The Scattered Disk as the source of the Jupiter Family comets

The short period Jupiter family comets (JFCs) are thought to originate in the Kuiper Belt; specifically, a dynamical subclass of the Kuiper Belt known as the `scattered disk' is argued to be the dominant source of JFCs. However, the best estimates from observational surveys indicate that this source may fall short by more than two orders of magnitude the estimates obtained from theoretical models of the dynamical evolution of Kuiper belt objects into JFCs. We re-examine the scattered disk as a source of the JFCs and make a rigorous estimate of the discrepancy. We find that the uncertainties in the dynamical models combined with a change in the size distribution function of the scattered disk at faint magnitudes (small sizes) beyond the current observational limit offer a possible but problematic resolution to the discrepancy. We discuss several other possibilities: that the present population of JFCs is a large fluctuation above their long term average, that larger scattered disk objects tidally break-up into multiple fragments during close planetary encounters as their orbits evolve from the trans-Neptune zone to near Jupiter, or that there are alternative source populations that contribute significantly to the JFCs. Well-characterized observational investigations of the Centaurs, objects that are transitioning between the trans-Neptune Kuiper belt region and the inner solar system, can test the predictions of the non-steady state and the tidal break-up hypotheses. The classical and resonant classes of the Kuiper belt are worth re-consideration as significant additional or alternate sources of the JFCs.Comment: 33 pages, 6 figures. Revised Content. To be published in The Astrophysical Journa

Superfluidity and binary-correlations within clusters of fermions

We propose a method for simulating the behaviour of small clusters of particles that explicitly accounts for all mean-field and binary-correlation effects. Our approach leads to a set of variational equations that can be used to study both the dynamics and thermodynamics of these clusters. As an illustration of this method, we explore the BCS-BEC crossover in the simple model of four fermions, interacting with finite-range potentials, in a harmonic potential. We find, in the crossover regime, that the particles prefer to occupy two distinct pair states as opposed to the one assumed by BCS theory

Dilute Bose gas with correlated disorder: A Path Integral Monte Carlo study

We investigate the thermodynamic properties of a dilute Bose gas in a correlated random potential using exact path integral Monte Carlo methods. The study is carried out in continuous space and disorder is produced in the simulations by a 3D speckle pattern with tunable intensity and correlation length. We calculate the shift of the superfluid transition temperature due to disorder and we highlight the role of quantum localization by comparing the critical chemical potential with the classical percolation threshold. The equation of state of the gas is determined in the regime of strong disorder, where superfluidity is suppressed and the normal phase exists down to very low temperatures. We find a $T^2$ dependence of the energy in agreement with the expected behavior in the Bose glass phase. We also discuss the major role played by the disorder correlation length and we make contact with a Hartree-Fock mean-field approach that holds valid if the correlation length is very large. The density profiles are analyzed as a function of temperature and interaction strength. Effects of localization and the depletion of the order parameter are emphasized in the comparison between local condensate and total density. At very low temperature we find that the energy and the particle distribution of the gas are very well described by the T=0 Gross-Pitaevskii theory even in the regime of very strong disorder.Comment: 27 pages, 20 figure

Equation of state of an interacting Bose gas at finite temperature: a Path Integral Monte Carlo study

By using exact Path Integral Monte Carlo methods we calculate the equation of state of an interacting Bose gas as a function of temperature both below and above the superfluid transition. The universal character of the equation of state for dilute systems and low temperatures is investigated by modeling the interatomic interactions using different repulsive potentials corresponding to the same s-wave scattering length. The results obtained for the energy and the pressure are compared to the virial expansion for temperatures larger than the critical temperature. At very low temperatures we find agreement with the ground-state energy calculated using the diffusion Monte Carlo method.Comment: 7 pages, 6 figure

Quasi-one-dimensional Bose gases with large scattering length

Bose gases confined in highly-elongated harmonic traps are investigated over a wide range of interaction strengths using quantum Monte Carlo techniques. We find that the properties of a Bose gas under tight transverse confinement are well reproduced by a 1d model Hamiltonian with contact interactions. We point out the existence of a unitary regime, where the properties of the quasi-1d Bose gas become independent of the actual value of the 3d scattering length. In this unitary regime, the energy of the system is well described by a hard rod equation of state. We investigate the stability of quasi-1d Bose gases with positive and negative 3d scattering length.Comment: 5 pages, 3 figure

Stochastic Paleoclimatology: Modeling the EPICA Ice Core Climate Records

We analyze and model the stochastic behavior of paleoclimate time series and assess the implications for the coupling of climate variables during the Pleistocene glacial cycles. We examine 800 kyr of carbon dioxide, methane, nitrous oxide, and temperature proxy data from the EPICA Dome-C ice core, which are characterized by 100~kyr glacial cycles overlain by fluctuations across a wide range of time scales. We quantify this behavior through multifractal time-weighted detrended fluctuation analysis, which distinguishes near red-noise and white-noise behavior below and above the 100~kyr glacial cycle respectively in all records. This allows us to model each time series as a one-dimensional periodic non-autonomous stochastic dynamical system, and assess the stability of physical processes and the fidelity of model-simulated time series. We extend this approach to a four-variable model with linear coupling terms, which we interpret in terms of the interrelationships between the time series. Methane and nitrous oxide are found to have significant destabilizing influences, while carbon dioxide and temperature have smaller stabilizing influences. We draw conclusions about causal relationships in glacial transitions and the climate processes that may have facilitated these couplings, and highlight opportunities to further develop stochastic modeling approaches.Comment: 14 pages, 6 figure

Can Minor Planets be Used to Assess Gravity in the Outer Solar System?

The twin Pioneer spacecraft have been tracked for over thirty years as they headed out of the solar system. After passing 20 AU from the Sun, both exhibited a systematic error in their trajectories that can be interpreted as a constant acceleration towards the Sun. This Pioneer Effect is most likely explained by spacecraft systematics, but there have been no convincing arguments that that is the case. The alternative is that the Pioneer Effect represents a real phenomenon and perhaps new physics. What is lacking is a means of measuring the effect, its variation, its potential anisotropies, and its region of influence. We show that minor planets provide an observational vehicle for investigating the gravitational field in the outer solar system, and that a sustained observation campaign against properly chosen minor planets could confirm or refute the existence of the Pioneer Effect. Additionally, even if the Pioneer Effect does not represent a new physical phenomenon, minor planets can be used to probe the gravitational field in the outer Solar System and since there are very few intermediate range tests of gravity at the multiple AU distance scale, this is a worthwhile endeavor in its own right.Comment: Accepted for publication in The Astrophysical Journa

Anomalous fluctuations of the condensate in interacting Bose gases

We find that the fluctuations of the condensate in a weakly interacting Bose gas confined in a box of volume $V$ follow the law $\sim V^{4/3}$. This anomalous behaviour arises from the occurrence of infrared divergencies due to phonon excitations and holds also for strongly correlated Bose superfluids. The analysis is extended to an interacting Bose gas confined in a harmonic trap where the fluctuations are found to exhibit a similar anomaly.Comment: 4 pages, RevTe