First-passage time in a bistable potential with colored noise

A precise digital simulation of a bistable system under the effect of colored noise is carried out. A set of data for the mean first-passage time is obtained. The results are interpreted and compared with presently available theories, which are revisited following a new insight. Discrepancies that have been discussed in the literature are understood within our framework.

The infrared behaviour of the static potential in perturbative QCD

The definition of the quark-antiquark static potential is given within an effective field theory framework. The leading infrared divergences of the static singlet potential in perturbation theory are explicitly calculated.

The QCD Potential at O(1/m2): Complete spin-dependent and spin-independent result

Within an effective field theory framework, we obtain an expression, with O(1/m2) accuracy, for the energies of the gluonic excitations between heavy quarks, which holds beyond perturbation theory. For the singlet heavy-quarkantiquark energy, in particular, we also obtain an expression in terms of Wilson loops. This provides, twenty years after the seminal work of Eichten and Feinberg, the first complete expression for the heavy quarkonium potential up to O(1/m2) for pure gluodynamics. Several errors present in the previous literature (also in the work of Eichten and Feinberg) have been corrected. We also briefly discuss the power counting of NRQCD in the nonperturbative regime.

Insight toward the first-passage time in a bistable potential with highly colored noise

The exponential coefficient in the first-passage-time problem for a bistable potential with highly colored noise is predicted to be (8/27 by all existing theories. On the other hand, we show herein that all existing numerical evidence seems to indicate that the coefficient is actually larger by about (4/3, i.e., that the numerical factor in the exponent is approximately (32/81. Existing data cover values of ¿V0/D up to ~20, where V0 is the barrier height, ¿ the correlation time of the noise, and D the noise intensity. We provide an explanation for the modified coefficinet, the explanation also being based on existing numerical simulations. Whether the value (8/27 predicted by all large-¿ theories is achieved for even larger values of ¿V0/D is unknown but appears questionable (except perhaps for enormously large, experimentally inaccessible values of this factor) in view of currently available results.

Dispersionless transport in a washboard potential

We study and characterize a new dynamical regime of underdamped particles in a tilted washboard potential. We find that for small friction in a finite range of forces the particles move essentially nondispersively, that is, coherently, over long intervals of time. The associated distribution of the particle positions moves at an essentially constant velocity and is far from Gaussian-like. This new regime is complementary to, and entirely different from, well-known nonlinear response and large dispersion regimes observed for other values of the external force.

Optical-model potential for electron and positron elastic scattering by atoms

An optical-model potential for systematic calculations of elastic scattering of electrons and positrons by atoms and positive ions is proposed. The electrostatic interaction is determined from the Dirac-Hartree-Fock self-consistent atomic electron density. In the case of electron projectiles, the exchange interaction is described by means of the local-approximation of Furness and McCarthy. The correlation-polarization potential is obtained by combining the correlation potential derived from the local density approximation with a long-range polarization interaction, which is represented by means of a Buckingham potential with an empirical energy-dependent cutoff parameter. The absorption potential is obtained from the local-density approximation, using the Born-Ochkur approximation and the Lindhard dielectric function to describe the binary collisions with a free-electron gas. The strength of the absorption potential is adjusted by means of an empirical parameter, which has been determined by fitting available absolute elastic differential cross-section data for noble gases and mercury. The Dirac partial-wave analysis with this optical-model potential provides a realistic description of elastic scattering of electrons and positrons with energies in the range from ~100 eV up to ~5 keV. At higher energies, correlation-polarization and absorption corrections are small and the usual static-exchange approximation is sufficiently accurate for most practical purposes.

η'-nucleus optical potential and possible η' bound states

Starting from a recent model of the η′N interaction, we evaluate the η ′-nucleus optical potential, including the contribution of lowest order in density, tρ/2mη′, together with the second-order terms accounting for η′ absorption by two nucleons. We also calculate the formation cross section of the η′bound states from (π, p) reactions on nuclei. The η′-nucleus potential suffers from uncertainties tied to the poorly known η′N interaction, which can be partially constrained by the experimental modulus of the η′N scattering length and/or the recently measured transparency ratios in η′nuclear photoproduction. Assuming an attractive interaction and taking the claimed experimental value |aη′N|= 0.1 fm, we obtain an η′optical potential in nuclear matter at saturation density of Vη′=−(8.7 + 1.8i) MeV, not attractive enough to produce η′bound states in light nuclei. Larger values of the scattering length give rise to deeper optical potentials, with moderate enough imaginary parts. For a value |aη′N|= 0.3 fm, which can still be considered to lie within the uncertainties of the experimental constraints, the spectra of light and medium nuclei show clear structures associated to η′-nuclear bound states and to threshold enhancements in the unbound region.

