论文标题
通过平滑电势快速定位本征函数
Fast localization of eigenfunctions via smoothed potentials
论文作者
论文摘要
我们研究了预测有限域中$（ - δ+v）ϕ =λ$ $ω\ subset \ mathbb {r}^d $的问题的问题$（δ+v）ϕ =λϕ $，以迅速变化。 Filoche＆Mayboroda引入了功能$ 1/U $，其中$（ - δ+ V）u = 1 $，作为$ V $的合适正规化，从其最小者可以预测具有很高准确性的特征函数的位置。我们提出了一种快速产生非常相似的景观的快速方法，可以用于相同的目的，并且可以非常有效地计算：例如，在$ n \ times n $ grid上的计算时间，例如，仅$ \ mathcal {o}（o}（n^2 \ log log {n}）$，这是两个Ffts的成本。
We study the problem of predicting highly localized low-lying eigenfunctions $(-Δ+V) ϕ= λϕ$ in bounded domains $Ω\subset \mathbb{R}^d$ for rapidly varying potentials $V$. Filoche & Mayboroda introduced the function $1/u$, where $(-Δ+ V)u=1$, as a suitable regularization of $V$ from whose minima one can predict the location of eigenfunctions with high accuracy. We proposed a fast method that produces a landscapes that is exceedingly similar, can be used for the same purposes and can be computed very efficiently: the computation time on an $n \times n$ grid, for example, is merely $\mathcal{O}(n^2 \log{n})$, the cost of two FFTs.
