In this paper, we present splitting schemes for the two-level Bloch model. After proposing two ways to split the Bloch equation, we show that it is possible in each case togenerate exact numerical solutions of the obt...In this paper, we present splitting schemes for the two-level Bloch model. After proposing two ways to split the Bloch equation, we show that it is possible in each case togenerate exact numerical solutions of the obtained sub-equations. These exact solutionsinvolve matrix exponentials which can be expensive to compute. Here, for 2×2 matriceswe develop equivalent formulations which reduce the computational cost. These splittingschemes are nonstandard ones and conserve all the physical properties (Hermicity, positiveness and trace) of Bloch equations. In addition, they are explicit, making effectivetheir implementation when coupled with the Maxwell’s equations.展开更多
文摘In this paper, we present splitting schemes for the two-level Bloch model. After proposing two ways to split the Bloch equation, we show that it is possible in each case togenerate exact numerical solutions of the obtained sub-equations. These exact solutionsinvolve matrix exponentials which can be expensive to compute. Here, for 2×2 matriceswe develop equivalent formulations which reduce the computational cost. These splittingschemes are nonstandard ones and conserve all the physical properties (Hermicity, positiveness and trace) of Bloch equations. In addition, they are explicit, making effectivetheir implementation when coupled with the Maxwell’s equations.
