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The spectrum of the weakly perturbed Landau Hamiltonian and orthogonal polynomials in the complex domain
Probability| Speaker: | Alexander Pushnitski, King's College London (visiting Caltech) |
| Location: | 693 Kerr |
| Start time: | Tue, Oct 18 2005, 3:10PM |
Description
The subject of the talk is the spectrum of a two-dimensional Schrodinger operator
with constant magnetic field and a compactly supported electric field.
The eigenvalues of such an operator form clusters around the Landau levels.
The eigenvalues in these clusters accumulate towards the Landau levels
super-exponentially fast. It appears that these eigenvalues can be related to a
certain sequence of orthogonal polynomials in the complex domain.
This allows one to accurately describe the rate of accumulation of eigenvalues
towards the Landau levels. This description involves the logarithmic capacity
of the support of the electric potential. The talk is based on a joint work
with Nikolai FIlonov from St.Petersburg.