By B. A. Van Tiggelen (auth.), Jean-Pierre Fouque (eds.)
The NATO complex examine Institute on Diffuse Waves in advanced Media was once held on the "Centre de body des Houches" in France from March 17 to 27, 1998. the colleges' clinical content material, wave propagation in heterogeneous me dia, has lined many parts of basic and utilized learn. at the one hand, the knowledge of wave propagation has significantly better over the past thirty years. New advancements and ideas corresponding to, speckle correlations, susceptible and powerful localization, time reversal, near-field propagation are lower than energetic study. however, wave propagation in random media is now being investigated in lots of diverse fields reminiscent of utilized arithmetic, acoustics, optics, atomic physics, geo physics or clinical sciences. each one neighborhood usually makes use of its personal langage to explain an identical phenomena. the purpose of the college used to be to collect around the world experts to light up numerous elements of wave propagation in random media. This quantity provides fourteen expository articles equivalent to classes and seminars given throughout the institution. they're prepared as follows. the 1st 3 articles care for the phenomena of localization of waves: B. van Tiggelen (p. 1) offers a serious overview of the physics of localization, J. Lacroix (p. sixty one) offers the mathematical conception and A. Klein (p. seventy three) describes fresh effects for randomized periodic media.
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Extra info for Diffuse Waves in Complex Media
The collision operator U can now be decomposed into By construction, the subset S is closed under the operation carried out Eq. (76), just like the total set r. Contrary to C it also exists classically. Physically it contains "loop" events that finally return to where they came from. In the theory of coherent backscattering, R describes "background" and C the "coherent peak". It is relation (76) that guarantees a coherent backscattering peak with an enhancement factor of approximately 2. It 44 is only approximately 2, because the vertex S does not give a peak, and contributes to background .
Typical contribution to the reducible vertex R. The present graph represents a totally incoherent event (a "ladder" diagram), where the phase cancels. B). Typical contribution to the vertex G ("most-crossed" diagram), obtained by time-reversing the lower path of the vertex R. ) Typical contribution to the vertex S which is here an incoherent path with equal start and end ("loop"). The relation (76) can be reformulated in wave number space, and the object 46 Cpp ' takes the form Cpp,(n, q) ~ 411" 12 1 -in + D(p + p')2 (81 ) Inserting Upp ' = S +Cpp' into Eq.
As a result, U obeys a diffusion equation too, with the same diffusion constant. In this way one can see that Eqs. (78) and (79) are in fact coupled equations for the diffusion constant D(w). This selfconsistency was first pointed out by G6tze  and worked out in detail by Vollhardt and Wolfle [7, 15, 16]. In the diffuse regime the Fourier transform of R( r) is (see Fig. :~:,,::,::' .... ,. , " ... ------- ... wtQ/2 ... - i,p+q/2 X~X~X~X~X~-X J, p'+ q/2 k,p- q/2 ~~x~x~x~x~x ---- w-Q/2 ,,' , I, p'- q/2 Figure 11.