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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Closure of quantum hydrodynamic moment equations
Keith H Hughes1, Steven M Parry, Irene Burghardt
1School of Chemistry, Bangor University, Bangor, Gwynedd LL57 2UW, United Kingdom. keith.hughes@bangor.ac.uk
The Journal of Chemical Physics
|February 12, 2009
Summary
A new closure scheme for quantum hydrodynamics simplifies calculations by reconstructing Wigner functions from known moments. This method aids in understanding the dynamics of quantum systems, including double-well and periodic potentials.
Area of Science:
- Quantum Mechanics
- Theoretical Physics
- Computational Chemistry
Background:
- The hydrodynamic formulation of quantum states relies on a hierarchy of coupled equations for Wigner function momentum moments.
- Solving this hierarchy requires a closure scheme to approximate unknown higher-order moments.
Purpose of the Study:
- To develop and apply a novel closure scheme for the Wigner function hierarchy in quantum hydrodynamics.
- To accurately approximate higher momentum moments using information from lower, known moments.
Main Methods:
- The study introduces a closure scheme based on expanding the Wigner function in a Gauss-Hermite orthonormal basis.
- This expansion utilizes known lower moments to reconstruct the Wigner function.
- Higher moments are obtained by integrating the reconstructed Wigner function over momentum space.
Main Results:
- The developed moment closure scheme effectively terminates the hierarchy of equations.
- The scheme was successfully applied to model both dissipative and nondissipative dynamics.
- Simulations were performed for two distinct systems: a double-well potential and a periodic potential.
Conclusions:
- The moment closure scheme provides an efficient method for solving quantum hydrodynamic equations.
- This approach facilitates the study of complex quantum systems and their dynamics.
- The technique is versatile and applicable to various potential landscapes.
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