Finite size melting of spherical solid-liquid aluminium interfaces

We have investigated the melting of nano-sized cone shaped aluminium needles coated with amorphous carbon using transmission electron microscopy. The interface between solid and liquid aluminium was found to have spherical topology. For needles with fixed apex angle, the depressed melting temperature of this spherical interface, with radius $R$, was found to scale linearly with the inverse radius $1/R$. However, by varying the apex angle of the needles we show that the proportionality constant between the depressed melting temperature and the inverse radius changes significantly. This lead us to the conclusion that the depressed melting temperature is not controlled solely by the inverse radius $1/R$. Instead we found a direct relation between the depressed melting temperature and the ratio between the solid-liquid interface area and the molten volume.Comment: to appear in Philosophical Magazine (2009

Asymmetric Bethe-Salpeter equation for pairing and condensation

The Martin-Schwinger hierarchy of correlations are reexamined and the three-particle correlations are investigated under various partial summations. Besides the known approximations of screened, ladder and maximally crossed diagrams the pair-pair correlations are considered. It is shown that the recently proposed asymmetric Bethe-Salpeter equation to avoid unphysical repeated collisions is derived as a result of the hierarchical dependencies of correlations. Exceeding the parquet approximation we show that an asymmetry appears in the selfconsistent propagators. This form is superior over the symmetric selfconsistent one since it provides the Nambu-Gorkov equations and gap equation for fermions and the Beliaev equations for bosons while from the symmetric form no gap equation results. The selfenergy diagrams which account for the subtraction of unphysical repeated collisions are derived from the pair-pair correlation in the three-particle Greenfunction. It is suggested to distinguish between two types of selfconsistency, the channel-dressed propagators and the completely dressed propagators, with the help of which the asymmetric expansion completes the Ward identity and is $\Phi$-derivable.Comment: 12 pages. 26 figure

Analysis of linear and nonlinear conductivity of plasma-like systems on the basis of the Fokker-Planck equation

The problems of high linear conductivity in an electric field, as well as nonlinear conductivity, are considered for plasma-like systems. First, we recall several observations of nonlinear fast charge transport in dusty plasma, molecular chains, lattices, conducting polymers and semiconductor layers. Exploring the role of noise we introduce the generalized Fokker-Planck equation. Second, one-dimensional models are considered on the basis of the Fokker-Planck equation with active and passive velocity-dependent friction including an external electrical field. On this basis it is possible to find the linear and nonlinear conductivities for electrons and other charged particles in a homogeneous external field. It is shown that the velocity dependence of the friction coefficient can lead to an essential increase of the electron average velocity and the corresponding conductivity in comparison with the usual model of constant friction, which is described by the Drude-type conductivity. Applications including novel forms of controlled charge transfer and non-Ohmic conductance are discussed.Comment: 14 pages with 6 figure

Asymmetric Primitive-Model Electrolytes: Debye-Huckel Theory, Criticality and Energy Bounds

Debye-Huckel (DH) theory is extended to treat two-component size- and charge-asymmetric primitive models, focussing primarily on the 1:1 additive hard-sphere electrolyte with, say, negative ion diameters, a--, larger than the positive ion diameters, a++. The treatment highlights the crucial importance of the charge-unbalanced ``border zones'' around each ion into which other ions of only one species may penetrate. Extensions of the DH approach which describe the border zones in a physically reasonable way are exact at high $T$ and low density, $\rho$, and, furthermore, are also in substantial agreement with recent simulation predictions for \emph{trends} in the critical parameters, $T_c$ and $\rho_c$, with increasing size asymmetry. Conversely, the simplest linear asymmetric DH description, which fails to account for physically expected behavior in the border zones at low $T$, can violate a new lower bound on the energy (which applies generally to models asymmetric in both charge and size). Other recent theories, including those based on the mean spherical approximation, have predicted trends in the critical parameters quite opposite to those established by the simulations.Comment: to appear in Physical Review

Nonlinear relaxation field in charged systems under high electric fields

The influence of an external electric field on the current in charged systems is investigated. The results from the classical hierarchy of density matrices are compared with the results from the quantum kinetic theory. The kinetic theory yields a systematic treatment of the nonlinear current beyond linear response. To this end the dynamically screened and field-dependent Lenard-Balescu equation is integrated analytically and the nonlinear relaxation field is calculated. The classical linear response result known as Debye - Onsager relaxation effect is only obtained if asymmetric screening is assumed. Considering the kinetic equation of one specie the other species have to be screened dynamically while the screening with the same specie itself has to be performed statically. Different other approximations are discussed and compared.Comment: language correction