6,721 research outputs found

    Existence of a Density Functional for an Intrinsic State

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    A generalization of the Hohenberg-Kohn theorem proves the existence of a density functional for an intrinsic state, symmetry violating, out of which a physical state with good quantum numbers can be projected.Comment: 6 page

    Constrained Orthogonal Polynomials

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    We define sets of orthogonal polynomials satisfying the additional constraint of a vanishing average. These are of interest, for example, for the study of the Hohenberg-Kohn functional for electronic or nucleonic densities and for the study of density fluctuations in centrifuges. We give explicit properties of such polynomial sets, generalizing Laguerre and Legendre polynomials. The nature of the dimension 1 subspace completing such sets is described. A numerical example illustrates the use of such polynomials.Comment: 11 pages, 10 figure

    Open problems in nuclear density functional theory

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    This note describes five subjects of some interest for the density functional theory in nuclear physics. These are, respectively, i) the need for concave functionals, ii) the nature of the Kohn-Sham potential for the radial density theory, iii) a proper implementation of a density functional for an "intrinsic" rotational density, iv) the possible existence of a potential driving the square root of the density, and v) the existence of many models where a density functional can be explicitly constructed.Comment: 10 page

    Two scenarios for quantum multifractality breakdown

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    We expose two scenarios for the breakdown of quantum multifractality under the effect of perturbations. In the first scenario, multifractality survives below a certain scale of the quantum fluctuations. In the other one, the fluctuations of the wave functions are changed at every scale and each multifractal dimension smoothly goes to the ergodic value. We use as generic examples a one-dimensional dynamical system and the three-dimensional Anderson model at the metal-insulator transition. Based on our results, we conjecture that the sensitivity of quantum multifractality to perturbation is universal in the sense that it follows one of these two scenarios depending on the perturbation. We also discuss the experimental implications.Comment: 5 pages, 4 figures, minor modifications, published versio

    Multifractality of quantum wave functions in the presence of perturbations

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    We present a comprehensive study of the destruction of quantum multifractality in the presence of perturbations. We study diverse representative models displaying multifractality, including a pseudointegrable system, the Anderson model and a random matrix model. We apply several types of natural perturbations which can be relevant for experimental implementations. We construct an analytical theory for certain cases, and perform extensive large-scale numerical simulations in other cases. The data are analyzed through refined methods including double scaling analysis. Our results confirm the recent conjecture that multifractality breaks down following two scenarios. In the first one, multifractality is preserved unchanged below a certain characteristic length which decreases with perturbation strength. In the second one, multifractality is affected at all scales and disappears uniformly for a strong enough perturbation. Our refined analysis shows that subtle variants of these scenarios can be present in certain cases. This study could guide experimental implementations in order to observe quantum multifractality in real systems.Comment: 20 pages, 27 figure

    Finite geometries and diffractive orbits in isospectral billiards

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    Several examples of pairs of isospectral planar domains have been produced in the two-dimensional Euclidean space by various methods. We show that all these examples rely on the symmetry between points and blocks in finite projective spaces; from the properties of these spaces, one can derive a relation between Green functions as well as a relation between diffractive orbits in isospectral billiards.Comment: 10 page

    Entanglement and localization of wavefunctions

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    We review recent works that relate entanglement of random vectors to their localization properties. In particular, the linear entropy is related by a simple expression to the inverse participation ratio, while next orders of the entropy of entanglement contain information about e.g. the multifractal exponents. Numerical simulations show that these results can account for the entanglement present in wavefunctions of physical systems.Comment: 6 pages, 4 figures, to appear in the proceedings of the NATO Advanced Research Workshop 'Recent Advances in Nonlinear Dynamics and Complex System Physics', Tashkent, Uzbekistan, 200

    Retrieving Nuclear Information from Protons Propagating through A Thick Target

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    The multiple scattering of high-energy particles in a thick target is fromulated in an impact parameter representation. A formalism similar but not identical to that of Moliere is obtained. We show that calculations of particle beam broadening due to multiple Coulomb scattering alone can be given in closed form. The focus of this study is on whether or not the broadening of the Coulomb angular distribution prevents the retrieval of nuclear-interaction information from mesauring the angular distributions of charged partiles scattered from a thick target. For this purpose, we study multiple scatterings with both the nuclear and Coulomb interactions included and we do not make a small-angle expansion. Condition for retrieving nuclear infomration from high-energy protons propagating through a block of material are obtained.Comment: 29 pages, 13 figure

    Ferromagnetic (Ga,Mn)N epilayers versus antiferromagnetic GaMn3_3N clusters

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    Mn-doped wurtzite GaN epilayers have been grown by nitrogen plasma-assisted molecular beam epitaxy. Correlated SIMS, structural and magnetic measurements show that the incorporation of Mn strongly depends on the conditions of the growth. Hysteresis loops which persist at high temperature do not appear to be correlated to the presence of Mn. Samples with up to 2% Mn are purely substitutional Ga1x_{1-x}Mnx_xN epilayers, and exhibit paramagnetic properties. At higher Mn contents, precipitates are formed which are identified as GaMn3_3N clusters by x-ray diffraction and absorption: this induces a decrease of the paramagnetic magnetisation. Samples co-doped with enough Mg exhibit a new feature: a ferromagnetic component is observed up to Tc175T_c\sim175 K, which cannot be related to superparamagnetism of unresolved magnetic precipitates.Comment: Revised versio
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