Universal bound states of two- and three-body quantum systems
Driscoll, Kevin Joseph
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When there is a low-energy resonance between two particles, the typical separation of physical length scales no longer holds, and quantum systems can form states that are much larger on average than the characteristic size of the underlying interaction. Within this regime, long-wavelength theories with weak scattering break down; however, broadly applicable results can be recovered by replacing the interaction potential with appropriately chosen boundary conditions. We investigate two such systems of spinless bosons: three particles with resonant two-body interactions and two particles resonantly interacting with a flat surface. In the former case, where the Efimov effect is known to occur, we give exact expressions for the two- and three-body contacts, which describe the two- and three-body correlations in the system, at the threshold where the least bound Efimov trimer disassociates. In the latter, we find a sequence of bound states between the bosons and the surface (which produces a resonant potential) that are much larger on average than the range of interaction, and we show a new method for relating the contacts, which appear in the distribution of particles with large momenta, to the short-range correlations. The methods that we improve and develop are applicable to many systems with large scattering length and resonant potentials which open a different avenue to investigate effective three-body interactions.