The condensate number in PIMC treatments of trapped bosons

In path integral Monte Carlo (PIMC) treatments of harmonically trapped boso ns, one cannot use the usual long-range constant limit of the one-body redu ced density matrix rho(1) to determine the condensate number n(0) because r ho(1) always approaches zero in a trap. W. Krauth found that the longest pe rmutation cycle arising in the simulation gives a consistent value of n(0). Our analytical studies of the ideal gas suggest other ways of using permut ation cycles to determine n(0). We test these approaches on simulations inv olving finite-size ideal and interacting gases and find that the methods ar e consistent. (C) 2000 Elsevier Science B.V. All rights reserved.