Rigorous Derivation of the Gross-Pitaevskii Equation

The time dependent Gross-Pitaevskii equation describes the dynamics of initially trapped Bose-Einstein condensates. We present a rigorous proof of this fact starting from a many-body bosonic Schroedinger equation with a short scale repulsive interaction in the dilute limit. Our proof shows the persistence of an explicit short scale correlation structure in the condensate.Comment: 4 pages, 1 figur

Stationary wave patterns generated by an impurity moving with supersonic velocity through a Bose-Einstein condensate

Formation of stationary 3D wave patterns generated by a small point-like impurity moving through a Bose-Einstein condensate with supersonic velocity is studied. Asymptotic formulae for a stationary far-field density distribution are obtained. Comparison with three-dimensional numerical simulations demonstrates that these formulae are accurate enough already at distances from the obstacle equal to a few wavelengths.Comment: 7 pages, 3 figure

Spontaneous Crystallization of Skyrmions and Fractional Vortices in the Fast-rotating and Rapidly-quenched Spin-1 Bose-Einstein Condensates

We investigate the spontaneous generation of crystallized topological defects via the combining effects of fast rotation and rapid thermal quench on the spin-1 Bose-Einstein condensates. By solving the stochastic projected Gross-Pitaevskii equation, we show that, when the system reaches equilibrium, a hexagonal lattice of skyrmions, and a square lattice of half-quantized vortices can be formed in a ferromagnetic and antiferromagnetic spinor BEC, respetively, which can be imaged by using the polarization-dependent phase-contrast method

Delocalization and Diffusion Profile for Random Band Matrices

We consider Hermitian and symmetric random band matrices $H = (h_{xy})$ in $d \geq 1$ dimensions. The matrix entries $h_{xy}$, indexed by x,y \in (\bZ/L\bZ)^d, are independent, centred random variables with variances s_{xy} = \E |h_{xy}|^2. We assume that $s_{xy}$ is negligible if $|x-y|$ exceeds the band width $W$. In one dimension we prove that the eigenvectors of $H$ are delocalized if $W\gg L^{4/5}$. We also show that the magnitude of the matrix entries \abs{G_{xy}}^2 of the resolvent $G=G(z)=(H-z)^{-1}$ is self-averaging and we compute \E \abs{G_{xy}}^2. We show that, as $L\to\infty$ and $W\gg L^{4/5}$, the behaviour of \E |G_{xy}|^2 is governed by a diffusion operator whose diffusion constant we compute. Similar results are obtained in higher dimensions

Exact eigenstate analysis of finite-frequency conductivity in graphene

We employ the exact eigenstate basis formalism to study electrical conductivity in graphene, in the presence of short-range diagonal disorder and inter-valley scattering. We find that for disorder strength, $W \ge$ 5, the density of states is flat. We, then, make connection, using the MRG approach, with the work of Abrahams \textit{et al.} and find a very good agreement for disorder strength, $W$ = 5. For low disorder strength, $W$ = 2, we plot the energy-resolved current matrix elements squared for different locations of the Fermi energy from the band centre. We find that the states close to the band centre are more extended and falls of nearly as $1/E_l^{2}$ as we move away from the band centre. Further studies of current matrix elements versus disorder strength suggests a cross-over from weakly localized to a very weakly localized system. We calculate conductivity using Kubo Greenwood formula and show that, for low disorder strength, conductivity is in a good qualitative agreement with the experiments, even for the on-site disorder. The intensity plots of the eigenstates also reveal clear signatures of puddle formation for very small carrier concentration. We also make comparison with square lattice and find that graphene is more easily localized when subject to disorder.Comment: 11 pages,15 figure

Negative phenotypic and genetic associations between copulation duration and longevity in male seed beetles

Reproduction can be costly and is predicted to trade-off against other characters. However, while these trade-offs are well documented for females, there has been less focus on aspects of male reproduction. Furthermore, those studies that have looked at males typically only investigate phenotypic associations, with the underlying genetics often ignored. Here, we report on phenotypic and genetic trade-offs in male reproductive effort in the seed beetle, Callosobruchus maculatus. We find that the duration of a male's first copulation is negatively associated with subsequent male survival, phenotypically and genetically. Our results are consistent with life-history theory and suggest that like females, males trade-off reproductive effort against longevity

Mapping gene associations in human mitochondria using clinical disease phenotypes

Nuclear genes encode most mitochondrial proteins, and their mutations cause diverse and debilitating clinical disorders. To date, 1,200 of these mitochondrial genes have been recorded, while no standardized catalog exists of the associated clinical phenotypes. Such a catalog would be useful to develop methods to analyze human phenotypic data, to determine genotype-phenotype relations among many genes and diseases, and to support the clinical diagnosis of mitochondrial disorders. Here we establish a clinical phenotype catalog of 174 mitochondrial disease genes and study associations of diseases and genes. Phenotypic features such as clinical signs and symptoms were manually annotated from full-text medical articles and classified based on the hierarchical MeSH ontology. This classification of phenotypic features of each gene allowed for the comparison of diseases between different genes. In turn, we were then able to measure the phenotypic associations of disease genes for which we calculated a quantitative value that is based on their shared phenotypic features. The results showed that genes sharing more similar phenotypes have a stronger tendency for functional interactions, proving the usefulness of phenotype similarity values in disease gene network analysis. We then constructed a functional network of mitochondrial genes and discovered a higher connectivity for non-disease than for disease genes, and a tendency of disease genes to interact with each other. Utilizing these differences, we propose 168 candidate genes that resemble the characteristic interaction patterns of mitochondrial disease genes. Through their network associations, the candidates are further prioritized for the study of specific disorders such as optic neuropathies and Parkinson disease. Most mitochondrial disease phenotypes involve several clinical categories including neurologic, metabolic, and gastrointestinal disorders, which might indicate the effects of gene defects within the mitochondrial system. The accompanying knowledgebase (http://www.mitophenome.org/) supports the study of clinical diseases and associated genes

Output feedback robust H∞ control with D-stability and variance constraints: A parametrization approach

This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2005 Springer Ltd.In this paper, we study the problem of robust H∞ controller design for uncertain continuous-time systems with variance and D-stability constraints. The parameter uncertainties are allowed to be unstructured but norm-bounded. The aim of this problem is the design of an output feedback controller such that, for all admissible uncertainties, the closed-loop poles be placed within a specified disk, the H∞ norm bound constraint on the disturbance rejection attenuation be guaranteed, and the steady-state variance for each state of the closed-loop system be no more than the prescribed individual upper bound, simultaneously. A parametric design method is exploited to solve the problem addressed. Sufficient conditions for the existence of the desired controllers are derived by using the generalized inverse theory. The analytical expression of the set of desired controllers is also presented. It is shown that the obtained results can be readily extended to the dynamic output feedback case and the discrete-time case