ROGUE WAVEFUNCTIONS DUE TO NOISY QUANTUM TUNNELING POTENTIALS

Abstract

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 nonlinearSchr¨odinger equation (NLSE) with a tunneling potential. We consider three differenttypes of potentials, namely; the single rectangular barrier, double rectangular barrier,and triangular barrier. For all these three cases, we show that white-noise given topotentials do not trigger modulation instability for tunneling of the sech type solitonsolutions of the NLSE. However, white-noised potentials trigger modulation instabilityfor tunneling of the sinusoidal wavefunctions; thus, such a wavefield turns into a chaoticone with many apparent peaks. We argue that peaks of such a field may be in the formof rational rogue wave solutions of the NLSE. Our results can be used to examine theeffects 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 alsobe used for developing the quantum science and technology with many possible applications including but are not limited to increasing the resolution and efficiency of scanningtunneling microscopes, enhancing proton tunneling for DNA mutation and enhancingsuperconducting properties of junctions