We investigate the phenomena of symmetry breaking and phase transition in theground state of Bose-Einstein condensates (BECs) trapped in a double square well and in an opticallattice well, respectively. By using stand...We investigate the phenomena of symmetry breaking and phase transition in theground state of Bose-Einstein condensates (BECs) trapped in a double square well and in an opticallattice well, respectively. By using standing-wave expansion method, we present symmetric andasymmetric ground state solutions of nonlinear Schroedinger equation (NLSE) with a symmetric doublesquare well potential for attractive nonlinearity. In particular, we study the ground state wavefunction's properties by changing the depth of potential and atomic interactions (here we restrictourselves to the attractive regime). By using the Fourier grid Hamiltonian method, we also reveal aphase transition of BECs trapped in one-dimensional optical lattice potential.展开更多
The Dirac equation is solved for Killingbeck potential. Under spin symmetry limit, the energy eigenvalues and the corresponding wave functions are obtained by using wave function ansatz method.
By introducing the Lucas-Riccati method and a linear variable separation method, new variable separation solutions with arbitrary functions are derived for a （2＋1）-dimensional modified dispersive water-wave system....By introducing the Lucas-Riccati method and a linear variable separation method, new variable separation solutions with arbitrary functions are derived for a （2＋1）-dimensional modified dispersive water-wave system. The main idea of this method is to express the solutions of this system as polynomials in the solution of the Riecati equation that the symmetrical Lucas functions satisfy. From the variable separation sohition and by selecting appropriate functions, some novel Jacobian elliptic wave structure with variable modulus and their interactions with dromions and peakons are investigated.展开更多
The Schrodinger equation with hyperbolic potential V （ x ）=- Vosinh 2q （ x / d） / cosh 6 （ x / d） （q= 0, 1, 2, 3） is studied by transforming it into the confluent Heun equation. We obtain genera/symmetric and ...The Schrodinger equation with hyperbolic potential V （ x ）=- Vosinh 2q （ x / d） / cosh 6 （ x / d） （q= 0, 1, 2, 3） is studied by transforming it into the confluent Heun equation. We obtain genera/symmetric and antisymmetric polynomial solutions of the SchrSdinger equation in a unified form via the Functional Bethe ansatz method. Furthermore, we discuss the characteristic of wavefunction of bound state with varying potential strengths. Particularly, the number of wavefunction＇s nodes decreases with the increase of potentiaJ strengths, and the particle tends to the bottom of the potential well correspondingly.展开更多
文摘We investigate the phenomena of symmetry breaking and phase transition in theground state of Bose-Einstein condensates (BECs) trapped in a double square well and in an opticallattice well, respectively. By using standing-wave expansion method, we present symmetric andasymmetric ground state solutions of nonlinear Schroedinger equation (NLSE) with a symmetric doublesquare well potential for attractive nonlinearity. In particular, we study the ground state wavefunction's properties by changing the depth of potential and atomic interactions (here we restrictourselves to the attractive regime). By using the Fourier grid Hamiltonian method, we also reveal aphase transition of BECs trapped in one-dimensional optical lattice potential.
文摘The Dirac equation is solved for Killingbeck potential. Under spin symmetry limit, the energy eigenvalues and the corresponding wave functions are obtained by using wave function ansatz method.
文摘By introducing the Lucas-Riccati method and a linear variable separation method, new variable separation solutions with arbitrary functions are derived for a （2＋1）-dimensional modified dispersive water-wave system. The main idea of this method is to express the solutions of this system as polynomials in the solution of the Riecati equation that the symmetrical Lucas functions satisfy. From the variable separation sohition and by selecting appropriate functions, some novel Jacobian elliptic wave structure with variable modulus and their interactions with dromions and peakons are investigated.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11047025,11075126 and 11031005the Ministry of Education Doctoral Program Funds under Grant Nos.20126101110004,20116101110017SRF for ROCS
文摘The Schrodinger equation with hyperbolic potential V （ x ）=- Vosinh 2q （ x / d） / cosh 6 （ x / d） （q= 0, 1, 2, 3） is studied by transforming it into the confluent Heun equation. We obtain genera/symmetric and antisymmetric polynomial solutions of the SchrSdinger equation in a unified form via the Functional Bethe ansatz method. Furthermore, we discuss the characteristic of wavefunction of bound state with varying potential strengths. Particularly, the number of wavefunction＇s nodes decreases with the increase of potentiaJ strengths, and the particle tends to the bottom of the potential well correspondingly.
