Landau Damping Of Collective Excitation In Bose-einstein Condensate Homogeneous System

Bose-Einstein condensate is the intersection of degenerate quantum multi-systems in atomic and molecular physics and so on.Elementary excitation is the basic research content of statistical and condensed matter physics.Collective excitation is an important research direction of BoseEinstein condensate.Then the research on collective excitation has a great theoretical guiding effect on the in-depth study of the ground state and thermodynamic properties of condensates.Especially the research concerning low-energy collective excitation has attracted extensive interest of scholars.Damping and frequency shift are two accompanying characteristic phenomena in collective excitation experiments.Damping and frequency shift have two mechanisms,Landau and Beliaev.Many theoretical works focus on the Landau mechanism,and damping is firstly studied.The research methods of collective excitation damping and frequency shift are mainly divided into two categories,one is two fluid theory,which is used for high temperature and high density,and the other is mean field theory,which is used for low temperature and low density.In this manuscript,the Landau damping of collective excitation in a homogeneous Bose-Einstein condensed system is studied by using Hartree-Fock-Bogoliubov mean field theory.Manuscript[Giorgini S,Phys.Rev.A,1998,57(4):2949-2957]is the pioneer work of constructing HartreeFock-Bogoliubov mean field theory of collective excitation damping of Bose-Einstein condensate,in which Landau damping of collective excitation in uniform systems is studied,but the conclusion is wrong.In the derivation of the conclusion,the quasi-particle resonance transition and collective excitation energy are used to approximate.Firstly,this manuscript does not strictly deduce the above two approximations and gives the functional relationship between damping and temperature in the range of large parameter changes,as well as obtains more reasonable and universal analytical calculation results.The functional relationship between damping and temperature under the two limit conditions of approaching absolute zero and critical temperature of phase transition is discussed,especially the functional relationship between damping and temperature of phonons whose energy is far less than that of particle interaction under the two limit temperature conditions.The error function is introduced to analyze the contribution of quasiparticle transition with different energy to damping,and the details of quasiparticle interaction are given.Then,the two approximations are used to correct the errors in the manuscript and the application scope of the two approximations is analyzed by using the calculation results of the above error function.In order to correct the errors in the manuscript,the derivation process of this manuscript is given completely and the details are put in the appendix.The outcomes of this manuscript does good to deepen the understanding of the significance of Hartree-Fock-Bogoliubov mean field theory in the study of the collective excitation multi-body properties of Bose-Einstein condensate,and study deeply the Landau damping and frequency shift of collective excitation in one-component BoseEinstein condensate.