The contribution to the Fokker-Planck eqttation. for the distribution function for gases, due to particle-particle interactions in which the fundamental two-body force obeys an inverse square law, is investigated. The coefficients in the equation, (~) (the average change in velocity in a short time) and f# ~), are obtained using the collision cross sections for such forces. These coefficients are obtained in terms of two fundamental integrals which are dependent on the distribution'function itself. The transformation of the equation to polar c.oordtnates in a case of axial symmetry is carried out. By expanding the distribution function in Legendre functions of the angle the equation is cast into the form of an infinite set of one dimensional coupled nonlinear integra-differential equations. If the distribution function is approximated by a finite series, the reaultant Fokker-~lanck equation may be treated numerically using a compUting machine. Keeping only one or two terms in the series corresponds to the approximations of Chandrasekhar, and Cohen, Spitzer and McRoutly, respectively .

Excitons in vertically stacked type-II quantum dots experience the topological magnetic phase and demonstrate the Aharonov-Bohm oscillations in the emission intensity. Photoluminescence of vertically stacked ZnTe/ZnSe quantum dots is measured in magnetic fields up to 31 T. The Aharonov-Bohm oscillations are found in the magnetic-field dependence of emission intensity. The positions of the peaks of the emission intensity are in a good agreement with numerical simulations of excitons in stacked quantum dots.Comment: 15 page

In a study of the low-temperature anomalies which appear in disordered solids we have measured the specific heat, thermal conductivity, thermal expansion, and dielectric dispersion for a carefully prepared series of (Si02)~"(K20)"and (Si02)~"(Na20)"glasses. Each sample had a known glass transition temperature Tg, mass density, phonon velocities, covalency, and density and concentration fluctuations. The only significant correlation occurred between the phonon mean free path and the glass-transition temperature. No explicit support was found for any model developed to explain the specific heat and/or thermal conductivity of glasses.

No abstract

No abstract