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Scar and antiscar quantum effects in open chaotic systems
1Department of Physics and Society of Fellows, Harvard University, Cambridge, Massachusetts 02138, USA. kaplan@physics.harvard.edu
Summary
Periodic orbits significantly influence quantum systems, enhancing long-term survival probabilities beyond standard predictions. These effects, observed in weakly open chaotic systems, are linked to specific orbital structures.
Area of Science:
- Quantum mechanics
- Classical chaos
- Statistical physics
Background:
- Weakly open quantum systems with chaotic classical limits exhibit complex behaviors.
- Periodic orbit effects are crucial for understanding resonance phenomena.
Purpose of the Study:
- To predict and numerically observe strong periodic orbit effects in weakly open quantum systems.
- To investigate the role of antiscars and unstable periodic orbits on system properties.
Main Methods:
- Numerical simulations of weakly open quantum systems.
- Analysis of resonance properties and long-time survival probabilities.
- Quantitative comparison with theoretical predictions based on stability matrices.
Main Results:
- Antiscars lead to exponentially narrow resonances when openings are on unstable periodic orbits.
- Long-time survival probability is exponentially enhanced compared to random matrix theory predictions.
- Remaining probability density shows non-trivial distributions influenced by other system orbits.
Conclusions:
- Periodic orbit effects provide a novel mechanism for enhanced quantum system survival.
- These quantum effects, appearing beyond Heisenberg time, lack classical counterparts.
- The stability matrix of periodic orbits quantitatively determines decay rates and survival probabilities.