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On the existence of impurity bound excitons in one-dimensional systems with zero range interactions
- Source :
- Journal of Mathematical Physics 58, 052106 (2017)
- Publication Year :
- 2017
-
Abstract
- We consider a three-body one-dimensional Schr\"odinger operator with zero range potentials, which models a positive impurity with charge $\kappa > 0$ interacting with an exciton. We study the existence of discrete eigenvalues as $\kappa$ is varied. On one hand, we show that for sufficiently small $\kappa$ there exists a unique bound state whose binding energy behaves like $\kappa^4$, and we explicitly compute its leading coefficient. On the other hand, if $\kappa$ is larger than some critical value then the system has no bound states.
- Subjects :
- Mathematical Physics
Subjects
Details
- Database :
- arXiv
- Journal :
- Journal of Mathematical Physics 58, 052106 (2017)
- Publication Type :
- Report
- Accession number :
- edsarx.1701.04302
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1063/1.4983921