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Abstract
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We consider the Fröhlich Hamiltonian with large coupling constant
.
For initial data of Pekar product form with coherent phonon field and
with the electron minimizing the corresponding energy, we provide
a norm-approximation of the evolution, valid up to times of order
. The
approximation is given in terms of a Pekar product state, evolved through the
Landau–Pekar equations, corrected by a Bogoliubov dynamics taking quantum
fluctuations into account. This allows us to show that the Landau–Pekar
equations approximately describe the evolution of the electron- and one-phonon
reduced density matrices under the Fröhlich dynamics up to times of order
.
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Keywords
polaron dynamics, Landau–Pekar equations, quantum
fluctuations, Bogoliubov dynamics
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Mathematical Subject Classification
Primary: 35Q40, 46N50
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Milestones
Received: 9 December 2020
Revised: 22 April 2021
Accepted: 26 May 2021
Published: 12 February 2022
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