Hai Wen-Hua

Solutions, bifurcations and chaos of the nonlinear Schrödinger equation with weak damping

Using the wave packet theory, we obtain all the solutions of the weakly damped nonlinear Schrodinger equation. These solutions are the static solution and solutions of planar wave, solitary wave, shock wave and elliptic function wave and chaos. The bifurcation phenomenon exists in both steady and non-steady solutions. The chaotic and periodic motions can coexist in a certain parametric space region.

Nonlinear dissipative dynamics of a two-component atomic condensate coupling with a continuum

We investigate the nonlinear dissipative coherence bifurcation and population dynamics of a two-component atomic Bose—Einstein condensate coupling with a continuum. The coupling between the two-component condensates and the continuum brings effective dissipations to the two-component condensates. The steady states and the coherence bifurcation depend on both dissipation and the nonlinear interaction between condensed atoms. The coherence among condensed atoms may be even enhanced by the effective dissipations. The combination of dissipation and nonlinearity allows one to control the switching between different self-trapped states or the switching between a self-trapped state and a non-self-trapped state.

Suppressing chaos by parametric perturbation at doubled frequency of periodic perturbation

An analysis of the chaos suppression of a nonlinear elastic beam (NLEB) is presented. In terms of modal transformation the equation of NLEB is reduced to the Duffing equation. It is shown that the chaotic behaviour of the NLEB is sensitively dependent on the parameters of perturbations and initial conditions. By adjusting the frequency of parametric perturbation to twice that of the periodic one and the amplitude of parametric perturbation to the same as the periodic one, the chaotic region of the nonlinear elastic beam driven by periodic force can be greatly suppressed.

CHAOTIC SOLITON IN COUPLED LONG JOSEPHSON JUNCTIONS

The interaction between soliton and sinusoidal wave in two weakly coupled long Josephson junctions is studied. Theoretical analysis reveals that the soliton may be embedded in Melnikov chaotic attractors and the Fiske-step-modes are implied in the boundedness condition of the system. Comparison between the chaotic soliton oscillators and synchronized soliton oscillators shows that the former possesses greater maximal velocity and energy.

A Method for Avoiding the Divergence Difficulties of Quant urn Mechanics

High-ordered correction of wavefunction for Schrodinger equation with one dimensional potential V(x) and interaction Hamiltonian has been found by introducing a new particular solution for . Convergence conditions of the wavefunction lead to the formulas of energy corrections and scattering amplitudes. It is shown that the result can avoid some divergence difficulties of quantum mechanics.

Quantum tunneling switch in a planar four-well system

We investigate the tunneling dynamics of a single atom in a planar four-well potential driven by a high-frequency ac field. The quasienergy spectrum exhibits anticrossing and crossing, which are related to selective coherent destruction of tunneling (CDT) with several selectable directions. By using the CDTs of different directions, the switchlike effect is shown for the six tunneling pathways among the four wells. Applying the present results, we suggest a scheme for designing a single-atom quantum motor with the driving field as a quantum starter.

Laser-Manipulating Macroscopic Quantum States of a Bose–Einstein Condensate Held in a Kronig–Penny Potential

We investigate the boundary value problem (BVP) of a quasi-one-dimensional Gross–Pitaevskii equation with the Kronig–Penney potential (KPP) of period d, which governs a repulsive Bose–Einstein condensate. Under the zero and periodic boundary conditions, we show how to determine n exact stationary eigenstates {Rn} corresponding to different chemical potentials {μn} from the known solutions of the system. The n-th eigenstate Rn is the Jacobian elliptic function with period 2d/n for n = 1,2,..., and with zero points containing the potential barrier positions. So Rn is differentiable at any spatial point and Rn2 describes n complete wave-packets in each period of the KPP. It is revealed that one can use a laser pulse modeled by a δ potential at site xi to manipulate the transitions from the states of {Rn} with zero point x ≠ xi to the states of {Rn} with zero point x = xi. The results suggest an experimental scheme for applying BEC to test the BVP and to observe the macroscopic quantum transitions.

Analytic study of a Bose-Einstein condensate in waveguide with an obstacle potential

We investigate the exact solutions of one-dimensional (1D) time-independent Gross–Pitaevskii equation (GPE), which governs a Bose–Einstein condensate (BEC) in the magnetic waveguide with a square-Sech potential. Both the bound state and transmission state are found and the corresponding spatial configurations and transport properties of BEC are analyzed. It is shown that the well-known absolute transmission of the linear system can occur in the considered nonlinear system.

Boundedness and convergence of perturbed corrections for helium-like ions in ground states

Applying the improved Rayleigh–Schrodinger perturbation theory based on an integral equation to helium-like ions in ground states and treating electron correlations as perturbations, we obtain the second-order corrections to wave-functions consisting of a few terms and the third-order corrections to energicity. It is demonstrated that the corrected wavefunctions are bounded and quadratically integrable, and the corresponding perturbation series is convergent. The results clear off the previous distrust for the convergence in the quantum perturbation theory and show a reciprocal development on the quantum perturbation problem of the ground state helium-like systems.

Generation and control of chaos in a Bose--Einstein condensate

For a Bose-Einstein condensate (BEC) confined in a double lattice consisting of two weak laser standing waves we find the Melnikov chaotic solution and chaotic region of parameter space by using the direct perturbation method. In the chaotic region, spatial evolutions of the chaotic solution and the corresponding distribution of particle number density are bounded but unpredictable between their superior and inferior limits. It is illustrated that when the relation k1 ≈ k2 between the two laser wave vectors is kept, the adjustment from k2 < k1 to k2 ≥ k1 can transform the chaotic region into regular one or the other way round. This suggests a feasible scheme for generating and controlling chaos, which could lead to an experimental observation in the near future.