Small-Angle X-ray and neutron scattering from diamond single crystals

Results of Small-Angle Scattering study of diamonds with various types of point and extended defects and different degrees of annealing are presented. It is shown that thermal annealing and/or mechanical deformation cause formation of nanosized planar and threedimensional defects giving rise to Small-Angle Scattering. The defects are often facetted by crystallographic planes 111, 100, 110, 311, 211 common for diamond. The scattering defects likely consist of clusters of intrinsic and impurity-related defects; boundaries of mechanical twins also contribute to the SAS signal. There is no clear correlation between concentration of nitrogen impurity and intensity of the scattering.Comment: 6 pages, 5 figures; presented at SANS-YuMO User Meeting 2011, Dubna, Russi

Universally-composable privacy amplification from causality constraints

We consider schemes for secret key distribution which use as a resource correlations that violate Bell inequalities. We provide the first security proof for such schemes, according to the strongest notion of security, the so called universally-composable security. Our security proof does not rely on the validity of quantum mechanics, it solely relies on the impossibility of arbitrarily-fast signaling between separate physical systems. This allows for secret communication in situations where the participants distrust their quantum devices.Comment: 4 page

A New Look at Pricing of the Russian Option

The “Russian option” was introduced and calculated with the help of the solution of the optimal stopping problem for a two-dimensional Markov process in [10]. This paper proposes a new derivation of the general results [10]. The key idea is to introduce the dual martingale measure which permits one to reduce the “two-dimensional” optimal stopping problem to a “one-dimensional” one. This approach simplifies the discussion and explain the simplicity of the answer found in [10]

Modification of Nanodiamonds by Xenon Implantation: A Molecular Dynamics Study

Xenon implantation into nanodiamonds is studied using molecular dynamics. The nanodiamonds range in size from 2-10 nm and the primary knock-on (PKA) energy extends up to 40 keV. For small nanodiamonds an energy-window effect occurs in which PKA energies of around 6 keV destroy the nanodiamond, while in larger nanodiamonds the radiation cascade is increasingly similar to those in bulk material. Destruction of the small nanodiamonds occurs due to thermal annealing associated with the small size of the particles and the absence of a heat-loss path. Simulations are also performed for a range of impact parameters, and for a series of double-nanodiamond systems in which a heat-loss path is present. The latter show that the thermal shock caused by the impact occurs on the timescale of a few picoseconds. These findings are relevant to ion-beam modification of nanoparticles by noble gases as well as meteoritic studies where implantation is proposed as the mechanism for xenon incorporation in pre-solar nanodiamonds

Almost Sure Convergence of Solutions to Non-Homogeneous Stochastic Difference Equation

We consider a non-homogeneous nonlinear stochastic difference equation X_{n+1} = X_n (1 + f(X_n)\xi_{n+1}) + S_n, and its important special case X_{n+1} = X_n (1 + \xi_{n+1}) + S_n, both with initial value X_0, non-random decaying free coefficient S_n and independent random variables \xi_n. We establish results on \as convergence of solutions X_n to zero. The necessary conditions we find tie together certain moments of the noise \xi_n and the rate of decay of S_n. To ascertain sharpness of our conditions we discuss some situations when X_n diverges. We also establish a result concerning the rate of decay of X_n to zero.Comment: 22 pages; corrected more typos, fixed LaTeX macro