Dynamics of classical quadrupole moment. I (Q1610041)

The authors of this interesting paper study the problem of whether the motion of the electric quadrupole moment of the nucleus perturbed by the alternating magnetic field is chaotic or not. This problem is similar to that of the kicked rotor, which is one of the simplest dynamical chaotic systems, but is a little more complicated. Taking into account the Heisenberg equation of motion as well commutation relation between the components of the angular moment operator \(\mathbf I =(I_x,I_y,I_z)\) and the notations \(\mathbf x=(x,y,z)\) for \(\mathbf I\) as \(x(t)=I_x(t)\), \(y(t)=I_y(t)\), \(z(t)=I_z(t)\) and scaling the time, \(t\to \hbar t/(6A)\) the authors obtain a simple form of the equations of motion. Here \(A\) is a quantity defined by the quadrupole moment of the nucleus (\(c\)-number). It is shown that chaotic behavior exists in the classical system of the nuclear quadrupole moment under perturbation of the delta function type. The structure of the transformation in the phase space is analyzed, and the phenomenology of the transformation discussed by the Poincaré map. For Part II, see ibid. 13, 1017-1030 (2002; Zbl 1019.81062).