Statistics of Lagrangian quantum turbulence

Abstract

We consider the dynamics of small tracer particles in turbulent quantum liquids. The complicated interaction processes of vortex filaments, the quantum constraints on vorticity and the varying influence of both the superfluid and the normal fluid on the tracer particle effectively lead to a superstatistical Langevin-like model that in a certain approximation can be solved analytically. An analytic expression for the PDF of velocity v of the tracer particle is derived that exhibits not only the experimentally observed $v^{-}3$ tails but also the correct behavior near the center of the distribution, in excellent agreement with experimental measurements and numerical simulations. Our results are universal and do not depend on details of the quantum fluid.

5 pages, 2 figures

References in corpus (20)

• Superstatistics
• Fluid Particle Accelerations in Fully Developed Turbulence
• Dynamical foundations of nonextensive statistical mechanics
• Measurement of Lagrangian velocity in fully developed turbulence
• From time series to superstatistics
• Kolmogorov spectrum of superfluid turbulence: numerical analysis of the Gross-Pitaevskii equation with the small scale dissipation
• Velocity Statistics Distinguish Quantum Turbulence from Classical Turbulence
• Energy Spectrum of Superfluid Turbulence without Normal Fluid
• Generalized entropies and the transformation group of superstatistics
• Quantum Turbulence in a Trapped Bose-Einstein Condensate
• Emergence and decay of turbulence in stirred atomic Bose-Einstein condensates
• Statistics of 3-dimensional Lagrangian turbulence
• Non classical velocity statistics in a turbulent atomic Bose Einstein condensate
• Lagrangian acceleration statistics in turbulent flows
• Visualization of Superfluid Helium Flow
• Lagrangian Dynamics in High-Dimensional Point-Vortex Systems
• Energy cascade and the four-fifths law in superfluid turbulence
• Quantum turbulent velocity statistics and quasiclassical limit
• Numerical Study of Velocity Statistics in Steady Counterflow Quantum Turbulence
• Classical small systems coupled to finite baths

Cited by in corpus (10)

• Continuous transition from the extensive to the non-extensive statistics in an agent-based herding model
• Transitions between superstatistical regimes: validity, breakdown and applications
• Quantum Turbulent Structure in Light
• Dimensionally regularized Tsallis' Statistical Mechanics and two-body Newton's gravitation
• Single-mode nonlinear Langevin emulation of magnetohydrodynamic turbulence
• Canonical Ensemble in Non-extensive Statistical Mechanics
• Lagrangian quantum turbulence model based on alternating superfluid/ normal fluid stochastic dynamics
• Extreme Value Laws for Superstatistics
• On the putative essential discreteness of q-generalized entropies
• A first order Tsallis theory