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On the existence of impurity localized excitons in 1D systems

Jonas Have
(Aalborg University)
Torsdag, 6 oktober, 2016, at 15:15-16:00, in Aud. D3 (1531-215)
Consider a three-body one-dimensional Schrodinger operator, with short range potentials, which models a positively charged impurity interacting with an exciton (a pair of two oppositely charged particles). Denote the charge of the impurity by $\kappa$. We study the existence of a ground state as a function of $\kappa$. We show that for small $\kappa$ there exists a unique bound state which goes like $\kappa^4$. If the potentials are modelled by Dirac distributions, we can explicitly compute the leading coefficient. Under the same assumption, if $\kappa$ is larger than some explicit critical value, then we prove the absence of the discrete spectrum. This is joint work with HD Cornean, TG Pedersen (Aalborg) and Hynek Kovarik (Brescia). 
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