The Formation of Star Clusters II: 3D Simulations of Magnetohydrodynamic Turbulence in Molecular Clouds

(Abridged) We present a series of decaying turbulence simulations that represent a cluster-forming clump within a molecular cloud, investigating the role of magnetic fields on the formation of potential star-forming cores. We present an exhaustive analysis of numerical data from these simulations that includes a compilation of all of the distributions of physical properties that characterize bound cores - including their masses, radii, mean densities, angular momenta, spins, magnetizations, and mass-to-flux ratios. We also present line maps of our models that can be compared with observations. Our simulations range between 5-30 Jeans masses of gas, and are representative of molecular cloud clumps with masses between 100-1000 solar masses. The cores have mass-to-flux ratios that are generally less than that of the original cloud, and so a cloud that is initially highly supercritical can produce cores that are slightly supercritical, similar to that seen by Zeeman measurements of molecular cloud cores. Clouds that are initially only slightly supercritical will instead collapse along the field lines into sheets, and the cores that form as these sheets fragment have a different mass spectrum than what is observed. The spin rates of these cores suggests that subsequent fragmentation into multiple systems is likely. The sizes of the bound cores that are produced are typically 0.02-0.2 pc and have densities in the range 10^4-10^5 cm^{-3} in agreement with observational surveys. Finally, our numerical data allow us to test theoretical models of the mass spectrum of cores, such as the turbulent fragmentation picture of Padoan-Nordlund. We find that while this model gets the shape of the core mass spectrum reasonably well, it fails to predict the peak mass in the core mass spectrum.Comment: Accepted by MNRAS. 28 pages, 16 figures. Substantial revision since last versio

Gravitational waves in preheating

We study the evolution of gravitational waves through the preheating era that follows inflation. The oscillating inflaton drives parametric resonant growth of scalar field fluctuations, and although super-Hubble tensor modes are not strongly amplified, they do carry an imprint of preheating. This is clearly seen in the Weyl tensor, which provides a covariant description of gravitational waves.Comment: 8 pages, 8 figures, Revte

Local contribution of a quantum condensate to the vacuum energy density

We evaluate the local contribution g_[mu nu]L of coherent matter with lagrangian density L to the vacuum energy density. Focusing on the case of superconductors obeying the Ginzburg-Landau equation, we express the relativistic invariant density L in terms of low-energy quantities containing the pairs density. We discuss under which physical conditions the sign of the local contribution of the collective wave function to the vacuum energy density is positive or negative. Effects of this kind can play an important role in bringing about local changes in the amplitude of gravitational vacuum fluctuations - a phenomenon reminiscent of the Casimir effect in QED.Comment: LaTeX, 8 pages. Final journal versio

Exact Perturbations for inflation with smooth exit

Toy models for the Hubble rate or the scalar field potential have been used to analyze the amplification of scalar perturbations through a smooth transition from inflation to the radiation era. We use a Hubble rate that arises consistently from a decaying vacuum cosmology, which evolves smoothly from nearly de Sitter inflation to radiation domination. We find exact solutions for super-horizon perturbations (scalar and tensor), and for sub-horizon perturbations in the vacuum- and radiation-dominated eras. The standard conserved quantity for super-horizon scalar perturbations is exactly constant for growing modes, and zero for the decaying modes.Comment: Minor errors correcte

Critical properties and Bose Einstein Condensation in dimer spin systems

We analyze the spin relaxation time $1/T_1$ for a system made of weakly coupled one dimensional ladders.This system allows to probe the dimensional crossover between a Luttinger liquid and a Bose-Einstein condensateof magnons. We obtain the temperature dependence of $1/T_1$ in the various dimensional regimes, and discuss the experimental consequences.Comment: 4 pages, RevTeX 4, 3 EPS figure

Dissipative Transport of a Bose-Einstein Condensate

We investigate the effects of impurities, either correlated disorder or a single Gaussian defect, on the collective dipole motion of a Bose-Einstein condensate of $^7$Li in an optical trap. We find that this motion is damped at a rate dependent on the impurity strength, condensate center-of-mass velocity, and interatomic interactions. Damping in the Thomas-Fermi regime depends universally on the disordered potential strength scaled to the condensate chemical potential and the condensate velocity scaled to the peak speed of sound. The damping rate is comparatively small in the weakly interacting regime, and the damping in this case is accompanied by strong condensate fragmentation. \textit{In situ} and time-of-flight images of the atomic cloud provide evidence that this fragmentation is driven by dark soliton formation.Comment: 14 pages, 20 figure

(Giant) Vortex - (anti) vortex interaction in bulk superconductors: The Ginzburg-Landau theory

The vortex-vortex interaction potential in bulk superconductors is calculated within the Ginzburg-Landau (GL) theory and is obtained from a numerical solution of a set of two coupled non-linear GL differential equations for the vector potential and the superconducting order parameter, where the merger of vortices into a giant vortex is allowed. Further, the interaction potentials between a vortex and a giant vortex and between a vortex and an antivortex are obtained for both type-I and type-II superconductors. Our numerical results agree asymptotically with the analytical expressions for large inter-vortex separations which are available in the literature. We propose new empirical expressions valid over the full interaction range, which are fitted to our numerical data for different values of the GL parameter

Conditions for one-dimensional supersonic flow of quantum gases

One can use transsonic Bose-Einstein condensates of alkali atoms to establish the laboratory analog of the event horizon and to measure the acoustic version of Hawking radiation. We determine the conditions for supersonic flow and the Hawking temperature for realistic condensates on waveguides where an external potential plays the role of a supersonic nozzle. The transition to supersonic speed occurs at the potential maximum and the Hawking temperature is entirely determined by the curvature of the potential

Transition from synchronous to asynchronous superfluid phase slippage in an aperture array

We have investigated the dynamics of superfluid phase slippage in an array of apertures. The magnitude of the dissipative phase slips shows that they occur simultaneously in all the apertures when the temperature is around 10 mK below the superfluid transition, and subsequently lose their simultaneity as the temperature is lowered. We find that when periodic synchronous phase slippage occurs, the synchronicity exists from the very first phase slip, and therefore is not due to mode locking of interacting oscillators. When the system is allowed to relax freely from a given initial energy, the total number of phase slips that occur and the energy left in the system after the last phase slip depends reproducibly on the initial energy. We find the energy remaining after the final phase slip is a periodic function of the initial system energy. This dependence directly reveals the discrete and dissipative nature of the phase slips and is a powerful diagnostic for investigation of synchronicity in the array. When the array slips synchronously, this periodic energy function is a sharp sawtooth. As the temperature is lowered and the degree of synchronicity drops, the peak of this sawtooth becomes rounded, suggesting a broadening of the time interval over which the array slips. The underlying mechanism for the higher temperature synchronous behavior and the following loss of synchronicity at lower temperatures is not yet understood. We discuss the implications of our measurements and pose several questions that need to be resolved by a theory explaining the synchronous behavior in this quantum system. An understanding of the array phase slip process is essential to the optimization of superfluid `dc-SQUID' gyroscopes and interferometers.Comment: 10 pages, 4 figure