Quantum dissipative dynamics in the Bose polaron problem and beyond

本课题的主要目的是研究玻色气体中的杂质在多重激发下的响应。课题的初期研究了一维和二维玻色-爱因斯坦凝聚体中的不同激发。在一维情况下，我利用多种理论和数值方法研究了冲击波形式的低能激发。此外，还研究了自旋轨道耦合玻色-爱因斯坦凝聚体中杂质的耗散运动。在二维的情况下，我研究了涡旋--旋转的BEC中出现的激发。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。这些成就导致在国际期刊上发表了四篇成功的论文。已发表的材料大多与玻色气体中的激发有关，而关于杂质的研究仍处于编写阶段，将在本报告提交之日起一两个月内准备提交。

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.