Dynamics of Dissipative Quantum Systems--from Path Integrals to Master Equations

The path integral approach offers not only an exact expression for the non- equilibrium dynamics of dissipative quantum systems, but is also a convenient starting point for perturbative treatments. An alternative way to explore the influence of friction in the quantum realm is based on master equations which require, however, in one or the other aspect approximations. Here it is discussed under which conditions and limitations Markovian master equations can be derived from exact path integrals thus providing a firm basis for their applicability.Comment: 10 pages, 1 figur

Direct reduction of synthetic rutile using the FFC process to produce low-cost novel titanium alloys

Typically, pure TiO2 in pellet form has been utilised as the feedstock for the production of titanium metal via the solid state extraction FFC process. For the first time, this paper reports the use of loose synthetic rutile powder as the feedstock, along with its full characterisation at each stage of the reduction. The kinetics and mechanism of the reduction of synthetic rutile to a low oxygen titanium alloy have been studied in detail using a combination of X-ray diffraction, scanning electron microscopy, oxygen analysis, and X-ray fluorescence techniques. Partial reductions of synthetic rutile enabled a reaction pathway to be determined, with full reduction to a low oxygen titanium alloy occurring at 16 h. Major remnant elements from the Becher process within the feedstock were followed throughout the process, with a particular emphasis placed on the reduction behaviour of iron within the alloy. Although impurities such as Fe, Al, and Mn are found in the feedstock and alloy, no major deviations from previously reported reaction mechanisms and phase transformations utilising a pure porous (25–30 % porosity) TiO2 precursor were found. Following reduction, the titanium alloy powder produced from synthetic rutile (approx. 3500 ppm oxygen) has been consolidated via an emerging rapid sintering technique, and its microstructure analysed. This work will act as the baseline for future alloy development projects aimed at producing low-cost titanium alloys directly from synthetic rutile. Producing titanium alloys directly from synthetic rutile may negate the use of master alloy additions to Ti in the future