Complex collisions of ultracold molecules: A toy model

We introduce a model to study the collisions of two ultracold diatomic molecules in one dimension interacting via pairwise potentials. present results for this system and argue that it offers lessons real molecular three dimensions. analyze distribution adiabatic potentials hyperspherical coordinate representation as well near-threshold four-body bound states, systematically studying effects properties, such interaction strength, range, atomic mass. It is found potential's nearest-neighbor energy level transitions from significant repulsion characteristic chaos (Brody distribution) nonchaotic (Poisson are separated. For four-atom case where all atoms have equal masses shows Poissonian spacing distribution, while unequal-mass exhibits characterized by nonzero Brody parameter. derive semiclassical formula density states extract simple scaling laws with potential depth range. find good agreement between predictions full quantum mechanical calculations.