Quantum diffusion

Basic ideas and results which characterize quantum diffusion of defects in quantum crystals like solid helium as a new phenomenon are presented. Quantum effects in such media lead to a delocalization of point defects (vacancies, impurities etc.) and they turn into quasiparticles of a new type—defectons, which are characterized not by their position in the crystal lattice but by their quasimomentum and dispersion law. Defecton-defecton and defecton-phonon scattering are considered and an interpolation formula for the diffusion coefficient valid in all interesting temperature and concentration regions is presented. A comparison with the experimental data is made. Some alternative points of view are discussed in detail and the inconsistency of the Kisvarsanyi-Sullivan theory is shown.     

Intermolecular interactions of p-nitrophenol with butyl acetate,according to IR spectroscopic data

Infrared difference spectroscopy has been used to study the association of p-nitrophenol (NP) with butyl acetate (BA) in CCl₄ and in undiluted BA. It has been shown that in CCl₄, an associate is formed, [NP·BA] ·BA (Ia), in which one molecule of BA is linked to the NP by a hydrogen bond, and the second BA molecule is linked to the H-complex NP·BA by outer-sphere (dipole-dipole) interaction. In undiluted BA with low concentrations of NP, (Ia) is formed; with high concentrations of NP, an associate [(NP)₂BA] ·mBA is formed, in which two molecules of NP are bonded successively to each other and with a BA molecule; and the number of outer-sphere BA molecules may depend on the concentration of free BA molecules in the solutions.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 3, pp. 593–599, March, 1991.     

Calibration of a basket option model applied to company valuation

Applying real options thinking to company valuation seems theoretically and intuitively appealing. However, the real option analogy of a single European option as well as the compound option proxy perform poorly when applied to company valuation. We therefore suggest to rework the building blocks of real option applications to corporate valuation.  We introduce a framework to delineate the distribution of the underlying asset in the risk neutral world, which is important in order to value any derivative. This is achieved by an algorithm to calibrate a basket option model using real world data of observed share prices. The fitting takes account of the class of stable distributions. The index of stability of asymmetric α stable distribution serves as an over-all parameter to characterise the specific distribution.     

Asymptotic expansions of integrals of two Bessel functions via the generalized hypergeometric and Meijer functions

Asymptotic expansions of certain finite and infinite integrals involving products of two Bessel functions of the first kind are obtained by using the generalized hypergeometric and Meijer functions. The Bessel functions involved are of arbitrary (generally different) orders, but of the same argument containing a parameter which tends to infinity. These types of integrals arise in various contexts, including wave scattering and crystallography, and are of general mathematical interest being related to the Riemann—Liouville and Hankel integrals. The results complete the asymptotic expansions derived previously by two different methods — a straightforward approach and the Mellin-transform technique. These asymptotic expansions supply practical algorithms for computing the integrals. The leading terms explicitly provide valuable analytical insight into the high-frequency behavior of the solutions to the wave-scattering problems.     

Rigidity of the scattering length spectrum

In this paper we consider properties of obstacles satisfying some non-degeneracy conditions that can be recovered from the scattering length spectrum (SLS). Clearly the latter tells us whether the obstacle K is trapping or non-trapping. If the set of trapped points is relatively small, then the SLS also determines the volume of the obstacle, the number of its connected components, and whether its boundary is convex everywhere or it has non-trivial concavities. Under the additional assumption that the curvature of the obstacle does not vanish of infinite order, it is proved that from the SLS one can recover certain information about the number of reflection points of any simply reflecting ray in the exterior of the obstacle. Finally, for some special classes of obstacles (e.g. star-shaped ones), it is shown that the SLS completely determines the obstacle. Received: 2 March 1999 / Revised version: 16 January 2001 / Published online: 5 September 2002     

On the interpretation of the RHEED intensity oscillations during the growth of vicinal faces

A quantitative treatment of the crystallization kinetics in MBE growth of vicinal surfaces results the relation l ²=2D _sK between the surface diffusion coefficient D _s, the time for a monolayer deposition and the interstep distance l at which the RHEED intensity oscillations disappear. The correction factor K depends on the size and the energy of the two-dimensional critical nucleus and it is estimated to be smaller than 10^–2. The currently used interpretation of the RHEED intensity oscillations ignores the correction factor K and, therefore, the calculated values of D _s are several orders of magnitude smaller than its real values. The surface transport during the time of growth interruption is discussed in connection with the tendency to three dimensional growth at every second interface (where a deposition of the material with strong intermolecular bonds starts) of a small period superlattice.