Lorentz Invariant Berry Phase for a Perturbed Relativistic Four Dimensional Harmonic Oscillator

We show the existence of Lorentz invariant Berry phases generated, in the Stueckelberg–Horwitz–Piron manifestly covariant quantum theory (SHP), by a perturbed four dimensional harmonic oscillator. These phases are associated with a fractional perturbation of the azimuthal symmetry of the oscillator. They are computed numerically by using time independent perturbation theory and the definition of the Berry phase generalized to the framework of SHP relativistic quantum theory.     

Flow-induced control of chemical turbulence

We report spatiotemporal chaos in the Oregonator model of the Belousov-Zhabotinsky reaction. Spatiotemporal chaos spontaneously develops in a regime, where the underlying local dynamics show stable limit cycle oscillations (diffusion-induced turbulence). We show that spatiotemporal chaos can be suppressed by a unidirectional flow in the system. With increasing flow velocity, we observe a transition scenario from spatiotemporal chaos via a regime of travelling waves to a stationary steady state. At large flow velocities, we recover the known regime of flow distributed oscillations.     

Crowding games are sequentially solvable

A sequential-move version of a given normal-form game Γ is an extensive-form game of perfect information in which each player chooses his action after observing the actions of all players who precede him and the payoffs are determined according to the payoff functions in Γ. A normal-form game Γ is sequentially solvable if each of its sequential-move versions has a subgame-perfect equilibrium in pure strategies such that the players' actions on the equilibrium path constitute an equilibrium of Γ.  A crowding game is a normal-form game in which the players share a common set of actions and the payoff a particular player receives for choosing a particular action is a nonincreasing function of the total number of players choosing that action. It is shown that every crowding game is sequentially solvable. However, not every pure-strategy equilibrium of a crowding game can be obtained in the manner described above. A sufficient, but not necessary, condition for the existence of a sequential-move version of the game that yields a given equilibrium is that there is no other equilibrium that Pareto dominates it. Received July 1997/Final version May 1998     

Rotational bands from shell-model Hamiltonians

Shell-model Hamiltonians with eigenstates forming rotational bands are considered. Such states have eigenvalues proportional to J(J+ 1) and can be projected from a Slater determinant of deformed orbitals. The latter are linear combinations of single-nucleon wave functions of j-orbits in a major shell. Conditions on matrix elements and single-nucleon energies are obtained in terms of the deformation parameters. An actual effective interaction is constructed yielding exact ground-state rotational bands for ²⁰Ne and ²⁴Mg which gives reasonable agreement with energies of other sd shell nuclei. Unlike the case of SU(3) symmetry, spin-orbit interaction and different single-nucleon energies can be accommodated and the procedure is not confined to oscillator major shells. Other welcome departures of our effective interaction from the SU(3) picture are the absence of rotational spectra in oxygen isotopes and that the ²⁴Mg ground-state band is projected from a Nilsson-type deformed state with axial symmetry.     

Binding energies in (1d, 2s) shell nuclei

Binding energies of nuclei throughout the (1d, 2s) shell were calculated with a modified surface delta interaction. The full energy matrices within the complete space of all configurations containing $\text{1}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$, $\text{2}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and $\text{1}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ protons and neutrons were diagonalized. In spite of the crudeness of the interaction used, fair agreement is obtained between calculated and experimental energies. In particular, the calculated curve of α-particle separation energies shows kinks closely following the experimental ones.     

Mercury concentrations in fish from the Great Smoky Mountains National Park

Excessive mercury concentrations ostensibly due to pollution have been widely reported in fish tissue. The concentrations of mercury occurring naturally in fish tissue have not been well defined. A collection for mercury analysis of 198 fish of five species was made in 1972 in three high altitude streams in the Great Smoky Mountains, 20–25 km from the nearest pollution source. Mercury concentrations were (means, p.p.m.): rainbow trout Salmo gairdneri, 0.036; brook trout Salvelinus fontinalis, 0.018 ; banded sculpin Cottus carolinae, 0.025; rosyside aceClinostomus funduloides, 0.044; stoneroller Campostoma anomalum, 0.039. There was no significant difference in mercury concentration among fish analyzed whole, with gastrointestinal tract removed, or a strip of axial musculature. There was a significant (P0.05) difference in mercury concentration among species in one stream and in three species from different streams. A second collection of fish of the same species in 1973 verified the 1972 results. Methylmercury constituted 93 ±2.6% of total mercury. These results indicate that all fish acquire about the same tissue concentrations of mercury at chronic exposure to very low levels.     

Splitting of magnetic dipole modes in anisotropic TiO2 micro‐spheres

Monocrystalline titanium dioxide (TiO₂) micro‐spheres support two orthogonal magnetic dipole modes at terahertz (THz) frequencies due to strong dielectric anisotropy. For the first time, we experimentally detected the splitting of the first Mie mode in spheres of radii m through near‐field time‐domain THz spectroscopy. By fitting the Fano lineshape model to the experimentally obtained spectra of the electric field detected by the sub‐wavelength aperture probe, we found that the magnetic dipole resonances in TiO₂ spheres have narrow linewidths of only tens of gigahertz. Anisotropic TiO₂ micro‐resonators can be used to enhance the interplay of magnetic and electric dipole resonances in the emerging THz all‐dielectric metamaterial technology.