Generalized Strichartz estimates for wave and Dirac equations in Aharonov-Bohm magnetic fields

Oscillatory patterns in the Ginzburg-Landau model driven by the Aharonov-Bohm potential (Derivation of the Aharanov-Bohm potential in the Ginzburg-Landau model)

We consider the Aharonov-Bohm magnetic potential and study the transition from normal to superconducting solutions within the Ginzburg-Landau model of superconductivity. We obtain oscillations consistent with the Little-Parks effect. We study the same problem but for a regularization of the Aharonov-Bohm potential, which leads to an interesting Aharonov-Bohm like magnetic field, and we prove that the transition between superconducting and normal solutions is not monotone too. Our results show a mechanism to derive the Aharonov-Bohm magnetic potential starting from a step magnetic field thereby…

Dispersive estimates for the Dirac equation in an Aharonov-Bohm field

We prove local smoothing and weighted Strichartz estimates for the Dirac equation with a Aharonov-Bohm potential. The proof relies on an explicit representation of the solution built in terms of spectral projections.

Optical Aharonov-Bohm effect: an inverse hyperbolic problems approach

We describe the general setting for the optical Aharonov-Bohm effect based on the inverse problem of the identification of the coefficients of the governing hyperbolic equation by the boundary measurements. We interpret the inverse problem result as a possibility in principle to detect the optical Aharonov-Bohm effect by the boundary measurements.

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 compute the corresponding diffraction coefficient which is the principal symbol of the diffractive propagator. This paper gives the first proof of propagation of singularities of the Aharonov-Bohm Hamiltonian.

量子隧穿与Aharonov-Bohm效应

Quantum Tunneling and the Aharonov-Bohm effect

研究含径向势阱和双极点Aharonov-Bohm矢量势的哈密顿量，推导基态与第二态能量分裂的半经典渐近，发现通量效应为低阶。

Aharonov-Bohm effect revisited

Aharonov-Bohm effect is a quantum mechanical phenomenon that attracted the attention of many physicists and mathematicians since the publication of the seminal paper of Aharonov and Bohm [1] in 1959. We consider different types of Aharonov-Bohm effect such as magnetic AB effect, electric AB effect, combined electromagnetic AB effect, AB effect for the Schrödinger equations with Yang-Mills potentials, and the gravitational analog of AB effect. We shall describe different approaches to prove the AB effect based on the inverse scattering problems, the inverse boundary value problems in the presen…

Weak dispersive estimates for fractional Aharonov-Bohm-Schrödinger groups

We prove local smoothing, local energy decay and weighted Strichartz inequalities for fractional Schrödinger equations with a Aharonov-Bohm magnetic field in 2D. Explicit representations of the flows in terms of spherical expansions of the Hamiltonians are involved in the study. An improvement of the free estimate is proved, when the total flux of the magnetic field through the unit sphere is not an integer.

Inverse problems for the Schrodinger equations with time-dependent electromagnetic potentials and the Aharonov-Bohm effect

We consider the inverse boundary value problem for the Schrodinger operator with time-dependent electromagnetic potentials in domains with obstacles. We extend the resuls of the author's works [E1], [E2], [E3] to the case of time-dependent potentials. We relate our results to the Aharonov-Bohm effect caused by magnetic and electric fluxes.

Decay and Strichartz estimates in critical electromagnetic fields

We study the $L^1\to L^\infty$-decay estimates for dispersive equations in the Aharonov-Bohm magnetic fields, and further prove Strichartz estimates for the Klein-Gordon equation with critical electromagnetic potentials. The novel ingredients are the construction of Schwartz kernels of the spectral measure and heat propagator for the Schrödinger operator in Aharonov-Bohm magnetic fields. In particular, we explicitly construct the representation of the spectral measure and resolvent of the Schrödinger operator with Aharonov-Bohm potentials, and show that the heat kernel in critical electromagne…

Gauge Equivalence and Inverse Scattering for Aharonov-Bohm Effect

We consider the Aharonov-Bohm effect for the Schroedinger operator and the related inverse problem in an exterior domain the 2-dim. Euclidean space with Dirichlet boundary condition. We study the structure and asymptotics of generalized eigenfunctions and show that the scattering operator determines the domain and the Hamiltonian up to Gauge equivalence under the equal flux condition. We also show that the flux is determined by the scattering operator if the obstacle is convex.