The diffusion Monte Carlo method is applied to describe a trapped atomic Bose-Einstein condensate at zero temperature, fully quantum mechanically and nonperturbatively. For low densities, ${n(0)a}^{3}<~2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$
[n(0), peak density; a, s-wave scattering length], our calculations confirm that the exact ground-state energy for a sum of two-body interactions depends to a good approximation on only the atomic-physics parameter a, and no other details of the two-body model potential. Corrections to the mean-field Gross-Pitaevskii energy range from being essentially negligible to about 20% for
N=2−−50 particles in the trap with positive s-wave scattering length
a=100−−10000a.u. Our numerical calculations confirm that inclusion of an additional effective potential term in the mean-field equation, which accounts for quantum fluctuations [see, e.g., E. Braaten and A. Nieto, Phys. Rev. B 56, 14 745 (1997)], leads to a greatly improved description of trapped Bose gases.
We have examined the current correlation functions is statistical mechanics from a scattering theory viewpoint. In the light of low energy theorems, we study the connection between the long wavelength, low-frequency correlation functions of conserved currents and the on-shell scattering matrix elements which describe the collision processes taking place in the thermodynamical system of interest. Explicit general formulas are derived for the leading correction terms to the ideal gas correlation functions. These correction terms include the effect of two-body scatterings and double scatterings in three-body events. They are expressed in terms of two-body cross section, time delay, and the quantum analog of the distance of closest approach. Their connection to the second virial coefficient is established through sum rules. Relationship between our results and the Boltzmann equation is discussed.
We consider strongly interacting one-dimensional electron liquids where elementary excitations carry either spin or charge. At small temperatures a spinon created at the bottom of its band scatters off low-energy spin and charge excitations and follows the diffusive motion of a Brownian particle in momentum space. We calculate the mobility characterizing these processes and show that the resulting diffusion coefficient of the spinon is parametrically enhanced at low temperatures compared to that of a mobile impurity in a spinless Luttinger liquid. We briefly discuss that this hints at the relevance of spin in the process of equilibration of strongly interacting one-dimensional electrons, and comment on implications for transport in clean single-channel quantum wires.