The classical noncompact algebraic approach to the highly excited multi-mode vibrational dynamics

The direct product of the classical noncompact SU(1, 1)/U(1) coset space representation is introduced for the study of the highly excited vibrational dynamics. The advantages and disadvantages of this formalism as compared with the compact SU(n) formalism are analyzed. Taking SU(1, 1)/U(1)1 ⊗ SU(1, 1)/U(1)2 for the coupled two-mode system as an example, the features of the noncompact formalism are addressed including its physical and numerical aspects. It is concluded that for large multi-mode systems in high vibrational excitation, the noncompact formalism provides a convenient and potentially powerful algorithm for treating the dynamics.