The polaron hydrogenic atom in a strong magnetic field
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Ghanta, Rohan
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Abstract
It is shown that: (1) The ground-state electron density of a polaron bound in a Coulomb potential and exposed to a homogeneous magnetic field of strength B–with its transverse electron coordinates integrated out and when scaled appropriately with the magnetic field strength–converges pointwise and in a weak sense as B → ∞ to the square of a hyperbolic secant function; (2) The ground state of a polaron bound in a symmetric Mexican hat- type potential, scaled appropriately with the electron-phonon coupling parameter, is unique and therefore rotation-invariant, but the minimizers of the corresponding Pekar problem are nonradial; in the strong-coupling limit under the assumption that these minimizers are unique up to rotation the ground-state electron density–when scaled appropriately with the electron-phonon coupling strength–converges in a weak sense to a rotational average of their densities.
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2019-07-19
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Dissertation