Multiple scattering in random media I. Restricted two-body additive approximation |
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Authors: | Eugene P Gross |
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Institution: | (1) Department of Physics, Brandeis University, 02254 Waltham, Massachusetts |
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Abstract: | We present a microscopic theory of the problem of finding the properties of a particle interacting with potentials located at random sites. The sites are governed by a general probability distribution. The starting point is the multiple scattering equations for the amplitude k
1|T
|k
2 in terms of the individual scattering amplitudes k
1|T
|k
2. We work with quantitiesA
defined by k
1|T
|k
2=k
1|T
|k
2expi(k
1–k
2)R
]. The theory is based on a splitting of the fundamental equation forA into equations for the mean A and the fluctuationsAA
. Neglect of the fluctuations yields the quasicrystalline approximation. We rearrange the equation forAA
to isolate the collective part of the fluctuations. We then make the simplest microscopic truncation which is thatAA
is a restricted two-body additive function of the site positions. With the contribution of the collective fluctuations, this yields results forA that are accurate to ordert
4.Work supported in part by the National Science Foundation under Contract No. NSF DMRWork supported in part by the National Science Foundation under Contract No. NSF DMR |
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Keywords: | Multiple scattering random media |
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