Effective operators on an attractive magnetic edge
arxiv(2023)
摘要
The semiclassical Laplacian with discontinuous magnetic field is considered in two dimensions. The magnetic field is sign changing with exactly two distinct values and is discontinuous along a smooth closed curve, thereby producing an attractive magnetic edge. Various accurate spectral asymptotics are established by means of a dimensional reduction involving a microlocal phase space localization allowing to deal with the discontinuity of the field.
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关键词
Magnetic Laplacian,discontinuous magnetic field,semiclassical analysis,spectrum
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