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

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 .

  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We study the inverse problem for the second-order self-adjoint hyperbolic equation with the boundary data given on a part of the boundary. This paper is the continuation of the author's paper (Eskin 2006 A new approach to hyperbolic inverse problems Inverse Problems 22 815–33), in which we presented the crucial local step of the proof. In this paper, we prove the global step. Our method is a modification of the BC method with some new ideas. In particular, the method of determination of the metric is new.
    Inverse Problems 10/2007; 23(6):2343. · 1.90 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: 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.
  • Source
    [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). · 1.97 Impact Factor

Full-text (2 Sources)

Available from