Two-dimensional Noncommutative Gravitational Quantum Well

In this paper we consider two kinds of noncommutative space-time commutation relations in two-dimensional configuration space and feature the absolute value of the minimal length from the generalized uncertainty relations associated to the particular commutation relations. We study the problem of the two-dimensional gravitational quantum well in the new Hermitian variables and confront the experimental results for the first lowest energy state of the neutrons in the Earth's gravitational field to estimate the upper bounds on the noncommutativity parameters. The absolute value of the minimum length is smaller than a few nanometers.Comment: 12 page

Effects of Securities Transaction Taxes on Depth and Bid-Ask Spread

This paper investigates the effects of transaction taxes on depth and bid-ask spread under asymmetric information. The paper uses a static model where a monopolistic market maker faces liquidity and informed traders. Introducing transaction taxes could, surprisingly, lead to increase in depth. Under some distributional assumptions, when market conditions are favorable to the dealer, the spread responds less than proportionally to an increase in the transaction tax while the depth actually increases. In contrast, when market conditions are unfavorable to the dealer, the spread widens more than proportionally and the depth decreases, potentially to zero, in response to an increase in the transaction tax. Our model sheds light on the disagreement in the empirical literature on the relative magnitude of transaction costs on trading volume.Asymmetric information, Securities transaction taxes, Liquidity

Free energy of formation of clusters of sulphuric acid and water molecules determined by guided disassembly

We evaluate the grand potential of a cluster of two molecular species, equivalent to its free energy of formation from a binary vapour phase, using a nonequilibrium molecular dynamics technique where guide particles, each tethered to a molecule by a harmonic force, move apart to disassemble a cluster into its components. The mechanical work performed in an ensemble of trajectories is analysed using the Jarzynski equality to obtain a free energy of disassembly, a contribution to the cluster grand potential. We study clusters of sulphuric acid and water at 300 K, using a classical interaction scheme, and contrast two modes of guided disassembly. In one, the cluster is broken apart through simple pulling by the guide particles, but we find the trajectories tend to be mechanically irreversible. In the second approach, the guide motion and strength of tethering are modified in a way that prises the cluster apart, a procedure that seems more reversible. We construct a surface representing the cluster grand potential, and identify a critical cluster for droplet nucleation under given vapour conditions. We compare the equilibrium populations of clusters with calculations reported by Henschel et al. [J. Phys. Chem. A 118, 2599 (2014)] based on optimised quantum chemical structures

Orbital symmetry and the optical response of single-layer monochalcogenides

The absorption spectra of single-layer GaSe and GaTe in the hexagonal phase feature exciton peaks with distinct polarization selectivity. We investigate these distinct features from first-principle calculations using the GW-BSE formalisms. We show that the brightness of the exciton absorption peaks is tunable with the polarization of the light. Due to the symmetry of the bands under z-axis mirror symmetry, the bound exciton states selectively couple to either in-plane or out-of-plane polarization of the light. In particular, for a p-polarized light absorption experiment, the absorption peaks of the s-like excitons emerge at large angle of incidence, while the overall absorbance reduces over the rest of the spectrum

Many-Body Electronic Structure of Americium metal

We report computer based simulations of energetics, spectroscopy and electron-phonon interaction of americium using a novel spectral density functional method. This approach gives rise to a new concept of a many-body electronic structure and reveals the unexpected mixed valence regime of Am 5f6 electrons which under pressure acquire the 5f7 valence state. This explains unique properties of Am and addresses the fundamental issue of how the localization delocalization edge is approached from the localized side in a closed shell system.Comment: 4 pages, 3 figure

Ground State Properties of Simple Elements from GW Calculations

A novel self-consistent implementation of Hedin's GW perturbation theory is introduced. This finite-temperature method uses Hartree-Fock wave functions to represent Green's function. GW equations are solved with full potential linear augmented plane wave (FLAPW) method at each iteration of a self-consistent cycle. With our approach we are able to calculate total energy as a function of the lattice parameter. Ground state properties calculated for Na, Al, and Si compare well with experimental data.Comment: 4 pages, 3figure

A Continuous-Discontinuous Second-Order Transition in the Satisfiability of Random Horn-SAT Formulas

We compute the probability of satisfiability of a class of random Horn-SAT formulae, motivated by a connection with the nonemptiness problem of finite tree automata. In particular, when the maximum clause length is 3, this model displays a curve in its parameter space along which the probability of satisfiability is discontinuous, ending in a second-order phase transition where it becomes continuous. This is the first case in which a phase transition of this type has been rigorously established for a random constraint satisfaction problem