Silicon isotopes: from cosmos to benthos

Silicon is the second most abundant element on the Earth and one of the more abundant elements in our Solar System. Variations in the relative abundance of the stable isotopes of Si (Si isotope fractionation) in different natural reservoirs, both terrestrial (surface and deep Earth) as well as extra-terrestrial (e.g. meteorites, lunar samples), are a powerful tracer of present and past processes involving abiotic as well as biotic systems. The versatility of the Si isotope tracer is reflected in its wide-ranging applications from understanding the origin of early Solar System objects, planetary differentiation, Moon formation, mantle melting and magma differentiation on the Earth, ancient sea-water composition, to modern-day weathering, clay formation and biological fractionation on land as well as in the oceans. The application of Si isotopes as tracers of natural processes started over six decades ago and its usage has seen a sudden increase over the last decade due to improvements in mass spectrometry, particularly the advent of multi-collector inductively coupled plasma mass spectrometers, which has made Si isotope measurements safe and relatively easy while simultaneously improving the accuracy and precision of measurements.

Directed Nonabelian Sandpile Models on Trees

We define two general classes of nonabelian sandpile models on directed trees (or arborescences), as models of nonequilibrium statistical physics. Unlike usual applications of the well-known abelian sandpile model, these models have the property that sand grains can enter only through specified reservoirs. In the Trickle-down sandpile model, sand grains are allowed to move one at a time. For this model, we show that the stationary distribution is of product form. In the Landslide sandpile model, all the grains at a vertex topple at once, and here we prove formulas for all eigenvalues, their multiplicities, and the rate of convergence to stationarity. The proofs use wreath products and the representation theory of monoids.

Statistics of an adiabatic charge pump

We investigate the effect of time-dependent cyclic-adiabatic driving on the charge transport in a quantum junction. We propose a nonequilibrium Green's function formalism to study the statistics of the charge pumped (at zero bias) through the junction. The formulation is used to demonstrate charge pumping in a single electronic level coupled to two (electronic) reservoirs with time-dependent couplings. An analytical expression for the average pumped current for a general cyclic driving is derived. It is found that for zero bias, for a certain class of driving, the Berry phase contributes only to the odd cumulants. In contrast, a quantum master equation formulation does not show a Berry-phase effect at all.

Isotopes in cosmochemistry: recipe for a Solar System

Extreme isotopic variations among extraterrestrial materials provide great insights into the origin and evolution of the Solar System. In this tutorial review, we summarize how the measurement of isotope ratios can expand our knowledge of the processes that took place before and during the formation of our Solar System and its subsequent early evolution. The continuous improvement of mass spectrometers with high precision and increased spatial resolution, including secondary ion mass spectrometry (SIMS), thermal ionization mass spectrometry (TIMS) and multi collector-inductively coupled plasma-mass spectrometry (MC-ICP-MS), along with the ever growing amounts of available extraterrestrial samples have significantly increased the temporal and spatial constraints on the sequence of events that took place since and before the formation of the first Solar System condensates (i.e., Ca-Al-rich inclusions). Grains sampling distinct stellar environments with a wide range of isotopic compositions were admixed to, but possibly not fully homogenized in, the Sun's parent molecular cloud or the nascent Solar System. Before, during and after accretion of the nebula, as well as the formation and subsequent evolution of planetesimals and planets, chemical and physical fractionation processes irrevocably changed the chemical and isotopic compositions of all Solar System bodies. Since the formation of the first Solar System minerals and rocks 4.568 Gyr ago, short-and long-lived radioactive decay and cosmic ray interaction also contributed to the modification of the isotopic framework of the Solar System, and permit to trace the formation and evolution of directly accessible and inferred planetary and stellar isotopic reservoirs.