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Stable direct dynamics with quantum potential: Lorentzian trajectory basis function is all you need.

Alexey V Akimov1

  • 1Chemistry Department, University at Buffalo, Buffalo, New York 14260, USA.

The Journal of Chemical Physics
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Summary

This study introduces Lorentzian trajectory basis functions (TBFs) to stabilize quantum trajectory methods. These functions improve the quantum potential, enhancing the robustness of quantum dynamics simulations.

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Area of Science:

  • Quantum mechanics
  • Computational chemistry
  • Theoretical physics

Background:

  • Quantum trajectory methods offer alternatives to wavefunction-based quantum mechanics.
  • Instability of the quantum potential is a key challenge in these methods, especially in low-density regions.

Purpose of the Study:

  • To develop a stable and robust strategy for trajectory-based quantum dynamics.
  • To address the challenge of quantum potential instability in quantum trajectory simulations.

Main Methods:

  • Constructing probability density using superposition of Lorentzian-shaped trajectory basis functions (TBFs).
  • Comparing Lorentzian TBFs with commonly used Gaussian TBFs.
  • Proposing a general principle for selecting TBFs for quantum potential construction.

Main Results:

  • Lorentzian TBFs result in bounded and smooth quantum potentials and well-behaved quantum forces.
  • The proposed method enhances the stability of quantum trajectory integration.
  • The approach offers improvements over Gaussian TBFs, particularly in low-density regions.

Conclusions:

  • Lorentzian TBFs provide a stable and robust approach for quantum trajectory simulations.
  • The findings benefit coupled-trajectory and quantum-classical methods.
  • The proposed TBFs are applicable to wavepacket propagation and electronic structure theory.