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Model

We now do not assume that the field E(t) is given, but solution to the Maxwell equations

t B + curl E = 0,

t E - c2 curl B = - ∂t P/ε.

The coupling with the Bloch equations is done via the expression of the polarization P=NaTr(pρ) and the space is a parameter in the Bloch equations via E(x,t).

Concerning the Cauchy problem for the Maxwell–Bloch system, we can find a unique solution for small times [Bid01]. For the long time, an answer is given with some extra assumptions in [Dum05]


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