We discuss phenomenology associated with turbulent hydrodynamics in quantum fluids from a condensed-matter perspective. We begin with weakly interacting superfluids, often modelled by a mean-field theory governed by the Gross-Pitaevskii (GP) equation. Considering the effect of quantum fluctuations beyond the mean-field approximation, we propose a study of many-body quantum effects in turbulent hydrodynamics, especially near zero temperature. We indicate examples of quantum many-body systems where such effects may be uncovered. These include bosons confined in a periodic potential in low spatial dimensions (one and two), and the associated quantum critical point of the superfluid-insulator transition, realized in present-day ultracold-atom and quantum computing platforms. We conclude by listing a set of (open) questions that may be answered using modern quantum many-body techniques. This article is part of the theme issue 'Frontiers of turbulence and statistical physics'.
We discuss phenomenology associated with turbulent hydrodynamics in quantum fluids from a condensed-matter perspective. We begin with weakly interacting superfluids, often modelled by a mean-field theory governed by the Gross-Pitaevskii (GP) equation. Considering the effect of quantum fluctuations beyond the mean-field approximation, we propose a study of many-body quantum effects in turbulent hydrodynamics, especially near zero temperature. We indicate examples of quantum many-body systems where such effects may be uncovered. These include bosons confined in a periodic potential in low spatial dimensions (one and two), and the associated quantum critical point of the superfluid-insulator transition, realized in present-day ultracold-atom and quantum computing platforms. We conclude by listing a set of (open) questions that may be answered using modern quantum many-body techniques. This article is part of the theme issue 'Frontiers of turbulence and statistical physics'.
We discuss phenomenology associated with turbulent hydrodynamics in quantum fluids from a condensed-matter perspective. We begin with weakly-interacting superfluids, often modeled by a mean-field theory governed by the Gross-Pitaevskii equation. Considering the effect of quantum fluctuations beyond the mean-field approximation, we propose a study of many-body quantum effects in turbulent hydrodynamics, especially near zero temperature. We motivate examples of quantum many-body systems where such effects may be uncovered. These include bosons confined in a periodic potential in low spatial dimensions (one and two), and the associated quantum critical point of the superfluid-insulator transition, realized in present-day ultracold-atom and quantum computing platforms. We conclude by listing a set of (open) questions that may be answered using modern quantum many-body techniques. This article is part of the theme issue 'Frontiers of turbulence and statistical physics'.
Quantum turbulence shares many similarities with classical turbulence in the isotropic and homogeneous case, despite the inviscid and quantized nature of its vortices. However, when quantum fluids are subjected to rotation, their turbulent dynamics depart significantly from the classical expectations. We explore the phenomenology of rotating quantum turbulence, emphasizing how rotation introduces new regimes with no classical analogues. We review recent theoretical, experimental and numerical developments, and present new numerical results that map out distinct dynamical regimes arising from the interplay of rotation, quantization, nonlinearities and condensed matter regimes. In particular, we show the importance of distinguishing the dynamics of rotating quantum fluids in the slowly rotating, rapidly rotating and low Landau level regimes. The findings have implications for the dynamics of liquid helium, atomic Bose-Einstein condensates and neutron stars, and show how rotating quantum fluids can serve as a unique platform bridging turbulence theory and condensed matter physics, revealing novel states of out-of-equilibrium quantum matter. This article is part of the theme issue 'Frontiers of turbulence and statistical physics'.
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.
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.
Quantum fluctuations play a pivotal role in determining the ground state properties and phase transitions of ultra-cold bosonic systems. This study presents a comprehensive theoretical investigation of fluctuation effects beyond mean-field theory in dilute Bose gases, examining their impact on the superfluid–Mott insulator transition, quantum droplet formation, and critical phenomena. Beginning with the Gross–Pitaevskii mean-field framework , we systematically incorporate quantum corrections through Bogoliubov theory, yielding the Lee–Huang–Yang (LHY) energy correction scaling as . The quantum depletion quantifies the fraction of atoms driven from the condensate by zero-point fluctuations. For the Bose–Hubbard model , quantum Monte Carlo simulations establish the superfluid–Mott insulator critical point at , shifted 15% from the mean-field prediction. Critical exponents and confirm 3D XY universality. Quantum droplets in binary mixtures are stabilized by the repulsive LHY correction against mean-field collapse, with equilibrium densities matching experimental observations in K mixtures. Finite-size scaling analysis and the Ginzburg criterion delineate regimes where fluctuation effects dominate. All theoretical predictions are validated against precision measurements in ultracold atomic gases.
Superfluids are inviscid flows in which vorticity is supported on filaments with quantized circulation. Such objects, known as quantum vortices, exhibit a hydrodynamical behavior. Experimentally, the dynamics of superfluids has been studied by using particles, which nowadays have become the main tool for visualizing quantum vortices. In this Thesis, we study numerically and analytically the dynamics of active and finite-size particles in superfluids. The superfluid is modeled with the Gross–Pitaevskii equation, while the particles are implemented as moving repulsive potentials coupled with the macroscopic wave function describing the superfluid. Firstly, the model is used to investigate the interaction between particles and quantum vortices at very low temperatures. This part aims to give a theoretical background to the current experiments in which macroscopic particles are used to sample superfluid vortices and quantum turbulence. Specifically, we address the following problems: the capture of a particle by a quantum vortex, the reconnections of vortex filaments and the propagation of Kelvin waves in presence trapped particles and the dynamics of particles in decaying quantum turbulence. In the last part of the manuscript, finite temperature effects are studied in the Fourier-truncated Gross–Pitaevskii model. The goal is to characterize the dynamics of impurities immersed in a thermal bath and how their presence modifies the statistical properties of the fluid. In particular, the random motion of the impurities and the temperature dependence of the friction coefficient are studied. Finally, the clustering of impurities and its effect on the phase transitions of the condensate are investigated.