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Temporal flooding of regular islands by chaotic wave packets
Lars Bittrich1, Arnd Bäcker1, Roland Ketzmerick1
1Technische Universität Dresden, Institut für Theoretische Physik and Center for Dynamics, 01062 Dresden, Germany and Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany.
Summary
Dynamical tunneling allows wave packets in mixed phase space systems to explore regular regions. This "flooding" effect shows universal scaling, explained by random matrix theory.
Area of Science:
- Quantum mechanics
- Chaos theory
- Statistical physics
Background:
- Investigating wave packet dynamics in systems exhibiting both regular and chaotic behavior.
- Understanding the phenomenon of dynamical tunneling in quantum systems.
Purpose of the Study:
- To quantify the increase in wave packet weight on regular islands within a chaotic sea.
- To explore the scaling behavior of this increased weight and its dependence on system parameters.
- To connect these observations to theoretical models like random matrix theory.
Main Methods:
- Simulating time evolution of wave packets in systems with mixed phase space.
- Analyzing the distribution of wave packet weight across regular and chaotic regions.
- Comparing results for quantum maps and the mushroom billiard.
- Utilizing random matrix models for theoretical validation.
Main Results:
- Observed an average increase in wave packet weight on quantized tori within regular islands due to dynamical tunneling.
- Found that this flooding weight initially increases linearly and then saturates.
- Demonstrated universal scaling of the asymptotic flooding weight with an effective tunneling coupling.
- Reproduced this universality using a random matrix model.
Conclusions:
- Dynamical tunneling plays a crucial role in wave packet spreading in mixed phase space systems.
- The asymptotic flooding weight exhibits universal scaling properties.
- Random matrix theory provides a successful framework for understanding this universality.
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