Quantum critical dynamics of the two-dimensional Bose gas

The dilute, two-dimensional Bose gas exhibits a novel regime of relaxational dynamics in the regime k(B)T greater than or similar to vertical bar mu vertical bar where T is the absolute temperature and mu is the chemical potential. This may also be interpreted as the quantum criticality of the zero density quantum critical point at mu=0. We present a theory for this dynamic, to leading order in 1/ln[Lambda/(k(B)T)], where Lambda is a high energy cutoff. Although pairwise interactions between the bosons are weak at low energy scales, the collective dynamics are strongly coupled even when ln(Lambda/T) is large. We argue that the strong-coupling effects can be isolated in an effective classical model, which is then solved numerically. Applications to experiments on the gap-closing transition of spin-gap antiferromagnets in an applied field are presented.