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Amplitude-free correlation function based on an algebra for coordinate transformation in semiclassical integrals.
1Department of Basic Science, Graduate School of Arts and Sciences, The University of Tokyo, Komaba, 153-8902, Tokyo, Japan. kaztak@mns2.c.u-tokyo.ac.jp
Summary
We developed a new algebra for coordinate transformations in semiclassical integrals. This method extracts a correlation function free from exponential divergence in chaotic systems.
Area of Science:
- Quantum mechanics
- Theoretical chemistry
- Mathematical physics
Background:
- Semiclassical methods are crucial for understanding quantum systems.
- Coordinate transformations are complex in semiclassical integrals.
- Chaotic systems pose challenges due to amplitude factor divergence.
Purpose of the Study:
- To introduce a novel algebraic framework for systematic coordinate transformations.
- To apply this algebra to Maslov-type semiclassical wave packet theory.
- To extract a robust semiclassical correlation function.
Main Methods:
- Development of a new algebra for coordinate transformations.
- Application to Maslov-type semiclassical wave packet theory.
- Extraction of a semiclassical correlation function.
Main Results:
- The proposed algebra systematically handles coordinate transformations.
- A semiclassical correlation function is successfully extracted.
- The extracted function is free from exponentially diverging amplitude factors in chaotic systems.
Conclusions:
- The new algebra provides a powerful tool for semiclassical calculations.
- This approach resolves issues with amplitude divergence in chaotic systems.
- It offers a more stable and accurate method for correlation function analysis.