Fractal Study Of Quantum Chaotic Wave Function Of Periodic Gyroscopic System

In this paper we study the fractal dimensions of wave function for the periodically kicked free top. We find that at weak kicking strength coefficient (?1), the motion in classical phase space is regular, the fractal dimension is about 1, as kicking strength coefficient increases, the motion in classical phase space becomes chaotic and the fractal dimension also increases. When the kicking strength coefficient?6, the phase space becomes completely chaotic, the fractal dimension reaches its maximum value 1.5 and will keep it.Then we study multifractal of the wave function for the periodically kicked free top. We find (1)/(a) is connected with the kicking strength of the system, as the kicking strength coefficient(?) increases, the motion in classical phase space becomes chaotic and f(a) also increases; (2) the range of a also can describe the situation of the system, for A= 0.01 a keeps a narrow range,for ?= 3 a extend over a much wider range, for ?= 8 the range of a is wider than ?= 0.01,but narrower than ?= 3; (3) when studying the time evolution of the system, we find that for ?= 3,the range of a shows distinctive variations, but for ?=8 it remains almost unchanged.