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Semiclassical propagation of Gaussian wave packets
Raphael N P Maia1, Fernando Nicacio, Raúl O Vallejos
1Centro Brasileiro de Pesquisas Físicas (CBPF), Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, Brazil.
Physical Review Letters
|June 4, 2008
Summary
We analyze Gaussian wave packets in chaotic systems, showing they become primitive WKB states. This allows standard time-dependent WKB propagation without complex trajectories for long-term analysis.
Area of Science:
- Quantum mechanics
- Chaos theory
- Statistical physics
Background:
- Understanding the long-time evolution of quantum wave packets in chaotic systems is crucial.
- Semiclassical methods offer a bridge between classical and quantum descriptions.
Purpose of the Study:
- To analyze the semiclassical evolution of Gaussian wave packets in chaotic systems.
- To determine if complex trajectories are needed for long-time propagation.
Main Methods:
- Semiclassical analysis of Gaussian wave packets.
- Application of the time-dependent WKB scheme.
- Examination of Wigner function evolution.
Main Results:
- Gaussian wave packets evolve into primitive WKB states after a short time.
- Standard time-dependent WKB propagation is sufficient for long-time evolution.
- The Wigner function exhibits classical filament structure with quantum oscillations.
Conclusions:
- Complex trajectories are not required for semiclassical wave packet propagation in chaotic systems.
- Geometric properties of classical manifolds determine the phase and amplitude of quantum oscillations.
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