This paper provides a brief introduction to quantum turbulence in simple superfluids, in which the required rotational motion in the superfluid component is due entirely to the topological defects that are identified as quantized vortices. Particular emphasis is placed on the basic dynamical behaviour of the quantized vortices and on turbulent decay mechanisms at a very low temperature. There are possible analogies with the behaviour of cosmic strings.
This paper provides a brief introduction to quantum turbulence in simple superfluids, in which the required rotational motion in the superfluid component is due entirely to the topological defects that are identified as quantized vortices. Particular emphasis is placed on the basic dynamical behaviour of the quantized vortices and on turbulent decay mechanisms at a very low temperature. There are possible analogies with the behaviour of cosmic strings.
This paper reviews recent developments in the physics of quantum turbulence (QT). QT was discovered in superfluid (4)He in the 1950s, while the research has taken a new direction since the middle of the 1990s. QT is comprised of quantized vortices that are definite topological defects and expected to give a prototype of turbulence much simpler than usual classical turbulence. We give a general introduction and brief review of classical turbulence followed by a description of the dynamics of quantized vortices. After mentioning the modern research trends in QT, we discuss the energy spectra, the energy cascade and the possible dissipation mechanism of QT at very low temperatures. The last part is devoted to QT in atomic Bose-Einstein condensates.
The term quantum turbulence denotes the turbulent motion of quantum fluids, systems such as superfluid helium and atomic Bose-Einstein condensates, which are characterized by quantized vorticity, superfluidity, and, at finite temperatures, two-fluid behavior. This article introduces their basic properties, describes types and regimes of turbulence that have been observed, and highlights similarities and differences between quantum turbulence and classical turbulence in ordinary fluids. Our aim is also to link together the articles of this special issue and to provide a perspective of the future development of a subject that contains aspects of fluid mechanics, atomic physics, condensed matter, and low-temperature physics.
This article reviews recent developments in quantum fluid dynamics and quantum turbulence (QT) for superfluid helium and atomic Bose–Einstein condensates. Quantum turbulence was discovered in superfluid 4He in the 1950s, but the field moved in a new direction starting around the mid-1990s. Quantum turbulence is comprised of quantised vortices that are definite topological defects arising from the order parameter appearing in Bose–Einstein condensation. Hence, QT is expected to yield a simpler model of turbulence than does conventional turbulence. A general introduction to this issue and a brief review of the basic concepts are followed by a description of vortex lattice formation in a rotating atomic Bose–Einstein condensate, typical of quantum fluid dynamics. Then we discuss recent developments in QT of superfluid helium such as the energy spectra and dissipative mechanisms at low temperatures, QT created by vibrating structures, and the visualisation of QT. As an application of these ideas, we end with a discussion of QT in atomic Bose–Einstein condensates.
Turbulence in classical fluids has been the subject of scientific study for centuries, yet there is still no complete general theory of classical turbulence connecting microscopic physics to macroscopic fluid flows, and this remains one of the open problems in physics. In contrast, the phenomenon of quantum turbulence in superfluids has well-defined theoretical descriptions, based on first principles and microscopic physics, and represents a realm of physics that can connect the classical and quantum worlds. Studies of quantum turbulence may thus be viewed as a path for progress on the long-standing problem of turbulence.A dilute-gas Bose-Einstein condensate (BEC) is, in most cases, a superfluid that supports quantized vortices, the primary structural elements of quantum turbulence. BECs are particularly convenient systems for the study of vortices, as standard techniques allow the microscopic structure and dynamics of the vortices to be investigated. Vortices in BECs can be created and manipulated using a variety of techniques, hence BECs are potentially powerful systems for the microscopic study of quantum turbulence.This dissertation focuses on quantized vortices in BECs, specifically experimental and numerical studies of their formation, dynamics, and decay, in an effort to understand the microscopic nature of vortices as elements of quantum turbulence. Four main experiments were performed, and are described in the main chapters of this dissertation, after introductions to vortices, experimental methods, and turbulence are presented. These experiments were aimed at understanding various aspects of how vortices are created and behave in a superfluid system. They involved vortex dipole nucleation in the breakdown of superfluidity, persistent current generation from a turbulent state in the presence of energy dissipation, decay of angular momentum of a BEC due to trapping potential impurities, and exploration of the spontaneous formation of vortices during the BEC phase transition. These experiments represent progress towards enhanced understanding of the formation, dynamics, and decay of vortices in BECs and thus may be foundational to more general studies of quantum turbulence in superfluids.
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.
Since the idea of quantum turbulence was first proposed by Feynman and later realized in experiments of superfluid helium and Bose-Einstein condensates, much emphasis has been put on finding signatures that distinguish quantum turbulence from its classical counterpart. Here we show that quantum turbulence in rotating condensates is fundamentally different from the classical case. While rotating quantum turbulence develops a negative temperature state with self-organization of the kinetic energy in quantized vortices, it also displays an anisotropic dissipation mechanism and a different, non-Kolmogorovian, scaling of the energy at small scales. This scaling is compatible with Vinen turbulence and also has been found in recent simulations of condensates with multicharged vortices. An elementary explanation for the scaling is presented in terms of disorder in the vortices positions.