31,972 research outputs found
Mapping the Berry Curvature from Semiclassical Dynamics in Optical Lattices
We propose a general method by which experiments on ultracold gases can be
used to determine the topological properties of the energy bands of optical
lattices, as represented by the map of the Berry curvature across the Brillouin
zone. The Berry curvature modifies the semiclassical dynamics and hence the
trajectory of a wave packet undergoing Bloch oscillations. However, in two
dimensions these trajectories may be complicated Lissajous-like figures, making
it difficult to extract the effects of Berry curvature in general. We propose
how this can be done using a "time-reversal" protocol. This compares the
velocity of a wave packet under positive and negative external force, and
allows a clean measurement of the Berry curvature over the Brillouin zone. We
discuss how this protocol may be implemented and explore the semiclassical
dynamics for three specific systems: the asymmetric hexagonal lattice, and two
"optical flux" lattices in which the Chern number is nonzero. Finally, we
discuss general experimental considerations for observing Berry curvature
effects in ultracold gases.Comment: 12 page
Rarefied flow past a flat plate at incidence
Results of a numerical study using the direct simulation Monte Carlo (DSMC) method are presented for the transitional flow about a flat plate at 40 deg incidence. The plate has zero thickness and a length of 1.0 m. The flow conditions simulated are those experienced by the Shuttle Orbiter during reentry at 7.5 km/s. The range of freestream conditions are such that the freestream Knudsen number values are between 0.02 and 8.4, i.e., conditions that encompass most of the transitional flow regime. The DSMC simulations show that transitional effects are evident when compared with free molecule results for all cases considered. The calculated results demonstrate clearly the necessity of having a means of identifying the effects of transitional flow when making aerodynamic flight measurements as are currently being made with the Space Shuttle Orbiter vehicles. Previous flight data analyses have relied exclusively on adjustments in the gas-surface interaction models without accounting for the transitional effect which can be comparable in magnitude. The present calculations show that the transitional effect at 175 km would increase the Space Shuttle Orbiter lift-drag ratio by 90 percent over the free molecule value
Van der Waals Frictional Drag induced by Liquid Flow in Low- Dimensional Systems
We study the van der Waals frictional drag force induced by liquid flow in
low-dimensional systems (2D and 1D electron systems, and 2D and 1D channels
with liquid). We find that for both 1D and 2D systems, the frictional drag
force induced by liquid flow may be several orders of magnitude larger than the
frictional drag induced by electronic current.Comment: 10 pages, 4 figure
Coulomb drag as a measure of trigonal warping in doped graphene
I suggest to use the effect of Coulomb drag between two closely positioned
graphite monolayers (graphene sheets) for experimental measurement of the
strength of weak non-linearities of the spectrum in graphene. I consider
trigonal warping as a representative mechanism responsible for the drag effect.
Since graphene is relatively defect-free, I evaluate the drag conductivity in
the ballistic regime and find that it is proportional to the fourth power of
the warping strength.Comment: 4 pages, 1 figur
The quantized Hall conductance of a single atomic wire: A proposal based on synthetic dimensions
We propose a method by which the quantization of the Hall conductance can be
directly measured in the transport of a one-dimensional atomic gas. Our
approach builds on two main ingredients: (1) a constriction optical potential,
which generates a mesoscopic channel connected to two reservoirs, and (2) a
time-periodic modulation of the channel, specifically designed to generate
motion along an additional synthetic dimension. This fictitious dimension is
spanned by the harmonic-oscillator modes associated with the tightly-confined
channel, and hence, the corresponding "lattice sites" are intimately related to
the energy of the system. We analyze the quantum transport properties of this
hybrid two-dimensional system, highlighting the appealing features offered by
the synthetic dimension. In particular, we demonstrate how the energetic nature
of the synthetic dimension, combined with the quasi-energy spectrum of the
periodically-driven channel, allows for the direct and unambiguous observation
of the quantized Hall effect in a two-reservoir geometry. Our work illustrates
how topological properties of matter can be accessed in a minimal
one-dimensional setup, with direct and practical experimental consequences.
Word Length Perturbations in Certain Symmetric Presentations of Dihedral Groups
Given a finite group with a generating subset there is a well-established
notion of length for a group element given in terms of its minimal length
expression as a product of elements from the generating set. Recently, certain
quantities called and have been defined that allow
for a precise measure of how stable a group is under certain types of small
perturbations in the generating expressions for the elements of the group.
These quantities provide a means to measure differences among all possible
paths in a Cayley graph for a group, establish a group theoretic analog for the
notion of stability in nonlinear dynamical systems, and play an important role
in the application of groups to computational genomics. In this paper, we
further expose the fundamental properties of and by
establishing their bounds when the underlying group is a dihedral group. An
essential step in our approach is to completely characterize so-called
symmetric presentations of the dihedral groups, providing insight into the
manner in which and interact with finite group
presentations. This is of interest independent of the study of the quantities
. Finally, we discuss several conjectures and open
questions for future consideration
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