On Orbits of Automorphism Groups

If G is a finite group and if A is a group of automorphisms of G whose fixed point subgroup is C _G (A) then every subgroup F of C _G (A) acts on the set of orbits of A in G. The peculiarities of this action are used here to derive several results on the number of orbits of A in an economical manner.Original Russian Text Copyright © 2005 Deaconescu M. and Walls G. L.__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 3, pp. 533–537, May–June, 2005.     

Measurement of isotope shifts,fine and hyperfine structure splittings of the lithium D lines

The lithium D lines were studied using a diode laser that was frequency modulated by an electro-optic modulator, to excite an atomic beam. The transmission of part of the laser beam through an etalon was monitored to correct for the nonlinearity of the laser scan. The results for the ^6,7Li 2 S _1/2 and 2 P _1/2 hyperfine splittings agree very well with the best existing data while those for the D1 isotope shift and ^6,7Li fine structure splittings disagree significantly from data obtained by a previous laser atomic beam experiment. Our result for the D1 isotope shift is very close to the latest value computed using Hylleraas variational theory. Received 8 April 2002 / Received in final form 26 June 2002 Published online 21 January 2003 RID="a" ID="a"e-mail: wvw@yorku.ca     

Quantum statistics of multimode parametric amplification

The effect of a multimode interaction on the squeezing attainable in parametric amplification is investigated. In the non degenerate case the maximum squeezing attainable is reduced from the single mode case, whereas in the degenerate case the squeezing is essentially unaffected by the multimode nature of the interaction.     

Higher order effects in the master equation for coupled systems

The usual derivations of the master equation for coupled systems such as the laser make an assumption of weak coupling both for the coupling of the components to their heat baths and for the internal coupling between the components. It is this second condition that we wish to relax. In the usual derivation of the irreversible part of the master equation the approximation is made that the density operator for the coupled system factorizes into a product of the density operators for the two components. However when strong coupling is present, such as in high intensity lasers this approximation is no longer valid. To illustrate how the irreversible part of the master equation may be derived without making the factorization ansatz we consider the case of two coupled boson fields. Our derivation leads to additional terms in the usual master equation arising from correlations between the heat baths introduced by the coupling. This modified master equation yields the correct stationary solution for the density operator of the coupled system, whereas the usual master equation leads to a stationary solution for the density operator correct for the free components only.     

Electrophoretic investigations by laser light scattering

The electrophoresis of various colloidal suspensions has been investigated by laser light scattering. The electric field was applied to the solution by means of a narrow gap electrode configuration using a frequency modulated square wave electric field. The power spectrum of the intensity fluctuations of the scattered light was determined by direct sampling of the light intensity using an A/D converter and an on-line minicomputer. This experimental arrangement is capable of measuring very small Doppler shifts.     

Correlations in stochastic theories of chemical reactions

A comprehensive study of correlations in linear and nonlinear chemical reactions is presented using coupled chemical and diffusion master equations. As a consequence of including correlations in linear reactions the approach to the steady-state Poisson distribution from an initial non-Poissonian distribution is given by a power law rather than the exponential predicted by neglecting correlations. In nonlinear reactions we show that a steadystate Poisson distribution is achieved in small volumes, whereas in large volumes a non-Poissonian distribution is built up via the correlation. The spatial correlation function is calculated for two examples, one which exhibits an instability, the other which exhibits a second-order phase transition, and correlation length and correlation time are calculated and shown to become infinite as the critical point is approached. The critical exponents are found to be classical.     

Detailed balance in open quantum Markoffian systems

Agarwal's definition of detailed balance for open quantum Markoffian systems is shown to arise from microreversibility in an analogous fashion to the familiar classical concept. It is therefore presented as the appropriate formal generalisation of the classical result to the quantum-mechanical regime. This fully quantum-mechanical approach is discussed in relation to the Fokker-Planck equations of the phase-space calculus and the Pauli master equation; two contexts in which a pseudo-classical form of detailed balance is well known. Our discussion is illustrated through the examples of the damped harmonic oscillator and the single mode laser.Supported by a New Zealand U.G.C. Post Graduate Scholarship.     

Quantum fluctuations in Josephson junction comparators

We have developed a method for calculation of quantum fluctuation effects, in particular, of the uncertainty zone developing at the potential curvature sign inversion, for a damped harmonic oscillator with arbitrary time dependence of frequency and for arbitrary temperature, within the Caldeira-Leggett model. The method has been applied to the calculation of the gray zone width Delta Ix of Josephson-junction balanced comparators. The calculated temperature dependence of Delta Ix in the range 1.5 to 4.2 K is in virtually perfect agreement with experimental data for Nb-trilayer comparators with critical current densities of 1.0 and 5.5 kA/cm2, without any fitting parameters.