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The Polaron Hydrogenic Atom in a Strong Magnetic Field

Rohan Ghanta
(AU)
Analysis Seminar
Thursday, 12 September, 2019, at 16:15-17:00, in Aud. D3 (1531-215)
Abstract:
An electron interacting with the vibrational modes of a ionic crystal is called a polaron. Polarons are the simplest Quantum Field Theory models, yet their most basic features such as the effective mass, ground-state energy and wave function cannot be evaluated explicitly. And while several successful theories have been proposed over the years to approximate the energy and effective mass of various polarons, they are built entirely on unjustified, even questionable, Ansätze for the wave function.

In this talk I shall provide an explicit description of the ground state of a polaron in an asymptotic regime: For the Fröhlich polaron localized in a Coulomb potential and exposed to a homogeneous magnetic field of strength $B$ it will be shown that any approximate ground-state electron density–with its transverse coordinates integrated out and when scaled appropriately with the magnetic field strength– converges pointwise and in a weak sense as $B\to\infty$ to the square of a hyperbolic secant function: a sharp contrast to the Gaussian wave functions suggested in the physics literature. 
Contact person: Jacob Schach Møller