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






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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

This article is cited in 3 scientific papers (total in 3 papers)

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:

Received: 01.03.2011

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}


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

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    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  crossref  mathscinet  zmath  adsnasa  isi  scopus
    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  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:266
    Full text:77
    References:22
    First page:4

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020