When Infinity Does Not Count

摘要

Classical fluid dynamics is an incredibly flexible mathematical tool that can describe fluids as diverse as water and the dense nuclear matter of neutron stars. However, when a fluid is cooled to temperatures close to 0 K and exhibits quantum effects, a more fundamental theory must be used. Yet, attempts to introduce quantum effects as perturbations to the classical theory have not been successful: The solutions diverge and give meaningless, infinitely large answers. On page 228 of this issue, Imambekov and Glazman (1) consider a quantum fluid that moves in one spatial dimension and investigate how quantum effects influence the decay of elementary excitations caused by the nonlinearity of fluid dynamics. The authors apply a universal, nonperturbative transformation of variables, and the new theoretical formulation generates finite results.