  In recent years, analysis and control of quantum chaos are increasingly
important, but the lack of the concept of trajectory makes it impossible to
analyze quantum chaos by the methods used in classical chaos. This research
aims to connect Newton's world to the quantum world by the complex mechanics so
that quantum chaos can be analyzed and controlled by the complex-extended
Newtonian mechanics. Through the bridge of complex mechanics, in this article,
we model quantum motions for 2D charged anisotropic harmonic oscillator by
complex-valued dynamic equations, based on which quantum chaos can be analyzed
by using well-known methods used in classical chaos. With the established
quantum dynamic model, we then apply the sliding-mode control method to control
the chaotic quantum behavior of the considered quantum system. The simulation
results show that chaotic motions can be changed into periodic motions by the
proposed chaos control and meanwhile, chaos synchronization can be achieved in
the presence of variations of initial conditions. Several signatures of chaos
are introduced here to justify the chaos of the periodicity process under the
sliding-mode control law.
