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Statistics of chaotic tunneling
1Division of Theoretical Mechanics, School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom.
Physical Review Letters
|September 16, 2000
Summary
We derived the distribution of tunneling rates in chaotic systems, finding it depends on orbit stability, not universal. It matches the Porter-Thomas form for unstable orbits.
Area of Science:
- Quantum mechanics
- Classical chaos
- Statistical physics
Background:
- Understanding quantum tunneling rates is crucial in various physical systems.
- Classical chaos can significantly influence quantum phenomena like tunneling.
- Previous models often assumed universality in tunneling rate distributions.
Purpose of the Study:
- To derive the distribution of quantum tunneling rates in systems exhibiting classical chaos.
- To investigate the dependence of this distribution on the stability of tunneling trajectories.
- To explore deviations from universal distributions and their causes.
Main Methods:
- Utilizing classical information on tunneling trajectories.
- Applying random matrix theory arguments to wave function overlaps.
- Analyzing the stability of specific tunneling orbits.
Main Results:
- The derived tunneling rate distribution is not universal but depends on tunneling orbit stability.
- The distribution converges to the universal Porter-Thomas form for highly unstable orbits.
- Systematic deviations from universality can occur due to scarring of periodic orbits.
Conclusions:
- The distribution of tunneling rates in chaotic systems is intrinsically linked to classical dynamics.
- The stability of classical orbits provides a key parameter for predicting tunneling rate distributions.
- Further research into orbit scarring may reveal new insights into quantum-classical correspondence.