论文标题
在弗拉索夫 - 雪丁格 - 波森系统的稳态上
On steady states for the Vlasov-Schrödinger-Poisson system
论文作者
论文摘要
Vlasov-Schrödinger-Poisson系统是一种描述准低尺寸电子气体的动力学量子杂种模型。对于该系统，我们在有限的自由能最小化器中构建了大型的2D动力学/1D量子稳态，并显示了它们有限的亚带结构，单调性，独特性和条件动力学稳定性。我们的证明是基于浓度 - 紧凑性原理的，但是由于缺乏紧凑性起源于杂种性质而出现了一些其他困难（请参阅注释1.9）。为了克服困难，我们通过重新排列和部分最小化问题引入了最小化顺序的三步完善，并且自由能的强化引理（Lemma 5.3）至关重要。
The Vlasov-Schrödinger-Poisson system is a kinetic-quantum hybrid model describing quasi-lower dimensional electron gases. For this system, we construct a large class of 2D kinetic/1D quantum steady states in a bounded domain as generalized free energy minimizers, and we show their finite subband structure, monotonicity, uniqueness and conditional dynamical stability. Our proof is based on the concentration-compactness principle, but some additional difficulties arise due to lack of compactness originated from the hybrid nature (see Remark 1.9). To overcome the difficulties, we introduce a 3-step refinement of a minimizing sequence by rearrangement and partial minimization problems, and the coercivity lemma for the free energy (Lemma 5.3) is crucially employed.
