Supergoop Dynamics

We initiate a systematic study of the dynamics of multi-particle systems with supersymmetric Van der Waals and electron-monopole type interactions. The static interaction allows a complex continuum of ground state configurations, while the Lorentz interaction tends to counteract this configurational fluidity by magnetic trapping, thus producing an exotic low temperature phase of matter aptly named supergoop. Such systems arise naturally in $\mathcal{N}=2$ gauge theories as monopole-dyon mixtures, and in string theory as collections of particles or black holes obtained by wrapping D-branes on internal space cycles. After discussing the general system and its relation to quiver quantum mechanics, we focus on the case of three particles. We give an exhaustive enumeration of the classical and quantum ground states of a probe in an arbitrary background with two fixed centers. We uncover a hidden conserved charge and show that the dynamics of the probe is classically integrable. In contrast, the dynamics of one heavy and two light particles moving on a line shows a nontrivial transition to chaos, which we exhibit by studying the Poincar\'e sections. Finally we explore the complex dynamics of a probe particle in a background with a large number of centers, observing hints of ergodicity breaking. We conclude by discussing possible implications in a holographic context.Comment: 35 pages,11 figures. v2: updated references to include a previous proof of classical integrability, exchanged a figure for a prettier versio

Planet Populations as a Function of Stellar Properties

Exoplanets around different types of stars provide a window into the diverse environments in which planets form. This chapter describes the observed relations between exoplanet populations and stellar properties and how they connect to planet formation in protoplanetary disks. Giant planets occur more frequently around more metal-rich and more massive stars. These findings support the core accretion theory of planet formation, in which the cores of giant planets form more rapidly in more metal-rich and more massive protoplanetary disks. Smaller planets, those with sizes roughly between Earth and Neptune, exhibit different scaling relations with stellar properties. These planets are found around stars with a wide range of metallicities and occur more frequently around lower mass stars. This indicates that planet formation takes place in a wide range of environments, yet it is not clear why planets form more efficiently around low mass stars. Going forward, exoplanet surveys targeting M dwarfs will characterize the exoplanet population around the lowest mass stars. In combination with ongoing stellar characterization, this will help us understand the formation of planets in a large range of environments.Comment: Accepted for Publication in the Handbook of Exoplanet