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Register a new userDensity functional formulation of the Random Phase Approximation for inhomogeneous fluids: application to the Gaussian core and Coulomb particles
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Using the adiabatic connection, we formulate the free energy in terms of the correlation function of a fictitious system, $h_{lambda}({bf r},{bf r})$, where $lambda$ determines the interaction strength. To obtain $h_{lambda}({bf r},{bf r})$ we use the Ornstein-Zernike equation, and the two equations constitute a general liquid-state framework for treating inhomogeneous fluids. As the two equations do not form a closed set, an approximate closure relation is required and it determines a type of an approximation. In the present work we investigate the random phase approximation (RPA) closure. We determine that this approximation is identical to the variational Gaussian approximation derived within the framework of the field-theory. We then apply our generalized RPA approximation to the Gaussian core model and Coulomb charges.
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We propose a simplified version of local molecular field (LMF) theory to treat Coulomb interactions in simulations of ionic fluids. LMF theory relies on splitting the Coulomb potential into a short-ranged part that combines with other short-ranged core interactions and is simulated explicitly. The averaged effects of the remaining long-ranged part are taken into account through a self-consistently determined effective external field. The theory contains an adjustable length parameter sigma that specifies the cut-off distance for the short-ranged interaction. This can be chosen to minimize the errors resulting from the mean-field treatment of the complementary long-ranged part. Here we suggest that in many cases an accurate approximation to the effective field can be obtained directly from the equilibrium charge density given by the Debye theory of screening, thus eliminating the need for a self-consistent treatment. In the limit sigma -> 0, this assumption reduces to the classical Debye approximation. We examine the numerical performance of this approximation for a simple model of a symmetric ionic mixture. Our results for thermodynamic and structural properties of uniform ionic mixtures agree well with similar results of Ewald simulations of the full ionic system. In addition we have used the simplified theory in a grand-canonical simulation of a nonuniform ionic mixture where an ion has been fixed at the origin. Simulations using short-ranged truncations of the Coulomb interactions alone do not satisfy the exact condition of complete screening of the fixed ion, but this condition is recovered when the effective field is taken into account. We argue that this simplified approach can also be used in the simulations of more complex nonuniform systems.
We use an analytic criterion for vanishing of exponential damping of correlations developed previously (Piasecki et al, J. Chem. Phys., 133, 164507, 2010) to determine the threshold volume fractions for structural transitions in hard sphere systems in dimensions D=3,4,5 and 6, proceeding from the YBG hierarchy and using the Kirkwood superposition approximation. We conclude that the theory does predict phase transitions in qualitative agreement with numerical studies. We also derive, within the superposition approximation, the asymptotic form of the analytic condition for occurence of a structural transition in the D->Infinity limit .
We construct a density functional for the lattice gas / Ising model on square and cubic lattices based on lattice fundamental measure theory. In order to treat the nearest-neighbor attractions between the lattice gas particles, the model is mapped to a multicomponent model of hard particles with additional lattice polymers where effective attractions between particles arise from the depletion effect. The lattice polymers are further treated via the introduction of polymer clusters (labelled by the numbers of polymer they contain) such that the model becomes a multicomponent model of particles and polymer clusters with nonadditive hard interactions. The density functional for this nonadditive hard model is constructed with lattice fundamental measure theory. The resulting bulk phase diagram recovers the Bethe-Peierls approximation and planar interface tensions show a considerable improvement compared to the standard mean-field functional and are close to simulation results in three dimensions. We demonstrate the existence of planar interface solutions at chemical potentials away from coexistence when the equimolar interface position is constrained to arbitrary real values.
Classical density functional theory for finite temperatures is usually formulated in the grand-canonical ensemble where arbitrary variations of the local density are possible. However, in many cases the systems of interest are closed with respect to mass, e.g. canonical systems with fixed temperature and particle number. Although the tools of standard, grand-canonical density functional theory are often used in an ad hoc manner to study closed systems, their formulation directly in the canonical ensemble has so far not been known. In this work, the fundamental theorems underlying classical DFT are revisited and carefully compared in the two ensembles showing that there are only trivial formal differences. The practicality of DFT in the canonical ensemble is then illustrated by deriving the exact Helmholtz functional for several systems: the ideal gas, certain restricted geometries in arbitrary numbers of dimensions and finally a system of two hard-spheres in one dimension (hard rods) in a small cavity. Some remarkable similarities between the ensembles are apparent even for small systems with the latter showing strong echoes of the famous exact of result of Percus in the grand-canonical ensemble.
We study the spin Coulomb drag in a quasi-two-dimensional electron gas beyond the random phase approximation (RPA). We find that the finite transverse width of the electron gas causes a significant reduction of the spin Coulomb drag. This reduction, however, is largely compensated by the enhancement coming from the inclusion of many-body local field effects beyond the RPA, thereby restoring good agreement with the experimental observations by C. P. Weber textit{et al.}, Nature, textbf{437}, 1330 (2005).
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