Threshold effects in a two-fermion system on an optical lattice View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2020-05-30

AUTHORS

S. N. Lakaev, S. H. Abdukhakimov

ABSTRACT

For a wide class of two-particle Schrödinger operators H(k) = H0(k) + V, k ∈ Td\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{T}^d$$\end{document}, corresponding to a two-fermion system on a d-dimensional cubic integer lattice (d ≥ 1), we prove that for any value k ∈ Td\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{T}^d$$\end{document} of the quasimomentum, the discrete spectrum of H(k) below the lower threshold of the essential spectrum is a nonempty set if the following two conditions are satisfied. First, the two-particle operator H(0) corresponding to a zero quasimomentum has either an eigenvalue or a virtual level on the lower threshold of the essential spectrum. Second, the one-particle free (nonperturbed) Schrödinger operator in the coordinate representation generates a semigroup that preserves positivity. More... »

PAGES

648-663

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1134/s0040577920050074

DOI

http://dx.doi.org/10.1134/s0040577920050074

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1128079354


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