Relaxation to quantum equilibrium for Dirac fermions in the de Broglie-Bohm pilot-wave theory

Numerical simulations indicate that the Born rule does not need to be postulated in the de Broglie-Bohm pilot-wave theory, but arises dynamically (relaxation to quantum equilibrium). These simulations were done for a particle in a two-dimensional box whose wave-function obeys the non-relativistic Schroedinger equation and is therefore scalar. The chaotic nature of the de Broglie-Bohm trajectories, thanks to the nodes of the wave-function which act as vortices, is crucial for a fast relaxation to quantum equilibrium. For spinors, we typically do not expect any node. However, in the case of the Dirac equation, the de Broglie-Bohm velocity field has vorticity even in the absence of nodes. This observation raises the question of the origin of relaxation to quantum equilibrium for fermions. In this article, we provide numerical evidence to show that Dirac particles also undergo relaxation, by simulating the evolution of various non-equilibrium distributions for two-dimensional systems (the 2D Dirac oscillator and the Dirac particle in a spherical 2D box).Comment: 11 pages, 9 figure

Fluids confined in wedges and by edges: Virial series for the line-thermodynamic properties of hard spheres

This work is devoted to analyze the relation between the thermodynamic properties of a confined fluid and the shape of its confining vessel. Recently, new insights in this topic were found through the study of cluster integrals for inhomogeneous fluids that revealed the dependence on the vessel shape of the low density behavior of the system. Here, the statistical mechanics and thermodynamics of fluids confined in wedges or by edges is revisited, focusing on their cluster integrals. In particular, the well known hard sphere fluid, which was not studied in this framework so far, is analyzed under confinement and its thermodynamic properties are analytically studied up to order two in the density. Furthermore, the analysis is extended to the confinement produced by a corrugated wall. These results rely on the obtained analytic expression for the second cluster integral of the confined hard sphere system as a function of the opening dihedral angle 0 < β < 2π. It enables a unified approach to both wedges and edges.Fil: Urrutia, Ignacio. Comisión Nacional de Energía Atómica. Centro Atómico Constituyentes; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

LISA Science Results in the Presence of Data Disturbances

Each spacecraft in the Laser Interferometer Space Antenna houses a proof mass which follows a geodesic through spacetime. Disturbances which change the proof mass position, momentum, and/or acceleration will appear in the LISA data stream as additive quadratic functions. These data disturbances inhibit signal extraction and must be removed. In this paper we discuss the identification and fitting of monochromatic signals in the data set in the presence of data disturbances. We also present a preliminary analysis of the extent of science result limitations with respect to the frequency of data disturbances

Fluctuations Do Matter: Large Noise-Enhanced Halos in Charged-Particle Beams

The formation of beam halos has customarily been described in terms of a particle-core model in which the space-charge field of the oscillating core drives particles to large amplitudes. This model involves parametric resonance and predicts a hard upper bound to the orbital amplitude of the halo particles. We show that the presence of colored noise due to space-charge fluctuations and/or machine imperfections can eject particles to much larger amplitudes than would be inferred from parametric resonance alone.Comment: 13 pages total, including 5 figure

Energy and variance optimization of many body wave functions

We present a simple, robust and efficient method for varying the parameters in a many-body wave function to optimize the expectation value of the energy. The effectiveness of the method is demonstrated by optimizing the parameters in flexible Jastrow factors, that include 3-body electron-electron-nucleus correlation terms, for the NO$_2$ and decapentaene (C$_{10}$H$_{12}$) molecules. The basic idea is to add terms to the straightforward expression for the Hessian that are zero when the integrals are performed exactly, but that cancel much of the statistical fluctuations for a finite Monte Carlo sample. The method is compared to what is currently the most popular method for optimizing many-body wave functions, namely minimization of the variance of the local energy. The most efficient wave function is obtained by optimizing a linear combination of the energy and the variance.Comment: 4 pages, 4 figures, minor corrections of inexact statements, missing

Boundary hopping and the mobility edge in the Anderson model in three dimensions

It is shown, using high-precision numerical simulations, that the mobility edge of the 3d Anderson model depends on the boundary hopping term t in the infinite size limit. The critical exponent is independent of it. The renormalized localization length at the critical point is also found to depend on t but not on the distribution of on-site energies for box and Lorentzian distributions. Implications of results for the description of the transition in terms of a local order-parameter are discussed

A Model for the Propagation of Sound in Granular Materials

This paper presents a simple ball-and-spring model for the propagation of small amplitude vibrations in a granular material. In this model, the positional disorder in the sample is ignored and the particles are placed on the vertices of a square lattice. The inter-particle forces are modeled as linear springs, with the only disorder in the system coming from a random distribution of spring constants. Despite its apparent simplicity, this model is able to reproduce the complex frequency response seen in measurements of sound propagation in a granular system. In order to understand this behavior, the role of the resonance modes of the system is investigated. Finally, this simple model is generalized to include relaxation behavior in the force network -- a behavior which is also seen in real granular materials. This model gives quantitative agreement with experimental observations of relaxation.Comment: 21 pages, requires Harvard macros (9/91), 12 postscript figures not included, HLRZ preprint 6/93, (replacement has proper references included

Linear and Non Linear Effects on the Newtonian Gravitational Constant as deduced from the Torsion Balance

The Newtonian gravitational constant has still 150 parts per million of uncertainty. This paper examines the linear and nonlinear equations governing the rotational dynamics of the torsion gravitational balance. A nonlinear effect modifying the oscillation period of the torsion gravitational balance is carefully explored.Comment: 11 pages, 2 figure

Quantum kinetic theory model of a continuous atom laser

We investigate the feasible limits for realising a continuously evaporated atom laser with high-temperature sources. A plausible scheme for realising a truly continuous atom laser is to outcouple atoms from a partially condensed Bose gas, whilst continuously reloading the system with non-condensed thermal atoms and performing evaporative cooling. Here we use quantum kinetic theory to model this system and estimate feasible limits for the operation of such a scheme. For sufficiently high temperatures, the figure of merit for the source is shown to be the phase-space flux. The dominant process limiting the usage of sources with low phase-space flux is the three-body loss of the condensed gas. We conclude that certain double-magneto-optical trap (MOT) sources may produce substantial mean condensate numbers through continuous evaporation, and provide an atom laser source with a narrow linewidth and reasonable flux.Comment: 28 pages, 5 figure

New set of measures to analyze non-equilibrium structures

We introduce a set of statistical measures that can be used to quantify non-equilibrium surface growth. They are used to deduce new information about spatiotemporal dynamics of model systems for spinodal decomposition and surface deposition. Patterns growth in the Cahn-Hilliard Equation (used to model spinodal decomposition) are shown to exhibit three distinct stages. Two models of surface growth, namely the continuous Kardar-Parisi-Zhang (KPZ) model and the discrete Restricted-Solid-On-Solid (RSOS) model are shown to have different saturation exponents