Quantum dissipative dynamics in the Bose polaron problem and beyond

这个科学项目的主要目标是研究嵌入在多重激发存在的玻色气体中的杂质的响应。该研究项目的最初部分集中于研究一维和二维玻色-爱因斯坦凝聚中出现的不同激发。在一维情况下，我使用多种理论和数值方法研究了激波形式的低能激发。此外，我还研究了自旋轨道耦合玻色-爱因斯坦凝聚体（BECs）中杂质的耗散运动。它们在物质的条纹相中呈现出奇异的低能激发。在二维的情况下，我研究了涡旋——这是在旋转的bec中出现的激励。对于这些研究，我使用了平均场方法以及基于机器学习算法的新技术。在机器学习研究中，我研究了在低能声子存在的情况下检测这种涡旋激发。这些成就已经在国际期刊上成功发表了四篇论文。已发表的材料多与玻色气体中的激发态有关，而杂质的研究仍处于写作阶段，将在本报告提交之日起一到两个月内准备提交。

The main goal of this scientific project is to study the response of an impurity embedded in a Bose gas in which multiple excitations exist.The initial part of the research project focused on investigating different excitation appearing in Bose-Einstein condensates in one and two dimensions.In the one-dimensional case, I have studied low-energy excitations in the form of shock waves using multiple theoretical and numerical approaches. In addition, I have also investigated dissipative motion of impurities in spin-orbit coupled Bose-Einstein condensates (BECs). These present exotic low-energy excitations in their stripe phase of matter.In the two-dimensional case, I have studied vortices - which are excitations appearing in rotating BECs. For these studies, I used mean field approaches as well as new techniques based on Machine Learning alorithms. In the Machine Learning study, I investigated the detection of such vortex excitations in the presence of low-energy phonons.These achievements have lead to four successful publications in international journals. The published material is mostly related to excitations in Bose gases, while the study on impurities is still in its writing stage and will be ready for submission within one or two months from the submission date of this report.