title: Scattering mean free path in continuous complex media: beyond the Helmholtz equation.
abstract: We present theoretical calculations of the ensemble-averaged (or effective or coherent) wave field propagating in a heterogeneous medium considered as one realization of a random process. In the literature, it is usually assumed that heterogeneity can be accounted for by a random scalar function of the space coordinates, termed the potential. Physically, this amounts to replacing the constant wave speed in Helmholtz' equation by a space-dependent speed. In the case of acoustic waves, we show that this approach leads to incorrect results for the scattering mean free path, no matter how weak the fluctuations. The detailed calculation of the coherent wave field must take into account both a scalar and an operator part in the random potential. When both terms have identical amplitudes, the correct value for the scattering mean free paths is shown to be more than 4 times smaller (13/3, precisely) in the low-frequency limit, whatever the shape of the correlation function. Based on the diagrammatic approach of multiple scattering, theoretical results are obtained for the self-energy and mean free path within Bourret's and on-shell approximations. They are confirmed by numerical experiments.
authors.affiliation: ESPCI ParisTech, PSL Research University, CNRS, Univ Paris Diderot, Sorbonne Paris Cité, Institut Langevin, 1 rue Jussieu, F-75005, Paris, France.
authors.forename: Ibrahim
authors.initials: I
authors.lastname: Baydoun
authors.affiliation: ESPCI ParisTech, PSL Research University, CNRS, Univ Paris Diderot, Sorbonne Paris Cité, Institut Langevin, 1 rue Jussieu, F-75005, Paris, France.
authors.forename: Diego
authors.initials: D
authors.lastname: Baresch
authors.affiliation: ESPCI ParisTech, PSL Research University, CNRS, Univ Paris Diderot, Sorbonne Paris Cité, Institut Langevin, 1 rue Jussieu, F-75005, Paris, France.
authors.forename: Romain
authors.initials: R
authors.lastname: Pierrat
authors.affiliation: ESPCI ParisTech, PSL Research University, CNRS, Univ Paris Diderot, Sorbonne Paris Cité, Institut Langevin, 1 rue Jussieu, F-75005, Paris, France.
authors.forename: Arnaud
authors.initials: A
authors.lastname: Derode