Phonon occupation number

This formula describes the exchange of a single phonon of wavevector Q, frequency co(0 ) and polarization e(Q,j). n is the Bose factor for annihilation (—) or creation (+) of a phonon, respectively, i.e. the phonon occupation number. 

There are two different temperature regimes of diffusive behavior they are analogous to those described by Holstein [1959] for polaron motion. At the lowest temperatures, coherent motion takes place in which the lattice oscillations are not excited transitions in which the phonon occupation numbers are not changed are dominant. The Frank-Condon factor is described by (2.51), and for the resonant case one has in the Debye model ... 

The e term refers to a unit polarization vector, is the first-order derivative of the susceptibility tensor with respect to the phonon amplitude, also known as the Raman tensor, and rij is the phonon occupation number for the /th mode, given by ... 

Another intriguing quality of Raman spectroscopy is its capability to measure local temperature quantitatively and precisely. This is possible in two distinct ways, arising due to two different characteristics of the Raman spectra in crystalline solids. The first characteristic is the presence of the phonon occupation number in the Raman scattering cross section in accordance with (17.3). While the relation to temperature of the strict intensity of a particular phonon peak is obfuscated by the numerous other components of the Raman scattering cross section, taking the ratio of integrated intensities of the Stokes (1 ) and anti-Stokes (Ias) peaks provides the following relationship by which to measure temperature ... 

The energy transfer rates given in Eqs. (32) and (34) predict the same temperature dependences which are contained in the phonon occupation number given in Eq, (33). The major difference in the two energy transfer rates is their dependence on energy mismatch. 

In the Orbach process the transfer rate is composed of a temperature-dependent part associated with the phonon-occupation number nq and a temperature independent part corresponding to energy transfer accompanied by spontaneous phonon emission. 

In Equation (8), A represents the anharmonic shift and F the anharmonic broadening. Both A and F are proportional to nj, the Bose phonon occupation numbers - 1)" ], and at temperatures such that kT fi(jjj, rij is propor-... 

Figure 7 demonstrates the regularity band of PP in the Raman spectrum and the relative phonon occupation number for the extended excited bonds, Nj/No, and that for the compressed excited bonds, Nq/Nq, where No is the equilibrium occupation number. It is clear that Nj/No > 1 and Np/No < 1. N is related with temperature by the expression [61] ... 

The relative intensities of the phonon assisted transitions in a given material are determined by the product f (Uq + h + h) -The effects of the oscillator strength are clearly manifested in phonon emission processes, for which ng <<1. For temperatures up to room ten5)erature this conditions is satisfied and fj becomes the principal factor governing the relative strengths. For phonon absorption processes, the phonon occupation number has a large effect on the relative intensities. In this case the role of... 

We conclude, therefore, that it is possible to measure the temperature dependence of the dephasing time of LO phonons in GaP and ZnSe and to account for the observation in terms of the simple Bose-Einstein dependence on phonon occupation numbers. Although this procedure does indeed yield quite good agreement between experiment and theory, no theoretical apparatus exists for the prediction of the magnitude of T2 at T=0K. 

The transformed problem is treatable only if one can assume that the carrier is still delocalized. In this case the bosonic component of Vei can be eliminated approximating Vei = e Veie with its thermal average (yei) - This is equivalent to the assumption that the phonon occupation number does not change during the transport, i.e., that inelastic processes are not important. In this limit we have for the Hamiltonian in Eq. (1) ... 

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