Abrasion of flat rotating shapes

We report on the erosion of flat linoleum "pebbles" under steady rotation in a slurry of abrasive grit. To quantify shape as a function of time, we develop a general method in which the pebble is photographed from multiple angles with respect to the grid of pixels in a digital camera. This reduces digitization noise, and allows the local curvature of the contour to be computed with a controllable degree of uncertainty. Several shape descriptors are then employed to follow the evolution of different initial shapes toward a circle, where abrasion halts. The results are in good quantitative agreement with a simple model, where we propose that points along the contour move radially inward in proportion to the product of the radius and the derivative of radius with respect to angle

Local correlation functional for electrons in two dimensions

We derive a local approximation for the correlation energy in two-dimensional electronic systems. In the derivation we follow the scheme originally developed by Colle and Salvetti for three dimensions, and consider a Gaussian approximation for the pair density. Then, we introduce an ad-hoc modification which better accounts for both the long-range correlation, and the kinetic-energy contribution to the correlation energy. The resulting functional is local, and depends parametrically on the number of electrons in the system. We apply this functional to the homogeneous electron gas and to a set of two-dimensional quantum dots covering a wide range of electron densities and thus various amounts of correlation. In all test cases we find an excellent agreement between our results and the exact correlation energies. Our correlation functional has a form that is simple and straightforward to implement, but broadly outperforms the commonly used local-density approximation

Construction of the B88 exchange-energy functional in two dimensions

We construct a generalized-gradient approximation for the exchange-energy density of finite two-dimensional systems. Guided by non-empirical principles, we include the proper small-gradient limit and the proper tail for the exchange-hole potential. The observed performance is superior to that of the two-dimensional local-density approximation, which underlines the usefulness of the approach in practical applications

Ab-initio angle and energy resolved photoelectron spectroscopy with time-dependent density-functional theory

We present a time-dependent density-functional method able to describe the photoelectron spectrum of atoms and molecules when excited by laser pulses. This computationally feasible scheme is based on a geometrical partitioning that efficiently gives access to photoelectron spectroscopy in time-dependent density-functional calculations. By using a geometrical approach, we provide a simple description of momentum-resolved photoe- mission including multi-photon effects. The approach is validated by comparison with results in the literature and exact calculations. Furthermore, we present numerical photoelectron angular distributions for randomly oriented nitrogen molecules in a short near infrared intense laser pulse and helium-(I) angular spectra for aligned carbon monoxide and benzene.Comment: Accepted for publication on Phys. Rev.

Antibonding Ground state of Adatom Molecules in Bulk Dirac Semimetals

The ground state of the diatomic molecules in nature is inevitably bonding, and its first excited state is antibonding. We demonstrate theoretically that, for a pair of distant adatoms placed buried in three-dimensional-Dirac semimetals, this natural order of the states can be reversed and an antibonding ground state occurs at the lowest energy of the so-called bound states in the continuum. We propose an experimental protocol with the use of a scanning tunneling microscope tip to visualize the topographic map of the local density of states on the surface of the system to reveal the emerging physics

Alloying effects on the optical properties of Ge1−x_{1-x}Six_x nanocrystals from TDDFT and comparison with effective-medium theory

We present the optical spectra of Ge$_{1-x}$Si$_x$ alloy nanocrystals calculated with time-dependent density-functional theory in the adiabatic local-density ap proximation (TDLDA). The spectra change smoothly as a function of the compositio n $x$. On the Ge side of the composition range, the lowest excitations at the ab sorption edge are almost pure Kohn-Sham independent-particle HOMO-LUMO transitio ns, while for higher Si contents strong mixing of transitions is found. Within T DLDA the first peak is slightly higher in energy than in earlier independent-par ticle calculations. However, the absorption onset and in particular its composit ion dependence is similar to independent-particle results. Moreover, classical depolarization effects are responsible for a very strong suppression of the abs orption intensity. We show that they can be taken into account in a simpler way using Maxwell-Garnett classical effective-medium theory. Emission spectra are in vestigated by calculating the absorption of excited nanocrystals at their relaxe d geometry. The structural contribution to the Stokes shift is about 0.5 eV. Th e decomposition of the emission spectra in terms of independent-particle transit ions is similar to what is found for absorption. For the emission, very weak tra nsitions are found in Ge-rich clusters well below the strong absorption onset.Comment: submitted to Phys. Rev.