Transition non-resonant

Beyond the systems and applications described in this chapter, projection-operator methods can, for example, be used to study the dynamics near glass transitions [77] and the propagation of wave functions in systems with non-resonant transitions. The latter application has recently been analyzed in connection with the decomposition of the spectral density [78] showing the wide range of applicability of the proposed schemes. 

It is known from experiments Gordiets et al. (1988) that in a vibrationally excited gas, near-resonant vibrational energy exchanges between molecules of the same chemical species proceed much faster than non-resonant transitions between different molecules, as well as transfers of vibrational energy to other modes and chemical reactions. Therefore the following relation between the characteristic relaxation times is fulfilled ... 

W2 will increase until A21 + 21 becomes negligible and then tiz/ni = gifgi- The required radiation densities are therefore about 10-100 mW for a resonant transition (/ = 0.1-1) and 1 W/cm for a non-resonant transition (/ = 0.001). Furthermore, the use of a continuous wave laser allows tii to be maximum and the use of multistep excitation may be helpful especially when high-energy terms (Rydberg states) have to be populated. 

Quasi-resonant and resonant transition switching power supplies have a much more attractive radiated spectral shape. This is because the transitions are forced to be at a lower frequency by the resonant elements, hence only the low frequency spectral components are exhibited (below 30MHz). The lower rate of change during the transitions are responsible for behavior. The higher frequency spectral components are almost non existent. The near-held radiated spectrum of a quasi-resonant, hyback converter are shown in Figure E-2. The quasi-resonant and soft switching families of converters are much quieter and easier to hlter. 

We chose a setup with a monochromatic IR field at resonance with the vibrational transition frequency in oscillator Vi, at, which is different from the transition frequency in oscillator V2, C02, and assumed that non-resonant effects can be neglected. The ultrashort UV pulse was approximated by a delta pulse ( A = 0). 

Taking the phonon source out of equilibrium at a certain frequency range may lead to enhancement in Ipc. On a speculative level, one may visualize shining the electrons with a high intensity beam of non-equilibrium phonons with a narrow frequency range around, say, w0. Icc, resulting from resonant transitions, will be significantly affected only when u>o is close to the differences e — Cj or c( — C(. The effect on the Debye-Waller factor will be small for a narrow-band beam. In this way, Icc will initially increase with the intensity of this radiation, until decoherence effects will take over and Ipc will disappear. 

The inner-shell hole 4d, produced by photoexcitation is filled by a non-radiative transition (radiative decay is negligible). Therefore, the resonance has a certain mean lifetime t which corresponds to a natural width T of approximately 114 meV for the xenon 4d5/2 -> 6p resonance. Autoionization produces many final ionic states, and the important branches are given by... 

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