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12:03
A Method for Tracking the Time Evolution of Steady-State Evoked Potentials
Published on: May 25, 2019
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Exponential propagators for the Schrödinger equation with a time-dependent potential.
Philipp Bader1, Sergio Blanes2, Nikita Kopylov2
1Departament de Matemàtiques, Universitat Jaume I, E-12071 Castellón, Spain.
The Journal of Chemical Physics
|July 2, 2018
Summary
New commutator-free (CF) propagators enhance numerical integration of the time-dependent Schrödinger equation. These advanced methods offer improved performance for complex quantum systems.
Area of Science:
- Quantum mechanics
- Computational physics
- Numerical analysis
Background:
- The Schrödinger equation governs quantum systems.
- Time-dependent Hamiltonians pose computational challenges.
- Commutator-free (CF) propagators offer efficiency for such problems.
Purpose of the Study:
- To develop novel, high-order CF propagators for time-dependent Schrödinger equations.
- To improve the computational efficiency and accuracy of numerical integration methods.
- To tailor CF propagators for Hamiltonians composed of kinetic energy and time-dependent potentials.
Main Methods:
- Developing new fourth- and sixth-order CF propagators.
- Introducing a novel sixth-order CF propagator with a cost-free double commutator term.
- Utilizing the Lanczos method for computing the action of exponential operators on vectors.
Main Results:
- Achieved considerably improved performance with the new CF propagators.
- Demonstrated the effectiveness of the novel sixth-order propagator.
- Validated the performance of the developed methods through numerical examples.
Conclusions:
- The proposed CF propagators offer significant advantages for integrating the time-dependent Schrödinger equation.
- The new methods provide a more efficient and accurate approach to solving complex quantum dynamics.
- The cost-free term in the novel propagator further enhances computational efficiency.
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