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Updated: Jul 22, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
A new method for solving the quantum hydrodynamic equations of motion: application to two-dimensional reactive
Denise K Pauler1, Brian K Kendrick
1Theoretical Division (T-12, MS-B268), Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
This study solves de Broglie-Bohm hydrodynamic equations using a novel meshless method. The approach accurately predicts reaction probabilities in quantum dynamics, offering a robust alternative to existing methods.
Area of Science:
- Quantum mechanics
- Computational chemistry
- Fluid dynamics
Background:
- The de Broglie-Bohm theory offers a deterministic interpretation of quantum mechanics.
- Solving the associated hydrodynamic equations presents significant computational challenges.
Purpose of the Study:
- To develop and validate a novel numerical method for solving the de Broglie-Bohm hydrodynamic equations.
- To accurately compute reaction probabilities in quantum systems.
Main Methods:
- A meshless method utilizing moving least squares and an arbitrary Lagrangian-Eulerian frame.
- A regridding algorithm for maintaining uniform particle spacing.
- Artificial viscosity to mitigate numerical instabilities.
Main Results:
- The method successfully solves the de Broglie-Bohm hydrodynamic equations.
- Accurate computation of reaction probabilities for a model collinear reaction.
- Excellent agreement with results from the quantum trajectory method.
Conclusions:
- The developed meshless method provides a stable and accurate approach for quantum dynamics simulations.
- This technique offers a viable alternative for studying chemical reactions at the quantum level.
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