Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inverse scattering for a random potential   In this paper we consider an inverse problem for the $n$-dimensional random
Schr\"{o}dinger equation $(\Delta-q+k^2)u = 0$. We study the scattering of
plane waves in the presence of a potential $q$ which is assumed to be a
Gaussian random function such that its covariance is described by a
pseudodifferential operator. Our main result is as follows: given the
backscattered far field, obtained from a single realization of the random
potential $q$, we uniquely determine the principal symbol of the covariance
operator of $q$. Especially, for $n=3$ this result is obtained for the full
non-linear inverse backscattering problem. Finally, we present a physical
scaling regime where the method is of practical importance.

24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics