BOSE-EINSTEIN CONDENSATION IN ONE-DIMENSIONAL POWER-LAW TRAPS - A PATH-INTEGRAL MONTE-CARLO SIMULATION

Bose-Einstein condensation is known to occur in one-dimensional power- law potentials V(x) proportional to\x\(eta) as a true phase transition for eta < 2, but only if there are no interactions between the partic les. We show, via a pathintegral quantum Monte Carlo scheme, that for both eta > 2 and eta = 2 the spatial distribution of finite numbers of hard-core bosons suddenly becomes bimodal below a certain temperature , with a central condensate of particles distributed according to the lowest single-particle eigenstate. At still lower temperatures, the ha rd-core interactions cause the single-particle ground state to become a poor description for the interacting gas. If eta < 2, the energy per particle undergoes a sudden decrease near the same temperature at whi ch the bimodal distribution appears. It is found that this drop in ene rgy disappears if the range of the interaction potential is sufficient ly large. [S1050-2947(98)09308-1].