Statistical mechanics of violent relaxation in stellar systems

We discuss the statistical mechanics of violent relaxation in stellar systems following the pioneering work of Lynden-Bell (1967). The solutions of the gravitational Vlasov-Poisson system develop finer and finer filaments so that a statistical description is appropriate to smooth out the small-scales and describe the ``coarse-grained'' dynamics. In a coarse-grained sense, the system is expected to reach an equilibrium state of a Fermi-Dirac type within a few dynamical times. We describe in detail the equilibrium phase diagram and the nature of phase transitions which occur in self-gravitating systems. Then, we introduce a small-scale parametrization of the Vlasov equation and propose a set of relaxation equations for the coarse-grained dynamics. These relaxation equations, of a generalized Fokker-Planck type, are derived from a Maximum Entropy Production Principle (MEPP). We make a link with the quasilinear theory of the Vlasov-Poisson system and derive a truncated model appropriate to collisionless systems subject to tidal forces. With the aid of this kinetic theory, we qualitatively discuss the concept of ``incomplete relaxation'' and the limitations of Lynden-Bell's theory

Schrödinger-Poisson-Vlasov-Poisson correspondence

The Schr\"odinger-Poisson equations describe the behavior of a superfluid Bose-Einstein condensate under self-gravity with a 3D wave function. As $\hbar/m\to 0$, $m$ being the boson mass, the equations have been postulated to approximate the collisionless Vlasov-Poisson equations also known as the collisionless Boltzmann-Poisson equations. The latter describe collisionless matter with a 6D classical distribution function. We investigate the nature of this correspondence with a suite of numerical test problems in 1D, 2D, and 3D along with analytic treatments when possible. We demonstrate that, while the density field of the superfluid always shows order unity oscillations as $\hbar/m\to 0$ due to interference and the uncertainty principle, the potential field converges to the classical answer as $(\hbar/m)^{2}$. Thus, any dynamics coupled to the superfluid potential is expected to recover the classical collisionless limit as $\hbar/m\to 0$. The quantum superfluid is able to capture rich phenomena such as multiple phase-sheets, shell-crossings, and warm distributions. Additionally, the quantum pressure tensor acts as a regularizer of caustics and singularities in classical solutions. This suggests the exciting prospect of using the Schr\"odinger-Poisson equations as a low-memory method for approximating the high-dimensional evolution of the Vlasov-Poisson equations. As a particular example we consider dark matter composed of ultra-light axions, which in the classical limit ($\hbar/m\to 0$) is expected to manifest itself as collisionless cold dark matter

Forming Planetesimals in Solar and Extrasolar Nebulae

Planets are built from planetesimals: solids larger than a kilometer which grow by colliding pairwise. Planetesimals themselves are unlikely to form by two-body collisions; sub-km objects have gravitational fields individually too weak, and electrostatic attraction is too feeble for growth beyond a few cm. We review the possibility that planetesimals form when self-gravity brings together vast ensembles of small particles. Even when self-gravity is weak, aerodynamic processes can accumulate solids relative to gas, paving the way for gravitational collapse. Particles pile up as they drift radially inward. Gas turbulence stirs particles, but can also seed collapse by clumping them. While the feedback of solids on gas triggers vertical shear instabilities that obstruct self-gravity, this same feedback triggers streaming instabilities that strongly concentrate particles. Numerical simulations find that solids 10-100 cm in size gravitationally collapse in turbulent disks. We outline areas for progress, including the possibility that still smaller objects self-gravitate.Comment: To appear in Annual Reviews. This review is intended to be both current and pedagogical. Incorporates suggestions from the community; further comments welcome. v2: Single-space

Dynamical Boson Stars

The idea of stable, localized bundles of energy has strong appeal as a model for particles. In the 1950s John Wheeler envisioned such bundles as smooth configurations of electromagnetic energy that he called {\em geons}, but none were found. Instead, particle-like solutions were found in the late 1960s with the addition of a scalar field, and these were given the name {\em boson stars}. Since then, boson stars find use in a wide variety of models as sources of dark matter, as black hole mimickers, in simple models of binary systems, and as a tool in finding black holes in higher dimensions with only a single killing vector. We discuss important varieties of boson stars, their dynamic properties, and some of their uses, concentrating on recent efforts.Comment: 79 pages, 25 figures, invited review for Living Reviews in Relativity; major revision in 201

On Landau damping

Going beyond the linearized study has been a longstanding problem in the theory of Landau damping. In this paper we establish exponential Landau damping in analytic regularity. The damping phenomenon is reinterpreted in terms of transfer of regularity between kinetic and spatial variables, rather than exchanges of energy; phase mixing is the driving mechanism. The analysis involves new families of analytic norms, measuring regularity by comparison with solutions of the free transport equation; new functional inequalities; a control of nonlinear echoes; sharp scattering estimates; and a Newton approximation scheme. Our results hold for any potential no more singular than Coulomb or Newton interaction; the limit cases are included with specific technical effort. As a side result, the stability of homogeneous equilibria of the nonlinear Vlasov equation is established under sharp assumptions. We point out the strong analogy with the KAM theory, and discuss physical implications.Comment: News: (1) the main result now covers Coulomb and Newton potentials, and (2) some classes of Gevrey data; (3) as a corollary this implies new results of stability of homogeneous nonmonotone equilibria for the gravitational Vlasov-Poisson equatio

Leakage current induced anomalies in the photoluminescence of GaAs coupled quantum wells

We have performed photoluminescence experiments on GaAs/AlGaAs coupled quantum wells as a function of bias voltage and photoexcitation intensity. Spatially indirect recombination appears at higher electric fields for weak photoexcitation instead of the spatially direct one which is dominant at zero bias voltage. However, for strong photoexcitation with photon energy larger than the band gap of the barrier layers, the spatially direct recombination remains dominant over a wide range of bias voltage. Under this condition, the exciton ring emission is observed in the PL image at positive biases for which a large leakage current flows through the device. These results suggest that the 2DEGs induced by the large leakage current is important for interpreting the behavior of the ring emission. (C) 2004 WILEY-VCH Verlag GmbH & Co. KGaA. Weinheim