Resonance free regions in magnetic scattering by two solenoidal fields at large separation

@article{Alexandrova2011ResonanceFR,
  title={Resonance free regions in magnetic scattering by two solenoidal fields at large separation},
  author={I. Alexandrova and H. Tamura},
  journal={Journal of Functional Analysis},
  year={2011},
  volume={260},
  pages={1836-1885}
}
Abstract We consider the problem of quantum resonances in magnetic scattering by two solenoidal fields at large separation in two dimensions. This system has trapped trajectories oscillating between two centers of the fields. We give a sharp lower bound on resonance widths when the distance between the two centers goes to infinity. The bound is described in terms of backward amplitudes calculated explicitly for scattering by each solenoidal field. The study is based on a new type of complex… Expand
Resonances in scattering by two magnetic fields at large separation and a complex scaling method
Abstract We study the quantum resonances in magnetic scattering in two dimensions. The scattering system consists of two obstacles by which the magnetic fields are completely shielded. TheExpand
Aharonov--Bohm effect in resonances of magnetic Schrödinger operators in two dimensions III
We study the Aharonov-Bohm effect (AB effect) in quan- tum resonances for magnetic scattering in two dimensions. The system consists of four scatters, two obstacles and two scalar potentials withExpand
The heat kernel for two Aharonov–Bohm solenoids in a uniform magnetic field
Abstract A non-relativistic quantum model is considered with a point particle carrying a charge e and moving in the plane pierced by two infinitesimally thin Aharonov–Bohm solenoids and subjected toExpand
Peierls substitution for magnetic Bloch bands
We consider the one-particle Schrodinger operator in two dimensions with a periodic potential and a strong constant magnetic field perturbed by slowly varying non-periodic scalar and vectorExpand
THE AHARONOV-BOHM HAMILTONIAN WITH TWO VORTICES REVISITED
We consider an invariant quantum Hamiltonian H = −Δ LB + V in the L 2 space based on a Riemannian manifold ˜M with a discrete symmetry group Γ. To any unitary representation Λ of Γ one can relateExpand
Resonance free regions for nontrapping manifolds with cusps
We prove resolvent estimates for nontrapping manifolds with cusps which imply the existence of arbitrarily wide resonance free strips, local smoothing for the Schrodinger equation, and resonant waveExpand
Nonlinear Bang–Bang Eigenproblems and Optimization of Resonances in Layered Cavities
We study optimization of quasi-normal-eigenvalues $$\omega $$ω associated with the equation $$y^{\prime \prime } = -\omega ^2 B y $$y″=-ω2By of two-side open optical and mechanical resonators. TheExpand
The wave trace and resonances of the magnetic Hamiltonian with singular vector potentials
We study leading order singularities of the wave trace of the Aharonov–Bohm Hamiltonian on R with multiple solenoids under a generic assumption that no three solenoids are collinear. Then we applyExpand
Diffraction of the Aharonov–Bohm Hamiltonian
In this paper, we compute the diffractive wave propagator of the Aharonov-Bohm effect on $\mathbf{R}^2$ with a single solenoid using a technique of moving solenoid location. In addition, we computeExpand

References

SHOWING 1-10 OF 25 REFERENCES
Aharonov-Bohm Effect in Scattering by Point-like Magnetic Fields at Large Separation
Abstract. The aim is to study the Aharonov-Bohm effect in the scattering by two point-like magnetic fields at large separation in two dimensions. We analyze the asymptotic behavior of scatteringExpand
Barrier Resonances in Strong Magnetic Fields
In this paper, we study the resonances of Schrodinger operators with a homogeneous magnetic field when the field strength tends to the infinity. We prove the existence of resonances and give completeExpand
Width of shape resonances for non globally analytic potentials
We consider the semiclassical Schroedinger operator with a "well in an island" potential, on which we assume smoothness only, except near infinity. We give the asymptotic expansion of the imaginaryExpand
The shape resonance
For a class of Schrödinger operatorsH:=−(ℏ2/2m)Δ+V onL2(ℝn), with potentials having minima embedded in the continuum of the spectrum and non-trapping tails, we show the existence of shape resonancesExpand
Aharonov-Bohm Effect with $δ$--type Interaction
A quantum particle interacting with a thin solenoid and a magnetic flux is described by a five-parameter family of Hamilton operators, obtained via the method of self-adjoint extensions. One of theExpand
Topological Effects in Quantum Mechanics
Preface. 1. Introduction. 2. Vector Potentials of Static Solenoids. 3. Electromagnetic Properties of Static Solenoids. 4. Interaction of Magnetisations with an External Electromagnetic Field and aExpand
A class of analytic perturbations for one-body Schrödinger Hamiltonians
We study a class of symmetric relatively compact perturbations satisfying analyticity conditions with respect to the dilatation group inRn. Absence of continuous singular part for the Hamiltonians isExpand
Lower bounds for resonance widths in potential and obstacle scattering
Explicit lower bounds are given for the size of the imaginary parts of resonances for Schrödinger operators with non-trapping or trapping potentials, and for the Dirichlet Laplacian in the exteriorExpand
Significance of Electromagnetic Potentials in the Quantum Theory
In this paper, we discuss some interesting properties of the electromagnetic potentials in the quantum domain. We shall show that, contrary to the conclusions of classical mechanics, there existExpand
Complex scaling and the distribution of scattering poles
The purpose of this paper is to establish sharp polynomial bounds on the number of scattering poles for a general class of compactly supported self-adjoint perturbations of the Laplacian in R', nExpand
...
1
2
3
...