  In this paper we study the effects of white-noised potentials on nonlinear
quantum tunneling. We use a split-step scheme to numerically solve the
nonlinear Schrodinger equation (NLSE) with a tunneling potential. We consider
three different types of potentials, namely; the single rectangular barrier,
double rectangular barrier and triangular barrier. For all these three cases we
show that white-noise given to potentials do not trigger modulation instability
for tunneling of the sech type soliton solutions of the NLSE. However
white-noised potentials trigger modulation instability for tunneling of the
sinusoidal wavefunctions, thus such a wavefield turns into a chaotic one with
many apparent peaks. We argue that peaks of such a field may be in the form of
rational rogue wave solutions of the NLSE. Our results can be used to examine
the effects of noise on quantum tunneling. Since a rogue wavefunction means a
higher probability of the tunneling particle to be at a given (x,t) coordinate,
our results may also be used for developing the quantum science and technology
with many possible applications including but are not limited to increasing the
resolution and efficiency of scanning tunneling microscopes, enhancing proton
tunneling for DNA mutation and enhancing superconducting properties of
junctions.
