Energy spectrum open systems

The subsurface liquid phase generally is an open system and its composition is a result of dynamic transformation of dissolved constituents in various chemical species over a range of reaction time scales. At any particular time the liquid phase is an electrolyte solution, potentially containing a broad spectrum of inorganic and organic ions and nonionized molecules. The presently accepted description of the energy characteristics of the liquid phase is based on the concept of matrix and osmotic potentials. The matrix potential is due to the attraction of water to the solid matrix, while the osmotic potential is due to the presence of solute in the subsurface water. 

The results of open-system pyrolysis (Rock-Eval II) have been used to specify the kinetic parameters controlling maturation. Hydrocarbon yield rates as determined by these experiments are shown in Fig. 6.9a. Both nonlinear optimization technique (Levenberg-Marquardt method Press et al. 1986 Issler and Snowdon 1990) and linear methods are used to determine the values of the reaction parameters Aj, Ej, andX, . This technique minimizes an error function by comparing the hydrocaibon release rates, Sj, calculated by Eq. 6.9 and those rates measured in open-system pyrolysis. An example of the spectrum of activation energies obtained from this analysis is shown in Fig. 6.9b. 

The particle density in an isolated bounded system is required to be zero at the boundary point at infinity. This introduces gaps (or discreteness) in the excitation spectrum, at low energy, which are not present in extended systems. The presence of shell structure, and whether the shells are open or closed, is... 

Figure 6.9 Generic five-state system for ultrafast efficient switching. The resonant two-state system of Figure 6.6 is extended by three target states for selective excitation. While the intermediate target state 4) is in exact two-photon resonance with the laser pulse, both outer target states 3) and 5) lie well outside the bandwidth of the two-photon spectrum. Therefore, these states are energetically inaccessible under weak-field excitation. Intense femtosecond laser pulses, however, utilize the resonant AC Stark effect to modify the energy landscape. As a result, new excitation pathways open up, enabling efficient population transfer to the outer target states as well.

Another remark is that the resonances exist only below the line defined by (2.18) and (2.19) so that there is a gap between the real energy axis and the resonance spectrum. This is the feature of a strongly open scattering system in which the decay process is ultrafast. This gap is given in terms of the topological pressure that is the leading zero, so(E) = P(fi E), of the inverse Ruelle zeta function,... 

Such considerations led to the early solar-system picture of the atom, in which an electron presumably revolved about the nucleus in one or another definite orbit but was unable to take a position between the orbits when the electron shifted from an outer orbit to an inner orbit, nearer the positively charged nucleus, it would give off the energy detected in the spectra. (It was an open question why an electron would be allowed in one orbit or another and yet be prohibited from taking an intermediate position between the orbits.) Bohr used such a picture and, with classical physical laws, drew up equations that described the supposed motion of the electron in its circular orbit. Using simple assumptions, he successfully explained the structure of the hydrogen spectrum. 

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