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Spectral Analysis of the 2 + 1 Fermionic Trimer with Contact Interactions

  • Simon Becker
  • Alessandro MichelangeliEmail author
  • Andrea Ottolini
Article

Abstract

We qualify the main features of the spectrum of the Hamiltonian of point interaction for a three-dimensional quantum system consisting of three point-like particles, two identical fermions, plus a third particle of different species, with two-body interaction of zero range. For arbitrary magnitude of the interaction, and arbitrary value of the mass parameter (the ratio between the mass of the third particle and that of each fermion) above the stability threshold, we identify the essential spectrum, localise the discrete spectrum and prove its finiteness, qualify the angular symmetry of the eigenfunctions, and prove the increasing monotonicity of the eigenvalues with respect to the mass parameter. We also demonstrate the existence or absence of bound states in the physically relevant regimes of masses.

Keywords

Particle systems with zero-range/contact interactions Ter-martirosyan-skornyakov hamiltonians Fermonic 2 + 1 system 

Mathematics Subject Classification (2010)

46N50 47A60 47B25 47N50 70F07 81Q10 

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Applied Mathematics and Theoretical PhysicsUniversity of CambridgeCambridgeUK
  2. 2.International School for Advanced Studies – SISSATriesteItaly
  3. 3.Department of MathematicsStanford UniversityStanfordUSA

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