Ubiquitous diffraction resonances in positronium formation from fullerenes

Due to the dominant electron capture by positrons from the molecular wall and the spatial dephasing across the wall-width, a powerful diffraction effect universally underlies the positronium (Ps) formation from fullerenes. This results into trains of resonances in the Ps formation cross section as a function of the positron beam energy, producing uniform structures in recoil momenta in analogy with classical single-slit diffraction fringes in the configuration space. The prediction opens a hitherto unknown avenue of Ps spectroscopy with nanomaterials.Comment: 6 pages, 3 figures, submitte

Hamiltonian Formulation of Quantum Hall Skyrmions with Hopf Term

We study the nonrelativistic nonlinear sigma model with Hopf term in this paper. This is an important issue beacuse of its relation to the currently interesting studies in skyrmions in quantum Hall systems. We perform the Hamiltonian analysis of this system in $CP^1$ variables. When the coefficient of the Hopf term becomes zero we get the Landau-Lifshitz description of the ferromagnets. The addition of Hopf term dramatically alters the Hamiltonian analysis. The spin algebra is modified giving a new structure and interpretation to the system. We point out momentum and angular momentum generators and new features they bring in to the system.Comment: 16pages, Latex file, typos correcte

The effect of Pressure in Higher Dimensional Quasi-Spherical Gravitational Collapse

We study gravitational collapse in higher dimensional quasi-spherical Szekeres space-time for matter with anisotropic pressure. Both local and global visibility of central curvature singularity has been studied and it is found that with proper choice of initial data it is possible to show the validity of CCC for six and higher dimensions. Also the role of pressure in the collapsing process has been discussed.Comment: 11 pages, 6 figures, RevTeX styl

CP1CP^{1} model with Hopf interaction: the quantum theory

The $CP^1$ model with Hopf interaction is quantised following the Batalin-Tyutin (BT) prescription. In this scheme, extra BT fields are introduced which allow for the existence of only commuting first-class constraints. Explicit expression for the quantum correction to the expectation value of the energy density and angular momentum in the physical sector of this model is derived. The result shows, in the particular operator ordering that we have chosen to work with, that the quantum effect has a divergent contribution of ${\cal O} (\hbar^2)$ in the energy expectation value. But, interestingly the Hopf term, though topological in nature, can have a finite ${\cal O} (\hbar)$ contribution to energy density in the homotopically nontrivial topological sector. The angular momentum operator, however, is found to have no quantum correction, indicating the absence of any fractional spin even at this quantum level. Finally, the extended Lagrangian incorporating the BT auxiliary fields is computed in the conventional framework of BRST formalism exploiting Faddeev-Popov technique of path integral method.Comment: LaTeX, 28 pages, no figures, typos corrected, journal ref. give

Optical Signatures of Spin-Orbit Interaction Effects in a Parabolic Quantum Dot

We demonstrate here that the dipole-allowed optical absorption spectrum of a parabolic quantum dot subjected to an external magnetic field reflects the inter-electron interaction effects when the spin-orbit interaction is also taken into account. We have investigated the energy spectra and the dipole-allowed transition energies for up to four interacting electrons parabolically confined, and have uncovered several novel features in those spectra that are solely due to the SO interaction.Comment: 4 pages, 3 figure