PreprintCC BY 4.0arXiv
The Fröhlich Polaron at large total momentum in d=3
Abstract
We consider the three-dimensional Fröhlich polaron at fixed coupling strength α>0 and total momentum P ∈ bbR3. We show that the bottom of the spectrum reaches the essential spectrum at a finite value of |P|, implying that the fiber Hamiltonian has no ground state at sufficiently large total momentum. This extends the known weak-coupling result to arbitrary coupling. Our approach describes states near the spectral threshold by a fully interacting polaron with small residual momentum and one additional phonon carrying almost all of the total momentum.
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BibTeX
@misc{schmidt2026fröhlich,
title = {{The Fröhlich Polaron at large total momentum in d=3}},
author = {Tobias Schmidt},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16081},
eprint = {2610.16081},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16081},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Fröhlich Polaron at large total momentum in d=3
AU - Tobias Schmidt
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16081
UR - https://arxiv.org/abs/2610.16081
AB - We consider the three-dimensional Fröhlich polaron at fixed coupling strength α>0 and total momentum P ∈ bbR^3. We show that the bottom of the spectrum reaches the essential spectrum at a finite value of |P|, implying that the fiber Hamiltonian has no ground state at sufficiently large total momentum. This extends the known weak-coupling result to arbitrary coupling. Our approach describes states near the spectral threshold by a fully interacting polaron with small residual momentum and one additional phonon carrying almost all of the total momentum.
ER -