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Ubiquity of bound states for the strongly coupled polaron

David Mitrouskas and Robert Seiringer
Vol. 5 (2023), No. 4, 973–1008
DOI: 10.2140/paa.2023.5.973
Abstract

We study the spectrum of the Fröhlich Hamiltonian for the polaron at fixed total momentum. We prove the existence of excited eigenvalues between the ground state energy and the essential spectrum at strong coupling. In fact, our main result shows that the number of excited energy bands diverges in the strong coupling limit. To prove this we derive upper bounds for the min-max values of the corresponding fiber Hamiltonians and compare them with the bottom of the essential spectrum, a lower bound on which was recently obtained by Brooks and Seiringer (Comm. Math. Phys. 404:1 (2023), 287–337). The upper bounds are given in terms of the ground state energy band shifted by momentum-independent excitation energies determined by an effective Hamiltonian of Bogoliubov type.

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Keywords
Fröhlich polaron, strong coupling limit, bound states
Mathematical Subject Classification
Primary: 81Q10, 81V70
Milestones
Received: 28 November 2022
Revised: 18 August 2023
Accepted: 14 October 2023
Published: 15 December 2023
Authors
David Mitrouskas
Institute of Science and Technology Austria
Klosterneuburg
Austria
Robert Seiringer
Institute of Science and Technology Austria
Klosterneuburg
Austria
© 2023 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers).