Complex absorbing potential and chebyshev propagation scheme

Area of Science:

• Computational physics
• Numerical methods

Background:

• Wave packet simulations require methods to handle boundary conditions.
• Complex absorbing potentials (CAPs) are used to absorb outgoing waves and prevent reflections.
• Numerical stability is crucial for accurate simulations.

Purpose of the Study:

• To analyze the effectiveness and limitations of complex absorbing potentials.
• To derive a condition for the maximum time step in wave packet propagation.
• To identify the failure point of the Chebyshev propagation scheme with CAPs.

Main Methods:

• Detailed mathematical analysis of complex absorbing potentials.
• Derivation of a limiting value for the propagation time step.
• Investigation of the Chebyshev propagation scheme's behavior with CAPs.

Main Results:

• A limiting value for the maximum propagation time step was derived.
• Exceeding this time step limit introduces significant errors.
• The Chebyshev propagation scheme was observed to fail beyond this limit.

Conclusions:

• Complex absorbing potentials are effective but have limitations related to time step size.
• Careful selection of the time step is necessary for accurate simulations using CAPs.
• The derived time step limit is critical for the stability of Chebyshev propagation with CAPs.