arXiv math/05055542005-05-26math.AP

Inverse problems for Schrodinger equations with Yang-Mills potentials in domains with obstacles and the Aharonov-Bohm effect

Gregory Eskin

备注：: 15 pages
发表信息：: Journal of Physics: Conference series 12(2005), 23-31
DOI：: 10.1088/1742-6596/12/1/003

英文摘要：

We study the inverse boundary value problems for the Schrödinger equations with Yang-Mills potentials in a bounded domain $Ω_0\subset\R^n$ containing finite number of smooth obstacles $Ω_j,1\leq j \leq r$. We prove that the Dirichlet-to-Neumann operator on $\partialΩ_0$ determines the gauge equivalence class of the Yang-Mills potentials. We also prove that the metric tensor can be recovered up to a diffeomorphism that is identity on $\partialΩ_0$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

On Aharonov-Bohm operators with two colliding poles

We consider Aharonov-Bohm operators with two poles and prove sharp asymptotics for simple eigenvalues as the poles collapse at an interior point out of nodal lines of the limit eigenfunction.

2016-12-13math.AP

Dispersive estimates for two-particles Schrödinger and wave equations in the Aharonov-Bohm field

We study the dispersive behaviors of two-particles Schrödinger and wave equations in the Aharonov-Bohm field. In particular, we prove the Strichartz estimates for Schrödinger and wave equations in this setting. The key point is to construct spectral measure of Schrödinger operator with an Aharonov-Bohm type potential in $\R^4$. As applications, we finally prove a scattering theory for the nonlinear defocusing subcritical two-particles Schrödinger equation with Aharonov-Bohm potential.

2021-10-13math.AP

Multiple Aharonov--Bohm eigenvalues: the case of the first eigenvalue on the disk

It is known that the first eigenvalue for Aharonov--Bohm operators with half-integer circulation in the unit disk is double if the potential's pole is located at the origin. We prove that in fact it is simple as the pole $a\neq 0$.

2018-03-05math.AP

Rate of convergence for eigenfunctions of Aharonov-Bohm operators with a moving pole

We study the behavior of eigenfunctions for magnetic Aharonov-Bohm operators with half-integer circulation and Dirichlet boundary conditions in a planar domain. We prove a sharp estimate for the rate of convergence of eigenfunctions as the pole moves in the interior of the domain.

2016-12-05math.AP

On the leading term of the eigenvalue variation for Aharonov-Bohm operators with a moving pole

We study the behavior of eigenvalues for magnetic Aharonov-Bohm operators with half-integer circulation and Dirichlet boundary conditions in a planar domain. We analyse the leading term in the Taylor expansion of the eigenvalue function as the pole moves in the interior of the domain, proving that it is a harmonic homogeneous polynomial and detecting its exact coefficients.

2015-05-28math.AP

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

We prove generalized Strichartz estimates for wave and massless Dirac equations in Aharonov-Bohm magnetic fields. Following a well established strategy to deal with scaling critical perturbations of dispersive PDEs, we make use of Hankel transform and rely on some precise estimates on Bessel functions. As a complementary result, we prove a local smoothing estimate for the Klein-Gordon equation in the same magnetic field.

2020-08-01math.AP

更多相关论文收起更多论文

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…

2020-08-05math-phmath.APmath.MP

多极Aharonov-Bohm哈密顿量的Schrödinger方程的Strichartz估计

Strichartz estimates for Schrödinger equations with the multipole Aharonov--Bohm Hamiltonian

Princeton University（普林斯顿大学）；Beijing Institute of Technology（北京理工大学）

本文证明了$\mathbb{R}^2$上多极Aharonov-Bohm哈密顿量的Schrödinger方程的全局时间Strichartz估计，并通过建立局部光滑估计作为中间步骤。

2026-05-23math-phmath.APmath.MP

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.

2016-12-30math-phmath.APmath.MP

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.

2007-10-18math-phmath.APmath.MP

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.

2021-06-11math-phmath.APmath.MP

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。

2024-07-23math-phmath.APmath.MP

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…

2015-04-19math-phmath.APmath.MP

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.

2016-04-10math-phmath.APmath.MP

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.

2006-11-12math-phmath.APmath.MP

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.

2010-03-02math-phmath.APmath.MP