Guishu Chong

Spatial chaos of trapped Bose–Einstein condensate in one-dimensional weak optical lattice potential

The spatially chaotic attractor in an elongated cloud of Bose-Einstein condensed atoms perturbed by a weak optical lattice potential is studied. The analytical insolvability and numerical incomputability of the atomic number density are revealed by a perturbed solution that illustrates the unpredictability of the deterministic chaos. Although this could lead the nonphysical explosion and unboundedness to the numerical solution, the theoretical analysis offers a criterion to avoid them. Moreover, the velocity field is investigated that exhibits the superfluid property of the chaotic system.

Chaotic atomic tunneling between two periodically driven Bose–Einstein condensates

The chaotic coherent atomic tunneling between two periodically driven and weakly coupled Bose-Einstein condensates has been investigated. The perturbed correction to the homoclinic orbit is constructed and its boundedness conditions are established that contain the Melnikov criterion for the onset of chaos. We analytically reveal that the chaotic coherent atomic tunneling is deterministic but not predictable. Our numerical calculation shows good agreement with the analytical result and exhibits nonphysically numerical instability. By adjusting the initial conditions, we propose a method to control the unboundedness, which leads the quantum coherent atomic tunneling to predictable periodical oscillation.

Transitions between chaos and order in rf-driven Josephson junction

We investigate transitions between the chaotic and regular states through a perturbed chaotic solution of a rf-driven Josephson system. It is shown that the transition from order to chaos may occur when the system initially near the heteroclinic points. The chaotic solution tends to an unstable periodic one for the initial values sufficiently nearing the heteroclinic orbit but going beyond the heteroclinic points. Thus the Josephson chaos can be analytically and numerically controlled, by adjusting the initial conditions.

Analytically bounded and numerically unbounded compound pendulum chaos

Abstract A compound pendulum with deterministically periodic perturbation is treated. In the analytical approximation, chaotic solution initially near the homoclinic one is constructed and its boundedness conditions are established. It is shown that the chaotic solution is analytically bounded and numerically unbounded, which describes a non-periodical vibration around unstable equilibrium of the corresponding unperturbed system.

CHAOTIC SOLUTION OF THE rf-DRIVEN JOSEPHSON SYSTEM WITH QUADRATIC DAMPING

The method of direct perturbation is applied to a rf-driven Josephson junction with strong and quadratic damping resistor. Perturbed correction to the heteroclinic orbit is constructed and its boundedness conditions are established to contain the Melnikov criterion for the onset of chaos. The result shows that the corrected heteroclinic orbit is unbounded, unless it is chaotic. The analytically deterministic chaotic solution exposes the incomputability of chaotic orbits, which is numerically demonstrated.

Exact Solutions for Hydrogenic Impurity States in Quantum Dots

According to the hydrogenic-effective-mass theory and assumed finite barrier height for a confining potential, the analytical solutions and quantum energy-level structure for a hydrogenic impurity located at the center of a spherical quantum dot (SQD) are obtained. The calculated results reveal that because of the spatial confinement of the quantum dots, the energy, quantum numbers and radius of the SQD must satisfy a certain relation which arises from the boundary conditions. Given a barrier height or energy, the relation allows for the existence of bound states only for some discrete values of the radius of the SQD. On the other hand, for a fixed radius the energies of the bound states are discrete.

CONTROLLING HYPERRADIANCE FROM CHAOTIC SOLITON OSCILLATOR IN JOSEPHSON JUNCTIONS

Using direct perturbation technology we study how to control the hyperradiance from chaotic soliton oscillator in two weakly coupled long Josephson junctions, by adjusting the bias current. The results reveal that the single soliton in a junction perturbed by a periodic solution of another junction possesses chaotic behavior. When the soliton is approximately synchronized with the periodic solution, the emitted power from the system rapidly increases. Although the boundedness conditions limit its maximal value, the chaotic soliton oscillator may emit much greater power than the soliton pair. Theoretical analysis and numerical simulation both demonstrate the results.