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Chaos Solitons & Fractals

Effects of the medium fractionality and oscillating potential profiles on the Superarrivals of the Gaussian wave packets

Davood Haji Taghi Tehrani, M. Solaimani

Published Jan 26, 2023• 5 citations
Publisher
DOI
10.1016/j.chaos.2023.113138

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In this study, we present a numerical investigation of wave packet dynamics in a nonlinear and dispersive medium described by the space-fractional Schrödinger equation, with direct relevance to quantum electronic device applications. Employing the Split-Step Finite Difference (SSFD) method, we analyse the superarrival phenomenon, where the arrival time of a Gaussian wave packet is accelerated due to the presence of a decelerating potential barrier. Two key configurations are explored: a barrier approaching the wave packet and a receding one. We show that the superarrival response is highly sensitive to system parameters such as the fractional order, nonlinearity, dispersion, and the barrier's motion profile. Our findings demonstrate that superarrival can be effectively tuned, offering new design strategies for emerging quantum electronic components such as ultrafast signal switches, wave-based logic gates, and controllable tunneling junctions in nano-engineered systems. This work bridges fundamental quantum transport with the functionality of next-generation electronic devices.
Superarrival, a quantum effect where a wave packet arrives earlier than its free-space counterpart, is investigated in fractional nanostructured media. We model a Gaussian wave packet interacting with a uniformly decelerating potential barrier or well using the fractional Schrödinger equation and the Split-Step Finite Difference method. The impact of the Lévy stability index, wave packet width, and initial distance on superarrival is analyzed. Results show that fractional media strongly enhance superarrival, especially for wider, low-energy packets interacting with barriers. These findings underscore the role of nonlocality in quantum transport and suggest potential applications in nanoscale optoelectronic devices such as tunable delay lines, ultrafast modulators, and quantum information processors.