185 research outputs found
Energy spectra of vortex distributions in two-dimensional quantum turbulence
We theoretically explore key concepts of two-dimensional turbulence in a
homogeneous compressible superfluid described by a dissipative two-dimensional
Gross-Pitaeveskii equation. Such a fluid supports quantized vortices that have
a size characterized by the healing length . We show that for the
divergence-free portion of the superfluid velocity field, the kinetic energy
spectrum over wavenumber may be decomposed into an ultraviolet regime
() having a universal scaling arising from the vortex
core structure, and an infrared regime () with a spectrum that
arises purely from the configuration of the vortices. The Novikov power-law
distribution of intervortex distances with exponent -1/3 for vortices of the
same sign of circulation leads to an infrared kinetic energy spectrum with a
Kolmogorov power law, consistent with the existence of an inertial
range. The presence of these and power laws, together with
the constraint of continuity at the smallest configurational scale
, allows us to derive a new analytical expression for the
Kolmogorov constant that we test against a numerical simulation of a forced
homogeneous compressible two-dimensional superfluid. The numerical simulation
corroborates our analysis of the spectral features of the kinetic energy
distribution, once we introduce the concept of a {\em clustered fraction}
consisting of the fraction of vortices that have the same sign of circulation
as their nearest neighboring vortices. Our analysis presents a new approach to
understanding two-dimensional quantum turbulence and interpreting similarities
and differences with classical two-dimensional turbulence, and suggests new
methods to characterize vortex turbulence in two-dimensional quantum fluids via
vortex position and circulation measurements.Comment: 19 pages, 8 figure
Snell's Law for a vortex dipole in a Bose-Einstein condensate
A quantum vortex dipole, comprised of a closely bound pair of vortices of
equal strength with opposite circulation, is a spatially localized travelling
excitation of a planar superfluid that carries linear momentum, suggesting a
possible analogy with ray optics. We investigate numerically and analytically
the motion of a quantum vortex dipole incident upon a step-change in the
background superfluid density of an otherwise uniform two-dimensional
Bose-Einstein condensate. Due to the conservation of fluid momentum and energy,
the incident and refracted angles of the dipole satisfy a relation analogous to
Snell's law, when crossing the interface between regions of different density.
The predictions of the analogue Snell's law relation are confirmed for a wide
range of incident angles by systematic numerical simulations of the
Gross-Piteavskii equation. Near the critical angle for total internal
reflection, we identify a regime of anomalous Snell's law behaviour where the
finite size of the dipole causes transient capture by the interface.
Remarkably, despite the extra complexity of the surface interaction, the
incoming and outgoing dipole paths obey Snell's law.Comment: 16 pages, 7 figures, Scipost forma
Mutual friction and diffusion of two-dimensional quantum vortices
We present a microscopic open quantum systems theory of thermally-damped
vortex motion in oblate atomic superfluids that includes previously neglected
energy-damping interactions between superfluid and thermal atoms. This
mechanism couples strongly to vortex core motion and causes dissipation of
vortex energy due to mutual friction, as well as Brownian motion of vortices
due to thermal fluctuations. We derive an analytic expression for the
dimensionless mutual friction coefficient that gives excellent quantitative
agreement with experimentally measured values, without any fitted parameters.
Our work closes an existing two orders of magnitude gap between dissipation
theory and experiments, previously bridged by fitted parameters, and provides a
microscopic origin for the mutual friction and diffusion of quantized vortices
in two-dimensional atomic superfluids
Spectral analysis for compressible quantum fluids
Turbulent fluid dynamics typically involves excitations on many different
length scales. Classical incompressible fluids can be cleanly represented in
Fourier space enabling spectral analysis of energy cascades and other
turbulence phenomena. In quantum fluids, additional phase information and
singular behaviour near vortex cores thwarts the direct extension of standard
spectral techniques. We develop a formal and numerical spectral analysis for
symmetry-breaking quantum fluids suitable for analyzing turbulent flows,
with specific application to the Gross-Pitaevskii fluid. Our analysis builds
naturally on the canonical approach to spectral analysis of velocity fields in
compressible quantum fluids, and establishes a clear correspondence between
energy spectral densities, power spectral densities, and autocorrelation
functions, applicable to energy residing in velocity, quantum pressure,
interaction, and potential energy of the fluid. Our formulation includes all
quantum phase information and also enables arbitrary resolution spectral
analysis, a valuable feature for numerical analysis. A central vortex in a
trapped planar Bose-Einstein condensate provides an analytically tractable
example with spectral features of interest in both the infrared and ultraviolet
regimes. Sampled distributions modelling the dipole gas, plasma, and clustered
regimes exhibit velocity correlation length increasing with vortex energy,
consistent with known qualitative behaviour across the vortex clustering
transition. The spectral analysis of compressible quantum fluids presented here
offers a rigorous tool for analysing quantum features of superfluid turbulence
in atomic or polariton condensates.Comment: 17 pages. Fixed error in appendix C presentation, added references.
Results and conclusions unchange
Scaling dynamics of the ultracold Bose gas
The large-scale expansion dynamics of quantum gases is a central tool for
ultracold gas experiments and poses a significant challenge for theory. In this
work we provide an exact reformulation of the Gross-Pitaevskii equation for the
ultracold Bose gas in a coordinate frame that adaptively scales with the system
size during evolution, enabling simulations of long evolution times during
expansion or similar large-scale manipulation. Our approach makes no
hydrodynamic approximations, is not restricted to a scaling ansatz, harmonic
potentials, or energy eigenstates, and can be generalized readily to
non-contact interactions via the appropriate stress tensor of the quantum
fluid. As applications, we simulate the expansion of the ideal gas, a
cigar-shaped condensate in the Thomas-Fermi regime, and a linear superposition
of counter propagating Gaussian wavepackets. We recover known scaling for the
ideal gas and Thomas-Fermi regimes, and identify a linear regime of
aspect-ratio preserving free expansion; analysis of the scaling dynamics
equations shows that an exact, aspect-ratio invariant, free expansion does not
exist for nonlinear evolution. Our treatment enables exploration of nonlinear
effects in matter-wave dynamics over large scale-changing evolution.Comment: 12 pages, 3 figures, 2 appendice
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