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The Landau–Pekar
equations: adiabatic theorem and accuracy
Nikolai Leopold, Simone Rademacher, Benjamin Schlein and Robert Seiringer |
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Vol. 14 (2021), No. 7, 2079–2100
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Abstract |
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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 Fröhlich Hamiltonian with large coupling constant . 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 . |
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Keywords
polaron, dynamics, adiabatic theorem
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Mathematical Subject Classification 2010
Primary: 35Q40, 46N50
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Milestones
Received: 9 May 2019
Revised: 2 March 2020
Accepted: 22 April 2020
Published: 10 November 2021
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Authors |
| Nikolai Leopold | |
| Institute of Science and Technology
Austria Klosterneuburg Austria |
Department of Mathematics and
Computer Science University of Basel Basel Switzerland |
| Simone Rademacher | |
| Institute of Mathematics University of Zurich Zurich Switzerland |
Institute of Science and Technology
Austria Klosterneuburg Austria |
| Benjamin Schlein | |
| Institute of Mathematics University of Zurich Zurich Switzerland |
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| Robert Seiringer | |
| Institute of Science and Technology
Austria Klosterneuburg Austria |
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