23,117 research outputs found
Correlated versus Ferromagnetic State in Repulsively Interacting Two-Component Fermi Gases
Whether a spin-1/2 Fermi gas will become ferromagnetic as the strength of
repulsive interaction increases is a long-standing controversial issue.
Recently this problem is studied experimentally by Jo et al, Science, 325, 1521
(2009) in which the authors claim a ferromagnetic transition is observed. This
work is to point out the results of this experiment can not distinguish whether
the system is in a ferromagnetic state or in a non-magnetic but strongly
short-range correlated state. A conclusive experimental demonstration of
ferromagnetism relies on the observation of ferromagnetic domains.Comment: 4 pages, 2 figures, published versio
Reducing the bias of the maximum likelihood estimator for the Poisson regression model
We derive expressions for the first-order bias of the MLE for a Poisson regression model and show how these can be used to adjust the estimator and reduce bias without increasing MSE. The analytic results are supported by Monte Carlo simulations and three illustrative empirical applications.Poisson regression, maximum likelihood estimation, bias reduction
On-Shell Gauge Invariant Three-Point Amplitudes
Assuming locality, Lorentz invariance and parity conservation we obtain a set
of differential equations governing the 3-point interactions of massless
bosons, which in turn determines the polynomial ring of these amplitudes. We
derive all possible 3-point interactions for tensor fields with polarisations
that have total symmetry and mixed symmetry under permutations of Lorentz
indices. Constraints on the existence of gauge-invariant cubic vertices for
totally symmetric fields are obtained in general spacetime dimensions and are
compared with existing results obtained in the covariant and light-cone
approaches. Expressing our results in spinor helicity formalism we reproduce
the perhaps mysterious mismatch between the covariant approach and the light
cone approach in 4 dimensions. Our analysis also shows that there exists a
mismatch, in the 3-point gauge invariant amplitudes corresponding to cubic
self-interactions, between a scalar field and an antisymmetric rank-2
tensor field . Despite the well-known fact that in 4 dimensions
rank-2 anti-symmetric fields are dual to scalar fields in free theories, such
duality does not extend to interacting theories.Comment: significantly revised, final version published in JHE
A Geometrical Test of the Cosmological Energy Contents Using the Lyman-alpha Forest
In this Letter we explore a version of the test of cosmological geometry
proposed by Alcock and Paczynski (1979), using observations of the Lyman-alpha
forest in the spectra of close quasar pairs. By comparing the correlations in
absorption in one quasar spectrum with correlations between the spectra of
neighboring quasars one can determine the relation of the redshift distance
scale to the angle distance scale at the redshift of the absorbers, . Since this relationship depends on the parameters of the cosmological
model, these parameters may be determined using the Lyman-alpha forest. While
this test is relatively insensitive to the density parameter in a
dust-dominated universe, it is more sensitive to the presence of a matter
component with large negative pressure (such as a cosmological constant
) and its equation of state. With only 25 pairs of quasar spectra at
angular separations , one can discriminate between an open universe () and an flat
(-dominated) universe at the level. The S/N can be enhanced
by considering quasar pairs at smaller angular separations, but requires proper
modeling of nonlinear redshift space distortions. Here the correlations and
redshift space distortions are modeled using linear theory.Comment: 13 pages, 2 ps figures, submitted to ApJ
Kernel-based machine learning protocol for predicting DNA-binding proteins
DNA-binding proteins (DNA-BPs) play a pivotal role in various intra- and extra-cellular activities ranging from DNA replication to gene expression control. Attempts have been made to identify DNA-BPs based on their sequence and structural information with moderate accuracy. Here we develop a machine learning protocol for the prediction of DNA-BPs where the classifier is Support Vector Machines (SVMs). Information used for classification is derived from characteristics that include surface and overall composition, overall charge and positive potential patches on the protein surface. In total 121 DNA-BPs and 238 non-binding proteins are used to build and evaluate the protocol. In self-consistency, accuracy value of 100% has been achieved. For cross-validation (CV) optimization over entire dataset, we report an accuracy of 90%. Using leave 1-pair holdout evaluation, the accuracy of 86.3% has been achieved. When we restrict the dataset to less than 20% sequence identity amongst the proteins, the holdout accuracy is achieved at 85.8%. Furthermore, seven DNA-BPs with unbounded structures are all correctly predicted. The current performances are better than results published previously. The higher accuracy value achieved here originates from two factors: the ability of the SVM to handle features that demonstrate a wide range of discriminatory power and, a different definition of the positive patch. Since our protocol does not lean on sequence or structural homology, it can be used to identify or predict proteins with DNA-binding function(s) regardless of their homology to the known ones
Negative electronic compressibility enables electrically-induced charge density waves in a two-dimensional electron liquid
We show that the negative electronic compressibility of two-dimensional
electronic systems at sufficiently low density enables the generation of charge
density waves through the application of a uniform force field, provided no
current is allowed to flow. The wavelength of the density oscillations is
controlled by the magnitude of the (negative) screening length, and their
amplitude is proportional to the applied force. Both are electrically tunable.Comment: 4 pages, 5 figure
A simple minimax estimator for quantum states
Quantum tomography requires repeated measurements of many copies of the
physical system, all prepared by a source in the unknown state. In the limit of
very many copies measured, the often-used maximum-likelihood (ML) method for
converting the gathered data into an estimate of the state works very well. For
smaller data sets, however, it often suffers from problems of rank deficiency
in the estimated state. For many systems of relevance for quantum information
processing, the preparation of a very large number of copies of the same
quantum state is still a technological challenge, which motivates us to look
for estimation strategies that perform well even when there is not much data.
In this article, we review the concept of minimax state estimation, and use
minimax ideas to construct a simple estimator for quantum states. We
demonstrate that, for the case of tomography of a single qubit, our estimator
significantly outperforms the ML estimator for small number of copies of the
state measured. Our estimator is always full-rank, and furthermore, has a
natural dependence on the number of copies measured, which is missing in the ML
estimator.Comment: 26 pages, 3 figures. v2 contains minor improvements to the text, and
an additional appendix on symmetric measurement
Stability of a Fully Magnetized Ferromagnetic state in Repulsively Interacting Ultracold Fermi Gases
We construct a variational wave function to study whether a fully polarized
Fermi sea is energetically stable against a single spin flip. Our variational
wave function contains sufficient short-range correlation at least to the same
level as Gutzwiller's projected wave function. For Hubbard lattice model and
continuum model with pure repulsive interaction, we show a fully polarized
Fermi sea is generally unstable even when the repulsive strength becomes
infinite. While for a resonance model, ferromagnetic state is possible if the
s-wave scattering length is positive and sufficiently large, and the system is
prepared in scattering state orthogonal to molecular bound state. However, we
can not rule out the possibility that more exotic correlation can destabilize
the ferromagnetic state.Comment: 4 pages, 3 figure
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