Superintegrable systems with spin and second-order integrals of motion

We investigate a quantum nonrelativistic system describing the interaction of two particles with spin 1/2 and spin 0, respectively. We assume that the Hamiltonian is rotationally invariant and parity conserving and identify all such systems which allow additional integrals of motion that are second order matrix polynomials in the momenta. These integrals are assumed to be scalars, pseudoscalars, vectors or axial vectors. Among the superintegrable systems obtained, we mention a generalization of the Coulomb potential with scalar potential $V_0=\frac{\alpha}{r}+\frac{3\hbar^2}{8r^2}$ and spin orbital one $V_1=\frac{\hbar}{2r^2}$.Comment: 32 page

Tunneling Time in the Landau-Zener Model

We give a general definition for the tunneling time in the Landau-Zener model. This definition allows us to compute numerically the Landau-Zener tunneling time at any sweeping rate without ambiguity. We have also obtained analytical results in both the adiabatic limit and the sudden limit. Whenever applicable, our results are compared to previous results and they are in good agreement.Comment: 7pages, 9 figure

Relativistic Coulomb problem for particles with arbitrary half-integer spin

Using relativistic tensor-bispinorial equations proposed in hep-th/0412213 we solve the Kepler problem for a charged particle with arbitrary half-integer spin interacting with the Coulomb potential.Comment: Misprints are correcte

Exotic solutions in string theory

Solutions of classical string theory, correspondent to the world sheets, mapped in Minkowsky space with a fold, are considered. Typical processes for them are creation of strings from vacuum, their recombination and annihilation. These solutions violate positiveness of square of mass and Regge condition. In quantum string theory these solutions correspond to physical states |DDF>+|sp> with non-zero spurious component.Comment: accepted in Il Nuovo Cimento A for publication in 199

Statistical theory for the reaction N + OH → NO + H: thermal low-temperature rate constants

The reaction N + OH → NO + H involves the intermediate formation of NOH adducts which in part rearrange to HNO conformers. A statistical treatment of the process is developed in which an initial adiabatic channel capture of the reactants is accompanied by partial primary redissociation of the N⋯OH collision pairs. A criterion for the extent of this primary redissociation in competition to the formation of randomized, long-lived, complex of NOH is proposed. The NOH adducts then may decompose to NO + H, rearrange in a unimolecular process to HNO, or undergo secondary redissociation back to the reactants N + OH, while HNO may also decompose to NO + H. As the reactants N(4S) + OH(2Π) have open electronic shells, non-Born–Oppenheimer effects have to be considered. Their influence on thermal rate constants of the reaction at low temperatures is illustrated and compared with such effects in other reactions such as C(3P) + OH(2Π)

Curve crossing in linear potential grids: the quasidegeneracy approximation

The quasidegeneracy approximation [V. A. Yurovsky, A. Ben-Reuven, P. S. Julienne, and Y. B. Band, J. Phys. B {\bf 32}, 1845 (1999)] is used here to evaluate transition amplitudes for the problem of curve crossing in linear potential grids involving two sets of parallel potentials. The approximation describes phenomena, such as counterintuitive transitions and saturation (incomplete population transfer), not predictable by the assumption of independent crossings. Also, a new kind of oscillations due to quantum interference (different from the well-known St\"uckelberg oscillations) is disclosed, and its nature discussed. The approximation can find applications in many fields of physics, where multistate curve crossing problems occur.Comment: LaTeX, 8 pages, 8 PostScript figures, uses REVTeX and psfig, submitted to Physical Review