308 research outputs found
ASYMPTOTIC ANALYSIS FOR GREEN FUNCTIONS OF AHARONOV-BOHM HAMILTONIAN WITH APPLICATION TO RESONANCE WIDTHS IN MAGNETIC SCATTERING
The Aharonov–Bohm Hamiltonian is the energy operator which governs quantum particles moving in a solenoidal field in two dimensions. We analyze asymptotic properties of its Green function with spectral parameters in the unphysical sheet. As an application, we discuss
the lower bound on resonance widths for scattering by two magnetic fields with compact supports at large separation. The bound is evaluated in terms of backward scattering amplitudes by a single magnetic field. A special emphasis is placed on analyzing how a trajectory oscillating between two magnetic fields gives rise to resonances near the real axis, as the distance between two supports goes to infinity. We also refer to the relation to the semiclassical resonance theory for scattering
by two solenoidal fields
Asymptotic distribution of eigenvalues for Schrödinger operators with homogeneous magnetic fields. II
Spectral and scattering theory for 3-particle Hamiltonian with stark effect : asymptotic completeness
Aharonov--Bohm effect in resonances of magnetic Schrödinger operators in two dimensions II
We study the Aharonov–Bohm effect (AB effect) in quantum resonances for magnetic scattering in two dimensions. The system consists of four scatters, two obstacles and two scalar potentials with compact support, which are largely separated from one another. The obstacles by which the magnetic fields are completely shielded are horizontally placed between the supports of the two potentials. The fields do not influence particles from a classical mechanical point of view, but quantum particles are influenced by the corresponding vector potential which does not necessarily vanish outside the obstacle. This quantum phenomenon is called the AB effect. The resonances are shown to be generated near the real axis by the trajectories trapped between two supports of the scalar potentials as the distances between the scatterers go to infinity. We analyze how the AB effect influences the location of resonances. The result is described in terms of the backward amplitudes for scattering by each of the scalar potentials, and it depends heavily on the ratios of the distances between the four scatterers as well as on the magnetic fluxes of the fields
Asymptotic properties in forward directions of resolvent kernels of magnetic Schrödinger operators in two dimensions
We study the asymptotic properties in forward directions of resolvent kernels with spectral parameters in the lower half plane (unphysical sheet) of the complex plane for magnetic Schrödinger operators in two dimensions. The asymptotic formula obtained has an application to the problem of quantum resonances in magnetic scattering, and it is especially helpful in studying how the Aharonov–Bohm effect influences the location of resonances. Here we mention only the results without proofs
Asymptotic distribution of eigenvalues for Schrödinger operators with homogeneous magnetic fields
Spectral and scattering theory for 3-particle Hamiltonian with Stark effect : nonexistence of bound states and resolvent estimate
Asymptotic distribution of eigenvalues for Schrodinger operators with homogeneous magnetic fields. II
Asymptotic distribution of negative eigen values for two dimensional Pauli operators with spherically symmetric magnetic fields
Error estimate in operator norm of exponential product formulas for propagators of parabolic evolution equations
- …