Collision models susceptibility

Third, the expression for the spectral function pertinent to the HO model is derived in detail using the ACF method. Some general results given in GT and VIG (and also in Section II) are confirmed by calculations, in which an undamped harmonic law of motion of the bounded charged particles is used explicitly. The complex susceptibility, depending on a type of a collision model,... 

In the second period, which was ended by review GT after the average perturbation theorem was proved, it became possible to get the Kubo-like expression for the spectral function L(z) (GT, p. 150). This expression is applicable to any axially symmetric potential well. Several collision models were also considered, and the susceptibility was expressed through the same spectral function L(z) (GT, p. 188). The law of motion of the particles should now be determined only by the steady state. So, calculations became much simpler than in the period (1). The best achievements of the period (2) concern the cone-confined rotator model (GT, p. 231), in which the dipoles were assumed to librate in space in an infinitely deep rectangular well, and applications of the theory to nonassociated liquids (GT, p. 329). 

Now we turn to calculation of the susceptibility component Xst( ) in Eq. (17). To extract it from Eq. (14c), one should replace there p for and account for an inhomogeneity of the induced distribution F(y). The latter is determined by a chosen collision model. Such models are described in detail in GT, Section IV.B, and in VIG, Section VI, where they are separated into the self-consistent and non-self-consistent models. For one simple example they are considered also in Section VII.C... 

We employ the Gross collision model for which this susceptibility xor[z(v)] is related to the correlator ( spectral function ) Lor of the hat model as... 

For other collision models (e.g., for the Gross model, see GT1) the susceptibility % is related to the spectral function by a rational relation different from (83). This leads to an essential change of the low-frequency spectrum. 

Second, the SF (254) is used in the case of the Gross collision model as a constitutive element of the formula for the complex susceptibility Xg I 1 this case the orientational distribution Fq, differing from FB, changes radically the calculated low-frequency spectrum, while the far-IR spectrum is very close to that given by the Boltzmann susceptibility Xb (252). We shall return to this point in Section IX.D. 

We should also remark that Kalmykov and Limonova, using a similar collision model applied to an isotropic dipolar medium, have obtained [58, 59] the following expression for the complex susceptibility ... 

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