---
_id: '14854'
abstract:
- lang: eng
  text: "\r\nAbstract\r\nWe 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."
article_processing_charge: No
article_type: original
author:
- first_name: David Johannes
  full_name: Mitrouskas, David Johannes
  id: cbddacee-2b11-11eb-a02e-a2e14d04e52d
  last_name: Mitrouskas
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Mitrouskas DJ, Seiringer R. Ubiquity of bound states for the strongly coupled
    polaron. <i>Pure and Applied Analysis</i>. 2023;5(4):973-1008. doi:<a href="https://doi.org/10.2140/paa.2023.5.973">10.2140/paa.2023.5.973</a>
  apa: Mitrouskas, D. J., &#38; Seiringer, R. (2023). Ubiquity of bound states for
    the strongly coupled polaron. <i>Pure and Applied Analysis</i>. Mathematical Sciences
    Publishers. <a href="https://doi.org/10.2140/paa.2023.5.973">https://doi.org/10.2140/paa.2023.5.973</a>
  chicago: Mitrouskas, David Johannes, and Robert Seiringer. “Ubiquity of Bound States
    for the Strongly Coupled Polaron.” <i>Pure and Applied Analysis</i>. Mathematical
    Sciences Publishers, 2023. <a href="https://doi.org/10.2140/paa.2023.5.973">https://doi.org/10.2140/paa.2023.5.973</a>.
  ieee: D. J. Mitrouskas and R. Seiringer, “Ubiquity of bound states for the strongly
    coupled polaron,” <i>Pure and Applied Analysis</i>, vol. 5, no. 4. Mathematical
    Sciences Publishers, pp. 973–1008, 2023.
  ista: Mitrouskas DJ, Seiringer R. 2023. Ubiquity of bound states for the strongly
    coupled polaron. Pure and Applied Analysis. 5(4), 973–1008.
  mla: Mitrouskas, David Johannes, and Robert Seiringer. “Ubiquity of Bound States
    for the Strongly Coupled Polaron.” <i>Pure and Applied Analysis</i>, vol. 5, no.
    4, Mathematical Sciences Publishers, 2023, pp. 973–1008, doi:<a href="https://doi.org/10.2140/paa.2023.5.973">10.2140/paa.2023.5.973</a>.
  short: D.J. Mitrouskas, R. Seiringer, Pure and Applied Analysis 5 (2023) 973–1008.
date_created: 2024-01-22T08:24:23Z
date_published: 2023-12-15T00:00:00Z
date_updated: 2024-01-23T12:55:12Z
day: '15'
department:
- _id: RoSe
doi: 10.2140/paa.2023.5.973
intvolume: '         5'
issue: '4'
keyword:
- General Medicine
language:
- iso: eng
month: '12'
oa_version: None
page: 973-1008
publication: Pure and Applied Analysis
publication_identifier:
  issn:
  - 2578-5885
  - 2578-5893
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
status: public
title: Ubiquity of bound states for the strongly coupled polaron
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 5
year: '2023'
...