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Magnetic wells in dimension two and three

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Periodic and Ergodic Spectral Problems

this talks deals with semiclassical asymptotics of the two- or three-dimensional magnetic Laplacians in presence of magnetic confinement. Using generic assumptions on the geometry of the confinement, we exhibit semiclassical scales and their corresponding effective quantum Hamiltonians, by means of microlocal normal forms extit{`a la Birkhoff} or Grushin’s problems. As a consequence, when the magnetic field admits a unique and non degenerate minimum, we are able to reduce the spectral analysis of the low-lying eigenvalues to a one-dimensional $hbar$-pseudo-differential operators.

This talk is part of the Isaac Newton Institute Seminar Series series.

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