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  • 1
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Physics Letters B 146 (1984), S. 183-186 
    ISSN: 0370-2693
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Physics
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 43 (1986), S. 197-205 
    ISSN: 1572-9613
    Keywords: Dielectric susceptibility ; Clausius-Mossotti relation ; phenomenological electrostatics ; Stillinger-Lovett sum rule ; linear response theory ; statistical mechanics ; one-component plasma ; disk and strip geometry ; thermodynamic limit
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract This paper reports exact and numerical results on the shape dependence of the dielectric susceptibility of the one-component plasma (O.C.P.) in two dimensions. Some apparently conflicting predictions of phenomenological electrostatics and statistical mechanics are resolved. We prove indeed that, for a disk shaped two-dimensional one-component plasma at the particular temperatureT 0 =q 2 (2K B )−1, the Clausius-Mossotti relation is exactly fulfilled. It yields a value of the susceptibility which is twice that given by the second moment Stillinger-Lovett sum rule. Similar results are reported for the strip geometry. These discrepancies are explained in terms of shape dependent versus shape independent thermodynamic limits. We report also exact and numerical results on the size dependence of the dielectric susceptibility of the systems quoted above.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 46 (1987), S. 599-633 
    ISSN: 1572-9613
    Keywords: One- and two-component plasmas ; dielectric susceptibility ; partial second moment ; shape-dependent effects
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract This paper deals with the shape dependence of the dielectric susceptibility (equivalently defined, in a canonical ensemble, by the mean square fluctuation of the electric polarization or by the second moment of the charge-charge correlation function) of classical Coulomb systems. The concept of partial second moment is introduced with the aim of analyzing the contributions to the total susceptibility of pairs of particles of increasing separation. For a diskshaped one-component plasma with coupling parameter γ=2 it is shown, numerically and algebraically for small and large systems, that (1) the correlation function of two particles close to the edge of the disk decays as the inverse of the square of their distance, and (2) the susceptibility is made up of a bulk contribution, which saturates rapidly toward the Stillinger-Lovett value, and of a surface contribution, which varies on the scale of the disk diameter and is described by a new law called the “arc sine” law. It is also shown that electrostatics and statistical mechanics with shape-dependent thermodynamic limits are consistent for the same model in a strip geometry, whereas the Stillinger-Lovett sum rule is verified for a boundary-free geometry such as the surface of a sphere. Some results of extensive computer simulations of one- and two-component plasmas in circular and elliptic geometries are shown. Anisotropy effects on the susceptibilities are clearly demonstrated and the “arc sine” law for a circular plasma is well confirmed.
    Type of Medium: Electronic Resource
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  • 4
    ISSN: 1572-9613
    Keywords: Phenomenological electrostatics ; shape-dependent effects ; dielectric susceptibility ; surface correlations ; Debye-Hückel approximation ; grand ensemble computer simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We report analytical and numerical studies of surface correlations in finite, homogeneously polarizable, classical Coulomb systems placed in an insulating or conducting environment. Their purpose is to understand the phenomenological, shape-dependent laws of electrostatics, from the point of view of statistical mechanics; we focus on the knowledge of the dielectric susceptibility of the system, a quantity proportional to the equilibrium fluctuation of the system's instantaneous polarization per unit volume. This goal has been achieved for a system in a conducting state. The picture is that the shape-dependent part of the susceptibilities results from the action of unbounded observables (the second moments of the instantaneous polarization of the system) on long-range surface correlations and that the relations of electrostatics are verified by means of shape-dependent thermodynamic limits. This picture is supported (i) by exact solutions and asymptotic analysis of the Debye-Hückel approximation of multicomponent plasmas in disks and spheres with insulating and conducting environment and also in ellipses in a vacuum, and (ii) by computer simulations of a one-component plasma in a disk with different environments, notably a conducting environment with permeable and impermeable wall. These observations have revealed for the first time the reason why the susceptibility of a conducting disk in a conductor with impermeable walls diverges linearly with the radius of the disk: this is due to the occurrence of long-range radial correlations in the conductor. These findings are quantitatively interpreted in terms of a novel “canonical” Debye-Huckel approximation as contrasted to the ordinary “grand canonical” version. Lastly a fresh look at the problem of the surface correlations of a conductor in a vacuum, which places the observer close to the surface of the conductor but in the vacuum, is presented and applied to the disk, the ellipse, the cylinder, the sphere, and the wedge.
    Type of Medium: Electronic Resource
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