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On the Discrete Spectrum of a Model Operator in Fermionic Fock Space

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Listed:
  • Zahriddin Muminov
  • Fudziah Ismail
  • Zainidin Eshkuvatov
  • Jamshid Rasulov

Abstract

We consider a model operator associated with a system describing three particles in interaction, without conservation of the number of particles. The operator acts in the direct sum of zero-, one-, and two-particle subspaces of the fermionic Fock space  over . We admit a general form for the "kinetic" part of the Hamiltonian , which contains a parameter to distinguish the two identical particles from the third one. (i) We find a critical value for the parameter that allows or forbids the Efimov effect (infinite number of bound states if the associated generalized Friedrichs model has a threshold resonance) and we prove that only for the Efimov effect is absent, while this effect exists for any . (ii) In the case , we also establish the following asymptotics for the number of eigenvalues of below , for all .

Suggested Citation

  • Zahriddin Muminov & Fudziah Ismail & Zainidin Eshkuvatov & Jamshid Rasulov, 2013. "On the Discrete Spectrum of a Model Operator in Fermionic Fock Space," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-12, May.
    • Handle: RePEc:hin:jnlaaa:875194
    DOI: 10.1155/2013/875194
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