TABLE OF CONTENTS At very low temperatures close to absolute zero, quantum effects begin to acquire primary importance in the properties of fluids. It is well-known that helium becomes a liquid phase below the (critical) temperature T c = 4 .22 K (under atmospheric pressure), and superfluid properties appear below T ? = 2 .172 K (discovered by P. L. Kapitza, 1938). [1]
Recently, there has been dramatic improvement in the Bose Einstein condensation of (magnetically) trapped alkali-atomic gases at ultra-low temperatures. Such an atomic-gas Bose Einstein condensation differs from the liquid-helium condensate in several ways. An example of this is that condensates of alkali-atomic gases are dilute. As a result, at low temperatures, the Gross Pitaevskii equation (11.23) below gives an extremely precise description of the atomic condensate, and its dynamics is described by potential flows of an ideal fluid with a uniform (vanishing) entropy.
In traditional fluid dynamics, the ideal fluid is a virtual idealized fluid which is characterized by vanishing transport coefficients such as viscosity and thermal conductivity. The superfluid at T = 0 K is a real ideal fluid which supports only potential flows of zero entropy. However, it is remarkable that it can support quantized circulations as well at excited states. The purpose of this chapter is to introduce such ideas of superfluid flows. [2]
[1]From T ? down to T = 0 K, the liquid is called helium II.
