All-optical determination of initial oxidation of Si(100) and its kinetics

By comparison of measured and ab initio calculated surface optical spectra we demonstrate that two main oxidation processes initially occur after dissociation of oxygen molecules, forming in both cases Si–O–Si entities: (i) breaking of Si dimers by incorporation of oxygen atoms; (ii) incorporation into the silicon backbonds. The kinetics up to half-monolayer coverage is determined, and explained in terms of Langmuir-like adsorption mechanisms with different probabilities.     

Geometry and electronic band structure of surfaces: the case of Ge(111):Sn and C(111)

We present an ab initio study of two semiconductor surfaces, the α phase of Sn on Ge(111) and the cleavage surface of diamond. The theoretical tools used (density functional theory (DFT) and many-body perturbation theory) are discussed in detail, and the advantages and disadvantages of the two approaches are pointed out. We show that in the case of diamond it is essential to go beyond the DFT single-particle approach, and to introduce quasiparticle effects through the GW approximation. PACS 73.20.-r; 73.20.At; 71.15.Mb     

Many-body perturbation theory using the density-functional concept: beyond the GW approximation

We propose an alternative formulation of many-body perturbation theory that uses the density-functional concept. Instead of the usual four-point integral equation for the polarizability, we obtain a two-point one, which leads to excellent optical absorption and energy-loss spectra. The corresponding three-point vertex function and self-energy are then simply calculated via an integration, for any level of approximation. Moreover, we show the direct impact of this formulation on the time-dependent density-functional theory. Numerical results for the band gap of bulk silicon and solid argon illustrate corrections beyond the GW approximation for the self-energy.     

Pricing vulnerable European options with stochastic default barriers

CF Lo and KC Ku Institute of Theoretical Physics and Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong, China Email: cho-hoi_hui{at}hkma.gov.hk Received on 31 July 2006. Accepted on 15 March 2007. This paper develops a valuation model of European options incorporatinga stochastic default barrier, which extends a constant defaultbarrier proposed in the Hull–White model. The defaultbarrier is considered as an option writer's liability. Closed-formsolutions of vulnerable European option values based on themodel are derived to study the impact of the stochastic defaultbarriers on option values. The numerical results show that negativecorrelation between the firm values and the stochastic defaultbarriers of option writers gives material reductions in optionvalues where the options are written by firms with leverageratios corresponding to BBB or BB ratings.     

Action functional and quasi‐potential for the burgers equation in a bounded interval

Consider the viscous Burgers equation u_t + f(u)_x = εu_xx on the interval [0,1] with the inhomogeneous Dirichlet boundary conditions u(t,0) = ρ₀, u(t,1) = ρ₁. The flux f is the function f(u) = u(1 − u), ε > 0 is the viscosity, and the boundary data satisfy 0 < ρ₀ < ρ₁ < 1. We examine the quasi‐potential corresponding to an action functional arising from nonequilibrium statistical mechanical models associated with the above equation. We provide a static variational formula for the quasi‐potential and characterize the optimal paths for the dynamical problem. In contrast with previous cases, for small enough viscosity, the variational problem defining the quasi‐potential admits more than one minimizer. This phenomenon is interpreted as a nonequilibrium phase transition and corresponds to points where the superdifferential of the quasi‐potential is not a singleton. © 2011 Wiley Periodicals, Inc.     

Coexistence of negatively and positively buckled isomers on n+-doped Si(111) − 2 × 1

A long-standing puzzle regarding the Si(111) ? 2 × 1 surface has been solved. The surface energy gap previously determined by photoemission on heavily n-doped crystals was not compatible with a strongly bound exciton known from other considerations to exist. New low-temperature angle-resolved photoemission and scanning tunneling microscopy data, together with theory, unambiguously reveal that isomers with opposite bucklings and different energy gaps coexist on such surfaces. The subtle energetics between the isomers, dependent on doping, leads to a reconciliation of all previous results.