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Finite element method for finite-size scaling in quantum mechanics
Winton Moy1, Marcelo A Carignano, Sabre Kais
1Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, USA.
The Journal of Physical Chemistry. A
|May 22, 2008
Summary
Researchers developed a systematic procedure using the finite element method and finite-size scaling to determine quantum critical parameters. This approach accurately calculated critical values for the Yukawa potential, showing promise for larger quantum systems.
Area of Science:
- Quantum physics
- Computational physics
Background:
- Determining quantum critical parameters is essential for understanding quantum systems.
- Existing numerical methods may have limitations in accuracy or scalability.
Purpose of the Study:
- To develop a systematic procedure for obtaining quantum critical parameters.
- To apply and validate this procedure for the Yukawa potential.
Main Methods:
- Combined the finite-size scaling (FSS) method with the finite element method (FEM).
- Solved the Yukawa potential using the finite element approach.
- Applied FSS to determine critical parameters.
Main Results:
- Calculated critical values for the Yukawa potential (l=0): lambda c = 0.83990345, alpha = 2.0002, nu = 1.002.
- Obtained results for alpha and nu that closely match theoretically exact values.
- Achieved lambda c values comparable to the best numerical estimations.
Conclusions:
- The combined FEM and FSS method provides a reliable procedure for calculating quantum critical parameters.
- The FEM approach is versatile and can be applied to more complex and larger quantum systems.
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