Semiclassical real-time tunneling by multiple spawning of classical trajectories

Area of Science:

• Quantum mechanics
• Computational chemistry
• Physical chemistry

Background:

• Semiclassical methods are crucial for simulating quantum dynamics.
• Real-time propagation methods offer a direct approach to solving time-dependent quantum problems.
• Gaussian wave packet methods provide a practical semiclassical approximation.

Purpose of the Study:

• To extend existing semiclassical real-time propagation methods.
• To improve the accuracy of semiclassical simulations for quantum systems.
• To apply the enhanced methods to the problem of barrier tunneling.

Main Methods:

• Systematic extension of semiclassical real-time propagation using Gaussian wave packets.
• Leveraging the composition property of the time-dependent quantum-mechanical Green function.
• Application to a benchmark model of reactive scattering involving barrier tunneling.

Main Results:

• Achieved good agreement between semiclassical and exact quantum mechanical calculations for transmission probability below the barrier top.
• Demonstrated the effectiveness of the extended method for the first time in barrier tunneling.
• Required only two insertions of unity for accurate results in the benchmark model.

Conclusions:

• The extended semiclassical real-time propagation method provides accurate results for barrier tunneling.
• This approach offers a computationally efficient alternative to exact quantum mechanical methods.
• The method shows promise for broader applications in quantum dynamics and reactive scattering.