Spectra of Euclidean Random Matrices

Details Spectra of Euclidean Random Matrices Spectra of Euclidean Random Matrices

1999-06-09

arxiv.org/abs/cond-mat/9906135v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

10 pages, 4 figures

Scientific paper

10.1016/S0550-3213(99)00428-9

We study the spectrum of a random matrix, whose elements depend on the Euclidean distance between points randomly distributed in space. This problem is widely studied in the context of the Instantaneous Normal Modes of fluids and is particularly relevant at the glass transition. We introduce a systematic study of this problem through its representation by a field theory. In this way we can easily construct a high density expansion, which can be resummed producing an approximation to the spectrum similar to the Coherent Potential Approximation for disordered systems.

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