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

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

1998-01-07

arxiv.org/abs/math/9801021v1

J. Math. Phys. 40 (1999), 4630-4638

Mathematics

Functional Analysis

a LateX file, 12 pages

Scientific paper

10.1063/1.532993

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.

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