RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 TMF: Year: Volume: Issue: Page: Find

 TMF, 2012, Volume 170, Number 3, Pages 393–408 (Mi tmf6774)

Existence and analyticity of bound states of a two-particle Schrödinger operator on a lattice

S. N. Lakaev, S. S. Ulashov

Samarkand State University, Samarkand, Uzbekistan

Abstract: We consider the two-particle discrete Schrödinger operator $H_\mu(K)$ corresponding to a system of two arbitrary particles on a $d$-dimensional lattice $\mathbb Z^d$, $d\ge3$, interacting via a pair contact repulsive potential with a coupling constant $\mu>0$ ($K\in\mathbb T^d$ is the quasimomentum of two particles). We find that the upper (right) edge of the essential spectrum can be either a virtual level (for $d=3,4)$ or an eigenvalue (for $d\ge5)$ of $H_\mu(K)$. We show that there exists a unique eigenvalue located to the right of the essential spectrum, depending on the coupling constant $\mu$ and the two-particle quasimomentum $K$. We prove the analyticity of the corresponding eigenstate and the analyticity of the eigenvalue and the eigenstate as functions of the quasimomentum $K\in\mathbb T^d$ in the domain of their existence.

Keywords: discrete Schrödinger operator, two-particle system, Hamiltonian, contact repulsive potential, virtual level, eigenvalue, lattice

DOI: https://doi.org/10.4213/tmf6774

Full text: PDF file (460 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2012, 170:3, 326–340

Bibliographic databases:

Citation: S. N. Lakaev, S. S. Ulashov, “Existence and analyticity of bound states of a two-particle Schrödinger operator on a lattice”, TMF, 170:3 (2012), 393–408; Theoret. and Math. Phys., 170:3 (2012), 326–340

Citation in format AMSBIB
\Bibitem{LakUla12} \by S.~N.~Lakaev, S.~S.~Ulashov \paper Existence and analyticity of bound states of a~two-particle Schr\"odinger operator on a~lattice \jour TMF \yr 2012 \vol 170 \issue 3 \pages 393--408 \mathnet{http://mi.mathnet.ru/tmf6774} \crossref{https://doi.org/10.4213/tmf6774} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3168848} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2012TMP...170..326L} \elib{http://elibrary.ru/item.asp?id=20732432} \transl \jour Theoret. and Math. Phys. \yr 2012 \vol 170 \issue 3 \pages 326--340 \crossref{https://doi.org/10.1007/s11232-012-0033-6} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000303456600006} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84860381632} 

• http://mi.mathnet.ru/eng/tmf6774
• https://doi.org/10.4213/tmf6774
• http://mi.mathnet.ru/eng/tmf/v170/i3/p393

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. S. N. Lakaev, Sh. U. Alladustov, “Positivity of eigenvalues of the two-particle Schrödinger operator on a lattice”, Theoret. and Math. Phys., 178:3 (2014), 336–346
2. S. N. Lakaev, G. Dell'Antonio, A. M. Khalkhuzhaev, “Existence of an isolated band in a system of three particles in an optical lattice”, J. Phys. A-Math. Theor., 49:14 (2016), 145204
3. S. N. Lakaev, Sh. S. Lakaev, “The existence of bound states in a system of three particles in an optical lattice”, J. Phys. A-Math. Theor., 50:33 (2017), 335202
•  Number of views: This page: 266 Full text: 77 References: 22 First page: 4