https://doi.org/10.1007/s100510050581
A path integral approach to effective non-linear medium
1
Commissariat à l'Énergie Atomique, Service de Physique de la Matière
Condensée, BP 12,
91680 Bruyères-Le-Chatel, France
2
Commissariat à l'Énergie Atomique, Service de Physique Théorique, 91191
Gif-Sur-Yvette Cedex, France
Corresponding author: a mark@argento.bu.edu
Received:
13
May
1998
Accepted:
27
July
1998
Published online: 15 December 1998
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 ε is fluctuating
from point to point), and to the case of weak non-linearity (i.e.
where ε and χ 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.
PACS: 72.20.Ht – High-field and nonlinear effects / 77.84.Lf – Composite materials
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1998
