52 research outputs found
Anomalous coupling between topological defects and curvature
We investigate a counterintuitive geometric interaction between defects and
curvature in thin layers of superfluids, superconductors and liquid crystals
deposited on curved surfaces. Each defect feels a geometric potential whose
functional form is determined only by the shape of the surface, but whose sign
and strength depend on the transformation properties of the order parameter.
For superfluids and superconductors, the strength of this interaction is
proportional to the square of the charge and causes all defects to be repelled
(attracted) by regions of positive (negative) Gaussian curvature. For liquid
crystals in the one elastic constant approximation, charges between 0 and
are attracted by regions of positive curvature while all other charges
are repelled.Comment: 5 pages, 4 figures, minor changes, accepted for publication in Phys.
Rev. Let
Stability of the vortex lattice in a rotating superfluid
We analyze the stability of the vortex lattice in a rotating superfluid
against thermal fluctuations associated with the long-wavelength Tkachenko
modes of the lattice. Inclusion of only the two-dimensional modes leads
formally to instability in infinite lattices; however, when the full
three-dimensional spectrum of modes is taken into account, the
thermally-induced lattice displacements are indeed finite.Comment: 16 page
Vortex lattices in rapidly rotating Bose-Einstein condensates: modes and correlation functions
After delineating the physical regimes which vortex lattices encounter in
rotating Bose-Einstein condensates as the rotation rate, , increases,
we derive the normal modes of the vortex lattice in two dimensions at zero
temperature. Taking into account effects of the finite compressibility, we find
an inertial mode of frequency , and a primarily transverse
Tkachenko mode, whose frequency goes from being linear in the wave vector in
the slowly rotating regime, where is small compared with the lowest
compressional mode frequency, to quadratic in the wave vector in the opposite
limit. We calculate the correlation functions of vortex displacements and
phase, density and superfluid velocities, and find that the zero-point
excitations of the soft quadratic Tkachenko modes lead in a large system to a
loss of long range phase correlations, growing logarithmically with distance,
and hence lead to a fragmented state at zero temperature. The vortex positional
ordering is preserved at zero temperature, but the thermally excited Tkachenko
modes cause the relative positional fluctuations to grow logarithmically with
separation at finite temperature. The superfluid density, defined in terms of
the transverse velocity autocorrelation function, vanishes at all temperatures.
Finally we construct the long wavelength single particle Green's function in
the rotating system and calculate the condensate depletion as a function of
temperature.Comment: 11 pages Latex, no figure
Polygonal N-vortex arrays: A Stuart model
Published versio
Coherently Scattering Atoms from an Excited Bose-Einstein Condensate
We consider scattering atoms from a fully Bose-Einstein condensed gas. If we
take these atoms to be identical to those in the Bose-Einstein condensate, this
scattering process is to a large extent analogous to Andreev reflection from
the interface between a superconducting and a normal metal. We determine the
scattering wave function both in the absence and the presence of a vortex. Our
results show a qualitative difference between these two cases that can be
understood as due to an Aharonov-Bohm effect. It leads to the possibility to
experimentally detect and study vortices in this way.Comment: 5 pages of ReVTeX and 2 postscript figure
Vortices and dynamics in trapped Bose-Einstein condensates
I review the basic physics of ultracold dilute trapped atomic gases, with
emphasis on Bose-Einstein condensation and quantized vortices. The hydrodynamic
form of the Gross-Pitaevskii equation (a nonlinear Schr{\"o}dinger equation)
illuminates the role of the density and the quantum-mechanical phase. One
unique feature of these experimental systems is the opportunity to study the
dynamics of vortices in real time, in contrast to typical experiments on
superfluid He. I discuss three specific examples (precession of single
vortices, motion of vortex dipoles, and Tkachenko oscillations of a vortex
array). Other unusual features include the study of quantum turbulence and the
behavior for rapid rotation, when the vortices form dense regular arrays.
Ultimately, the system is predicted to make a quantum phase transition to
various highly correlated many-body states (analogous to bosonic quantum Hall
states) that are not superfluid and do not have condensate wave functions. At
present, this transition remains elusive. Conceivably, laser-induced synthetic
vector potentials can serve to reach this intriguing phase transition.Comment: Accepted for publication in Journal of Low Temperature Physics,
conference proceedings: Symposia on Superfluids under Rotation (Lammi,
Finland, April 2010
Physics of Neutron Star Crusts
The physics of neutron star crusts is vast, involving many different research
fields, from nuclear and condensed matter physics to general relativity. This
review summarizes the progress, which has been achieved over the last few
years, in modeling neutron star crusts, both at the microscopic and macroscopic
levels. The confrontation of these theoretical models with observations is also
briefly discussed.Comment: 182 pages, published version available at
<http://www.livingreviews.org/lrr-2008-10
The Flux-Line Lattice in Superconductors
Magnetic flux can penetrate a type-II superconductor in form of Abrikosov
vortices. These tend to arrange in a triangular flux-line lattice (FLL) which
is more or less perturbed by material inhomogeneities that pin the flux lines,
and in high- supercon- ductors (HTSC's) also by thermal fluctuations. Many
properties of the FLL are well described by the phenomenological
Ginzburg-Landau theory or by the electromagnetic London theory, which treats
the vortex core as a singularity. In Nb alloys and HTSC's the FLL is very soft
mainly because of the large magnetic penetration depth: The shear modulus of
the FLL is thus small and the tilt modulus is dispersive and becomes very small
for short distortion wavelength. This softness of the FLL is enhanced further
by the pronounced anisotropy and layered structure of HTSC's, which strongly
increases the penetration depth for currents along the c-axis of these uniaxial
crystals and may even cause a decoupling of two-dimensional vortex lattices in
the Cu-O layers. Thermal fluctuations and softening may melt the FLL and cause
thermally activated depinning of the flux lines or of the 2D pancake vortices
in the layers. Various phase transitions are predicted for the FLL in layered
HTSC's. The linear and nonlinear magnetic response of HTSC's gives rise to
interesting effects which strongly depend on the geometry of the experiment.Comment: Review paper for Rep.Prog.Phys., 124 narrow pages. The 30 figures do
not exist as postscript file
Particles-vortex interactions and flow visualization in He4
Recent experiments have demonstrated a remarkable progress in implementing
and use of the Particle Image Velocimetry (PIV) and particle tracking
techniques for the study of turbulence in He4. However, an interpretation of
the experimental data in the superfluid phase requires understanding how the
motion of tracer particles is affected by the two components, the viscous
normal fluid and the inviscid superfluid. Of a particular importance is the
problem of particle interactions with quantized vortex lines which may not only
strongly affect the particle motion, but, under certain conditions, may even
trap particles on quantized vortex cores. The article reviews recent
theoretical, numerical, and experimental results in this rapidly developing
area of research, putting critically together recent results, and solving
apparent inconsistencies. Also discussed is a closely related technique of
detection of quantized vortices negative ion bubbles in He4.Comment: To appear in the J Low Temperature Physic
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