For a Nelson-type Hamiltonian on a soft quantum waveguide, the essential spectrum of the curved guide is a half-line whose threshold combines the straight-guide ionization threshold and the one-boson mass; a negative eigenstate of an effective 1D operator implies a bound state.
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Spectral Analysis of a Soft Quantum Waveguide Coupled to a Massive Quantum Scalar Field
For a Nelson-type Hamiltonian on a soft quantum waveguide, the essential spectrum of the curved guide is a half-line whose threshold combines the straight-guide ionization threshold and the one-boson mass; a negative eigenstate of an effective 1D operator implies a bound state.