The dynamics of the weak non//near matter sofitary waves in a spin-1 condensates with harmonic external potential are investigated analytically by a perturbation method. It is shown that, in the small amplitude limit,...The dynamics of the weak non//near matter sofitary waves in a spin-1 condensates with harmonic external potential are investigated analytically by a perturbation method. It is shown that, in the small amplitude limit, the dynamics of the solitary waves are governed by a variable-coetficient Korteweg-de Vries （KdV） equation. The reduction to the （KdV） equation may be useful to understand the dynamics of nonlinear matter waves in spinor BECs. The analytical expressions for the evolution of soliton show that the small-amplitude vector solitons of the mixed types perform harmonic oscillations in the presence of the trap. Furthermore, the emitted radiation profiles and the soliton oscillation frequency are also obtained.展开更多
The stability of the ground state of two-component Bose-Einstein condensates （BEGs） loaded into the central well of an axially symmetric Bessel lattices （BLs） potential with attractive or repulsive atoms interacti...The stability of the ground state of two-component Bose-Einstein condensates （BEGs） loaded into the central well of an axially symmetric Bessel lattices （BLs） potential with attractive or repulsive atoms interactions is studied using the time-dependent Gross-Pitaevskii equation （GPE）. By using the variational method, we find that stable ground state of two-component BEGs can exist in BLs. The BLs＇s depth and the intra-species atom interaction play an important role in the stability of ground state. The collapse of two-component BEGs in BLs is also studied and a collapse condition for trapped two-component BEGs is obtained. It is shown that the two-component BEGs exhibit rich collapse dynamics. That is, the two-component BEGs can collapse in the system with both intra- and inter-attractive, or with intra-attractive and inter-repulsive, or with intra-repulsive and inter-attractive atom interactions. Furthermore, the control of the collapse of the two-component BEGs in BLs is discussed in detail. The stability diagram of the ground state in parameter space is obtained. The results show that the collapse of two-component BEGs can be controlled by temporal modulation of the atom interaction.展开更多
The kinetic behavior of an aggregation-annihilation system with two species groups is studied in this paper.We propose that an aggregation reaction occurs only between the same species and an irreversible joint annihi...The kinetic behavior of an aggregation-annihilation system with two species groups is studied in this paper.We propose that an aggregation reaction occurs only between the same species and an irreversible joint annihilation reaction occurs only between the two species belonging to distinct groups. Based on the mean-field theory, we investigate the rate equations of the process with constant reaction rates and obtain the asymptotic descriptions of the cluster-mass distributions for the symmetrical cases. We find that the cluster-mass distribution of each species obeys a standard scaling description in certain cases. Meanwhile, breakdown of the standard scaling description is also found for the distribution in some special cases and the cluster-mass distribution comes in a peculiar scaling regime. The evolutionbehaviour of the system depends crucially on the reaction rates and the ratio of initial concentrations between the two groups. Moreover, the species numbers of the two groups also play important roles in the properties of the cluster distributions.展开更多
Recently the mass and the basic structure of SM Higgs boson （H^0） have been discussed by the author with obtaining asymptotic solution for the equation of motion of nonlinear Klein-Gordon type partial differential e...Recently the mass and the basic structure of SM Higgs boson （H^0） have been discussed by the author with obtaining asymptotic solution for the equation of motion of nonlinear Klein-Gordon type partial differential equation. In this paper, we will treat with above in mind： masses of glueball （GB） of ground state and of certain fo mesons, ur, Higgs boson （ur-H^0） which will consist of a number of GBs and/or fo above for respective fullerene structure, a representation of these fo mesons＇ masses by masses of n octet and GB, and transformation of ur-H^0 into H^0.展开更多
We obtain soliton and plane wave solutions for the coupled nonlinear Schrotinger equations, which describe the dynamics of the three-component Bose-Einstein condensates by using the Hirota method. Meanwhile we find th...We obtain soliton and plane wave solutions for the coupled nonlinear Schrotinger equations, which describe the dynamics of the three-component Bose-Einstein condensates by using the Hirota method. Meanwhile we find that the system which has attractive atomic interaction will only possess a shape changing （inelastic） collision property due to intensity redistribution in the absence of the spin-exchange interaction. As a discussed example, we investigate the one-soliton, two-soliton solutions and collisional effects between bright two-soliotn solution, which lead to the intensity redistribu tion.展开更多
By using the invariant theory, we study the phases of two-component Bose-Einstein condensates with a coupling drive under the case that the strength of the interatomic interaction in each condensate equals the intersp...By using the invariant theory, we study the phases of two-component Bose-Einstein condensates with a coupling drive under the case that the strength of the interatomic interaction in each condensate equals the interspecies interaction. The dynamical and geometric phases are presented respectively. The Aharonov-Anandan phase is also obtained under the cyclical evolution.展开更多
