The effective mass problem for the Landau-Pekar equations

Article Mathematics, Applied

The Strongly Coupled Polaron on the Torus: Quantum Corrections to the Pekar Asymptotics

Dario Feliciangeli et al.

Summary: The study investigates the Frohlich polaron model on a three-dimensional torus, providing a proof of the second-order quantum corrections to its ground-state energy in the strong-coupling limit. The presence of translational symmetry (and its breakdown in the Pekar approximation) makes the analysis significantly more challenging than in previous studies in confined cases.

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS (2021)

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Article Physics, Mathematical

Persistence of the spectral gap for the Landau-Pekar equations

Dario Feliciangeli et al.

Summary: By providing a class of specific initial data, the Landau-Pekar equations exhibit a uniform spectral gap for all times, allowing for the extension of results on the adiabatic theorem to larger time scales.

LETTERS IN MATHEMATICAL PHYSICS (2021)

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Article Mathematics, Applied

THE LANDAU-PEKAR EQUATIONS: ADIABATIC THEOREM AND ACCURACY

Nikolai Leopold et al.

Summary: An adiabatic theorem is proved for the Landau-Pekar equations, allowing the derivation of new results on their accuracy as effective equations for time evolution generated by the Frohlich Hamiltonian with a large coupling constant alpha. It is shown that the time evolution of Pekar product states under coherent phonon fields, with the electron trapped by the phonons, is well approximated by the Landau-Pekar equations until times shorter than alpha squared.

ANALYSIS & PDE (2021)

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Article Physics, Mathematical

A note on the Frohlich dynamics in the strong coupling limit

David Mitrouskas

Summary: Our study revises a previous result on the Frohlich dynamics in the strong coupling limit, showing that the electron ground state remains close to its initial state for a certain period of time, while the phonon fluctuations can be described by a Bogoliubov transformation.

LETTERS IN MATHEMATICAL PHYSICS (2021)

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Review Nanoscience & Nanotechnology

Polarons in materials

Cesare Franchini et al.

Summary: Polarons, arising from the interaction of electrons with lattice vibrations, strongly influence materials properties. This Review provides a map of the theoretical models and experimental techniques used to study polarons in materials, presenting paradigmatic examples of different types of polarons and polaron-driven phenomena.

NATURE REVIEWS MATERIALS (2021)

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Article Physics, Mathematical