Kinetic theory for scalar fields with nonlocal quantum coherence

We derive quantum kinetic equations for scalar fields undergoing coherent evolution either in time (coherent particle production) or in space (quantum reflection). Our central finding is that in systems with certain space-time symmetries, quantum coherence manifests itself in the form of new spectral solutions for the dynamical 2-point correlation function. This spectral structure leads to a consistent approximation for dynamical equations that describe coherent evolution in presence of decohering collisions. We illustrate the method by solving the bosonic Klein problem and the bound states for the nonrelativistic square well potential. We then compare our spectral phase space definition of particle number to other definitions in the nonequilibrium field theory. Finally we will explicitly compute the effects of interactions to coherent particle production in the case of an unstable field coupled to an oscillating background.Comment: 33 pages, 7 figures, replaced with the version published in JHE

Formation and Evolution of Binary Asteroids

Satellites of asteroids have been discovered in nearly every known small body population, and a remarkable aspect of the known satellites is the diversity of their properties. They tell a story of vast differences in formation and evolution mechanisms that act as a function of size, distance from the Sun, and the properties of their nebular environment at the beginning of Solar System history and their dynamical environment over the next 4.5 Gyr. The mere existence of these systems provides a laboratory to study numerous types of physical processes acting on asteroids and their dynamics provide a valuable probe of their physical properties otherwise possible only with spacecraft. Advances in understanding the formation and evolution of binary systems have been assisted by: 1) the growing catalog of known systems, increasing from 33 to nearly 250 between the Merline et al. (2002) Asteroids III chapter and now, 2) the detailed study and long-term monitoring of individual systems such as 1999 KW4 and 1996 FG3, 3) the discovery of new binary system morphologies and triple systems, 4) and the discovery of unbound systems that appear to be end-states of binary dynamical evolutionary paths. Specifically for small bodies (diameter smaller than 10 km), these observations and discoveries have motivated theoretical work finding that thermal forces can efficiently drive the rotational disruption of small asteroids. Long-term monitoring has allowed studies to constrain the system's dynamical evolution by the combination of tides, thermal forces and rigid body physics. The outliers and split pairs have pushed the theoretical work to explore a wide range of evolutionary end-states.Comment: 42 pages, 4 figures, contribution to the Asteroids 4 boo

Evolution of central dark matter of early-type galaxies up to z ~ 0.8

We investigate the evolution of dark and luminous matter in the central regions of early-type galaxies (ETGs) up to z ~ 0.8. We use a spectroscopically selected sample of 154 cluster and field galaxies from the EDisCS survey, covering a wide range in redshifts (z ~ 0.4-0.8), stellar masses ($\log M_{\star}/ M_{\odot}$ ~ 10.5-11.5 dex) and velocity dispersions ($\sigma_{\star}$ ~ 100-300 \, km/s). We obtain central dark matter (DM) fractions by determining the dynamical masses from Jeans modelling of galaxy aperture velocity dispersions and the $M_{\star}$ from galaxy colours, and compare the results with local samples. We discuss how the correlations of central DM with galaxy size (i.e. the effective radius, $R_{\rm e}$), $M_{\star}$ and $\sigma_{\star}$ evolve as a function of redshift, finding clear indications that local galaxies are, on average, more DM dominated than their counterparts at larger redshift. This DM fraction evolution with $z$ can be only partially interpreted as a consequence of the size-redshift evolution. We discuss our results within galaxy formation scenarios, and conclude that the growth in size and DM content which we measure within the last 7 Gyr is incompatible with passive evolution, while it is well reproduced in the multiple minor merger scenario. We also discuss the impact of the IMF on our DM inferences and argue that this can be non-universal with the lookback time. In particular, we find the Salpeter IMF can be better accommodated by low redshift systems, while producing stellar masses at high-$z$ which are unphysically larger than the estimated dynamical masses (particularly for lower-$\sigma_{\star}$ systems).Comment: 14 pages, 6 figures, 3 tables, MNRAS in pres

