Study of dynamical behaviour and fermionization of a bosonic gas in funnel potential

This paper presents a funnel external potential model to investigate dynamic properties of ultracold Bose gas. By using variational method, we obtain the ground-state energy and density properties of ultracold Bose atoms. The results show that the ultracold Bose gas confined in a funnel potential experiences the transition from three-dimensional regime to quasi-one-dimensional regime in a small aspect ratio, and undergoes fermionization process as the aspect ratio increases.     

Photoassociation of ultracold RbCs molecules into the （2）0- state （v = 189,190） below the 5S1/2 ＋ 6P1/2 dissociation limit

Ultracold polar RbCs molecules are produced via photoassociation in a laser-cooled mixture of 85Rb and 133Cs atoms. The a 3Σ+ state molecules which decay from electronically excited (2)0- state RbCs molecules are detected by resonance-enhanced two-photon ionization. The new rovibrational levels (v = 189, 190) in the (2)0- state are also observed, which exist in theory and have not been observed in experiments yet. The corresponding rotational constants are measured by photoassociation spectroscopy, which are consistent with theoretical calculations using a nonrigid rotor model.     

Novel Quantum Phases of Ultracold Bosonic Atoms in Honeycomb Optical Lattice

We study the quantum phase transition of ultracold atoms in the honeycomb optical lattice. The Hamiltonian of ultracold bosonic atoms in the honeycomb optical lattice is derived. We take the mean-field approximation and further solve the Hamiltonian with the numerical diagonalization method. We obtain the phase diagram and find that the Mort-insulator （MI）, density wave （DW） and modulated superfluid （MS） phases appear. Furthermore, the phase diagram is analyzed according to the order parameter and the average number of particles.     

Effect of Spatial Dimension and External Potential on Joule-Thomson Coefficients of Ideal Bose Gases

Based on the form of the n-dimensional generic power-law potential, the state equation and the heat capacity, the analytical expressions of the Joule-Thomson coefficient （3TC） for an ideal Bose gas are derived in n-dimensional potential. The effect of the spatial dimension and the external potential on the JTC are discussed, respectively. These results show that： （i） For the free ideal Bose gas, when n/s ≤ 2 （n is the spatial dimension, s is the momentum index in the relation between the energy and the momentum）, and T → Tc （Tc is the critical temperature）, the JTC can obviously improve by means of changing the throttle valve＇s shape and decreasing the spatial dimension of gases. （ii） For the inhomogeneous external potential, the discriminant △= [1 - y∏^ni=1（kT/εi）^1/tiГ（1/ti＋1）] （k is the Boltzmann Constant, T is the thermodynamic temperature, ε is the external field＇s energy）, is obtained. The potential makes the JTC increase when △ 〉 0, on the contrary, it makes the JTC decrease when A 〈△. （iii） In the homogenous strong external potential, the JTC gets the maximum on the condition of kTεi〈〈1.     

Bose-Einstein Condensation in Linear Sigma Model at Hartree Approximation

The BEG of charged pions is investigated in the framework of O（4） linear sigma model. By using Cornwall- Jackiw-Tomboufis formalism, we have derived the gap equations for the effective masses of the mesons at finite temperature and finite isospin density. The critical temperature and phase diagram of BEG are discussed in the non-chiral limit at Hartree approximation.     

Elliptic Function Waves of Spinor Bose-Einstein Condensates in an Optical Lattice

An improved nonlinear Schrodinger equation different from usual one of spinor Bose-Einstein condensates （BECs） in an optical lattice are obtained by taking into account a nonlinear term in the equation of motion for probability amplitude of spins carefully. The elliptic function wave solutions of the model are found under specific boundary condition, for example, the two ends of the atomic chain are fixed. In the case of limit the elliptic function wave solutions are reduced into spin-wave-like or solitons.     

Landau-Zener Tunnelling of Two-Component Bose-Einstein Condensates in Optical Lattices

We investigate the Landau-Zener tunnelling of two-component Bose-Einstein condensates （BECs） in optical lattices. In the neighborhood of the Brillouin zone edge, the system can be reduced to two coupled nonlinear two-level models. From the models, we calculate the change of the tunnelling probability for each component with the linear sweeping rate. It is found that the probability for each component exhibits regular oscillating behavior for the larger sweeping rate, but for smaller rate the oscillation is irregular. Moreover, the asymmetry of the tunnelling between the two components can be induced by the unbalanced initial populations or the inequality of the two self-interactions when the cross-interaction between the components exists. The result can not be found in the single component BECs.     

Systematically investigating the polarization gradient cooling in an optical molasses of ultracold cesium atoms

We systematically investigate the polarization gradient cooling （PGC） process in an optical molasses of ultracold cesium atoms. The SR mode for changing the cooling laser, which means that the cooling laser frequency is stepped to the setting value while its intensity is ramped, is found to be the best for the PGC, compared with other modes studied. We verify that the heating effect of the cold atoms, which appears when the cooling laser intensity is lower than the saturation intensity, arises from insufficient polarization gradient cooling. Finally, an exponential decay function with a statistical explanation is introduced to explain the dependence of the cold atom temperature on the PGC interaction time.     

Unconventional Energy Bands and Chirality of Ultracold Atoms in Trilayer Honeycomb Lattice

We investigate ultracold fermionic atoms in the trilayer honeycomb lattice. In the low energy approximation, we derive an effective Hamiltonian for pseudospins. The energy spectrum shows a cubic form of the wavevector and is gapless. The quasiparticles and quasiholes are ehiral and show Berry＇s phase π when the wavevector adiabatically evolves along a closed circle, Furthermore, the experimental detection of the energy spectrum is proposed with Bragg scattering techniques.     

