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Teoreticheskaya i Matematicheskaya Fizika, 1996, Volume 107, Number 1, Pages 75–85
DOI: https://doi.org/10.4213/tmf1139 (Mi tmf1139) 		 
This article is cited in 9 scientific papers (total in 9 papers)

The Iorio–O'Carroll theorem for $N$-particle lattice Hamiltonian

Yu. V. Zhukov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (246 kB) Citations (9)
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DOI: https://doi.org/10.4213/tmf1139
Abstract: The unitary equivalence of the full and free Hamiltonians for a $N$-particle quantum lattice system with the small coupling constant is proved. This result is obtained by means of the mathematical scattering theory: we prove the existence and asymptotic completeness of the wave operators. Here we construct a special representation for the exponent of the Hamiltonian.
Received: 12.10.1995
English version:
Theoretical and Mathematical Physics, 1996, Volume 107, Issue 1, Pages 478–486
DOI: https://doi.org/10.1007/BF02071455
Bibliographic databases:
Language: Russian
Citation: Yu. V. Zhukov, “The Iorio–O'Carroll theorem for $N$-particle lattice Hamiltonian”, TMF, 107:1 (1996), 75–85; Theoret. and Math. Phys., 107:1 (1996), 478–486
Citation in format AMSBIB
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\by Yu.~V.~Zhukov
\paper The Iorio--O'Carroll theorem for $N$-particle lattice Hamiltonian
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\jour Theoret. and Math. Phys.
\yr 1996
\vol 107
\issue 1
\pages 478--486
\crossref{https://doi.org/10.1007/BF02071455}
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  • https://doi.org/10.4213/tmf1139
  • https://www.mathnet.ru/eng/tmf/v107/i1/p75
    • This publication is cited in the following 9 articles:
    1. Tulkin H. Rasulov, Elyor B. Dilmurodov, Khilola G. Khayitova, PHYSICAL MESOMECHANICS OF CONDENSED MATTER: Physical Principles of Multiscale Structure Formation and the Mechanisms of Nonlinear Behavior: MESO2022, 2899, PHYSICAL MESOMECHANICS OF CONDENSED MATTER: Physical Principles of Multiscale Structure Formation and the Mechanisms of Nonlinear Behavior: MESO2022, 2023, 030005  crossref
    2. Yu. Kh. Eshkabilov, D. J. Kulturaev, “On discrete spectrum of one two-particle lattice Hamiltonian”, Ufa Math. J., 14:2 (2022), 97–107  mathnet  crossref
    3. Yu. Kh. Èshkabilov, “Spectrum of a model three-particle Schrödinger operator”, Theoret. and Math. Phys., 186:2 (2016), 268–279  mathnet  crossref  crossref  mathscinet  isi  elib
    4. R. R. Kucharov, Yu. Kh. Eshkabilov, “On the number of negative eigenvalues of a partial integral operator”, Siberian Adv. Math., 25:3 (2015), 179–190  mathnet  crossref  mathscinet
    5. G. P. Arzikulov, Yu. Kh. Eshkabilov, “On the essential and the discrete spectra of a Fredholm type partial integral operator”, Siberian Adv. Math., 25:4 (2015), 231–242  mathnet  crossref  mathscinet
    6. Yu. Kh. Eshkabilov, R. R. Kucharov, “Essential and discrete spectra of the three-particle Schrödinger operator on a lattice”, Theoret. and Math. Phys., 170:3 (2012), 341–353  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    7. È. R. Akchurin, R. A. Minlos, “Scattering theory for a class of two-particle operators of mathematical physics (the case of weak interaction)”, Izv. Math., 76:6 (2012), 1077–1109  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    8. Yu. Kh. Eshkabilov, “On the discrete spectrum of partial integral operators”, Siberian Adv. Math., 23:4 (2013), 227–233  mathnet  crossref  mathscinet  elib
    9. Yu. Kh. Eshkabilov, “O spektralnykh svoistvakh operatorov v modeli Fridrikhsa s nekompaktnym yadrom v prostranstve dvukh peremennykh funktsii”, Vladikavk. matem. zhurn., 8:3 (2006), 53–67  mathnet  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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