A novel algorithm of Diagrammatic Quantum Monte Carlo in momentum representation is reported in details. New models can be studied with this algorithm. For Bose systems with attractive interaction, the algorithm is free of the well-known minus-sign problem, while in other models it is weaker than in real-space methods. Using this algorithm, we present the results of an exact numeric simulation of N one-dimensional bosons with attractive delta-functional interaction in a rotating ring. We prove that in the large-N limit the system can be described by conventional methods of weakly interacting gas, the dimensionless parameter of weak interaction being just 1/N. When the strength of interaction is less then a certain threshold value, the dependence of angular momentum on the rotation frequency features plateaus characteristic of the irrotational fluid (the Hess-Fairbank effect).
We consider a three-dimensional weakly interacting Bose gas in the fluctuation region (and its vicinity) of the normal-fluid--superfluid phase transition point. We establish relations between basic thermodynamic functions: density $n(T,\ensuremath{\mu})$, superfluid density ${n}_{s}(T,\ensuremath{\mu})$, and condensate density ${n}_{\text{cnd}}(T,\ensuremath{\mu})$. Being universal for all weakly interacting ${\ensuremath{\mid}\ensuremath{\psi}\ensuremath{\mid}}^{4}$ systems, these relations are obtained from Monte Carlo simulations of the classical ${\ensuremath{\mid}\ensuremath{\psi}\ensuremath{\mid}}^{4}$ model on a lattice. Comparing with the mean-field results yields a quantitative estimate of the fluctuation region size. Away from the fluctuation region, on the superfluid side, all the data perfectly agree with the predictions of the quasicondensate mean-field theory. This demonstrates that the only effect of the leading above-the-mean-field corrections in the condensate-based treatments is to replace the condensate density with the quasicondensate one in all local thermodynamic relations. Surprisingly, we find that a significant fraction of the density profile of a loosely trapped atomic gas might correspond to the fluctuation region.
Relaxation of far-from-equilibrium quantum fluids, intimately related to the emergence of long-range order, is theoretically associated with the decay of a turbulent isotropic tangle of vortex lines. We observe and study such decaying quantum turbulence in a homogeneous 3D atomic Bose gas. Using matter-wave techniques to magnify the gas density distribution, and then imaging a thin slice of the magnified cloud, we observe imprints of randomly oriented vortex lines and measure the vortex line-length density
L. The observed decay of
L agrees with the prediction for Vinen `ultraquantum' turbulence. Although our weakly interacting gases are highly compressible, their large-scale dynamics are consistent with the behavior of an incompressible hydrodynamic fluid, with the decay of
L not depending on the strength of the interatomic interactions and being similar to that in the strongly interacting superfluid helium.