Spinor dynamics in an antiferromagnetic spin-1 thermal Bose gas

We present experimental observations of coherent spin-population oscillations in a cold thermal, Bose gas of spin-1 sodium-23 atoms. The population oscillations in a multi-spatial-mode thermal gas have the same behavior as those observed in a single-spatial-mode antiferromagnetic spinor Bose Einstein condensate. We demonstrate this by showing that the two situations are described by the same dynamical equations, with a factor of two change in the spin-dependent interaction coefficient, which results from the change to particles with distinguishable momentum states in the thermal gas. We compare this theory to the measured spin population evolution after times up to a few hundreds of ms, finding quantitative agreement with the amplitude and period. We also measure the damping time of the oscillations as a function of magnetic field.Comment: 5 pages, 3 figure

The Einstein Equations of Evolution - A Geometric Approach

In this paper the exterior Einstein equations are explored from a differential geometric point of view. Using methods of global analysis and infinite-dimensional geometry, we answer sharply the question: "In what sense are the Einstein equations, written as equations of evolution, a Lagrangian dynamical system?" By using our global methods, several aspects of the lapse function and shift vector field are clarified. The geometrical significance of the shift becomes apparent when the Einstein evolution equations are written using Lie derivatives. The evolution equations are then interpreted as evolution equations as seen by an observer in space coordinates. Using the notion of body-space transitions, we then find the relationship between solutions with different shifts by finding the flow of a time-dependent vector field. The use of body and space coordinates is shown to be somewhat analogous to the use of such coordinates in Euler's equations for a rigid body and the use of Eulerian and Lagrangian coordinates in hydrodynamics. We also explore the geometry of the lapse function, and show how one can pass from one lapse function to another by integrating ordinary differential equations. This involves integrating what we call the "intrinsic shift vector field." The essence of our method is to extend the usual configuration space [fraktur M]=Riem(M) of Riemannian metrics to [script T]×[script D]×[fraktur M], where [script T]=C[infinity](M,R) is the group of relativistic time translations and [script D]=Diff(M) is the group of spatial coordinate transformations of M. The lapse and shift then enter the dynamical picture naturally as the velocities canonically conjugate to the configuration fields (xit,etat)[is-an-element-of][script T]×[script D]. On this extended configuration space, a degenerate Lagrangian system is constructed which allows precisely for the arbitrary specification of the lapse and shift functions. We reinterpret a metric given by DeWitt for [fraktur M] as a degenerate metric on [script D]×[fraktur M]. On [script D]×[fraktur M], however, the metric is quadratic in the velocity variables. The groups [script T] and [script D] also serve as symmetry groups for our dynamical system. We establish that the associated conserved quantities are just the usual "constraint equations." A precise theorem is given for a remark of Misner that in an empty space-time we must have [script H]=0. We study the relationship between the evolution equations for the time-dependent metric gt and the Ricci flat condition of the reconstructed Lorentz metric gL. Finally, we make some remarks about a possible "superphase space" for general relativity and how our treatment on [script T]×[script D]×[fraktur M] is related to ordinary superspace and superphase space

Asymmetric collapse by dissolution or melting in a uniform flow

An advection--diffusion-limited dissolution model of an object being eroded by a two-dimensional potential flow is presented. By taking advantage of the conformal invariance of the model, a numerical method is introduced that tracks the evolution of the object boundary in terms of a time-dependent Laurent series. Simulations of a variety of dissolving objects are shown, which shrink and then collapse to a single point in finite time. The simulations reveal a surprising exact relationship whereby the collapse point is the root of a non-analytic function given in terms of the flow velocity and the Laurent series coefficients describing the initial shape. This result is subsequently derived using residue calculus. The structure of the non-analytic function is examined for three different test cases, and a practical approach to determine the collapse point using a generalized Newton--Raphson root-finding algorithm is outlined. These examples also illustrate the possibility that the model breaks down in finite time prior to complete collapse, due to a topological singularity, as the dissolving boundary overlaps itself rather than breaking up into multiple domains (analogous to droplet pinch-off in fluid mechanics). In summary, the model raises fundamental mathematical questions about broken symmetries in finite-time singularities of both continuous and stochastic dynamical systems.Comment: 20 pages, 11 figure