Dielectric tensor definition

If we ignore the small effect of two-phonon transitions on the dispersion of the refraction index n, then in the region of the energies E = hu>, corresponding to the excitation of two-particle states, the absorption coefficient n is found to be directly associated with the density of two-particle states. In fact, for light polarized, for instance, along the x-axis, which coincides, by definition, with the direction of the vector dBB, the dielectric tensor has a nonvanishing component... 

To proceed we have to express the x-component of the polarization in layer 1 in terms of Ex and its z-component in terms of Dz. We can obtain these relations if we take into account that the displacement vector by definition is D = e i(w, A )E = eooE + 47rP. For the dielectric tensor in layer 1 we can take the... 

Figure 83. The definitions of the molecular axes and components of the dielectric tensor.

The definitions of the dielectric tensor components in the local molecular frame, and main alignment structures sandwiched SmC materials in thin films. For testing the dielectric constant, small electric fields, not enough to cause any reorientation, are applied across the plates. 

In the OKE response only the off-diagonal elements, i j, of the dielectric tensor are involved, so the isotropic polarizability, a, does not contribute. Furthermore, the experimental q wave-vector value is zero, hence the translational part of (2.27) is not relevant. Concerning the OKE response the susceptibility tensor definition can be simplified as... 

In the previous section we connected the susceptibility tensor directly to the microscopic parameters, the molecular polarizabilities. Indeed, this point of view clarifies the molecular aspects of the x tensor, but the connection with the dynamical model is complicated by the extremely large number of variables that must be considered. An alternative possibility is represented by a coarsegrained definition of the susceptibility function, in fact if we disregard to the microscopic information we gain a more direct link to the dynamic model. The polarizability of a rigid symmetric-top molecule can be described by (2.29), hence the dielectric tensor becomes... 

Measurements of dipole moments, Kerr constants, and dielectric absorption have been employed (81RCR336) widely to obtain information on the conformational equilibrium in acyl heterocycles. Details on conformer structures and populations depend on the choice of additive scheme, group moments, or polarizability tensor in the case of Kerr constants. Several early conclusions, especially for furan- and thiophene-2-carboxaldehyde, appeared contradictory, owing to the choice of these quantities. A more precise definition of polarizability tensors for several heterocycles and a choice of group moments and additive schemes tested on a large amount of available experimental results and supported by accurate theoretical calculations have led to more confidence in the use of experimental dipole moments and Kerr constants in conformational analysis. A limitation of the method is that the... 

In the continuum approach to the surrounding medium one has by definition, m = 0. Medium effects are therefore presented by a reaction field term in Eq. (24). Three types of environment can be represented in this framework i) an anisotropic medium without spatial dispersion, where the permitivity tensor is defined with the ansatz c(r — r ) = c(r) (5(r — r ), that leads to a distance dependent dielectric system dependance ii) an isotropic medium which is characterized by s(r — r ) = e(r)1 (r — r ) hi) a homogeneous and isotropic medium, the permitivity tensor is the unit tensor multiplied by the static dielectric constant Thus the effective Schrodinger equation for each case is obtained from Eq. (24) after integration of the r -variable with the corresponding ansatz for the permitivity tensor. 

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