Coherent Spin Dynamics into Space Quantization

We propose a mechanism to describe how a physical quantity, which initially can take continuous values, is restricted within some discrete values after a measurement. As an example of the present theory, in which interplay between coherence of motion and fluctuation from disturbance plays an important role, we investigate motion of a spin state in a magnetic field. First, we point out that discrete eigenstates are formed from continuous states as a result of coherence of precession motion of a spin. Next, by assuming disturbance from environmental electromagnetic fields, we investigate temporal change of direction of a spin state by applying the first order perturbation theory and the Monte Carlo technique. Results of simulations show that the spins, whose directions are randomly distributed at the initial time, are reoriented toward only two directions due to fluctuation guided by coherence.