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Scientific Reports

Wave packet splitter and rectificator based on the Dirac delta potentials in a fractional medium

M. Solaimani

Published Feb 14, 2025• 0 citations
Publisher

Abstract

In this work, we have investigated the Gaussian and Airy wave packets colliding on the Dirac delta potentials. We have used the time-dependent space-fractional Schrodinger equation and solved it by using the slit step finite difference method. Here, we have presented some exclusive exotic propagation properties of Dirac delta potential that cannot be observed for other very similar potentials such as one-dimensional coulomb potential. We can now rectify any number of colliding wave packets provided that the correct parameters adjustment is possible. We have also addressed the wave packet speed control, wave packet splitting, wave packet rectification through collision process, wave packet dispersion, etc. The effects of different parameters such as the nonlinearity, fractitionality, dispersion, etc. on the wave packet-delta potential collision are also considered.

DOI
10.1038/s41598-025-87001-y

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In this work, we have investigated the Gaussian and Airy wave packets colliding on the Dirac delta potentials. We have used the time-dependent space-fractional Schrodinger equation and solved it by using the slit step finite difference method. Here, we have presented some exclusive exotic propagation properties of Dirac delta potential that cannot be observed for other very similar potentials such as one-dimensional coulomb potential. We can now rectify any number of colliding wave packets provided that the correct parameters adjustment is possible. We have also addressed the wave packet speed control, wave packet splitting, wave packet rectification through collision process, wave packet dispersion, etc. The effects of different parameters such as the nonlinearity, fractitionality, dispersion, etc. on the wave packet-delta potential collision are also considered.
We investigate a traveling Gaussian wave packet transport through a rectangular quantum barrier of lévy crystals in fractional quantum mechanics formalism. We study both standard and fractional Schrödinger equations in linear and nonlinear regimes by using a split-step finite difference (SSFD) method. We evaluate the reflection, trapping, and transmission coefficients of the wave packet and the wave packet spreading by using time-dependent inverse participation ratio (IPR) and second moment. By simultaneously adjusting the fractional and nonlinear terms, we create sharp pulses, which is an essential issue in optoelectronic devices. We illustrate that the effects of barrier height and width on the transmission coefficient are strangely different for the standard and fractional Schrödinger equations. We observe fortunately soliton-like localized wave packets in the fractional regime. Thus, we can effectively control the behavior of the wave evolution by adjusting the available parameters, which can excite new ideas in optics.
We investigate numerically the time-dependent Schrödinger equation on a two-dimensional comb in the presence of a localized Dirac delta potential on the backbone. The geometric constraint and the point interaction are both regularized via narrow Gaussian approximations, and the resulting equation is discretized with second-order finite differences and integrated with a fourth-order Runge–Kutta scheme on a finite domain. Two initial states are considered—a Gaussian wave packet and a comb-like wave function—and two barrier configurations are studied: a potential centered at the origin and one displaced along the backbone. In both cases, the Dirac delta interaction suppresses the probability density at the barrier position and reorganizes the wave packet into a persistent split-peak profile, in contrast to the single spreading maximum observed in the free case. When the barrier is displaced, due to reflection from the barrier, the left–right symmetry is broken and the density remains asymmetrically concentrated near the interaction site. To elucidate the results further, we also analyze the second moment, which undoubtedly confirms that the anomalous dynamics features, such as the subdiffusive behavior on comb-like structures in classical systems are retained in the quantum case as well.
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.
In this study, we investigate the transport properties of Airy and Hermit-Gaussian wavepackets traveling through a Gaussian potential well in the standard and fractional media. We use a split step Fourier method to solve the corresponding two-dimensional fractional nonlinear linear Schrodinger equation. We study the interference phenomenon, Huygens principle and trapping properties of the system in different situations. For this purpose, the position of the system has also selected inside the potential well to consider the wavepacket evolution. Then, the effect of the well and incident wavepackets parameters on the evolution the transport properties of employed wavepackets have properly been considered.
Localization of relativistic particles have been of great research interests over many decades. We investigate the time evolution of the Gaussian wave packets governed by the one dimensional Dirac equation. For the free Dirac equation, we obtain the evolution profiles analytically in many approximation regimes, and numerical simulations consistent with other numerical schemes. Interesting behaviors such as Zitterbewegung and Klein paradox are exhibited. In particular, the dispersion rate as a function of mass is calculated, and it yields an interesting result that super-massive and massless particles both exhibit no dispersion in free space. For the Dirac equation with random potential or mass, we employ the Chebyshev polynomials expansion of the propagator operator to numerically investigate the probability profiles of the displacement distribution when the potential or mass is uniformly distributed. We observe that the widths of the Gaussian wave packets decrease approximately with the power law of order o(s−ν)o(s^{-ν})o(s−ν) with $\frac{1}{2}
We solve numerically the time-dependent Dirac equation for a quantum wave packet tunneling through a potential barrier. We analyze the spatial probability distribution of the transmitted wave packet in the context of the possibility of effectively superluminal peak and front velocities of the electron during tunneling. Both the Dirac and Schr\"odinger theories predict superluminal tunneling speeds. However, in contrast to the Dirac theory the Schr\"odinger equation allows a possible violation of causality. Based on an analysis of the tunneling process in full temporal and spatial resolution, we introduce an instantaneous tunneling speed that can be computed inside the potential barrier.