Fluctuation-dissipation theorem susceptibilities

Let us first analyze the effect of the bias field on the magnetic SR in the framework of the linear response theory formulated for SR [96,97,99]. The main idea of the linear response treatment is a direct use of the fluctuation-dissipation theorem, which expresses the thermal (fluctuational) power spectrum Qn(a>) of the magnetic moment of the system, namely, magnetic noise, through the imaginary component of its linear dynamic susceptibility ImX = to a weak probing ac field of an arbitrary frequency co as... 

Note that all throughout our consideration we use the usual definition of % as the magnetic susceptibility of a unit volume of the disperse system. Therefore, to keep up with the meaning of the fluctuation-dissipation theorem, in formula (4.278) the total volume Vt of the system is introduced. In terms of the total number N of the magnetic particles V, = N/c = NV/< >. 

The fluctuation-dissipation theorem relates the correlations to absorption in other words, the scattering function is proportional to the imaginary part of a generalised (Q and to dependent) susceptibility, In the zero-frequency, zero-wavevector... 

The second, more practical, expression is in terms of the dynamic magnetic susceptibility x iQ> T). Its connection to the correlation function described by eq. (2) is given via the fluctuation dissipation theorem,... 

Once the dynamic spin susceptibility has been obtained both, fNS measurements and NMR experiments, can be explored. Probed by INS from the fluctuation-dissipation theorem the -dependent and co-dependent spin structure factor is related to the dynamical susceptibility by... 

Equation 10 is a general result based on the fluctuation-dissipation theorem [3,4,9]. So the susceptibility can independently be evaluated from AG which in the case of the mean field FH theory leads to a similar result as the RPA,... 

Quasilocal soft modes modulate the local dielectric susceptibility of the glass Scik oc aikx and therefore, causes the inelastic light scattering. As a consequence of the fluctuation-dissipation theorem the frequency and temperature dependence of the stokes Raman scattering intensity are determined by... 

The Einstein relation is a special case of a more general result known as the fluctuation-dissipation theorem (FDT). The FDT relates the strength of the random thermal fluctuations (here D) to the corresponding susceptibility to external perturbations (here in such a way that ensures that the probability distribution converges to the proper equilibriiun result at stea state. 

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