By Cox, Kilian, Leighton, Shamoon

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In the form it has been written down, it applies to any dimension. It can be adapted for anisotropy or inelastic scattering or absorption [7]. e. n f:. 0 will be discussed in the next Chapter. The wavenumber integral in Eq. (82) suffers from a number of divergencies that should be considered in more detail. In dimensions d :::; 2 it diverges at small wave numbers. This corresponds physically to long wave trajectories, for which the approximations leading to Eq. (82) should apply. This catastrophe implies that interference effects inhibit classical diffusion in d :::; 2 completely, as argued many times already in the present paper.

W.

S +t (94) The correlation function depends on one parameter Y = n~ (w )/ Vo only . e. the inverse time to travel one localization length. This also confirms that Inl ~ Iwl as has been assumed earlier. At low frequencies w -+ 0 the localization length ~ rv w- 2 is large and dephasing occurs rapidly. Equation (94) can be transformed into one for the power spectrum S(w, r) of fluctuations with frequency w in a time window r. The result is S(w,r) = J 1 X dtexp(-iwt) (p(r+t)p(t))= IF(wWX- ( )2' (95) -00 r 1 +X 11 oo where X = Irlvo/~(w).

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