Continuous quantum measurement of a Bose-Einstein condensate: a stochastic Gross-Pitaevskii equation

We analyze the dynamics of a Bose-Einstein condensate undergoing a continuous dispersive imaging by using a Lindblad operator formalism. Continuous strong measurements drive the condensate out of the coherent state description assumed within the Gross-Pitaevskii mean-field approach. Continuous weak measurements allow instead to replace, for timescales short enough, the exact problem with its mean-field approximation through a stochastic analogue of the Gross-Pitaevskii equation. The latter is used to show the unwinding of a dark soliton undergoing a continuous imaging.Comment: 13 pages, 10 figure

New Approximability Results for the Robust k-Median Problem

We consider a robust variant of the classical $k$-median problem, introduced by Anthony et al. \cite{AnthonyGGN10}. In the \emph{Robust $k$-Median problem}, we are given an $n$-vertex metric space $(V,d)$ and $m$ client sets $\set{S_i \subseteq V}_{i=1}^m$. The objective is to open a set $F \subseteq V$ of $k$ facilities such that the worst case connection cost over all client sets is minimized; in other words, minimize $\max_{i} \sum_{v \in S_i} d(F,v)$. Anthony et al.\ showed an $O(\log m)$ approximation algorithm for any metric and APX-hardness even in the case of uniform metric. In this paper, we show that their algorithm is nearly tight by providing $\Omega(\log m/ \log \log m)$ approximation hardness, unless ${\sf NP} \subseteq \bigcap_{\delta >0} {\sf DTIME}(2^{n^{\delta}})$. This hardness result holds even for uniform and line metrics. To our knowledge, this is one of the rare cases in which a problem on a line metric is hard to approximate to within logarithmic factor. We complement the hardness result by an experimental evaluation of different heuristics that shows that very simple heuristics achieve good approximations for realistic classes of instances.Comment: 19 page

Galerkin FEM for fractional order parabolic equations with initial data in H−s, 0<s≤1H^{-s},~0 < s \le 1

We investigate semi-discrete numerical schemes based on the standard Galerkin and lumped mass Galerkin finite element methods for an initial-boundary value problem for homogeneous fractional diffusion problems with non-smooth initial data. We assume that $\Omega\subset \mathbb{R}^d$, $d=1,2,3$ is a convex polygonal (polyhedral) domain. We theoretically justify optimal order error estimates in $L_2$- and $H^1$-norms for initial data in $H^{-s}(\Omega),~0\le s \le 1$. We confirm our theoretical findings with a number of numerical tests that include initial data $v$ being a Dirac $\delta$-function supported on a $(d-1)$-dimensional manifold.Comment: 13 pages, 3 figure

Recursion and Path-Integral Approaches to the Analytic Study of the Electronic Properties of C60C_{60}

The recursion and path-integral methods are applied to analytically study the electronic structure of a neutral $C_{60}$ molecule. We employ a tight-binding Hamiltonian which considers both the $s$ and $p$ valence electrons of carbon. From the recursion method, we obtain closed-form {\it analytic} expressions for the $\pi$ and $\sigma$ eigenvalues and eigenfunctions, including the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) states, and the Green's functions. We also present the local densities of states around several ring clusters, which can be probed experimentally by using, for instance, a scanning tunneling microscope. {}From a path-integral method, identical results for the energy spectrum are also derived. In addition, the local density of states on one carbon atom is obtained; from this we can derive the degree of degeneracy of the energy levels.Comment: 19 pages, RevTex, 6 figures upon reques

Diffuse interstitial and multiple cavitary lung lesions due to Talaromyces marneffei infection in a non-HIV patient

AbstractA 57-year-old man presented with unproductive cough and dyspnea for 6 months in Fujian Province, China. His misuse of a large amount of steroids (accumulated dose equivalent to 3530 mg prednisolone) resulted in Talaromyces marneffei infection. Chest computed tomographic scan revealed diffuse interstitial and multiple cavitary lung lesions. Treatment with amphotericin B combined with itraconazole resulted in total recovery, with marked regression of lung lesions

Supporting Interoperability of Virtual Factories

The manufacturing industry is entering a new era. This emerging era starts with the integration of new ICT technologies and collaboration applications into traditional manufacturing practices and processes, such as manufacturing 2.0. Manufacturing 2.0 has been conceptualised as a system that goes beyond the factory floor, and paradigms of “manufacturing as an ecosystem” have emerged. The virtual factory is one of the important concepts and foundations central to the realization of future manufacturing. In this paper, we take a look into the current research on virtual factories and propose a new approach to improve interoperability through the integration of different proprietary, legacy and existing solutions

Three-Particle Correlations from Parton Cascades in Au+Au Collisions

We present a study of three-particle correlations among a trigger particle and two associated particles in Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV using a multi-phase transport model (AMPT) with both partonic and hadronic interactions. We found that three-particle correlation densities in different angular directions with respect to the triggered particle (`center', `cone', `deflected', `near' and `near-away') increase with the number of participants. The ratio of `deflected' to `cone' density approaches to 1.0 with the increasing of number of participants, which indicates that partonic Mach-like shock waves can be produced by strong parton cascades in central Au+Au collisions.Comment: 9 pages, 6 figures; Final version to appear in Physics Letters

Heat to Electricity Conversion by a Graphene Stripe with Heavy Chiral Fermions

A conversion of thermal energy into electricity is considered in the electrically polarized graphene stripes with zigzag edges where the heavy chiral fermion (HCF) states are formed. The stripes are characterized by a high electric conductance Ge and by a significant Seebeck coefficient S. The electric current in the stripes is induced due to a non-equilibrium thermal injection of "hot" electrons. This thermoelectric generation process might be utilized for building of thermoelectric generators with an exceptionally high figure of merit Z{\delta}T \simeq 100 >> 1 and with an appreciable electric power densities \sim 1 MW/cm2.Comment: 8 pages, 3 figure

Supersymmteric Null-like Holographic Cosmologies

We construct a new class of 1/4-BPS time dependent domain-wall solutions with null-like metric and dilaton in type II supergravities, which admit a null-like big bang singularity. Based on the domain-wall/QFT correspondence, these solutions are dual to 1/4-supersymmetric quantum field theories living on a boundary cosmological background with time dependent coupling constant and UV cutoff. In particular we evaluate the holographic $c$ function for the 2-dimensional dual field theory living on the corresponding null-like cosmology. We find that this $c$ function runs in accordance with the $c$-theorem as the boundary universe evolves, this means that the number of degrees of freedom is divergent at big bang and suggests the possible resolution of big bang singularity.Comment: 26 pages;v2 references adde