On the number of particles which a curved quantum waveguide can bind

Abstract

We discuss the discrete spectrum of N particles in a curved planar waveguide. If they are neutral fermions, the maximum number of particles which the waveguide can bind is given by a one-particle Birman-Schwinger bound in combination with the Pauli principle. On the other hand, if they are charged, e.g., electrons in a bent quantum wire, the Coulomb repulsion plays a crucial role. We prove a sufficient condition under which the discrete spectrum of such a system is empty.

a LateX file, 12 pages

References in corpus (4)

• Bound states and scattering in quantum waveguides coupled laterally through a boundary window
• Bound-state asymptotic estimates for window-coupled Dirichlet strips and layers
• Asymptotic estimates for bound states in quantum waveguides coupled laterally through a narrow window
• Bound states in a locally deformed waveguide: the critical case

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• Geometrically induced two-particle binding in a wave guide