Conditions for the formation of a moving bound state of a pair of quasiparticles

The spectra and the necessary criteria for the existence of a bound state of a pair of activation or Goldstone quasiparticles, whose energy depends on the momentum according to a power law with index n ≤ 2, are derived. In a space of dimensions d ≥ 2 a bound state forms with an arbitrarily weak attraction independently of the magnitude of the total momentum of the pair 2Q, while in a space of dimension > 2 the bound state forms only it 2Q is less than a critical value 2Qc. For Q > Qc the bound state is destroyed by a kinetic mechanism.

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