Dynamics of solutions to the Gross-Pitaevskii equation describing dipolar Bose-Einstein condensates
Dynamics of solutions to the Gross-Pitaevskii equation describing dipolar Bose-Einstein condensates
复制标题
DOI：
--
复制
发表时间：
2021-10
期刊：
影响因子：
--
通讯作者：
J. Bellazzini;Luigi Forcella
中科院分区：
文献类型：
--
作者：
J. Bellazzini;Luigi Forcella
本文综述了非囚禁偶极量子气体的Gross-Pitaevskii方程（GPE）解的长时间动力学的一些最新结果。我们描述的渐近行为的解决方案，为不同的初始配置的初始数据在能量空间中，特别是数据低于，高于，并在质量-能量阈值。利用抛物型双调和方程的热核的衰减性质，我们重新讨论了Riesz变换的幂的一些性质。这些衰减特性在建立所研究的GPE的解决方案的动力学特征中发挥着重要作用。
We review some recent results on the long time dynamics of solutions to the Gross-Pitaevskii equation (GPE) governing non-trapped dipolar Quantum Gases. We describe the asymptotic behaviours of solutions for different initial configurations of the initial datum in the energy space, specifically for data below, above, and at the Mass-Energy threshold. We revisit some properties of powers of the Riesz transforms by means of the decay properties of the heat kernel associated to the parabolic biharmonic equation. These decay properties play a fundamental tool in establishing the dynamical features of the solutions to the studied GPE.