Article

# Inverse problems for Schrödinger equations with Yang–Mills potentials in domains with obstacles and the Aharonov–Bohm effect

04/2005; 12(1). DOI: 10.1088/1742-6596/12/1/003
Source: arXiv

ABSTRACT We study the inverse boundary value problems for the Schrödinger equations with Yang-Mills potentials in a bounded domain Ω 0 ⊂ R n containing finite number of smooth obstacles Ω j , 1 ≤ j ≤ r. We prove that the Dirichlet-to-Neumann opeartor on ∂Ω 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 ∂Ω 0 .

0 Bookmarks
·
57 Views
• Source
##### Article: A Simple Proof of Magnetic and Electric Aharonov-Bohm Effects
[Hide abstract]
ABSTRACT: Magnetic Aharonov-Bohm effect (AB effect) was studied in hundreds of papers starting with the seminal paper of Aharonov and Bohm (Phys Rev 115:485, 1959). We give a new proof of the magnetic Aharonov-Bohm effect without using the scattering theory and the theory of inverse boundary value problems. We consider separately the cases of one and several obstacles. The electric AB effect was studied much less. We give the first proof of the electric AB effect in domains with moving boundaries. When the boundary does not move with the time the electric AB effect is absent.
Communications in Mathematical Physics 08/2013; 321(3). DOI:10.1007/s00220-013-1727-9 · 1.90 Impact Factor
• Source
##### Article: Inverse problems for general second order hyperbolic equations with time-dependent coefficients
[Hide abstract]
ABSTRACT: We study the inverse problems for the second order hyperbolic equations of general form with time-dependent coefficients assuming that the boundary data are given on a part of the boundary. The approach of this paper is a variant of the Boundary Control (BC) method developed in [E1], [E2]. We extend the results and simplify the proofs of author's earlier works [E1], [E2], [E3], [E4] to the general case of arbitrary Lorentzian time-dependent metrics.
• Source
##### Article: Mathematical Modeling for Tomography in Domains with Reflecting Obstacles
[Hide abstract]
ABSTRACT: This work develops new numerical methods for the solution of the tomography problem in domains with reflecting obstacles. We compare the solution's performance for Lambertian reflection, for classical tomography with ubroken rays and for specular reflection. Our numerical method using Lambertian reflection improves the solution's accuracy by an order of magnitude compared to classical tomography with ubroken rays and for tomography in the presence of a specularly reflecting obstacle the numerical method improves the solution's accuracy approximately by a factor of three times. We present efficient new algorithms for the solution's software implementation and analyze the solution's performance and effectiveness.
Journal of Physics Conference Series 02/2013; 410(1):2170-. DOI:10.1088/1742-6596/410/1/012170