Hearing the zero locus of a magnetic field |
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Authors: | Richard Montgomery |
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Institution: | (1) Department of Mathematics, University of California, 95064 Santa Cruz, CA, USA |
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Abstract: | We investigate the ground state of a two-dimensional quantum particle in a magnetic field where the field vanishes nondegenerately along a closed curve. We show that the ground state concentrates on this curve ase/h tends to infinity, wheree is the charge, and that the ground state energy grows like (e/h)2/3. These statements are true for any energy level, the level being fixed as the charge tends to infinity. If the magnitude of the gradient of the magnetic field is a constantb
0 along its zero locus, then we get the precise asymptotics(e/h)
2/3
(b
0)
2/3
E
* +O(1) for every energy level. The constantE
* .5698 is the infimum of the ground state energiesE( ) of the anharmonic oscillator family
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Keywords: | |
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