Thermal projector

We introduce the thermal projectors as in (56) and find the equation of motion for the reduced density matrix ps of system 1... 

We have already encountered the projection operator formalism in Appendix 9A, where an apphcation to the simplest system-bath problem—a single level interacting with a continuum, was demonstrated. This formalism is general can be applied in different ways and flavors. In general, a projection operator (or projector) P is defined with respect to a certain sub-space whose choice is dictated by the physical problem. By definition it should satisfy the relationship = P (operators that satisfy this relationship are called idempotent), but other than that can be chosen to suit our physical intuition or mathematical approach. For problems involving a system interacting with its equilibrium thermal environment a particularly convenient choice is the thermal projector. An operator that projects the total system-bath density operator on a product of the system s reduced density operator and the... 

The last term on the right-hand side of Eq. (10.100) also has a clear physical interpretation This is a contribution to force exerted on the system at time t, associated with the initial (Z = Zo) correlations between the system and the bath embedded in the term Qp tf). There are many situations where this contribution to the relevant time evolution can be disregarded, at least at long time, and it is identically zero if 2p(to) = 0. The last situation appears when P is the thermal projector (10.87) if we assume that until time Zo the system and bath were uncoupled with the bath kept at thermal equilibrium. 

We end this discussion with two comments. First, we note that the Nakajima-Zwanzig equation (10.100) is exact no approximations whatever were made in its derivation. Second, this identity can be used in many ways, depending on the choice of the projection operator P. The thermal projector (10.87) is a physically motivated choice. In what follows we present a detailed derivation of the quantum master equation using this projector and following steps similar to those taken above, however, we will sacrifice generality in order to get practical usable results. 

Derivation of the quantum master equation using the thermal projector... 

Gemini North Observatory/CTI Mode-locked SFG Laser. CTT is developing the first commercial solid-state Na LGS system. It will be installed on the center section of the 8-m Gemini North telescope, with the output beam relayed to a projector behind the secondary mirror. The projected beam is required to be 10-20 W power, with M2 < 1.5. The architecture is based on sum-frequency mixing two mode-locked solid-state Nd YAG lasers. The mode-locked format provides significantly higher peak intensity than CW, enabling more efficient SFG conversion. The laser is also free of the thermal and intensity transients that are inherent in the macro pulse format. The chosen... 

One major problem is that heated structures cool down during inspection, so that defects disappear rapidly. Thus storing of thermographs is essential. It was found that the relationship between the size of a hot spot on a thermograph and the size of a defect is a complex function of the defect depth and the thermal properties of the composite material inspected [82]. Impact energies of 6.00 J on 1.14 mm thick graphite poxy plates, heated to 15 C above room temperature with a 1 second pulse from one 1000 W projector, have been detected by thermography [73]. 

F-MAS condition to analyse polymorphs of YAFG peptides [21] (Fig. 2.9). Obtained NMR structural constraints combined with theoretical gauge-including projector augmented wave (GIFAW) calculation data were used to deduce a molecular arrangement of peptides in the crystal lattice after thermal rearrangement. 

Formulations similar to those used in Dry Silver but without the AgX component are light stable but can be imaged thermally. The silver behenate develops to form a black silver image where (and only where) heat is applied. Materials of this type were originally intended for reflex exposure. Here the film is sandwiched with a document and exposed to a source of infrared radiation. The ink on the document absorbs the infrared and converts it to heat, which initiates development of the film, where it is in contact with the ink image on the paper. Overhead projector transparencies, sometimes called view graphs, ... 

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