We consider the problem of rigorously computing periodic minimizers to the Ohta–Kawasaki energy. We develop a method to prove existence of solutions and determine rigorous bounds on the distance between our numerical approximations and the true infinite dimensional solution and also on the energy. We use a method with prescribed symmetries to explore the phase space, computing candidate minimizers both with and without experimentally observed symmetries. We find qualitative differences between the phase diagram of the Ohta–Kawasaki energy and self consistent field theory when well away from the weak segregation limit.

中文翻译：

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Ohta-Kawasaki问题中具有一般空间群对称性的最优周期结构

我们考虑严格计算周期性的极小值到Ohta-Kawasaki能量的问题。我们开发了一种方法来证明解的存在，并确定我们的数值逼近与真正的无穷维解之间的距离以及能量的严格界限。我们使用具有规定对称性的方法来探索相空间，计算具有和不具有实验观察到的对称性的候选最小化器。当远离弱偏析极限时，我们发现大田-川崎能量的相图与自洽场论之间存在质的差异。