On the inequivalence of statistical ensembles

We investigate the relation between various statistical ensembles of finite systems. If ensembles differ at the level of fluctuations of the order parameter, we show that the equations of states can present major differences. A sufficient condition for this inequivalence to survive at the thermodynamical limit is worked out. If energy consists in a kinetic and a potential part, the microcanonical ensemble does not converge towards the canonical ensemble when the partial heat capacities per particle fulfill the relation $c_{k}^{-1}+c_{p}^{-1}<0$.Comment: 4 pages, 4 figure

On the Resolution of the Time-Like Singularities in Reissner-Nordstrom and Negative-Mass Schwarzschild

Certain time-like singularities are shown to be resolved already in classical General Relativity once one passes from particle probes to scalar waves. The time evolution can be defined uniquely and some general conditions for that are formulated. The Reissner-Nordstrom singularity allows for communication through the singularity and can be termed "beam splitter" since the transmission probability of a suitably prepared high energy wave packet is 25%. The high frequency dependence of the cross section is w^{-4/3}. However, smooth geometries arbitrarily close to the singular one require a finite amount of negative energy matter. The negative-mass Schwarzschild has a qualitatively different resolution interpreted to be fully reflecting. These 4d results are similar to the 2d black hole and are generalized to an arbitrary dimension d>4.Comment: 47 pages, 5 figures. v2: See end of introduction for an important note adde

Transient backbending behavior in the Ising model with fixed magnetization

The physical origin of the backbendings in the equations of state of finite but not necessarily small systems is studied in the Ising model with fixed magnetization (IMFM) by means of the topological properties of the observable distributions and the analysis of the largest cluster with increasing lattice size. Looking at the convexity anomalies of the IMFM thermodynamic potential, it is shown that the order of the transition at the thermodynamic limit can be recognized in finite systems independently of the lattice size. General statistical mechanics arguments and analytical calculations suggest that the backbending in the caloric curve is a transient behaviour which should not converge to a plateau in the thermodynamic limit, while the first order transition is signalled by a discontinuity in other observables.Comment: 24 pages, 11 figure

Accelerating electromagnetic magic field from the C-metric

Various aspects of the C-metric representing two rotating charged black holes accelerated in opposite directions are summarized and its limits are considered. A particular attention is paid to the special-relativistic limit in which the electromagnetic field becomes the "magic field" of two oppositely accelerated rotating charged relativistic discs. When the acceleration vanishes the usual electromagnetic magic field of the Kerr-Newman black hole with gravitational constant set to zero arises. Properties of the accelerated discs and the fields produced are studied and illustrated graphically. The charges at the rim of the accelerated discs move along spiral trajectories with the speed of light. If the magic field has some deeper connection with the field of the Dirac electron, as is sometimes conjectured because of the same gyromagnetic ratio, the "accelerating magic field" represents the electromagnetic field of a uniformly accelerated spinning electron. It generalizes the classical Born's solution for two uniformly accelerated monopole charges.Comment: 22 pages, 5 figure

Premelting of Thin Wires

Recent work has raised considerable interest on the nature of thin metallic wires. We have investigated the melting behavior of thin cylindrical Pb wires with the axis along a (110) direction, using molecular dynamics and a well-tested many-body potential. We find that---in analogy with cluster melting---the melting temperature $T_m (R)$ of a wire with radius $R$ is lower than that of a bulk solid, $T_m^b$, by $T_m (R) = T_m^b -c/R$. Surface melting effects, with formation of a thin skin of highly diffusive atoms at the wire surface, is observed. The diffusivity is lower where the wire surface has a flat, local (111) orientation, and higher at (110) and (100) rounded areas. The possible relevance to recent results on non-rupturing thin necks between an STM tip and a warm surface is addressed.Comment: 10 pages, 4 postscript figures are appended, RevTeX, SISSA Ref. 131/94/CM/S

The Approach to Ergodicity in Monte Carlo Simulations

The approach to the ergodic limit in Monte Carlo simulations is studied using both analytic and numerical methods. With the help of a stochastic model, a metric is defined that enables the examination of a simulation in both the ergodic and non-ergodic regimes. In the non-ergodic regime, the model implies how the simulation is expected to approach ergodic behavior analytically, and the analytically inferred decay law of the metric allows the monitoring of the onset of ergodic behavior. The metric is related to previously defined measures developed for molecular dynamics simulations, and the metric enables the comparison of the relative efficiencies of different Monte Carlo schemes. Applications to Lennard-Jones 13-particle clusters are shown to match the model for Metropolis, J-walking and parallel tempering based approaches. The relative efficiencies of these three Monte Carlo approaches are compared, and the decay law is shown to be useful in determining needed high temperature parameters in parallel tempering and J-walking studies of atomic clusters.Comment: 17 Pages, 7 Figure

Molecular dynamics simulation of the order-disorder phase transition in solid NaNO2_2

We present molecular dynamics simulations of solid NaNO$_2$ using pair potentials with the rigid-ion model. The crystal potential surface is calculated by using an \emph{a priori} method which integrates the \emph{ab initio} calculations with the Gordon-Kim electron gas theory. This approach is carefully examined by using different population analysis methods and comparing the intermolecular interactions resulting from this approach with those from the \emph{ab initio} Hartree-Fock calculations. Our numerics shows that the ferroelectric-paraelectric phase transition in solid NaNO$_2$ is triggered by rotation of the nitrite ions around the crystallographical c axis, in agreement with recent X-ray experiments [Gohda \textit{et al.}, Phys. Rev. B \textbf{63}, 14101 (2000)]. The crystal-field effects on the nitrite ion are also addressed. Remarkable internal charge-transfer effect is found.Comment: RevTeX 4.0, 11 figure

Electrically tunable solid-state silicon nanopore ion filter

We show that a nanopore in a silicon membrane connected to a voltage source can be used as an electrically tunable ion filter. By applying a voltage between the heavily doped semiconductor and the electrolyte, it is possible to invert the ion population inside the nanopore and vary the conductance for both cations and anions in order to achieve selective conduction of ions even in the presence of significant surface charges in the membrane. Our model based on the solution of the Poisson equation and linear transport theory indicates that in narrow nanopores substantial gain can be achieved by controlling electrically the width of the charge double layer

Coalescence of nanoscale metal clusters: Molecular-dynamics study

We study the coalescence of nanoscale metal clusters in an inert-gas atmosphere using constant-energy molecular dynamics. The coalescence proceeds via atomic diffusion with the release of surface energy raising the temperature. If the temperature exceeds the melting point of the coalesced cluster, a molten droplet forms. If the temperature falls between the melting point of the larger cluster and those of the smaller clusters, a metastable molten droplet forms and freezes.Comment: 5 figure