We study quantum tunneling through a potential barrier whose height fluctuates in time and is modeled by Gaussian white noise. Exploiting the correspondence between Gaussian white-noise dynamics and Lindblad evolution, we recast the noise-averaged dynamics as a time-independent density-matrix scattering problem and derive fully analytical solutions. For nonrelativistic particles described by the Schrödinger equation, noise introduces dissipation, suppresses Fabry-Pérot oscillations, and produces exponentially decaying transmission. Applying the same formalism to graphene, we show that noise induces a complex longitudinal wave vector within the barrier, leading to strong suppression of transmission and Klein tunneling even at normal incidence. Within the present model, the analytical results show how the noise strength controls the attenuation of electron transmission through graphene barriers. More broadly, the formalism provides an analytical basis for investigating noisy multibarrier structures, including graphene quantum-dot confinement; assessing qubit performance, however, will require extending the treatment to explicit confinement geometries and accounting for coherence.

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• Electrical properties
• Noise
• Graphene
• Lindblad equation