Unconventional Landau Levels of Ultracold Fermionic Atoms on Two-Dimensional Honeycomb Lattice

We investigate the unconventional Landau levels of ultracold fermionic atoms on the two-dimensional honeycomb optical lattice subjected to an effective magnetic field, which is created with optical means. In the presence of the effective magnetic field, the energy spectrum of the unconventional Landau levels is calculated. Furthermore, we propose to detect the unconventional Landau levels with Bragg scattering techniques.     

Crossover from one to three dimensions for a gas of hard-core bosons

We develop a variational theory of the crossover from the one-dimensional (1D) regime to the 3D regime for ultracold Bose gases in thin waveguides. Within the 1D regime we map out the parameter space for fermionization, which may span the full 1D regime for suitable transverse confinement.     

Tunneling of Bose-Einstein condensate and interference effect in a harmonic trap with a Gaussian energy barrier

The tunneling effect of Bose-Einstein condensate (BEC) in a harmonic trap with a Gaussian energy barrier is studied in this paper. The initial condensate evolves into two separate moving condensates after the tunneling time under certain conditions. The interference pattern between the two moving condensates is given as a comparison and as a further demonstration of the existence of the global phase.     

Groupoids, Discrete Mechanics, and Discrete Variation

After introducing some of the basic definitions and results from the theory of groupoid and Lie algebroid, we investigate the discrete Lagrangian mechanics from the viewpoint of groupoid theory and give the connection between groupoids variation and the methods of the first and second discrete variational principles.     

Higher-Dimensional Lie Algebra and New Integrable Coupling of Discrete KdV Equation

Based on semi-direct sums of Lie subalgebra G, a higher-dimensional 6 × 6 matrix Lie algebra sμ（6） is constructed. A hierarchy of integrable coupling KdV equation with three potentials is proposed, which is derived from a new discrete six-by-six matrix spectral problem. Moreover, the Hamiltonian forms is deduced for lattice equation in the resulting hierarchy by means of the discrete variational identity -- a generalized trace identity. A strong symmetry operator of the resulting hierarchy is given. Finally, we prove that the hierarchy of the resulting Hamiltonian equations is Liouville integrable discrete Hamiltonian systems.     

Variational regularization method of solving the Cauchy problem for Laplace＇s equation： Innovation of the Grad-Shafranov （GS） reconstruction

The simplified linear model of Grad-Shafranov （GS） reconstruction can be reformulated into an inverse boundary value problem of Laplace＇s equation. Therefore, in this paper we focus on the method of solving the inverse boundary value problem of Laplace＇s equation. In the first place, the variational regularization method is used to deal with the ill- posedness of the Cauchy problem for Laplace＇s equation. Then, the ＇L-Curve＇ principle is suggested to be adopted in choosing the optimal regularization parameter. Finally, a numerical experiment is implemented with a section of Neumann and Dirichlet boundary conditions with observation errors. The results well converge to the exact solution of the problem, which proves the efficiency and robustness of the proposed method. When the order of observation error δ is 10-1, the order of the approximate result error can reach 10-3.     

Research on the discrete variational method for a Birkhoffian system

In this paper, we present a new integration algorithm based on the discrete Pfaff-Birkhoff principle for Birkhoffian systems. It is proved that the new algorithm can preserve the general symplectic geometric structures of Birkhoffian systems. A numerical experiment for a damping oscillator system is conducted. The result shows that the new algorithm can better simulate the energy dissipation than the R-K method, which illustrates that we can numerically solve the dynamical equations by the discrete variational method in a Birkhoffian framework for the systems with a general symplectic structure. Furthermore, it is demonstrated that the results of the numerical experiments are determined not by the constructing methods of Birkhoffian functions but by whether the numerical method can preserve the inherent nature of the dynamical system.     

Two Integrable Couplings of Modified Tu Hierarchy

Two different integrable couplings of the modified Tu hierarchy are obtained under the zero curvature equation by using two higher dimension Lie algebras. Furthermore, a complex Hamiltonian structures of the second integrable couplings is presented by taking use of the variational identity.     

Hamiltonian Forms for a Hierarchy of Discrete Integrable Coupling Systems

A semi-direct sum of two Lie algebras of four-by-four matrices is presented, and a discrete four-by-four matrix spectral problem is introduced. A hierarchy of discrete integrable coupling systems is derived. The obtained integrable coupling systems are all written in their Hamiltonian forms by the discrete variational identity. Finally, we prove that the lattice equations in the obtained integrable coupling systems are all Liouville integrable discrete Hamiltonian systems.     

A new $N^{}$ resonance as a hadronic molecular state

We report our recent work on a hadronic molecule state of the KKN system with I =1/2 and jR = 1/2＋. We assume that the A（1405） resonance and the scalar mesons, f0（980）, ao（980）, are reproduced as quasi-bound states of KN and KK, respectively. Performing non-relativistic three-body calculations with a variational method for this system, we find a quasibound state of the KIlN system around 1910 MeV below the three-body breakup threshold. This state corresponds to a new baryon resonance of N＊ with JP ： 1/2＋. We find also that this resonance has the cluster structure of the two-body bound states keeping their properties as in the isolated two-particle systems. We also briefly discuss another hadronic molecular state composed by two K and one N, which corresponds to a resonance.     

Study of electronic structures and absorption bands of BaMgF4 crystal with F colour centre

The electronic structures of BaMgF 4 crystals containing an F colour centre are studied within the framework of the fully relativistic self-consistent Direc-Slater theory,using a numerically discrete variational (DV-Xα) method. It is concluded from the calculated results that the energy levels of the F colour centre are located in the forbidden band. The optical transition energy from the ground state to the excited state for the F colour centre is about 5.12 eV,which corresponds to the 242-nm absorption band. These calculated results can explain the origin of the absorption bands.