We investigate tunneling and self-trapping of superfluid Fermi gases under a two-mode ansatz in different regimes of the crossover from Bardeen-Cooper-Schrieffer （BCS） superfluid to Bose-Einstein condensates （BEC）...We investigate tunneling and self-trapping of superfluid Fermi gases under a two-mode ansatz in different regimes of the crossover from Bardeen-Cooper-Schrieffer （BCS） superfluid to Bose-Einstein condensates （BEC）. Starting from a generalized equation of state, we derive the coupled equations of relative atom-pair number and relative phase about superfluid Fermi gases in a double-well system and then classify the different oscillation behaviors by the tunneling strength and interactions between atoms. Tunneling and self-trapping behaviors are considered in the whole BCS-BEC crossover in the ease of a symmetric double-well potential. We show that the nonlinear interaction between atoms makes the self-trapping more easily realized in BCS regime than in the BEC regime and stability analysis is also given.展开更多
We study Bose-Einstein condensation in a linear trap with a dimple potential where we model dimple potentials by Dirac δ function. Attractive and repulsive dimple potentials are taken into account. This model allows ...We study Bose-Einstein condensation in a linear trap with a dimple potential where we model dimple potentials by Dirac δ function. Attractive and repulsive dimple potentials are taken into account. This model allows simple, explicit numerical and analytical investigations of noninteracting gases. Thus, the Schrdinger equation is used instead of the Gross-Pitaevski equation. We calculate the atomic density, the chemical potential, the critical temperature and the condensate fraction. The role of the relative depth of the dimple potential with respect to the linear trap in large condensate formation at enhanced temperatures is clearly revealed. Moreover, we also present a semi-classical method for calculating various quantities such as entropy analytically. Moreover, we compare the results of this paper with the results of a previous paper in which the harmonic trap with a dimple potential in 1D is investigated.展开更多
The coupled Gross–Pitaevskii equations for two-species BEC have been solved analytically under the Thomas-Fermi approximation(TFA). Based on the analytical solution, two formulae are derived to relate the particle nu...The coupled Gross–Pitaevskii equations for two-species BEC have been solved analytically under the Thomas-Fermi approximation(TFA). Based on the analytical solution, two formulae are derived to relate the particle numbers N_A and N_B with the root mean square radii of the two kinds of atoms. Only the case that both kinds of atoms have nonzero distribution at the center of an isotropic trap is considered. In this case the TFA has been found to work nicely. Thus, the two formulae are applicable and are useful for the evaluation of N_A and N_B.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos.10774120 and 10975114the Natural Science Foundation of Gansu Province under Grant No.1010RJZA012Natural Science Foundation of Northwest Normal University under Grant No.NWNU-KJCXGC-03-48
文摘The dynamics of the weak non//near matter sofitary waves in a spin-1 condensates with harmonic external potential are investigated analytically by a perturbation method. It is shown that, in the small amplitude limit, the dynamics of the solitary waves are governed by a variable-coetficient Korteweg-de Vries （KdV） equation. The reduction to the （KdV） equation may be useful to understand the dynamics of nonlinear matter waves in spinor BECs. The analytical expressions for the evolution of soliton show that the small-amplitude vector solitons of the mixed types perform harmonic oscillations in the presence of the trap. Furthermore, the emitted radiation profiles and the soliton oscillation frequency are also obtained.
基金National Natural Science Foundation of China under Grant Nos.10774120 and 10475066the Natural Science Foundation of Gansu Province under Grant No.3ZS051-A25-013the Creation of Science and Technology of Northwest Normal University,China under Gant No.NWNU-KJCXGC-03-17
文摘The stability of the ground state of two-component Bose-Einstein condensates （BEGs） loaded into the central well of an axially symmetric Bessel lattices （BLs） potential with attractive or repulsive atoms interactions is studied using the time-dependent Gross-Pitaevskii equation （GPE）. By using the variational method, we find that stable ground state of two-component BEGs can exist in BLs. The BLs＇s depth and the intra-species atom interaction play an important role in the stability of ground state. The collapse of two-component BEGs in BLs is also studied and a collapse condition for trapped two-component BEGs is obtained. It is shown that the two-component BEGs exhibit rich collapse dynamics. That is, the two-component BEGs can collapse in the system with both intra- and inter-attractive, or with intra-attractive and inter-repulsive, or with intra-repulsive and inter-attractive atom interactions. Furthermore, the control of the collapse of the two-component BEGs in BLs is discussed in detail. The stability diagram of the ground state in parameter space is obtained. The results show that the collapse of two-component BEGs can be controlled by temporal modulation of the atom interaction.
