Dimensional crossover of nonrelativistic bosons - Lammers, Sören; Böttcher, Igor; Wetterich, Christof (Physical review, 2016)
We investigate how confining a transverse spatial dimension influences the few- and many-body properties of nonrelativistic bosons with pointlike interactions. Our main focus is on the dimensional crossover from three to two dimensions, which is of relevance for ultracold-atom experiments. Using functional-renormalization-group equations and T-matrix calculations we study how the phase transition temperature changes as a function of the spatial extent of the transverse dimension and relate the three- and two-dimensional s-wave scattering lengths. The analysis reveals how the properties of the lower-dimensional system are inherited from the higher-dimensional one during renormalization-group evolution. We limit the discussion to confinements in a potential well with periodic boundary conditions and argue why this qualitatively captures the physics of other compactifications such as transverse harmonic confinement as in cold-atom experiments.
Gesehen am 12.06.2020