Article

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

Journal of Physics Conference Series 04/2005; 12(1). DOI: 10.1088/1742-6596/12/1/003

Source: arXiv

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**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-. - [Show abstract] [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). · 1.90 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We consider the inverse problem for the second order self-adjoint hyperbolic equation in a bounded domain in R n with lower order terms depending analytically on the time variable. We prove that, assuming the BLR condition, the time-dependent Dirichlet-to-Neumann operator prescribed on a part of the boundary uniquely determines the coefficients of the hyperbolic equation up to a diffeomorphism and a gauge transformation. As a by-product we prove a similar result for the nonself-adjoint hyperbolic operator with time-independent coefficients.Communications in Partial Differential Equations 11/2007; 32(11):1737-1758. · 1.03 Impact Factor

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