# Mathematics Colloquia and Seminars

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### The spectrum of the weakly perturbed Landau Hamiltonian and orthogonal polynomials in the complex domain

**Mathematical Physics & Probability**

Speaker: | Alexander Pushnitski, King's College London (visiting Caltech) |

Location: | 693 Kerr |

Start time: | Tue, Oct 18 2005, 3:10PM |

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.