41 research outputs found
Supersolid He Likely Has Nearly Isotropic Superflow
We extend previous calculations of the zero temperature superfluid fraction
(SFF) {\it vs} localization, from the fcc lattice to the experimentally
realized (for solid He) hcp and bcc lattices. The superfluid velocity is
assumed to be a one-body function, and dependent only on the local density,
taken to be a sum over sites of gaussians of width . Localization is
defined as , with the nearest-neighbor distance. As expected, for
fcc and bcc lattices the superfluid density tensor is proportional to the unit
tensor. To numerical accuracy of three-places (but no more), the hcp superfluid
density tensor is proportional to the unit tensor. This implies that a larger
spread in data on , if measured on pure crystals, is unlikely to be due to
crystal orientation. In addition, to three decimal places (but no more) the
curves of {\it vs} are the same for both the hcp and fcc
cases. An expected value for the localization gives an in reasonable
agreement with experiment. The bcc lattice has a similar curve of {\it
vs} , but is generally smaller because the lattice is more dilute.Comment: 9 pages, 1 figure, 3 table
Fractional quantum Hall edge: Effect of nonlinear dispersion and edge roton
According to Wen's theory, a universal behavior of the fractional quantum
Hall edge is expected at sufficiently low energies, where the dispersion of the
elementary edge excitation is linear. A microscopic calculation shows that the
actual dispersion is indeed linear at low energies, but deviates from linearity
beyond certain energy, and also exhibits an "edge roton minimum." We determine
the edge exponent from a microscopic approach, and find that the nonlinearity
of the dispersion makes a surprisingly small correction to the edge exponent
even at energies higher than the roton energy. We explain this insensitivity as
arising from the fact that the energy at maximum spectral weight continues to
show an almost linear behavior up to fairly high energies. We also formulate an
effective field theory to describe the behavior of a reconstructed edge, taking
into account multiple edge modes. Experimental consequences are discussed.Comment: 15 pages with 10 figures. Submitted to Physical Review
Epidemic spreading on preferred degree adaptive networks
We study the standard SIS model of epidemic spreading on networks where
individuals have a fluctuating number of connections around a preferred degree
. Using very simple rules for forming such preferred degree networks,
we find some unusual statistical properties not found in familiar
Erd\H{o}s-R\'{e}nyi or scale free networks. By letting depend on the
fraction of infected individuals, we model the behavioral changes in response
to how the extent of the epidemic is perceived. In our models, the behavioral
adaptations can be either `blind' or `selective' -- depending on whether a node
adapts by cutting or adding links to randomly chosen partners or selectively,
based on the state of the partner. For a frozen preferred network, we find that
the infection threshold follows the heterogeneous mean field result
and the phase diagram matches the predictions of
the annealed adjacency matrix (AAM) approach. With `blind' adaptations,
although the epidemic threshold remains unchanged, the infection level is
substantially affected, depending on the details of the adaptation. The
`selective' adaptive SIS models are most interesting. Both the threshold and
the level of infection changes, controlled not only by how the adaptations are
implemented but also how often the nodes cut/add links (compared to the time
scales of the epidemic spreading). A simple mean field theory is presented for
the selective adaptations which capture the qualitative and some of the
quantitative features of the infection phase diagram.Comment: 21 pages, 7 figure
Modeling interacting dynamic networks: I. Preferred degree networks and their characteristics
We study a simple model of dynamic networks, characterized by a set preferred
degree, . Each node with degree attempts to maintain its
and will add (cut) a link with probability (). As
a starting point, we consider a homogeneous population, where each node has the
same , and examine several forms of , inspired by
Fermi-Dirac functions. Using Monte Carlo simulations, we find the degree
distribution in steady state. In contrast to the well-known Erd\H{o}s-R\'{e}nyi
network, our degree distribution is not a Poisson distribution; yet its
behavior can be understood by an approximate theory. Next, we introduce a
second preferred degree network and couple it to the first by establishing a
controllable fraction of inter-group links. For this model, we find both
understandable and puzzling features. Generalizing the prediction for the
homogeneous population, we are able to explain the total degree distributions
well, but not the intra- or inter-group degree distributions. When monitoring
the total number of inter-group links, , we find very surprising behavior.
explores almost the full range between its maximum and minimum allowed
values, resulting in a flat steady-state distribution, reminiscent of a simple
random walk confined between two walls. Both simulation results and analytic
approaches will be discussed.Comment: Accepted by JSTA
Microscopic study of the 2/5 fractional quantum Hall edge
This paper reports on our study of the edge of the 2/5 fractional quantum
Hall state, which is more complicated than the edge of the 1/3 state because of
the presence of a continuum of quasi-degenerate edge sectors corresponding to
different partitions of composite fermions in the lowest two {\Lambda} levels.
The addition of an electron at the edge is a non-perturbative process and it is
not a priori obvious in what manner the added electron distributes itself over
these sectors. We show, from a microscopic calculation, that when an electron
is added at the edge of the ground state in the [N_1, N_2] sector, where N_1
and N_2 are the numbers of composite fermions in the lowest two {\Lambda}
levels, the resulting state lies in either [N_1 + 1, N_2] or [N_1, N_2 + 1]
sector; adding an electron at the edge is thus equivalent to adding a composite
fermion at the edge. The coupling to other sectors of the form [N_1 + 1 + k,
N_2 - k], k integer, is negligible in the asymptotically low-energy limit. This
study also allows a detailed and substantial comparison with the two-boson
model of the 2/5 edge. We compute the spectral weights and find that while the
individual spectral weights are complicated and non-universal, their sum is
consistent with an effective two-boson description of the 2/5 edge.Comment: 11 pages, 7 figure
Electron operator at the edge of the 1/3 fractional quantum Hall liquid
This study builds upon the work of Palacios and MacDonald (Phys. Rev. Lett.
{\bf 76}, 118 (1996)), wherein they identify the bosonic excitations of Wen's
approach for the edge of the 1/3 fractional quantum Hall state with certain
operators introduced by Stone. Using a quantum Monte Carlo method, we extend to
larger systems containing up to 40 electrons and obtain more accurate
thermodynamic limits for various matrix elements for a short range interaction.
The results are in agreement with those of Palacios and MacDonald for small
systems, but offer further insight into the detailed approach to the
thermodynamic limit. For the short range interaction, the results are
consistent with the chiral Luttinger liquid predictions.We also study
excitations using the Coulomb ground state for up to nine electrons to
ascertain the effect of interactions on the results; in this case our tests of
the chiral Luttinger liquid approach are inconclusive.Comment: 10 pages, 2 figure
Spatial Modeling of Spread of Dengue Cellular Automata and Reaction Diffusion methods
by Shivakumar Jola