Darboux transformations for a twisted derivation and quasideterminant solutions to the super KdV equation

This paper is concerned with a generalized type of Darboux transformations defined in terms of a twisted derivation $D$ satisfying $D(AB)=D(A)+\sigma(A)B$ where $\sigma$ is a homomorphism. Such twisted derivations include regular derivations, difference and $q$-difference operators and superderivatives as special cases. Remarkably, the formulae for the iteration of Darboux transformations are identical with those in the standard case of a regular derivation and are expressed in terms of quasideterminants. As an example, we revisit the Darboux transformations for the Manin-Radul super KdV equation, studied in Q.P. Liu and M. Ma\~nas, Physics Letters B \textbf{396} 133--140, (1997). The new approach we take enables us to derive a unified expression for solution formulae in terms of quasideterminants, covering all cases at once, rather than using several subcases. Then, by using a known relationship between quasideterminants and superdeterminants, we obtain expressions for these solutions as ratios of superdeterminants. This coincides with the results of Liu and Ma\~nas in all the cases they considered but also deals with the one subcase in which they did not obtain such an expression. Finally, we obtain another type of quasideterminant solutions to the Main-Radul super KdV equation constructed from its binary Darboux transformations. These can also be expressed as ratios of superdeterminants and are a substantial generalization of the solutions constructed using binary Darboux transformations in earlier work on this topic

Correlations of chaotic eigenfunctions: a semiclassical analysis

We derive a semiclassical expression for an energy smoothed autocorrelation function defined on a group of eigenstates of the Schr\"odinger equation. The system we considered is an energy-conserved Hamiltonian system possessing time-invariant symmetry. The energy smoothed autocorrelation function is expressed as a sum of three terms. The first one is analogous to Berry's conjecture, which is a Bessel function of the zeroth order. The second and the third terms are trace formulae made from special trajectories. The second term is found to be direction dependent in the case of spacing averaging, which agrees qualitatively with previous numerical observations in high-lying eigenstates of a chaotic billiard.Comment: Revtex, 13 pages, 1 postscript figur

Elliptic flow in heavy ion collisions near the balance energy

The proton elliptic flow in collisions of Ca on Ca at energies from 30 to 100 MeV/nucleon is studied in an isospin-dependent transport model. With increasing incident energy, the elliptic flow shows a transition from positive to negative flow. Its magnitude depends on both the nuclear equation of state (EOS) and the nucleon-nucleon scattering cross section. Different elliptic flows are obtained for a stiff EOS with free nucleon-nucleon cross sections and a soft EOS with reduced nucleon-nucleon cross sections, although both lead to vanishing in-plane transverse flow at the same balance energy. The study of both in-plane and elliptic flows at intermediate energies thus provides a means to extract simultaneously the information on the nuclear equation of state and the nucleon-nucleon scattering cross section in medium.Comment: 6 pages, 2 figure

Stabilization of solitons in PT models with supersymmetry by periodic management

We introduce a system based on dual-core nonlinear waveguides with the balanced gain and loss acting separately in the cores. The system features a "supersymmetry" when the gain and loss are equal to the inter-core coupling. This system admits a variety of exact solutions (we focus on solitons), which are subject to a specific subexponential instability. We demonstrate that the application of a "management", in the form of periodic simultaneous switch of the sign of the gain, loss, and inter-coupling, effectively stabilizes solitons, without destroying the supersymmetry. The management turns the solitons into attractors, for which an attraction basin is identified. The initial amplitude asymmetry and phase mismatch between the components transforms the solitons into quasi-stable breathers.Comment: In press EPL 201

Photoproduction and Radiative Decay of Spin 1/2 and 3/2 Pentaquarks

We study photoproduction and radiative decays of pentauqarks paying particular attention to the differences between spin-1/2 and spin-3/2, positive and negative parities of pentaquarks. Detailed study of these processes can not only give crucial information about the spin, but also the parity of pentaquarks.Comment: 14 pages, 7 figure

Directed flow of neutral strange particles at AGS

Directed flow of neutral strange particles in heavy ion collisions at AGS is studied in the ART transport model. Using a lambda mean-field potential which is 2/3 of that for a nucleon as predicted by the constituent quark model, lambdas are found to flow with protons but with a smaller flow parameter as observed in experiments. For kaons, their repulsive potential, which is calculated from the impulse approximation using the measured kaon-nucleon scattering length, leads to a smaller anti-flow than that shown in the preliminary E895 data. Implications of this discrepancy are discussed.Comment: 6 pages, 2 figure

Kaon differential flow in relativistic heavy-ion collisions

Using a relativistic transport model, we study the azimuthal momentum asymmetry of kaons with fixed transverse momentum, i.e., the differential flow, in heavy-ion collisions at beam momentum of 6 GeV/c per nucleon, available from the Alternating Gradient Synchrotron (AGS) at the Brookhaven National Laboratory (BNL). We find that in the absence of kaon potential the kaon differential flow is positive and increases with transverse momentum as that of nucleons. The repulsive kaon potential as predicted by theoretical models, however, reduces the kaon differetnial flow, changing it to negative for kaons with low momenta. Cancellation between the negative differential flow at low mementa and the positive one at high momenta is then responsible for the experimentally observed nearly vanishing in-plane transverse flow of kaons in heavy ion experiments.Comment: Phys. Rev. C in pres

Generation of a High-Visibility Four-Photon Entangled State and Realization of a Four-Party Quantum Communication Complexity Scenario

We obtain a four-photon polarization-entangled state with a visibility as high as (95.35\pm 0.45)% directly from a single down-conversion source. A success probability of (81.54\pm 1.38)% is observed by applying this entangled state to realize a four-party quantum communication complexity scenario (QCCS), which comfortably surpass the classical limit of 50%. As a comparison, two Einstein-Podolsky-Rosen (EPR) pairs are shown to implement the scenario with a success probability of (73.89\pm 1.33)%. This four-photon state can be used to fulfill decoherence-free quantum information processing and other advanced quantum communication schemes.Comment: REVTEX 4.0, 4 pages, 4 figures, 1 tabl

On the QCD corrections to the charged Higgs decay of a heavy quark

Using dimensional regularization for both infrared and ultraviolet divergences, we confirm that the QCD corrections to the decay width $\Gamma(t\to H^+b)$ are equal to those to $\Gamma(t\to W^+b)$ in the limit of a large $t$ quark mass.Comment: 6 pages, report Alberta Thy-25-9