Multi-phonon resonance

The solution to the Hamiltonian of a vibration system is a Fourier series with multiple terms of frequencies being fold of that of the primary mode [30]. For example, the frequency of the secondary 2D mode should be twofold that of the primary D mode of diamond. Instead of the multi-phonon resonant scattering, Raman frequencies are the characteristics of the solution. Generally, one can measure the Raman frequency of a particular x mode as co = co o + Aco, where cOxO is the reference point from which the Raman shift Aco proceeds. The cOxo may vary with the frequency of the incident radiation and substrate conditions, but not the nature and the trends induced by the applied stimuli. By expanding the interatomic potential in a Taylor series at its equilibrium and considering the effective atomic z, one can derive the vibration frequency shift of a harmonic system,... 

R is the effective radius of the dislocation core, p is the density of the crystal. G is the shear modulus, v is the Poisson ratio. The second term in Equation (6) applies to very rapid deformation processes due to strong shock loading and is dominated by the resonant condition Ei - E. i T(T,U)vo /d that occurs as T(i,U) 1. This term leads to resonant multi-phonon molecular excitation and dissociation associated with detonation and is discussed elsewhere [18]. 

Fig. 1.11 Energy spectrum of nuclear resonant scattering from -Fe foil at room temperature, reported by Seto et al. [29]. Dotted line is a contribution of multi-phonon excitations [29]...

Fig. 2 a Energy migration, that is multi-step energy transfer between chemically identical chromophores. b Within the inhomogeneous distribution it can proceed via an resonant process (straight arrow) or via a phonon-assisted process whereby the energy mismatch between the donor and the acceptor is made up by lattice phonons (curly arrows)... 

Energy transfer between two inorganic ions can occur either by multipolar interaction or an exchange mechanism in dilute systems (Reisfeld and Jorgensen, 1977 Reisfeld, 1973, 1975, 1976a), or by multi-step migration in concentrated systems (Powell and Blasse, 1980). In addition to resonant transfer, phonon-assisted transfer is a quite common phenomenon (Reisfeld, 1976a, 1986). 

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