Model-independent bounds for the potential and kinetic energy of liquid 4He at zero temperature

Using the experimental values of the chemical potentials of liquid 4He and of a 3He impurity in liquid 4He, we derive a model-independent lower (upper) bound to the kinetic (potential) energy per particle at zero temperature. The values of the bounds at the experimental saturation density are 13.42 K for the kinetic energy and -20.59 K for the potential energy. All the theoretical calculations based on the Lennard-Jones potential violate the upper-bound condition for the potential energy.

Albert Lewin. Pandora and the Flying Dutchman: the Semiologic Potential of a Greek Myth

Albert Lewin, a well-known Hollywood cinema director who is significantly influenced by the surrealistic movement, brings together the myth f Pandora and the legend of the flying Dutchman in order to create an exemplary love story, a crazy love story which goes beyond the limits of human reason. Bearing in mind, then, that if one wants to believe in this sort of love story must not be guided by human reason stricto sensu, he builds a world of signs, a semiologic world which this article aims at helping to interpret.

Static and dynamic structure of liquid metals: Role of the different parts of the interaction potential

The influence of different parts of the interaction potential on the microscopic behavior of simple liquid metals is investigated by molecular dynamics simulation. The role of the soft-core repulsive, short-range attractive, and long-range oscillatory forces on the properties of liquid lithium close to the triple point is analyzed by comparing the results from simulations of identical systems but truncating the potential at different distances. Special attention is paid to dynamic collective properties such as the dynamic structure factors, transverse current correlation functions, and transport coefficients. It is observed that, in general, the effects of the short-range attractive forces are important. On the contrary, the influence of the oscillatory long-range interactions is considerably less, being the most pronounced for the dynamic structure factor at long wavelengths. The results of this work suggest that the influence of the attractive forces becomes less significant when temperature and density increase.

Liquid-liquid phase transition for soft-core attractive potential

Using event-driven molecular dynamics simulations, we study a three-dimensional one-component system of spherical particles interacting via a discontinuous potential combining a repulsive square soft core and an attractive square well. In the case of a narrow attractive well, it has been shown that this potential has two metastable gas-liquid critical points. Here we systematically investigate how the changes of the parameters of this potential affect the phase diagram of the system. We find a broad range of potential parameters for which the system has both a gas-liquid critical point C1 and a liquid-liquid critical point C2. For the liquid-gas critical point we find that the derivatives of the critical temperature and pressure, with respect to the parameters of the potential, have the same signs: they are positive for increasing width of the attractive well and negative for increasing width and repulsive energy of the soft core. This result resembles the behavior of the liquid-gas critical point for standard liquids. In contrast, for the liquid-liquid critical point the critical pressure decreases as the critical temperature increases. As a consequence, the liquid-liquid critical point exists at positive pressures only in a finite range of parameters. We present a modified van der Waals equation which qualitatively reproduces the behavior of both critical points within some range of parameters, and gives us insight on the mechanisms ruling the dependence of the two critical points on the potential¿s parameters. The soft-core potential studied here resembles model potentials used for colloids, proteins, and potentials that have been related to liquid metals, raising an interesting possibility that a liquid-liquid phase transition may be present in some systems where it has not yet been observed.

Difussion in a titled periodic potential: Enhancement, universality, and scaling

An exact analytical expression for the effective diffusion coefficient of an overdamped Brownian particle in a tilted periodic potential is derived for arbitrary potentials and arbitrary strengths of the thermal noise. Near the critical tilt (threshold of deterministic running solutions) a scaling behavior for weak thermal noise is revealed and various universality classes are identified. In comparison with the bare (potential-free) thermal diffusion, the effective diffusion coefficient in a critically tilted periodic potential may be, in principle, arbitrarily enhanced. For a realistic experimental setup, an enhancement by 14 orders of magnitude is predicted so that thermal diffusion should be observable on a macroscopic scale at room temperature.

Velocity cross-correlations and atomic momentum transfer in simple liquids with different potential cores

Time correlation functions between the velocity of a tagged particle and velocities of particles within specified ranges of initial separations have been obtained by molecular dynamics simulation. These correlation functions have allowed us to analyze the momentum transfer between particles in different coordination shells. Two simple liquids at very different densities and two purely repulsive potentials with very different softnesses have been considered. The longitudinal correlations, which are the velocity cross-correlations along the initial direction defined by the centers of two given particles, have been calculated separately. It has been proven that these correlations should be attributed to particles both in front of and behind the central one. As with propagating longitudinal modes, they are strongly dependent on the softness of the potential core. Some characteristic features of the velocity correlation functions after the initial rise should be related to nonlongitudinal correlations. It has been shown that velocity cross-correlations between distinct particles cannot only be attributed to the direct interactions among particles, but also to the motions induced by the movement of a tagged particle on their neighbors.