---
OA_place: repository
OA_type: green
_id: '14854'
abstract:
- lang: eng
  text: 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.
article_processing_charge: No
article_type: original
arxiv: 1
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.
corr_author: '1'
date_created: 2024-01-22T08:24:23Z
date_published: 2023-12-15T00:00:00Z
date_updated: 2025-04-23T14:21:39Z
day: '15'
department:
- _id: RoSe
doi: 10.2140/paa.2023.5.973
external_id:
  arxiv:
  - '2211.03606'
intvolume: '         5'
issue: '4'
keyword:
- General Medicine
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2211.03606
month: '12'
oa: 1
oa_version: Preprint
page: 973-1008
publication: Pure and Applied Analysis
publication_identifier:
  eissn:
  - 2578-5885
  issn:
  - 2578-5893
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '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'
...