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Abstract: A model of a quantum dot with impurity in the Lobachevsky plane isconsidered. Relying on explicit formulae for the Green function and the Krein$Q-$function which have been derived in a previous work we focus on thenumerical analysis of the spectrum. The analysis is complicated by the factthat the basic formulae are expressed in terms of spheroidal functions withgeneral characteristic exponents. The effect of the curvature on eigenvaluesand eigenfunctions is investigated. Moreover, there is given an asymptoticexpansion of eigenvalues as the curvature radius tends to infinity the flatcase limit.



Author: P. Stovicek, M. Tusek

Source: https://arxiv.org/







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