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Characterizing classical periodic orbits from quantum Green's functions in two-dimensional integrable systems:
Y F Chen1, J C Tung1, P H Tuan1
1Department of Electrophysics, National Chiao Tung University, 1001 Ta-Hsueh Rd., Hsinchu 30010, Taiwan.
Physical Review. E
|February 18, 2017
Summary
A new method links quantum Green's functions to classical periodic orbits in 2D systems. This approach reveals how classical features emerge from quantum mechanics in harmonic oscillators and quantum billiards.
Area of Science:
- Quantum mechanics
- Classical mechanics
- Mathematical physics
Background:
- Classical periodic orbits are fundamental in understanding dynamical systems.
- Connecting classical and quantum descriptions remains a key challenge in physics.
Purpose of the Study:
- To develop a general method for characterizing classical periodic orbits from quantum Green's functions.
- To establish a quantitative link between quantum Green's functions and classical periodic orbits in 2D integrable systems.
Main Methods:
- Derivation of a decomposing formula involving the beta function to connect quantum Green's functions with classical periodic orbits.
- Numerical analysis of 2D commensurate harmonic oscillators and integrable quantum billiards to validate the method.
Main Results:
- The study successfully links quantum Green's functions to classical periodic orbits.
- For harmonic oscillators, classical features arise from the superposition of degenerate states.
- For quantum billiards, a damping factor is crucial for exhibiting classical features in the mesoscopic regime by enabling coherent superposition of nearly degenerate eigenstates.
Conclusions:
- The developed method provides a powerful tool for analyzing the relationship between classical and quantum mechanics in integrable systems.
- The findings offer insights into the emergence of classical behavior from quantum phenomena.
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