Efimov effect in an internal spectral gap of a three-particle lattice Hamiltonian
Abstract
We prove the existence of an Efimov sequence in an internal gap of the essential spectrum of a three-particle lattice Hamiltonian. The system consists of two identical spinless fermions and one distinguishable particle on Z3, with repulsive pair interactions. For each fixed fermion-to-third-particle mass ratio γ>γ*≈13.6069657 and total quasi-momentum near π1, the mixed zero-range coupling is tuned to a simultaneous upper-threshold resonance. Sufficiently strong nearest-neighbour repulsion between the fermions separates the upper fermion-pair two-cluster spectrum from the free three-particle band. Infinitely many discrete eigenvalues accumulate at the lower endpoint of the resulting gap, which coincides with the free upper edge. We establish logarithmic eigenvalue-counting asymptotics with the same positive coefficient as at zero fermion--fermion coupling. This coefficient also governs accumulation above the essential spectrum throughout the closed weak-coupling interval, including its critical endpoint. We classify the channel spectrum near the free upper edge for all nonnegative fermion couplings.
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BibTeX
@misc{lakaev2026efimov,
title = {{Efimov effect in an internal spectral gap of a three-particle lattice Hamiltonian}},
author = {Saidakhmat N. ~Lakaev},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26284},
eprint = {2610.26284},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26284},
}
RIS
TY - UNPB
TI - Efimov effect in an internal spectral gap of a three-particle lattice Hamiltonian
AU - Saidakhmat N. ~Lakaev
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26284
UR - https://arxiv.org/abs/2610.26284
AB - We prove the existence of an Efimov sequence in an internal gap of the essential spectrum of a three-particle lattice Hamiltonian. The system consists of two identical spinless fermions and one distinguishable particle on Z^3, with repulsive pair interactions. For each fixed fermion-to-third-particle mass ratio γ>γ_*≈13.6069657 and total quasi-momentum near π1, the mixed zero-range coupling is tuned to a simultaneous upper-threshold resonance. Sufficiently strong nearest-neighbour repulsion between the fermions separates the upper fermion-pair two-cluster spectrum from the free three-particle band. Infinitely many discrete eigenvalues accumulate at the lower endpoint of the resulting gap, which coincides with the free upper edge. We establish logarithmic eigenvalue-counting asymptotics with the same positive coefficient as at zero fermion--fermion coupling. This coefficient also governs accumulation above the essential spectrum throughout the closed weak-coupling interval, including its critical endpoint. We classify the channel spectrum near the free upper edge for all nonnegative fermion couplings.
ER -