Hydrodynamics of a Superfluid Condensate.

K. Weiss, H. Haug

Eric D. Siggia, Andrei E. Ruckenstein

The thermodynamic, hydrodynamic, and kinetic properties of a variety of metastable states accessible to spin-polarized hydrogen are examined. The state with Bose condensation in the two lowest hyperfine levels will phase separate at a rate determined from superfluid hydrodynamics. The transverse and longitudinal magnetic relaxation times are evaluated in the classical, quantum, and superfluid regimes.

Zygmunt M. Galasiewicz

Since 1974 there have been serious experimental and also theoretical pointers to the possibility that no Bose condensation occurs in superfluid He4. Evans presented a theoretical argument against a condesate, suggesting a “pairing” model of superfluid helium. As yet, experiment connot decide if the concept of a one-particle condensate can be replaced by the idea of a two-particle condensate. March and Galasiewicz have argued that, if there is no one-particle condensate in He4, a ground state wave function cannot be built from a product of pairs but must fundamentally include three-particle correlations at least. So the idea of a three (not two) particle condensate seems worth some attention. It is demonstrated here that assuming a three-particle condensate we can regain from microscopic theory the Landau hydrodynamic equation for the superfluid velocity.

Luca Salasnich

Makoto Tsubota, Kenichi Kasamatsu

Abstract This book serves as a comprehensive textbook on quantum hydrodynamics and quantum turbulence, focusing on the hydrodynamics of quantum-condensed systems at low temperatures. A defining feature of these systems is the presence of an order parameter, leading to unique phenomena such as inviscid superfluid flow and vortex quantization—characteristics absent in classical hydrodynamics. The turbulence arising in these systems is known as quantum turbulence. This field lies at the intersection of several disciplines, including low-temperature condensed matter physics, fluid dynamics, quantum mechanics, statistical mechanics, and nonlinear and non-equilibrium physics. The primary systems discussed in this book are superfluid 4He, superfluid 3He, and atomic Bose-Einstein condensates (BECs). The study of quantum hydrodynamics began with the discovery of quantum turbulence in superfluid 4He in the 1950s. Superfluid 3He, discovered in 1972, was the first anisotropic superfluid, providing a platform to explore various topological defects. The realization of atomic BECs in 1995 through laser cooling marked a significant breakthrough, offering precise control over condensates and enabling the visualization of quantized vortices. In crafting this book, we aimed to present a unified narrative that emphasizes the common physics underlying these systems, rather than treating them in isolation. The content is tailored for first-year graduate students, ensuring clarity without the need for supplementary references. As both authors are theorists, we have placed a stronger emphasis on theoretical aspects over experimental findings.