Journal
ANALYSIS & PDE
Volume 14, Issue 7, Pages 2079-2100Publisher
MATHEMATICAL SCIENCE PUBL
DOI: 10.2140/apde.2021.14.2079
Keywords
polaron; dynamics; adiabatic theorem
Categories
Funding
- European Research Council (ERC) under the European Union [694227]
- Swiss National Science Foundation [200020_172623]
- NCCR SwissMAP
- Swiss National Science Foundation (SNF) [200020_172623] Funding Source: Swiss National Science Foundation (SNF)
- European Research Council (ERC) [694227] Funding Source: European Research Council (ERC)
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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.
We prove an adiabatic theorem for the Landau-Pekar equations. This allows us to derive new results on the accuracy of their use as effective equations for the time evolution generated by the Frohlich Hamiltonian with large coupling constant alpha. In particular, we show that the time evolution of Pekar product states with coherent phonon field and the electron being trapped by the phonons is well approximated by the Landau-Pekar equations until times short compared to alpha(2).
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