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Numerical Implementation for Linear Evolution on Uniform Mesh with FFT Approximation

This study focuses on implementing a numerical splitting scheme for discretizing linear evolution operators on a uniform mesh using a three-element vector FFT. It aims to approximate the solution of the evolution governed by conduction and valence bands. The analysis includes momentum and space coordinates, emphasizing stationary states and thermal distributions.

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Numerical Implementation for Linear Evolution on Uniform Mesh with FFT Approximation

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  1. Numerical implementation: splitting scheme We discretize the linear evolution operator, Uniform mesh: is a three element vector FFT Approximate solution of the evolution governed by A

  2. Numerical implementation: splitting scheme We discretize the linear evolution operator, Uniform mesh: is a three element vector Approximate solution of the evolution governed by B

  3. Conduction band x p Momentum coordinate Space coordinate

  4. Valence band x p Space coordinate Momentum coordinate Conduction band x p Momentum coordinate Space coordinate

  5. Stationary state: Thermal distribution Conduction band Valence band

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