Tunable Superarrival in Fractional Quantum Media

Document Type : Original Article

Authors

1 Faculty of Physics, Semnan University, Semnan 35195-363, Iran

2 Department of Physics, Qom University of Technology, Qom 1519-37195, Iran

Abstract

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.

Keywords

Main Subjects

© 2025 The Author(s). Progress in Physics of Applied Materials published by Semnan University Press. This is an open access article under the CC-BY 4.0 license. (https://creativecommons.org/licenses/by/4.0/)

References

[1] Ozawa, T., Price, H.M., Amo, A., Goldman, N., Hafezi, M., Lu, L., Rechtsman, M.C., Schuster, D., Simon, J., Zilberberg, O. and Carusotto, I., 2019. Topological photonics. Reviews of Modern Physics, 91(1), p.015006.
[2] Zimmermann, M., Efremov, M.A., Zeller, W., Schleich, W.P., Davis, J.P. and Narducci, F.A., 2019. Representation-free description of atom interferometers in time-dependent linear potentials. New Journal of Physics, 21(7), p.073031.
[3] Boyko, I., Petryk, M. and Lebovka, N., 2024. Tunnel transport problem for open multilayer nitride nanostructures with an applied constant magnetic field and time-dependent potential: An exact solution. Physical Review B, 110(4), p.045438.
[4] Iserles, A., Kropielnicka, K. and Singh, P., 2018. Magnus--Lanczos methods with simplified commutators for the Schrödinger equation with a time-dependent potential. SIAM Journal on Numerical Analysis, 56(3), pp.1547-1569.
[5] Louwen, A., Van Sark, W., Schropp, R. and Faaij, A., 2016. A cost roadmap for silicon heterojunction solar cells. Solar Energy Materials and Solar Cells, 147, pp.295-314.
[6] Quach, J.Q., Su, C.H., Martin, A.M., Greentree, A.D. and Hollenberg, L.C., 2011. Reconfigurable quantum metamaterials. Optics express, 19(12), pp.11018-11033.
[7] Kulik, I.O., 2007. Mesoscopic Aharonov-Bohm loops in a time-dependent potential: Quasistationary electronic states and quantum transitions. Physical Review B—Condensed Matter and Materials Physics, 76(12), p.125313.
[8] Alamir, A., Capuzzi, P. and Vignolo, P., 2013. Dynamical properties of a condensate in a moving random potential. The European Physical Journal Special Topics, 217(1), pp.63-68.
[9] Hernandez-Tenorio, C., Belyaeva, T.L. and Serkin, V.N., 2007. Parametric resonance for solitons in the nonlinear Schrödinger equation model with time-dependent harmonic oscillator potential. Physica B: Condensed Matter, 398(2), pp.460-463.
[10] Fring, A. and Tenney, R., 2020. Time-independent approximations for time-dependent optical potentials. The European Physical Journal Plus, 135(2), p.163.
[11] Yakubo, K., Feng, S. and Hu, Q., 1996. Simulation studies of photon-assisted quantum transport. Physical Review B, 54(11), p.7987.
[12] Ahmed, A., 2024. Tunneling Probability of Quantum Wavepacket in Time-Dependent Potential Well. Quanta, 13(1).
[13] Dimeo, R.M., 2014. Wave packet scattering from time-varying potential barriers in one dimension. American Journal of Physics, 82(2), pp.142-152.
[14] Laskin, N., 2000. Fractional quantum mechanics and Lévy path integrals. Physics Letters A, 268(4-6), pp.298-305.
[15] Manikandan, K., Aravinthan, D., Sudharsan, J.B. and Reddy, S.R.R., 2022. Soliton and rogue wave solutions of the space–time fractional nonlinear Schrödinger equation with PT-symmetric and time-dependent potentials. Optik, 266, p.169594.
[16] Li, M., 2019. A high-order split-step finite difference method for the system of the space fractional CNLS. The European Physical Journal Plus, 134(5), p.244.
[17] Zhang, L., Yang, R., Zhang, L. and Wang, L., 2021. A Conservative Crank‐Nicolson Fourier Spectral Method for the Space Fractional Schrödinger Equation with Wave Operators. Journal of Function Spaces, 2021(1), p.5137845.
