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TMF, 1995, Volume 103, Number 1, Pages 63–81 (Mi tmf1287)  

This article is cited in 14 scientific papers (total in 14 papers)

Spectrum and scattering in a model “spin-boson” with at most three photons

Yu. V. Zhukova, R. A. Minlosb

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Institute for Information Transmission Problems, Russian Academy of Sciences

Abstract: A model of radiative decay with a fixed atom and not more than three photons is studied. A spectral analysis of the Hamiltonian is made. This is done by means of scattering theory in a pair of spaces with a specially chosen embedding. The existence of wave operators and their asymptotic completeness are proved. The constructions are based on a detailed analysis of the resolvent of the Hamiltonian.

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English version:
Theoretical and Mathematical Physics, 1995, 103:1, 398–411

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Received: 13.07.1994

Citation: Yu. V. Zhukov, R. A. Minlos, “Spectrum and scattering in a model “spin-boson” with at most three photons”, TMF, 103:1 (1995), 63–81; Theoret. and Math. Phys., 103:1 (1995), 398–411

Citation in format AMSBIB
\by Yu.~V.~Zhukov, R.~A.~Minlos
\paper Spectrum and scattering in a~model ``spin-boson'' with at most three photons
\jour TMF
\yr 1995
\vol 103
\issue 1
\pages 63--81
\jour Theoret. and Math. Phys.
\yr 1995
\vol 103
\issue 1
\pages 398--411

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    This publication is cited in the following articles:
    1. T. H. Rasulov, “Discrete spectrum of a model operator in Fock space”, Theoret. and Math. Phys., 152:3 (2007), 1313–1321  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Albeverio, S, “On the spectrum of an Hamiltonian in Fock space. Discrete spectrum asymptotics”, Journal of Statistical Physics, 127:2 (2007), 191  crossref  mathscinet  zmath  adsnasa  isi
    3. T. H. Rasulov, “On the Structure of the Essential Spectrum of a Model Many-Body Hamiltonian”, Math. Notes, 83:1 (2008), 80–87  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. T. H. Rasulov, “The Faddeev equation and the location of the essential spectrum of a model operator for several particles”, Russian Math. (Iz. VUZ), 52:12 (2008), 50–59  mathnet  crossref  mathscinet  zmath
    5. T. H. Rasulov, “Investigation of the spectrum of a model operator in a Fock space”, Theoret. and Math. Phys., 161:2 (2009), 1460–1470  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. T. H. Rasulov, “Study of the essential spectrum of a matrix operator”, Theoret. and Math. Phys., 164:1 (2010), 883–895  mathnet  crossref  crossref  adsnasa  isi
    7. Rasulov T.H., “Investigations of the Essential Spectrum of a Hamiltonian in Fock Space”, Applied Mathematics & Information Sciences, 4:3 (2010), 395–412  isi
    8. T. Kh. Rasulov, “On the number of eigenvalues of a matrix operator”, Siberian Math. J., 52:2 (2011), 316–328  mathnet  crossref  mathscinet  isi
    9. T. Kh. Rasulov, I. O. Umarova, “Spektr i rezolventa odnoi blochno-operatornoi matritsy”, Sib. elektron. matem. izv., 11 (2014), 334–344  mathnet
    10. M. I. Muminov, T. H. Rasulov, “Infiniteness of the number of eigenvalues embedded in the essential spectrum of a $2\times2$ operator matrix”, Eurasian Math. J., 5:2 (2014), 60–77  mathnet
    11. G. R. Yodgorov, F. Ismail, Z. I. Muminov, “A description of the location and structure of the essential spectrum of a model operator in a subspace of a Fock space”, Sb. Math., 205:12 (2014), 1761–1774  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    12. T. H. Rasulov, “Branches of the essential spectrum of the lattice spin-boson model with at most two photons”, Theoret. and Math. Phys., 186:2 (2016), 251–267  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    13. Ibrogimov O.O., Tretter Ch., “On the Spectrum of An Operator in Truncated Fock Space”, Indefinite Inner Product Spaces, Schur Analysis, and Differential Equations: a Volume Dedicated to Heinz Langer, Operator Theory Advances and Applications, 263, eds. Alpay D., Kirstein B., Birkhauser Verlag Ag, 2018, 321–334  crossref  mathscinet  zmath  isi  scopus
    14. Ibrogimov O.O., “Spectral Analysis of the Spin-Boson Hamiltonian With Two Photons For Arbitrary Coupling”, Ann. Henri Poincare, 19:11 (2018), 3561–3579  crossref  mathscinet  zmath  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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