A general local control theory for manipulating quantum system dynamics is developed. Basic concept of the present theory is lying in the realization of monotonous increasing condition of the performance index,which is locally defined to major how the present quantum state satisfies the current objective. The local control field is designed to atisfy the above condition taking into account the equation of motion of the system. It is found,through the formulation,that the monotonous increasing condition can be achieved as long as the performance index is given as a function of expectation values of time-dependent observable operators,whose equation of motion is governed by the field-free system Hamiltonina or Liouvillian. It is also shown that the present theory is a generalization of molecular dynamics control problems. As for the special cases,performance indices for "transition path control," "population distriubtion control," and "wave packet shaping" are proposed. The theory is applied to vibrational control problems of the one-dimensional model system of hydrogen fluoride. The results show that the present method works effectively for the populationdynamics control as well as the wave packet shaping.
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