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Short-periodic-orbit method for excited chaotic eigenfunctions
F Revuelta1, E Vergini2, R M Benito1
1Grupo de Sistemas Complejos, Escuela Técnica Superior de Ingeniería Agronómica, Alimentaria y de Biosistemas, Universidad Politécnica de Madrid, Avenida Puerta de Hierro 2-4, 28040 Madrid, Spain.
Physical Review. E
|November 20, 2020
Summary
A new method uses wave functions on unstable orbits to calculate chaotic eigenfunctions efficiently. This approach requires fewer basis functions, significantly speeding up calculations in chaotic systems.
Area of Science:
- Quantum mechanics
- Chaos theory
- Computational physics
Background:
- Calculating excited chaotic eigenfunctions is computationally intensive.
- Existing methods face challenges with arbitrary energy windows.
- Understanding quantum chaos requires efficient numerical techniques.
Purpose of the Study:
- To present an alternative, efficient method for calculating excited chaotic eigenfunctions.
- To demonstrate the feasibility of using localized wave functions as basis sets.
- To reduce the computational cost for analyzing chaotic quantum systems.
Main Methods:
- Utilizing wave functions localized on unstable periodic orbits as basis sets.
- Applying the method to classically chaotic systems.
- Illustrating the approach with a coupled two-dimensional quartic oscillator.
Main Results:
- The proposed method is feasible and efficient.
- The number of required basis functions scales with the ratio of Heisenberg time (tH) to Ehrenfest time (tE).
- Convincing results were obtained for the quartic oscillator model.
Conclusions:
- Localized wave functions on unstable periodic orbits provide an efficient basis set for calculating chaotic eigenfunctions.
- This method offers a significant improvement in computational efficiency for quantum chaos studies.
- The approach is applicable to various classically chaotic systems.
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