Bénard–von Kármán Vortex Street In A Dipolar BEC

Bose-Einstein condensation(BEC)with dipolar interactions,since its novel physical phenomena,have received much attention recently from both experimental and theoretical studies.With the realization of a dipolar Chromium BEC,it is now possible to go beyond such isotropic interactions in BEC.Dipolar interactions have a long-range and anisotropic component.These features crucially influence the ground-state properties,stability,and dynamics of the BEC.Vortex street in superfluid is one of the hot spots in the field of cold atoms.However,vortex street formation was not found in these studies,probably because the parameter region for which a vortex street emerges is narrow.In this paper,we plan to study the vortex street in dipolar BEC.In the first chapter,the physical background and basic knowledge of the study are briefly introduced,including the introduction of BEC and its realization in experiment,the characteristics of BEC and the nonlinear Schrodinger equation in BEC.Then we introduce the discovery of phenomenon,its application in real life and the negative effect Bénard–von Kármán vortex street brings to our production and life.Finally,the research status and significance of Bénard–von Kármán vortex street in BEC are introduced.In the second chapter,we mainly introduces the research significance of dipole BEC,the characteristics of dipole interaction,and the current situation and development of dipole BEC at home and abroad.At the same time,the theoretical basis and numerical research methods involved of this research are simply sorted out,including the simplification process of GP equation,virtual time evolution method and time splitting spectrum method.In the third chapter,the main work of this paper is mainly introduced.Firstly,in the mean-field theory,we processe the three-dimensional GP equations,and obtain a dimensionless GP equation to describ the dipole BEC system.We numerically solve GP equation in two dimensions under the periodic boundary condition using the virtual time evolution method.The initial state is the stationary state of GP equation after plusing a small amount of noise to break the symmetry.Then,we consider a dipole BEC of atoms with an obstacle potential moving with a certain velocity in it,we want to find out the dynamic behavior of the dipole BEC.It is important to study the cases of various shapes and sizes of obstacle potentiasl,various speeds of obstacle potentiasl,and various dipolar interactions of the BEC systerms,all of which play important role in the creation of the votex street.We also want to know the parameter range in which a vortex street emerges and get the vortex phase diagram of the dipole BEC.In the end,it is worthy to study the mechanical mechanism of vortex pairs by caculating the drag force on the obstacle,for providing a mathematical description of the alternate creation of the votex pairs.The research of this project is beneficial to the further understanding of the dipole BEC system,and it is of great significance to the study of the quantum vortex structure.