Fokker-Planck approximation for N-dimensional nonmarkovian langevin equations

The Fokker-Planck approximation for n-dimensional nonmarkovian Langevin equations is discussed through an expansion in powers of the correlation time of the noise. Exact cases are considered and an application to brownian motion is presented.     

Generalised Ramsey numbers for small graphs

The generalised Ramsey number R(G₁, G₂,..., G_k) is defined as the smallest integer n such that, if the edges of K_n, the complete graph on n vertices, are coloured using k colours C₁, C₂,..., C_k, then for some i(1≤i≤k) there is a subgraph G_i of K_n with all of its edges colour C_i. When G₁=G₂=...,G_k=G, we use the more compact notation R_k(G).The generalised Ramsey numbers R_k(G) are investigated for all graphs G having at most four vertices (and no isolates). This extends the work of Chvátal and Harary, who made this investigation in the case k=2.     

Non-equilibrium quantum statistical mechanics of a damped harmonic oscillator

we give some general remarks on the quantization of systems where the energy operator is not conserved in time. Explicitly, we consider a damped harmonic oscillator and transform the corresponding Schrödinger-Langevin equation to the dual picture where the observables are time dependent but not the states. In this picture the time evolution will be described by a completely positive dynamical semigroup. At finite temperatures the situation is more complicated.     

Solid electrochemical modification of semiconductors

It is shown that the properties of semiconductors can be modified by solid electrochemical cells. These cells can be used as dopant sources for introduction of impurities into the semiconductor lattice. The solid electrolyte is so chosen that the ionic conducting species are the desired dopants. The controllability of the doping operation is very sensitive and either a constant concentration or a specified concentration profile can be achieved. These cells can also be used to modify the semiconductor surfaces such that only limited penetration of impurities is achieved.     

A case of hadwiger's conjecture

Sufficient conditions are established for Hadwiger's Conjecture to be valid in thecase r = 5.     

Observation of helicon-excited electron paramagnetic resonance in a high-mobility semiconductor

Helicon waves can be exploited in EPR studies of localized magnetic moments in high-conductivity semiconductors when the free carriers have small effective mass and high mobility. In an electron plasma helicons have precisely the polarization required to elicit EPR, and the plasma background actually enhances the resonance intensity. Microwave transmission experiments on Hg_1-xMn_xTe, a narrow-gap semiconductor with localized Mn⁺⁺ magnetic moments, are described to illustrate this effect.     

Contribution of inner-sphere reorganization in electron-transfer reaction in solution

A recently published paper in which the inner- and outer-sphere contributions in redox reactions are compared is incorrect. If one uses the experimental values for the force constants, rather than those calculated from the Urey—Bradley method, one finds R_inner = 1.6 R_out, where R represents the reorganization energy.     

Raman and IR spectra of crystalline phosphine in the γ phase

The γ phase of crystalline phosphine has been studied using IR and Raman spectroscopy. The observations include both pure phases, PH₃ and PD₃, and many of the modes of PH₃, PH₂D and PHD₂ dilute in PD₃ as well as of PD₃, PD₂H and PDH₃ dilute in PH₃. The phase transition β → γ is very slow for PH₃, but much more rapid for PD₃.Evidence is adduced pointing to the existence of inequivalent sites in this crystal, but none of a number of suggested models for the unit cell is entirely consistent with the numbers of multiplet components of the internal modes, nor with the numbers of external (lattice) modes observed in the IR and Raman.     

Resonance Raman scattering near a threshold for dissociation

The threshold behavior of Raman amplitudes for photon energies near dissociation of the intermediate potential surface of a diatomic molecule is determined. Structure in the Raman amplitudes is calculated and found to be due to resonance of the intermediate potential surface.