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Published on: August 2, 2019
Chaos regularization of quantum tunneling rates
Louis M Pecora1, Hoshik Lee, Dong-Ho Wu
1Materials Physics and Sensors, US Naval Research Laboratory, Washington, DC 20375, USA.
Summary
Quantum tunneling rates are influenced by the shape of potential wells. Chaotic dynamics regularize tunneling rates, while regular dynamics cause significant fluctuations, a finding explained by random-plane-wave theory.
Area of Science:
- Quantum mechanics
- Classical dynamics
- Chemical physics
Background:
- Quantum tunneling is a fundamental phenomenon in quantum mechanics.
- The behavior of quantum systems can be influenced by the geometry of their potential energy surfaces.
- Understanding tunneling rates is crucial for various fields, including quantum computing and molecular dynamics.
Purpose of the Study:
- To investigate the relationship between classical billiard dynamics and quantum tunneling rates in double-well potentials.
- To explore how the shape of potential wells affects tunneling rate fluctuations.
- To introduce and validate the concept of 'regularization of tunneling rates' in chaotic systems.
Main Methods:
- Simulating quantum tunneling rates through barriers in two-dimensional, symmetric double-well potentials.
- Analyzing the correlation between classical billiard trajectories (regular vs. chaotic) and tunneling rate variations.
- Comparing simulation results with predictions from a random-plane-wave theory of tunneling.
Main Results:
- Tunneling rates strongly depend on the shape of the potential wells, which dictates the classical dynamics.
- Regular (integrable) classical dynamics lead to large fluctuations (over two orders of magnitude) in tunneling rates with eigenenergies.
- Chaotic classical dynamics result in significantly reduced fluctuations in tunneling rates, termed 'regularization of tunneling rates'.
- A random-plane-wave theory accurately predicts the mean tunneling rates and small fluctuation variances for chaotic systems.
Conclusions:
- The shape-induced classical dynamics profoundly impact quantum tunneling rates.
- Chaotic dynamics in potential wells lead to a regularization of tunneling rates, reducing their variability.
- Random-plane-wave theory provides a robust framework for understanding tunneling in systems with chaotic classical limits.
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