QLunch: Oliver Matte

Speaker: Oliver Matte, AAU

Title: Low energy spectrum of a polaron in a weak constant magnetic field

Abstract: We consider a Fröhlich Hamiltonian generating the dynamics of a polaron in a constant magnetic field pointing in the z-direction for a fixed,  sufficiently small value of the z-component of the system’s total momentum. For weak magnetic field strengths, we show that the low-lying spectrum of this Hamiltonian exhibits a Landau band structure, with band spacings determined by the renormalized polaron mass. A key technique in the proof, borrowed from the magnetic perturbation theory of periodic Schrödinger operators, is the construction of an effective Hamiltonian acting in the sub-Hilbert space generated by a system of magnetic quasi-Wannier functions for the polaron.

The talk is based on joint work in progress with Horia Cornean und Rohan Ghanta.