/pdf/hydrodynamic-and-hydromagnetic-stability-3nl34xcht5.pdf

Hydrodynamic and Hydromagnetic Stability

This paper reviews recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases. It focuses on effects beyond standard weak-coupling descriptions, such as the Mott-Hubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation. Strong correlations in fermionic gases are discussed in optical lattices or near-Feshbach resonances in the BCS-BEC crossover.

/pdf/many-body-physics-with-ultracold-gases-552s10zfdn.pdf

Many-Body Physics with Ultracold Gases

A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented, with emphasis on comparisons between theory and quantitative experiments. Examples include patterns in hydrodynamic systems such as thermal convection in pure fluids and binary mixtures, Taylor-Couette flow, parametric-wave instabilities, as well as patterns in solidification fronts, nonlinear optics, oscillatory chemical reactions and excitable biological media. The theoretical starting point is usually a set of deterministic equations of motion, typically in the form of nonlinear partial differential equations. These are sometimes supplemented by stochastic terms representing thermal or instrumental noise, but for macroscopic systems and carefully designed experiments the stochastic forces are often negligible. An aim of theory is to describe solutions of the deterministic equations that are likely to be reached starting from typical initial conditions and to persist at long times. A unified description is developed, based on the linear instabilities of a homogeneous state, which leads naturally to a classification of patterns in terms of the characteristic wave vector q0 and frequency ω0 of the instability. Type Is systems (ω0=0, q0≠0) are stationary in time and periodic in space; type IIIo systems (ω0≠0, q0=0) are periodic in time and uniform in space; and type Io systems (ω0≠0, q0≠0) are periodic in both space and time. Near a continuous (or supercritical) instability, the dynamics may be accurately described via "amplitude equations," whose form is universal for each type of instability. The specifics of each system enter only through the nonuniversal coefficients. Far from the instability threshold a different universal description known as the "phase equation" may be derived, but it is restricted to slow distortions of an ideal pattern. For many systems appropriate starting equations are either not known or too complicated to analyze conveniently. It is thus useful to introduce phenomenological order-parameter models, which lead to the correct amplitude equations near threshold, and which may be solved analytically or numerically in the nonlinear regime away from the instability. The above theoretical methods are useful in analyzing "real pattern effects" such as the influence of external boundaries, or the formation and dynamics of defects in ideal structures. An important element in nonequilibrium systems is the appearance of deterministic chaos. A greal deal is known about systems with a small number of degrees of freedom displaying "temporal chaos," where the structure of the phase space can be analyzed in detail. For spatially extended systems with many degrees of freedom, on the other hand, one is dealing with spatiotemporal chaos and appropriate methods of analysis need to be developed. In addition to the general features of nonequilibrium pattern formation discussed above, detailed reviews of theoretical and experimental work on many specific systems are presented. These include Rayleigh-Benard convection in a pure fluid, convection in binary-fluid mixtures, electrohydrodynamic convection in nematic liquid crystals, Taylor-Couette flow between rotating cylinders, parametric surface waves, patterns in certain open flow systems, oscillatory chemical reactions, static and dynamic patterns in biological media, crystallization fronts, and patterns in nonlinear optics. A concluding section summarizes what has and has not been accomplished, and attempts to assess the prospects for the future.

/pdf/pattern-formation-outside-of-equilibrium-1601b9znum.pdf

Pattern formation outside of equilibrium

The phenomenon of Bose-Einstein condensation of dilute gases in traps is reviewed from a theoretical perspective. Mean-field theory provides a framework to understand the main features of the condensation and the role of interactions between particles. Various properties of these systems are discussed, including the density profiles and the energy of the ground-state configurations, the collective oscillations and the dynamics of the expansion, the condensate fraction and the thermodynamic functions. The thermodynamic limit exhibits a scaling behavior in the relevant length and energy scales. Despite the dilute nature of the gases, interactions profoundly modify the static as well as the dynamic properties of the system; the predictions of mean-field theory are in excellent agreement with available experimental results. Effects of superfluidity including the existence of quantized vortices and the reduction of the moment of inertia are discussed, as well as the consequences of coherence such as the Josephson effect and interference phenomena. The review also assesses the accuracy and limitations of the mean-field approach.

