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Semiclassical description of wave packet revival
Fabricio Toscano1, Raúl O Vallejos, Diego Wisniacki
1Instituto de Física, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ, Brazil. toscano@if.ufrj.br
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2009
Summary
Semiclassical theories accurately describe quantum wave packet revival in a quartic oscillator. Both time-dependent WKB and Van Vleck methods show impressive agreement up to and beyond revival times.
Area of Science:
- Quantum mechanics
- Theoretical physics
- Chemical physics
Background:
- Quantum wave packet revival is a complex long-time phenomenon.
- Understanding revival dynamics is crucial for quantum state control.
- Semiclassical methods offer computational advantages for quantum dynamics.
Purpose of the Study:
- To quantitatively assess semiclassical theories for wave packet revival.
- To investigate the accuracy of time-dependent WKB and Van Vleck propagation.
- To determine the long-time validity of these semiclassical approaches.
Main Methods:
- Applied semiclassical theory, specifically time-dependent WKB and Van Vleck propagation.
- Studied the one-dimensional quartic oscillator (Kerr type Hamiltonian).
- Analyzed the autocorrelation function and wave function evolution.
Main Results:
- Both time-dependent WKB and Van Vleck propagation accurately described wave packet revival.
- Impressive quantitative agreement was observed up to and beyond the revival time.
- The Van Vleck approach demonstrated analytical agreement extending to arbitrary long times.
Conclusions:
- Semiclassical theories provide a highly accurate description of quantum wave packet revival.
- The Van Vleck method offers a robust and analytically verifiable approach for long-time quantum dynamics.
- These findings support the utility of semiclassical methods in studying complex quantum systems.
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