Abstract:
In this article, we propose a new method to compute the effective properties of non-linear disordered media. We use the fact that the effective constants can be defined through the minimum of an energy functional. We express this minimum in terms of a path integral allowing us to use many-body techniques. We obtain the perturbation expansion of the effective constants to second order in disorder, for any kind of non-linearity. We apply our method to the case of strong non-linearities (i.e. , where is fluctuating from point to point), and to the case of weak non-linearity (i.e. where and fluctuate from point to point). Our results are in agreement with previous ones, and could be easily extended to other types of non-linear problems in disordered systems.
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Received: 13 May 1998 / Accepted: 27 July 1998
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Barthélémy, M., Orland, H. A path integral approach to effective non-linear medium. Eur. Phys. J. B 6, 537–541 (1998). https://doi.org/10.1007/s100510050581
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DOI: https://doi.org/10.1007/s100510050581