Corpus ID: 234681521

The wave trace and resonances of the magnetic Hamiltonian with singular vector potentials

@inproceedings{Yang2021TheWT,
  title={The wave trace and resonances of the magnetic Hamiltonian with singular vector potentials},
  author={Mengxuan Yang},
  year={2021}
}
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 apply our formula to get a lower bound of scattering resonances in a logarithmic neighborhood near the real axis. 

Figures from this paper

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 50 REFERENCES
On the Aharonov–Bohm Hamiltonian
Using the theory of self-adjoint extensions, we construct all the possible Hamiltonians describing the nonrelativistic Aharonov–Bohm effect. In general, the resulting Hamiltonians are notExpand
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
The Aharonov–Bohm effect in spectral asymptotics of the magnetic Schrödinger operator
We show that in the absence of a magnetic field the spectrum of the magnetic Schr\"odinger operator in an annulus depends on the cosine of the flux associated with the magnetic potential. This resultExpand
Contribution of periodic diffractive geodesics
Abstract On an euclidean surface with conical singularities, the wave-trace is expected to be singular at L where L is the length of some diffractive periodic geodesic. In this paper, we compute theExpand
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
Time delay in scattering by potentials and by magnetic fields with two supports at large separation
Abstract We study the asymptotic behavior of the time delay (defined as the trace of the Eisenbud–Wigner time delay operator) for scattering by potential and by magnetic field with two compactExpand
Semiclassical Analysis for Magnetic Scattering by Two Solenoidal Fields
That vector potentials have a direct significance to quantum particles moving in magnetic fields is known as the A-B (Aharonov-Bohm) effect. We study scattering by two solenoidal magnetic fieldsExpand
The green function for the two-solenoid Aharonov-Bohm effect
Abstract Applying the universal covering space technique we have calculated the Green function for the two-solenoid Aharonov-Bohm effect. The gauge group is allowed to be non-Abelian.
Resonance free regions in magnetic scattering by two solenoidal fields at large separation
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 betweenExpand
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
...
1
2
3
4
5
...