https://arxiv.org/pdf/cond-mat/9806038.pdf

Theory of Bose-Einstein condensation in trapped gases

One of Feynman's early applications of path integrals was to superfluid $^{4}\mathrm{He}$. He showed that the thermodynamic properties of Bose systems are exactly equivalent to those of a peculiar type of interacting classical "ring polymer." Using this mapping, one can generalize Monte Carlo simulation techniques commonly used for classical systems to simulate boson systems. In this review, the author introduces this picture of a boson superfluid and shows how superfluidity and Bose condensation manifest themselves. He shows the excellent agreement between simulations and experimental measurements on liquid and solid helium for such quantities as pair correlations, the superfluid density, the energy, and the momentum distribution. Major aspects of computational techniques developed for a boson superfluid are discussed: the construction of more accurate approximate density matrices to reduce the number of points on the path integral, sampling techniques to move through the space of exchanges and paths quickly, and the construction of estimators for various properties such as the energy, the momentum distribution, the superfluid density, and the exchange frequency in a quantum crystal. Finally the path-integral Monte Carlo method is compared to other quantum Monte Carlo methods.

Path integrals in the theory of condensed helium

Preface 1. Background on classical vortices 2. Background on liquid helium II 3. Vortex dynamics and mutual friction 4. The structure of quantized vortices 5. Vortex arrays 6. Vortex waves 7. Quantum turbulence 8. Nucleation of quantized vortices Index.

Quantized Vortices in Helium II

Turbulent convection occurs when the Rayleigh number (Ra)--which quantifies the relative magnitude of thermal driving to dissipative forces in the fluid motion--becomes sufficiently high. Although many theoretical and experimental studies of turbulent convection exist, the basic properties of heat transport remain unclear. One important question concerns the existence of an asymptotic regime that is supposed to occur at very high Ra. Theory predicts that in such a state the Nusselt number (Nu), representing the global heat transport, should scale as Nu proportional to Ra(beta) with beta = 1/2. Here we investigate thermal transport over eleven orders of magnitude of the Rayleigh number (10(6) < or = Ra < or = 10(7)), using cryogenic helium gas as the working fluid. Our data, over the entire range of Ra, can be described to the lowest order by a single power-law with scaling exponent beta close to 0.31. In particular, we find no evidence for a transition to the Ra(1/2) regime. We also study the variation of internal temperature fluctuations with Ra, and probe velocity statistics indirectly.

/pdf/turbulent-convection-at-very-high-rayleigh-numbers-4f2ocrdibo.pdf

Turbulent convection at very high Rayleigh numbers

The equilibrium and transport properties of liquid 4He are deduced from experimental observations at the saturated vapor pressure. In each case, the bibliography lists all known measurements. Quantities reported here include density, thermal expansion coefficient, dielectric constant, superfluid and normal fluid densities, first, second, third, and fourth sound velocities, specific heat, enthalpy, entropy, surface tension, ion mobilities, mutual friction, viscosity and kinematic viscosity, dispersion curve, structure factor, thermal conductivity, latent heat, saturated vapor pressure, thermal diffusivity and Prandtl number of helium I, and displacement length and vortex core parameter in helium II.

The observed properties of liquid helium at the saturated vapor pressure

Turbulent convection occurs when the Rayleigh number (Ra)—which quantifies the relative magnitude of thermal driving to dissipative forces in the fluid motion—becomes sufficiently high. Although many theoretical and experimental studies of turbulent convection exist, the basic properties of heat transport remain unclear. One important question concerns the existence of an asymptotic regime that is supposed to occur at very high Ra. Theory predicts that in such a state the Nusselt number (Nu), representing the global heat transport, should scale as Nu ∝ Raβ with β = 1/2. Here we investigate thermal transport over eleven orders of magnitude of the Rayleigh number (106 ≤ Ra ≤ 10 17), using cryogenic helium gas as the working fluid. Our data, over the entire range of Ra, can be described to the lowest order by a single power-law with scaling exponent β close to 0.31. In particular, we find no evidence for a transition to the Ra1/2 regime. We also study the variation of internal temperature fluctuations with Ra, and probe velocity statistics indirectly.

