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Scarring effects on tunneling in chaotic double-well potentials
W E Bies1, L Kaplan, E J Heller
1Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA. bies@fas.harvard.edu
Summary
This study reveals that scarring in chaotic double-well potentials influences level splitting oscillations, with periodicity linked to Planck
Area of Science:
- Quantum mechanics
- Chemical physics
- Mathematical physics
Background:
- Chaotic systems exhibit complex dynamics.
- Double-well potentials are fundamental in quantum mechanics.
- Scarring and tunneling are key phenomena in these systems.
Purpose of the Study:
- Investigate the relationship between scarring and tunneling.
- Analyze level splitting distributions in chaotic double-well potentials.
- Connect semiclassical theory with observable phenomena.
Main Methods:
- Analysis of level splitting distributions.
- Energy-dependent measurements of mean level splitting.
- Application of Creagh and Whelan's theoretical framework.
Main Results:
- Observed oscillations in mean level splitting as a function of energy.
- Identified periodic spacing of oscillations related to action.
- Correlated oscillation amplitude with scarring strength.
Conclusions:
- Scarring significantly impacts level splitting in chaotic double-well potentials.
- Results align with semiclassical predictions and finite quantum effects.
- Findings offer insights into reaction rates and resonance phenomena.