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TMF, 2007, Volume 153, Number 3, Pages 381–387 (Mi tmf6143)  

This article is cited in 7 scientific papers (total in 7 papers)

Positivity of the two-particle Hamiltonian on a lattice

M. I. Muminov

A. Navoi Samarkand State University

Abstract: We consider a two-particle Hamiltonian on the $d$-dimensional lattice $\mathbb Z^d$. We find a sufficient condition for the positivity of a family of operators $h(k)$ appearing after the "separation of the center of mass" of a system of two particles depending on the values of the total quasimomentum $k\in T^d$ (where $T^d$ is a $d$-dimensional torus). We use the obtained result to show that the operator $h(k)$ has positive eigenvalues for nonzero $k\in T^d$.

Keywords: two-particle Hamiltonian on a lattice, virtual level, regular point, positive operator, discrete spectrum

DOI: https://doi.org/10.4213/tmf6143

Full text: PDF file (428 kB)
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English version:
Theoretical and Mathematical Physics, 2007, 153:3, 1671–1676

Bibliographic databases:

Received: 15.01.2007
Revised: 02.05.2007

Citation: M. I. Muminov, “Positivity of the two-particle Hamiltonian on a lattice”, TMF, 153:3 (2007), 381–387; Theoret. and Math. Phys., 153:3 (2007), 1671–1676

Citation in format AMSBIB
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    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. M. I. Muminov, A. M. Hurramov, “Spectral properties of a two-particle Hamiltonian on a lattice”, Theoret. and Math. Phys., 177:3 (2013), 1693–1705  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. 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
    3. M. I. Muminov, A. M. Hurramov, “Multiplicity of virtual levels at the lower edge of the continuous spectrum of a two-particle Hamiltonian on a lattice”, Theoret. and Math. Phys., 180:3 (2014), 1040–1050  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    4. M. E. Muminov, A. M. Khurramov, “Spectral properties of two particle Hamiltonian on one-dimensional lattice”, Ufa Math. J., 6:4 (2014), 99–107  mathnet  crossref
    5. Muminov M.I. Murid A.H.M., “Spectral analysis of the two-particle Schrödinger operator on a lattice”, THE 22ND NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES (SKSM22): Strengthening Research and Collaboration of Mathematical Sciences in Malaysia (Selangor, Malaysia, 24–26 November 2014), AIP Conference Proceedings, 1682, ed. Mohamed I. How L. Mui A. Bin W., Amer Inst Physics, 2015, 040017  crossref  isi  scopus
    6. M. E. Muminov, E. M. Shermatova, “On finiteness of discrete spectrum of three-particle Schrödinger operator on a lattice”, Russian Math. (Iz. VUZ), 60:1 (2016), 22–29  mathnet  crossref  isi
    7. Muminov M.I., Khurramov A.M., “Spectral properties of a two-particle Hamiltonian on a d-dimensional lattice”, Nanosyst.-Phys. Chem. Math., 7:5 (2016), 880–887  crossref  zmath  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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