Molecular predissociation resonances below an energy level crossing
We study the resonances of $2\times 2$ systems of one dimensional Schrodinger operators which are related to the mathematical theory of molecular predissociation. We determine the precise positions of the resonances with real parts below the energy where bonding and anti-bonding potentials intersect transversally. In particular, we find that imaginary parts (widths) of the resonances are exponentially small and that the indices are determined by Agmon distances for the minimum of two potentials.
Scattering theory for multistate Schrödinger operators
We study multistate Schrodinger operators related to molecular dynamics. We consider potentials which do not necessarily decay and prove the absence of the singular continuous spectrum and propagation estimates which mean the scattering at speed larger than a positive constant and decay of the state with potentials higher than the considered energy at infinity. We also consider the multistate Schrodinger operators with many-body structures. We obtain the Mourre estimate and the minimal velocity estimate for the many-body operators. The lower bound of the velocity is determined by the distance between the energy and thresholds below the energy.
Geomagnetic micropulsations due to the motion of ocean waves
When sea waves move in the magnetic field of the earth, electric currents are generated in the water volume. These currents give rise to a small magnetic field which perturbs the earth's field. For plane trochoidal waves, this perturbing field decays exponentially with altitude and lies in a vertical plane which is oriented in the direction of wave propagation. The magnitude of the perturbing field also depends upon the magnitude and dip angle of the earth's field, and upon the height, wavelength, and propagation direction of the sea waves. For north-south waves, sea state 5, and an altitude of 100 feet, the perturbation is of the order of 0.1 gamma.