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We study the divergence of the solution to a Schr\"odinger-type amplifierdriven by the square of a Gaussian noise in presence of a random potential. Wefollow the same approach as Mounaix, Collet, and Lebowitz (MCL) in terms of adistributional formulation of the amplified field and the use of thePaley-Wiener theorem [Commun. Math. Phys. {\bf 264}, 741-758 (2006) and {\bf280}, 281-283 (2008)]. Our results show that the divergence is not affected bythe random potential, in the sense that it occurs at exactly the same couplingconstant as what was found by MCL without a potential. It follows {\it afortiori} that the breakdown of the amplifier is not affected by the possibleexistence of a localized regime in the amplification free limit.

Wave localization does not affect the breakdown of a Schr\"odinger-type amplifier driven by the square of a Gaussian field