5,886 research outputs found

    Self-consistent equation for an interacting Bose gas

    Full text link
    We consider interacting Bose gas in thermal equilibrium assuming a positive and bounded pair potential V(r)V(r) such that 0<\int d\br V(r) = a<\infty. Expressing the partition function by the Feynman-Kac functional integral yields a classical-like polymer representation of the quantum gas. With Mayer graph summation techniques, we demonstrate the existence of a self-consistent relation ρ(μ)=F(μaρ(μ))\rho (\mu)=F(\mu-a\rho(\mu)) between the density ρ\rho and the chemical potential μ\mu, valid in the range of convergence of Mayer series. The function FF is equal to the sum of all rooted multiply connected graphs. Using Kac's scaling V_{\gamma}(\br)=\gamma^{3}V(\gamma r) we prove that in the mean-field limit γ0\gamma\to 0 only tree diagrams contribute and function FF reduces to the free gas density. We also investigate how to extend the validity of the self-consistent relation beyond the convergence radius of Mayer series (vicinity of Bose-Einstein condensation) and study dominant corrections to mean field. At lowest order, the form of function FF is shown to depend on single polymer partition function for which we derive lower and upper bounds and on the resummation of ring diagrams which can be analytically performed.Comment: 33 pages, 6 figures, submitted to Phys.Rev.

    Topological indices of total graph of the ring Zո × Zm

    Get PDF
    In this paper, we compute some distance-based topological indices namely Wiener index, hyper Wiener index and reverse Wiener index of the total graph of the ring Zn × Zm. We also compute some eccentricity-based topological indices namely first Zagreb eccentricity index, second Zagreb eccentricity index, eccentric connectivity index, connective eccentricity index and eccentric distance sum index of the total graph of the ring Zn × Zm. Finally, we compute some degree-based topological indices namely second Zagreb index, product-connectivity index, sum connectivity index, atom-bond connectivity index and geometric arithmetic index of the total graph of the ring Zn ×Zm when both n and m are even, when n or m is even, and the case when n and m are both prime numbers (not neccesarily distinct).Publisher's Versio

    Functionals of the Brownian motion, localization and metric graphs

    Full text link
    We review several results related to the problem of a quantum particle in a random environment. In an introductory part, we recall how several functionals of the Brownian motion arise in the study of electronic transport in weakly disordered metals (weak localization). Two aspects of the physics of the one-dimensional strong localization are reviewed : some properties of the scattering by a random potential (time delay distribution) and a study of the spectrum of a random potential on a bounded domain (the extreme value statistics of the eigenvalues). Then we mention several results concerning the diffusion on graphs, and more generally the spectral properties of the Schr\"odinger operator on graphs. The interest of spectral determinants as generating functions characterizing the diffusion on graphs is illustrated. Finally, we consider a two-dimensional model of a charged particle coupled to the random magnetic field due to magnetic vortices. We recall the connection between spectral properties of this model and winding functionals of the planar Brownian motion.Comment: Review article. 50 pages, 21 eps figures. Version 2: section 5.5 and conclusion added. Several references adde

    The topology of fullerenes

    Get PDF
    Fullerenes are carbon molecules that form polyhedral cages. Their bond structures are exactly the planar cubic graphs that have only pentagon and hexagon faces. Strikingly, a number of chemical properties of a fullerene can be derived from its graph structure. A rich mathematics of cubic planar graphs and fullerene graphs has grown since they were studied by Goldberg, Coxeter, and others in the early 20th century, and many mathematical properties of fullerenes have found simple and beautiful solutions. Yet many interesting chemical and mathematical problems in the field remain open. In this paper, we present a general overview of recent topological and graph theoretical developments in fullerene research over the past two decades, describing both solved and open problems. WIREs Comput Mol Sci 2015, 5:96–145. doi: 10.1002/wcms.1207 Conflict of interest: The authors have declared no conflicts of interest for this article. For further resources related to this article, please visit the WIREs website

    Convolutional Deblurring for Natural Imaging

    Full text link
    In this paper, we propose a novel design of image deblurring in the form of one-shot convolution filtering that can directly convolve with naturally blurred images for restoration. The problem of optical blurring is a common disadvantage to many imaging applications that suffer from optical imperfections. Despite numerous deconvolution methods that blindly estimate blurring in either inclusive or exclusive forms, they are practically challenging due to high computational cost and low image reconstruction quality. Both conditions of high accuracy and high speed are prerequisites for high-throughput imaging platforms in digital archiving. In such platforms, deblurring is required after image acquisition before being stored, previewed, or processed for high-level interpretation. Therefore, on-the-fly correction of such images is important to avoid possible time delays, mitigate computational expenses, and increase image perception quality. We bridge this gap by synthesizing a deconvolution kernel as a linear combination of Finite Impulse Response (FIR) even-derivative filters that can be directly convolved with blurry input images to boost the frequency fall-off of the Point Spread Function (PSF) associated with the optical blur. We employ a Gaussian low-pass filter to decouple the image denoising problem for image edge deblurring. Furthermore, we propose a blind approach to estimate the PSF statistics for two Gaussian and Laplacian models that are common in many imaging pipelines. Thorough experiments are designed to test and validate the efficiency of the proposed method using 2054 naturally blurred images across six imaging applications and seven state-of-the-art deconvolution methods.Comment: 15 pages, for publication in IEEE Transaction Image Processin
    corecore