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 However when strong coupling is present, such as in high intensity lasers this approximation is no longer valid.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.     

Measurement of dipolar couplings in partially oriented molecules by local field NMR spectroscopy with low-power decoupling

Low-power phase-modulated Lee–Goldburg homonuclear decoupling was used to record PDLF spectra of fluorine-substituted benzene derivatives dissolved in nematic thermotropic liquid crystalline solvents. The low-power decoupling minimizes sample heating during RF irradiation while still achieving highly resolved PDLF spectra. The method is illustrated by recording spectra for 1,3-dichloro-4-fluoro-5-nitrobenzene, 1,3-dichloro-4-fluorobenzene, and 1,2-difluorobenzene dissolved in different nematic solvents.