Abstract
The [Formula: see text]-wave resonances induce an infinite number of negative eigenvalues accumulating at the origin for the system of three identical particles in two dimensions, provided that the energy operator is restricted on the subspace of wave functions which are antisymmetric with respect to the permutations. This quantum phenomenon is called the super Efimov effect and corresponds to the Efimov effect in three dimensions. It has been predicted in physics literature [ 10 ] and a mathematical proof has been given by Gridnev [ 5 ]. In this paper, we prove this effect for a wider class of pair interactions and improve the results obtained by [ 5 ]. We do not necessarily assume that the interactions are radially symmetric, have a definite signature and fall off exponentially at infinity. The essence of the proof is put in the asymptotic analysis of the singular behavior at low energy for resolvents of the Schrödinger operators with [Formula: see text]-wave resonances at zero energy.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
