Strang splitting schemes for N-level Bloch models

TL;DR

This paper introduces a computationally efficient splitting scheme for N-level Bloch models that preserves qualitative properties and avoids costly matrix exponential calculations by using Newton interpolation.

Contribution

It extends splitting schemes to N-level Bloch models and employs Newton interpolation to reduce computational costs while maintaining qualitative properties.

Findings

The scheme preserves all qualitative properties of the Bloch equations.

Numerical simulations demonstrate the scheme's efficiency and accuracy.

Compared to other methods, it offers reduced computational cost.

Abstract

We extend to the N-level Bloch model the splitting scheme which use exact numerical solutions of sub-equations. These exact solutions involve matrix exponentials which we want to avoid to calculate at each time step. We use Newton interpolation to reduce the computational cost. The resulting scheme is nonstandard and preserves all qualitative properties of the Bloch equations. We show numerical simulations to compare this approach with a few other schemes.