)) x 10^{-4} for the product branching fraction BF(Upsilon(3S)-->pi0 h_b) x BF(h_b-->gamma eta_b).Comment: 8 pages, 4 postscript figures, submitted to Phys. Rev. D (Rapid Communications

Study of Bbar --> Xu l nubar decays in BBbar events tagged by a fully reconstructed B-meson decay and determination of |V_{ub}|

We report measurements of partial branching fractions for inclusive charmless semileptonic B decays Bbar --> Xu l nubar, and the determination of the CKM matrix element |V_{ub}|. The analysis is based on a sample of 467 million Upsilon(4S) --> BBar decays recorded with the BaBar detector at the PEP-II e^+ e^- storage rings. We select events in which the decay of one of the B mesons is fully reconstructed and an electron or a muon signals the semileptonic decay of the other B meson. We measure partial branching fractions DeltaB in several restricted regions of phase space and determine the CKM element |V_{ub}| based on four different QCD predictions. For decays with a charged lepton momentum p_l^* > 1.0 GeV in the B meson rest frame, we obtain DeltaB = (1.80 \pm 0.13 (stat.) \pm 0.15 (sys.) \pm 0.02 (theo.)) \times 10^{-3} from a fit to the two-dimensional mX-q^2 distribution. Here, mX refers to the invariant mass of the final state hadron X and q^2 is the invariant mass squared of the charged lepton and neutrino. From this measurement we extract |V_{ub}| = (4.33\pm 0.24 (exp.) \pm 0.15 (theo.)) \times 10^{-3} as the arithmetic average of four results obtained from four different QCD predictions of the partial rate. We separately determine partial branching fractions for B^0 and B^- decays and derive a limit on the isospin breaking in Bbar --> Xu l nubar decays.Comment: 26 pages, 9 postscript figures, 9 tables, accepted for publication in PR