11,839 research outputs found
Counter-ions at single charged wall: Sum rules
For inhomogeneous classical Coulomb fluids in thermal equilibrium, like the
jellium or the two-component Coulomb gas, there exists a variety of exact sum
rules which relate the particle one-body and two-body densities. The necessary
condition for these sum rules is that the Coulomb fluid possesses good
screening properties, i.e. the particle correlation functions or the averaged
charge inhomogeneity, say close to a wall, exhibit a short-range (usually
exponential) decay. In this work, we study equilibrium statistical mechanics of
an electric double layer with counter-ions only, i.e. a globally neutral system
of equally charged point-like particles in the vicinity of a plain hard wall
carrying a fixed uniform surface charge density of opposite sign. At large
distances from the wall, the one-body and two-body counter-ion densities go to
zero slowly according to the inverse-power law. In spite of the absence of
screening, all known sum rules are shown to hold for two exactly solvable cases
of the present system: in the weak-coupling Poisson-Boltzmann limit (in any
spatial dimension larger than one) and at a special free-fermion coupling
constant in two dimensions. This fact indicates an extended validity of the sum
rules and provides a consistency check for reasonable theoretical approaches.Comment: 7 pages, 1 figur
Can Google Trends search queries contribute to risk diversification?
Portfolio diversification and active risk management are essential parts of
financial analysis which became even more crucial (and questioned) during and
after the years of the Global Financial Crisis. We propose a novel approach to
portfolio diversification using the information of searched items on Google
Trends. The diversification is based on an idea that popularity of a stock
measured by search queries is correlated with the stock riskiness. We penalize
the popular stocks by assigning them lower portfolio weights and we bring
forward the less popular, or peripheral, stocks to decrease the total riskiness
of the portfolio. Our results indicate that such strategy dominates both the
benchmark index and the uniformly weighted portfolio both in-sample and
out-of-sample.Comment: 11 pages, 3 figure
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