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- W2962840911 abstract "Abstract We consider the Laplace operator in a tubular neighbourhood of a conical surface of revolution, subject to an Aharonov-Bohm magnetic field supported on the axis of symmetry and Dirichlet boundary conditions on the boundary of the domain. We show that there exists a critical total magnetic flux depending on the aperture of the conical surface for which the system undergoes an abrupt spectral transition from infinitely many eigenvalues below the essential spectrum to an empty discrete spectrum. For the critical flux, we establish a Hardy-type inequality. In the regime with an infinite discrete spectrum, we obtain sharp spectral asymptotics with a refined estimate of the remainder and investigate the dependence of the eigenvalues on the aperture of the surface and the flux of the magnetic field." @default.
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- W2962840911 date "2019-01-26" @default.
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- W2962840911 title "Spectral transitions for Aharonov-Bohm Laplacians on conical layers" @default.
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- W2962840911 doi "https://doi.org/10.1017/prm.2018.64" @default.
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