This paper studies dynamics of a modulation-doped GaAs/AlGaAs heterostructure under transverse magnetic fields and microwave radiations. It finds that negative differential conductivity, due to the real-space electron transfer and delayed dielectric relaxation of the interface potential barrier, can lead to complex behaviours when a relatively small magnetic field is applied. Quasiperiodicity, frequency-locking and the routes from period-doubling to chaos are found. Under a large magnetic field, however, two time-independent homogeneous steady states exist; and the longitudinal resistance of the system shows an interesting oscillation with period tuned by the ratio of microwave radiation frequency w to the cyclotron frequency Wc and local minima at ω/ωc = integer ＋ 1/4.
The charge distribution in thin mesoscopic superconducting ring is studied by the phenomenological GinzburgLandau theory. In the giant vortex states we find that the mesoscopic rings may present three kinds of charge distribution while the disk only owns the first two kinds. The charge near the inner radius may change its sign from negative to positive with increasing applied field. In the multivortex state we find that there exist saddle-point states and stable multivortex states. The distribution of charge and the superconducting electron density in the （0：2） saddle states and the （0：4）, and （1：5） stable multivortex states has also been studied. The contour plot of the charge distribution and the Cooper pair density distribution are given.
