  Quantum hydrodynamics in superfluid helium and atomic Bose-Einstein
condensates (BECs) has been recently one of the most important topics in low
temperature physics. In these systems, a macroscopic wave function appears
because of Bose-Einstein condensation, which creates quantized vortices.
Turbulence consisting of quantized vortices is called quantum turbulence (QT).
The study of quantized vortices and QT has increased in intensity for two
reasons. The first is that recent studies of QT are considerably advanced over
older studies, which were chiefly limited to thermal counterflow in 4He, which
has no analogue with classical traditional turbulence, whereas new studies on
QT are focused on a comparison between QT and classical turbulence. The second
reason is the realization of atomic BECs in 1995, for which modern optical
techniques enable the direct control and visualization of the condensate and
can even change the interaction; such direct control is impossible in other
quantum condensates like superfluid helium and superconductors. Our group has
made many important theoretical and numerical contributions to the field of
quantum hydrodynamics of both superfluid helium and atomic BECs. In this
article, we review some of the important topics in detail. The topics of
quantum hydrodynamics are diverse, so we have not attempted to cover all these
topics in this article. We also ensure that the scope of this article does not
overlap with our recent review article (arXiv:1004.5458), "Quantized vortices
in superfluid helium and atomic Bose--Einstein condensates", and other review
articles.