[18] Liu, S., Zhang, Y., Malomed, B.A. and Karimi, E., 2023. Experimental realisations of the fractional Schrödinger equation in the temporal domain. Nature Communications, 14(1), p.222.
[19] Nizam, E. and Rahman, K., 2023, December. A Compact Split-step Finite Difference Method for Solving the Nonlinear Schrödinger Equation. In Journal of Physics: Conference Series (Vol. 2660, No. 1, p. 012027). IOP Publishing.
[20] Zhu, X., Wan, H. and Zhang, Y., 2024. A split-step finite element method for the space-fractional Schrödinger equation in two dimensions. Scientific Reports, 14(1), p.24257.
[21] Wang, P. and Huang, C., 2016. Split-step alternating direction implicit difference scheme for the fractional Schrödinger equation in two dimensions. Computers & Mathematics with Applications, 71(5), pp.1114-1128.
[22] Home, D., Majumdar, A.S. and Matzkin, A., 2012. Effects of a transient barrier on wavepacket traversal. Journal of Physics A: Mathematical and Theoretical, 45(29), p.295301.
[23] Mousavi, S.V. and Miret-Artés, S., 2019. On non-linear Schrödinger equations for open quantum systems. The European Physical Journal Plus, 134(9), p.431.
[24] Ali, M.M., Majumdar, A.S. and Home, D., 2002. Understanding quantum superarrivals using the Bohmian model. Physics Letters A, 304(3-4), pp.61-66.
[25] Balaž, A., Vidanović, I., Bogojević, A., Belić, A. and Pelster, A., 2011. Fast converging path integrals for time-dependent potentials: II. Generalization tomany-body systems and real-time formalism. Journal of Statistical Mechanics: Theory and Experiment, 2011(03), p.P03005.
[26] Wagner, T., Çelik, H., Gaebel, S., Berger, D., Lu, P.H., Häusler, I., Owschimikow, N., Lehmann, M., Dunin-Borkowski, R.E., Koch, C.T. and Hatami, F., 2025. Dynamic Imaging of Projected Electric Potentials of Operando Semiconductor Devices by Time-Resolved Electron Holography. Electronics, 14(1), p.199.
[27] Baek, S.K., Yi, S.D. and Kim, M., 2016. Particle in a box with a time-dependent δ-function potential. Physical Review A, 94(5), p.052124.
[28] Ehsani, M.H., Sabzevar, M. and Soleimani, M., 2025. Fractional Wave Propagation in Asymmetric Nonlinear Media: Implications for Metamaterial-Based Wave Control. Progress in Physics of Applied Materials, 5(2), pp.107-116.
[29] Shegelski, M.R., Poole, T. and Thompson, C., 2013. Capture of a quantum particle by a moving trapping potential. European Journal of Physics, 34(3), p.569.
[30] Xia, F., Wang, H., Xiao, D., Dubey, M. and Ramasubramaniam, A., 2014. Two-dimensional material nanophotonics. Nature photonics, 8(12), pp.899-907.
[31] Kilbas, A.A., 2006. Theory and applications of fractional differential equations. North-Holland Mathematics Studies, 204.
[32] Solaimani, M., 2020. Nontrivial wave-packet collision and broadening in fractional Schrodinger equation formalism. Journal of Modern Optics, 67(12), pp.1128-1137.
[33] Farag, N.G., Eltanboly, A.H., El-Azab, M.S. and Obayya, S.S., 2023. Numerical Solutions of the (2+ 1)-Dimensional Nonlinear and Linear Time-Dependent Schrödinger Equations Using Three Efficient Approximate Schemes. Fractal and Fractional, 7(2), p.188.
[34] Shegelski, M.R., Poole, T. and Thompson, C., 2013. Capture of a quantum particle by a moving trapping potential. European Journal of Physics, 34(3), p.569.
[35] Bandyopadhyay, S., Majumdar, A.S. and Home, D., 2002. Quantum-mechanical effects in a time-varying reflection barrier. Physical Review A, 65(5), p.052718.
[36] Majumdar, A.S. and Home, D., 2002. Quantum superarrivals and information transfer through a time-varying boundary. Pramana, 59(2), pp.321-328.
 
Progress in Physics of Applied Materials
Volume 6, Issue 1 - Serial Number 10
In Progress
May 2026
Pages 69-76

Files

History

  • Receive Date: 31 July 2025
  • Revise Date: 02 September 2025
  • Accept Date: 11 September 2025

Share

How to cite

Statistics