Impurity-bound excitons in one and two dimensions
Mathematical Physics
2018-07-05 v1 Other Condensed Matter
math.MP
Spectral Theory
Abstract
We study three-body Schr\"odinger operators in one and two dimensions modelling an exciton interacting with a charged impurity. We consider certain classes of multiplicative interaction potentials proposed in the physics literature. We show that if the impurity charge is larger than some critical value, then three-body bound states cannot exist. Our spectral results are confirmed by variational numerical computations based on projecting on a finite dimensional subspace generated by a Gaussian basis.
Cite
@article{arxiv.1807.01523,
title = {Impurity-bound excitons in one and two dimensions},
author = {Horia Cornean and Hynek Kovarik and Thomas G. Pederesen},
journal= {arXiv preprint arXiv:1807.01523},
year = {2018}
}