文摘The kinetic behavior of an aggregation-annihilation system with two species groups is studied in this paper.We propose that an aggregation reaction occurs only between the same species and an irreversible joint annihilation reaction occurs only between the two species belonging to distinct groups. Based on the mean-field theory, we investigate the rate equations of the process with constant reaction rates and obtain the asymptotic descriptions of the cluster-mass distributions for the symmetrical cases. We find that the cluster-mass distribution of each species obeys a standard scaling description in certain cases. Meanwhile, breakdown of the standard scaling description is also found for the distribution in some special cases and the cluster-mass distribution comes in a peculiar scaling regime. The evolutionbehaviour of the system depends crucially on the reaction rates and the ratio of initial concentrations between the two groups. Moreover, the species numbers of the two groups also play important roles in the properties of the cluster distributions.
文摘Recently the mass and the basic structure of SM Higgs boson （H^0） have been discussed by the author with obtaining asymptotic solution for the equation of motion of nonlinear Klein-Gordon type partial differential equation. In this paper, we will treat with above in mind： masses of glueball （GB） of ground state and of certain fo mesons, ur, Higgs boson （ur-H^0） which will consist of a number of GBs and/or fo above for respective fullerene structure, a representation of these fo mesons＇ masses by masses of n octet and GB, and transformation of ur-H^0 into H^0.
基金The project supported by the Natural Science Foundation of Yunnan Province under Grant No. 2005A20002M.Acknowledgments We express our sincere thanks to Ke-Zhao Zhou and Bo Xiong for helpful discussions.
文摘We obtain soliton and plane wave solutions for the coupled nonlinear Schrotinger equations, which describe the dynamics of the three-component Bose-Einstein condensates by using the Hirota method. Meanwhile we find that the system which has attractive atomic interaction will only possess a shape changing （inelastic） collision property due to intensity redistribution in the absence of the spin-exchange interaction. As a discussed example, we investigate the one-soliton, two-soliton solutions and collisional effects between bright two-soliotn solution, which lead to the intensity redistribu tion.
基金The project supported by National Natural Science Foundation of China under Grant No. 10574060 and Natural Science Foundation of Beijing under Grant No. 1072010
文摘By using the invariant theory, we study the phases of two-component Bose-Einstein condensates with a coupling drive under the case that the strength of the interatomic interaction in each condensate equals the interspecies interaction. The dynamical and geometric phases are presented respectively. The Aharonov-Anandan phase is also obtained under the cyclical evolution.
基金Supported by Supported by National Natural Science Foundation of China under Grant Nos. 10864006,11047101,11091240227,and11105039by Ph.D. Program Scholarship Fund of East China Normal University under Grant No. 20080044by Research Fund of Jiangsu University of Science and Technology under Grant No. 35051002
文摘We investigate tunneling and self-trapping of superfluid Fermi gases under a two-mode ansatz in different regimes of the crossover from Bardeen-Cooper-Schrieffer （BCS） superfluid to Bose-Einstein condensates （BEC）. Starting from a generalized equation of state, we derive the coupled equations of relative atom-pair number and relative phase about superfluid Fermi gases in a double-well system and then classify the different oscillation behaviors by the tunneling strength and interactions between atoms. Tunneling and self-trapping behaviors are considered in the whole BCS-BEC crossover in the ease of a symmetric double-well potential. We show that the nonlinear interaction between atoms makes the self-trapping more easily realized in BCS regime than in the BEC regime and stability analysis is also given.
文摘We study Bose-Einstein condensation in a linear trap with a dimple potential where we model dimple potentials by Dirac δ function. Attractive and repulsive dimple potentials are taken into account. This model allows simple, explicit numerical and analytical investigations of noninteracting gases. Thus, the Schrdinger equation is used instead of the Gross-Pitaevski equation. We calculate the atomic density, the chemical potential, the critical temperature and the condensate fraction. The role of the relative depth of the dimple potential with respect to the linear trap in large condensate formation at enhanced temperatures is clearly revealed. Moreover, we also present a semi-classical method for calculating various quantities such as entropy analytically. Moreover, we compare the results of this paper with the results of a previous paper in which the harmonic trap with a dimple potential in 1D is investigated.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11372122,11274393,11574404,and 11275279the Open Project Program of State Key Laboratory of Theoretical Physics,Institute of Theoretical Physics,Chinese Academy of Sciences,China+1 种基金the National Basic Research Program of China(2013CB933601)Guangdong Natural Science Foundation(2016A030313313)
文摘The coupled Gross–Pitaevskii equations for two-species BEC have been solved analytically under the Thomas-Fermi approximation(TFA). Based on the analytical solution, two formulae are derived to relate the particle numbers N_A and N_B with the root mean square radii of the two kinds of atoms. Only the case that both kinds of atoms have nonzero distribution at the center of an isotropic trap is considered. In this case the TFA has been found to work nicely. Thus, the two formulae are applicable and are useful for the evaluation of N_A and N_B.
