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<p>In this paper, we conceptualize an autonomous quantum particle as a wave–particle entity (WPE) and explore its dynamics within a one-dimensional double-well potential. Building on the mathematical foundations of the Schrödinger equation, we investigate the emergence of complex, quantum-like behaviors governed by an integro-differential equation. Under specific parameter regimes, the WPE exhibits chaotic motion, revealing instability analogous to quantized eigenstates. Our analysis demonstrates how chaos in the system manifests as wave-like characteristics in the particle’s positional probability distribution, closely mirroring behaviors in real quantum systems. We characterize the chaotic dynamics using Lyapunov exponents, bifurcation diagrams, time series, and two-dimensional and three-dimensional phase portraits. Additionally, the system displays rich nonlinear phenomena, including strange attractors and period-doubling routes to chaos, triggered by variations in control parameters. Finally, we assess the stability of the system at equilibrium points and apply multiple chaos quantification tools to evaluate its dynamical behavior. This study offers new insights into the interplay between classical chaos and quantum-like dynamics in wave–particle dual systems.</p>

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Chaotic dynamics and stability of quantum wave–particle entities in double-well potentials

  • 期刊论文

  • 发表日期：

    2026年3月5日

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  • Sanjay Kumar,
  • Arun Kumar Tiwary,
  • Ram Pravesh Prasad,
  • Chandrashekhar Nishad,
  • Ahmed Ezzat Matouk,
  • Krishan Pal

摘要

In this paper, we conceptualize an autonomous quantum particle as a wave–particle entity (WPE) and explore its dynamics within a one-dimensional double-well potential. Building on the mathematical foundations of the Schrödinger equation, we investigate the emergence of complex, quantum-like behaviors governed by an integro-differential equation. Under specific parameter regimes, the WPE exhibits chaotic motion, revealing instability analogous to quantized eigenstates. Our analysis demonstrates how chaos in the system manifests as wave-like characteristics in the particle’s positional probability distribution, closely mirroring behaviors in real quantum systems. We characterize the chaotic dynamics using Lyapunov exponents, bifurcation diagrams, time series, and two-dimensional and three-dimensional phase portraits. Additionally, the system displays rich nonlinear phenomena, including strange attractors and period-doubling routes to chaos, triggered by variations in control parameters. Finally, we assess the stability of the system at equilibrium points and apply multiple chaos quantification tools to evaluate its dynamical behavior. This study offers new insights into the interplay between classical chaos and quantum-like dynamics in wave–particle dual systems.