2025, Vol. 6, Issue 2, Part E
Periodic partial differential equations as a tool for quantum dynamics simulation
Author(s): Rusul Mohammed Hussein AL-shmary and Najat Abbas Abd Ali Al-Taie
Abstract: In the study, a quantum-inspired framework of solving one-dimensional periodic-boundary periodic partial differential equations (PDEs) is proposed. This model uses a mixture of the Crank-Nicolson time-stepping algorithm with spectral differencing to solve the time-dependence of a normalized wave function in 200 femtoseconds (fs) domain. The proposed hybrid numerical scheme has probability norm conservation with a relative accuracy of within +-0.5 percent, energy deviation of less than 1 percent and a stability index of 99.4 that is very good numerically and stable. The current method saves the computational time by approximately 31 percent compared to the traditional finite-differentiate methods but has both high spatial and temporal accuracy (root mean square error < 0.5 percent) and temporal precision (propagation of errors less than 1.2 percent). The simulations manage to reproduce periodic soliton like oscillations at the boundary and maintain the periodicity of the boundaries without introducing phase distortion, which proves the reliability of the method in simulating the stable dynamics of waves. All in all, the findings suggest that the deterministic PDE solvers with quantum-inspired transformations can be used to attain the neo-quantum stability and efficiency using classical hardware. This work offers a generalized and demystifying basis of future quantum-classical hybrid solvers in the modeling of complex multiscale dynamical systems.
DOI: https://doi.org/10.22271/math.2025.v6.i2e.274
Pages: 761-770 | Views: 73 | Downloads: 27
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How to cite this article:
Rusul Mohammed Hussein AL-shmary and Najat Abbas Abd Ali Al-Taie. Periodic partial differential equations as a tool for quantum dynamics simulation. Journal of Mathematical Problems, Equations and Statistics. 2025; 6(2): 761-770. DOI: 10.22271/math.2025.v6.i2e.274
