Absence of a Finite-Temperature Melting Transition in the Classical Two-Dimensional One-Component Plasma

Vortices in thin-film superconductors are often modelled as a system of particles interacting via a repulsive logarithmic potential. Arguments are presented to show that the hypothetical (Abrikosov) crystalline state for such particles is unstable at any finite temperature against proliferation of screened disclinations. The correlation length of crystalline order is predicted to grow as $\sqrt{1/T}$ as the temperature $T$ is reduced to zero, in excellent agreement with our simulations of this two-dimensional system.Comment: 3 figure

Non-ergodic effects in the Coulomb glass: specific heat

We present a numerical method for the investigation of non-ergodic effects in the Coulomb glass. For that, an almost complete set of low-energy many-particle states is obtained by a new algorithm. The dynamics of the sample is mapped to the graph formed by the relevant transitions between these states, that means by transitions with rates larger than the inverse of the duration of the measurement. The formation of isolated clusters in the graph indicates non-ergodicity. We analyze the connectivity of this graph in dependence on temperature, duration of measurement, degree of disorder, and dimensionality, studying how non-ergodicity is reflected in the specific heat.Comment: Submited Phys. Rev.

Fluctuations of the correlation dimension at metal-insulator transitions

We investigate numerically the inverse participation ratio, $P_2$, of the 3D Anderson model and of the power-law random banded matrix (PRBM) model at criticality. We found that the variance of $\ln P_2$ scales with system size $L$ as $\sigma^2(L)=\sigma^2(\infty)-A L^{-D_2/2d}$, being $D_2$ the correlation dimension and $d$ the system dimension. Therefore the concept of a correlation dimension is well defined in the two models considered. The 3D Anderson transition and the PRBM transition for $b=0.3$ (see the text for the definition of $b$) are fairly similar with respect to all critical magnitudes studied.Comment: RevTex, 5 pages, 4 eps figures, to be published in Phys. Rev. Let

Dielectric susceptibility of the Coulomb-glass

We derive a microscopic expression for the dielectric susceptibility $\chi$ of a Coulomb glass, which corresponds to the definition used in classical electrodynamics, the derivative of the polarization with respect to the electric field. The fluctuation-dissipation theorem tells us that $\chi$ is a function of the thermal fluctuations of the dipole moment of the system. We calculate $\chi$ numerically for three-dimensional Coulomb glasses as a function of temperature and frequency

Uncorrelated scattering approximation for the scattering and break-up of weakly bound nuclei on heavy targets

The scattering of a weakly bound (halo) projectile nucleus by a heavy target nucleus is investigated. A new approach, called the Uncorrelated Scattering Approximation, is proposed. The main approximation involved is to neglect the correlation between the fragments of the projectile in the region where the interaction with the target is important. The formalism makes use of hyper-spherical harmonics, Raynal-Revay coefficients and momentum-localized wave functions to expand projectile channel wave functions in terms of products of the channel wave function of the individual fragments. Within this approach, the kinetic energy and angular momentum of each fragment is conserved during the scattering process. The elastic, inelastic and break-up S-matrices are obtained as an analytic combination involving the bound wave function of the projectile and the product of the S-matrices of the fragments. The approach is applied to describe the scattering of deuteron on $^{58}$Ni at several energies. The results are compared with experimental data and continuum-discretized coupled-channels calculations.Comment: 34 pages, 5 figures, accepted for publication in Nucl. Phys.

Factorizing operators on Banach function spaces through spaces of multiplication operators

In order to extend the theory of optimal domains for continuous operators on a Banach function space X(μ) over a finite measure μ, we consider operators T satisfying other type of inequalities than the one given by the continuity which occur in several well-known factorization theorems (for instance, Pisier Factorization Theorem through Lorentz spaces, pth-power factorable operators . . . ). We prove that such a T factorizes through a space of multiplication operators which can be understood in a certain sense as the optimal domain for T . Our extended optimal domain technique does not need necessarily the equivalence between μ and the measure defined by the operator T and, by using δ-rings, μ is allowed to be infinite. Classical and new examples and applications of our results are also given, including some new results on the Hardy operator and a factorization theorem through Hilbert spaces.Generalitat Valenciana TSGD-07Ministerio de Educación y Ciencia MTM2006-13000-C03-0

Dielectric susceptibility of the Coulomb-glass

We derive a microscopic expression for the dielectric susceptibility X of a Coulomb glass, which corresponds to the definition used in classical electrodynamics, the derivative of the polarization with respect to the electric field. The fluctuation–dissipation theorem tells us that is a function of the thermal fluctuations of the dipole moment of the system. We calculate X numerically for three–dimensional Coulomb glasses as a function of temperature and frequency.We acknowledge financial support from the DGES project number PB96-1118, SMWK, and DFG (SFB 393). A great part of this work was performed during A. D.-S.’s visit at the IFW Dresden; A. D.-S. thanks the IFW for its hospitality