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Analysis of barrier scattering with real and complex quantum trajectories
Brad A Rowland1, Robert E Wyatt
1Institute for Theoretical Chemistry and Department of Chemistry and Biochemistry, The University of Texas at Austin, 1 University Station A5300, Austin, Texas 78712, USA. browland@mail.utexas.edu
The Journal of Physical Chemistry. A
|July 25, 2007
Summary
Approximate quantum trajectories, using the derivative propagation method (DPM), accurately model scattering problems. Complex-valued DPM and complex-classical trajectories show high accuracy, especially for deep tunneling through thick barriers.
Area of Science:
- Quantum mechanics
- Computational physics
- Chemical physics
Background:
- Scattering problems in quantum mechanics are crucial for understanding particle interactions.
- Simulating quantum phenomena, especially deep tunneling, presents significant computational challenges.
- Approximate methods are needed to efficiently solve complex quantum scattering scenarios.
Purpose of the Study:
- To analyze one-dimensional Eckart and Gaussian barrier scattering using approximate quantum trajectories.
- To evaluate the accuracy of real-valued and complex-valued derivative propagation methods (DPM).
- To investigate the efficacy of DPM for deep tunneling and high-energy scattering through thick barriers.
Main Methods:
- Computation of individual quantum trajectories using the derivative propagation method (DPM).
- Employment of both real-valued and complex-valued DPM quantum trajectories.
- Analysis of complex-extended barrier potentials and complex forces.
- Investigation of isochrones as specific initial conditions for complex-valued DPM trajectories.
Main Results:
- Real-valued DPM trajectories accurately reproduce transmitted probabilities for high-energy scattering at low orders.
- Complex-valued DPM accurately reproduces transmitted probabilities for both deep tunneling and high-energy scattering even at low orders.
- Complex-classical trajectories closely approximate exact results for deep barrier tunneling.
- Complex DPM demonstrates good convergence for thick barrier scattering problems at high orders.
Conclusions:
- Complex-valued DPM offers a highly accurate and efficient method for quantum scattering problems, particularly deep tunneling.
- The study elucidates the dynamics of complex-valued DPM trajectories, including the role of isochrones.
- Complex-valued DPM provides a robust approach for simulating quantum scattering phenomena with thick barriers.
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