Quantum hydrodynamics

Abstract

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 (order parameter) 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 4 He, 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.

Numerical Studies of Quantum Turbulence

“…Figure 1 shows a schematic representation of thermal counterflow. Superfluid 4 He is assumed to be confined in a channel of circular cross-section of radius A, with one closed end and the other end connected to a helium bath. We suppose that heat W per unit time is injected into the system near the closed end.…”

“…However, this model is not applicable to ST including randomly oriented vortices. If we confine ourselves to the scales much larger than the intervortex spacing, this model works well and the numerical simulation leads to the Kolmogorov's −5/3 and 4/5 laws 3 in superfluid 4 He [25]. This article does not address the HVBK model, because it is just beyond the scope.…”

“…QT was first discovered in superfluid 4 He and was recently discovered in atomic Bose-Einstein condensates (BECs). As a result, QT has become one of the most important topics in low temperature physics.…”

“…Though there are several existing review articles on QT [1,2,3,4,5,6], this articles focuses on the numerical studies of QT. The contents of this article are as follows.…”

Realization of inverse Kibble–Zurek scenario with trapped Bose gases

“…This was done by solving the nonlinear Schrödinger equation (8) by the methods of static [36] and dynamic [37] simulations. The dissipation is taken into account by introducing the phenomenological factor γ [38,39]. This dissipation slightly diminishes the number of atom in time, although not more than 10%.…”