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Dissipative quantum chaos: transition from wave packet collapse to explosion.
Gabriel G Carlo1, Giuliano Benenti, Dima L Shepelyansky
1Center for Nonlinear and Complex Systems, Università degli Studi dell'Insubria and Istituto Nazionale per la Fisica della Materia, Unità di Como, Italy.
Physical Review Letters
|October 26, 2005
Summary
Quantum trajectories reveal how dissipative chaotic systems behave. Strong dissipation causes wave packet collapse, while weak dissipation leads to explosion, with a transition dependent on dissipation and Ehrenfest time scales.
Area of Science:
- Quantum mechanics
- Chaos theory
- Statistical physics
Background:
- Dissipative chaotic systems exhibit complex dynamics.
- The Zaslavsky map is a model for such systems.
- Understanding quantum effects in chaos is crucial.
Purpose of the Study:
- Investigate quantum dynamics of a dissipative chaotic system.
- Analyze the role of dissipation strength.
- Determine the transition between collapse and explosion phenomena.
Main Methods:
- Quantum trajectories approach.
- Phase space analysis.
- Study of the Zaslavsky map.
Main Results:
- Strong dissipation leads to wave function collapse into a compact packet.
- Weak dissipation causes quantum wave packet explosion on the Ehrenfest time scale.
- Transition from collapse to explosion occurs when dissipation time exceeds Ehrenfest time.
Conclusions:
- Quantum effects significantly alter chaotic system dynamics.
- Dissipation strength is key in determining system behavior.
- Integrable systems show predominantly collapse, not explosion.