Demos.CrossingTully.Extended
The most demanding of the three standard examples is a situation with an extended region of strong nonadiabatic coupling. This example poses a severe challenge to quantum-classical algorithms.
| Method | Visualization |
|---|---|
| Quant.-mech. wavefunction |
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| Fewest switches surface hopping |
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| Single switch surface hopping |
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For strongly negative values of the position coordinate, the two adiabatic potentials are essentially parallel with a rather small energetic gap. A wavepacket coming from that direction undergoes strong nonadiabatic transitions in the extended coupling region between -10 and 0 while the transport on the two potentials is essentially the same. When it reaches positive coordinates where the two potentials start to deviate and the two densities evolve in a strongly different way: Lower state population is transmitted, accelerated, and eventually absorbed near the edge of the grid, while population on the upper state is reflected. On the way back, it passes the extended crossing zone again, and another phase of strongly nonadiabatic behavior is observed.
Apart from the periodic boundary conditions (not implemented in any of the trajectory-based methods), the quantum wavepacket dynamics is reproduced surprisingly well by the surface hopping trajectory approximation for t ≤ 2000.
