Coherent Pumping of Vibrations

So far the up-pumping models discussed above describe the behavior of molecules in a thermalized field of incoherent phonons. With incoherent vibrational up-pumping, the vibrational population grows linearly in time until the populations (Eq. 11) or quasitemperatures (Eq. 12) equalize [50]. 

There is a formal similarity in the mathematics used to describe vibrational transitions pumped by a resonant radiation field [148] and vibrational transitions pumped by phonons in a crystal lattice. In the lowest-order approximations, the radiation field and the vibrational transition are coupled by a transition dipole matrix element that is a linear function of a coordinate. The transition dipole describes charge displacement that occurs during the transition. Some of the cubic anharmonic coupling terms described by Eq. (10) result in a similar coupling between vibrational transitions and a phonon coordinate. These generally have the form / vibVph, so that the energy of the vibration with normal coordinate /vib is linearly proportional to the phonon coordinate /ph. Thus either an incoherent photon field or an incoherent phonon field can result in incoherent 

There are several unresolved issues in the problem of coherent vibrational pumping by shock fronts. These include (1) to what degree can a shock front be viewed as a coherent phonon source (2) can a shock front coherently drive vibrational excitations, and (3) could shock front coherent pumping cause selective bond breaking, especially bonds other than those broken by ordinary thermochemical reactions One way to look at the first issue is to look at the shock front as a superposition of phonons. Since phonons form a complete set 

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