Basis Of Semiclassical Approach Research Articles

Restoration of Symmetry Violation Based on Classical Quantization of Time-Dependent Mean Field

We investigate the restoration of the symmetry breakdown inherent to the ground state from a viewpoint of the classical quantization of time-dependent mean field. We take two examples of trans· lational motion of nuclei and rotation of pseudo-spin in the degenerate BCS model. A possible extension is also suggested. The collective motion inherent to the degeneracy of the ground state is a characteris­ tics in quantum many-body theory. Rotational motion of nuclei is known to be a typical example which is understood to be caused by the degeneracy of the intrinsic state with respect to the orientation of nuclei. The violation of rotational symmetry is usually restored by the angular momentum projection. 1 > The projection method is very general and fully quantum mechanical but it lacks intuitive appeal. An intuitive way of pursuing the collective motion associated with such broken symmetry can be performed on the basis of semiclassical approach. The time-dependent mean field or Hartree-Fock theory (TDHF) has long been known to provide a promising tool for such semiclassical approach.