Turbulent Convection at Very High Rayleigh Numbers

to Superfluid Vortices and Turbulence.- Turbulence Experiments.- An Introduction to Experiments on Superfluid Turbulence.- The Experimental Evidence for Vortex Nucleation in 4He.- Applications of Superfluid Helium in Large-Scale Superconducting Systems.- The Temperature Dependent Drag Crisis on a Sphere in Flowing Helium II.- Experiments on Quantized Turbulence at mK Temperatures.- Grid-Generated He II Turbulence in a Finite Channel - Experiment.- Intermittent Switching Between Turbulent and Potential Flow Around a Sphere in He II at mK Temperatures.- Vortex Dynamics.- Vortex Filament Methods for Superfluids.- to HVBK Dynamics.- Magnus Force, Aharonov-Bohm Effect, and Berry Phase in Superfluids.- Using the HVBK Model to Investigate the Couette Flow of Helium II.- Turbulence Theory.- An Introduction to the Theory of Superfluid Turbulence.- Numerical Methods for Coupled Normal-Fluid and Superfluid Flows in Helium II.- From Vortex Reconnections to Quantum Turbulence.- Vortices and Stability in Superfluid Boundary Layers.- Grid Generated He II Turbulence in a Finite Channel-Theoretical Interpretation.- Vortex Tangle Dynamics Without Mutual Friction in Superfluid 4He.- Applications of the Gaussian Model of the Vortex Tangle in the Superfluid Turbulent He II.- Stochastic Dynamics of a Vortex Loop. Thermal Equilibrium.- Stochastic Dynamics of a Vortex Loop. Large-Scale Stirring Force.- Nonequilibrium Vortex Dynamics in Superfluid Phase Transitions and Superfluid Turbulence.- The NLSE and Superfluidity.- The Nonlinear Schrodinger Equation as a Model of Superfluidity.- Vortex Nucleation and Limit Speed for a Flow Passing Nonlinearly Around a Disk in the Nonlinear Schrodinger Equation.- Vortices in Nonlocal Condensate Models of Superfluid Helium.- Ginzburg-Landau Description of Vortex Nucleation in a Rotating Superfluid.- Weak Turbulence Theory for the Gross-Pitaevskii Equation.- Dissipative Vortex Dynamics and Magnus Force.- Transition to Dissipation in Two- and Three-Dimensional Superflows.- Bose-Einstein Condensation.- Motion of Objects Through Dilute Bose-Einstein Condensates.- Stability of a Vortex in a Rotating Trapped Bose-Einstein Condensate*.- Kinetics of Strongly Non-equilibrium Bose-Einstein Condensation.- Quantum Nucleation of Phase Slips in Bose-Einstein Condensates.- Vortex Reconnections and Classical Aspects.- Vortex Reconnection in Normal and Superfluids.- Helicity in Hydro and MHD Reconnection.- Tropicity and Complexity Measures for Vortex Tangles.- The Geometry of Magnetic and Vortex Reconnection.- Current-Sheet Formation near a Hyperbolic Magnetic Neutral Line.- Nonlocality in Turbulence.- Helium 3 and Other Systems.- Quantized Vorticity in Superfluid 3He-A: Structure and Dynamics.- Vortices in Metastable 4He Films.- Quantum Hall E.ect Breakdown Steps and Possible Analogies with Classical and Super.uid Hydrodynamics.- Atomic Bose Condensate with a Spin Structure: The Use of Bloch State.- Quantum Dynamics of Vortex-Antivortex Pairs in a Circular Box.

Russell J. Donnelly

Papers

Quantized Vortices in Helium II

Turbulent convection at very high Rayleigh numbers

The observed properties of liquid helium at the saturated vapor pressure

Turbulent Convection at Very High Rayleigh Numbers

Quantized Vortex Dynamics and Superfluid Turbulence