Utility of su(1,1)-algebra in a schematic nuclear su(2)-model

The su(2)-algebraic model interacting with an environment is investigated from the viewpoint of treating a dissipative system. By using a time-dependent variational approach with a coherent state and with the help of the canonicity condition, the time-evolution of this quantum many-body system is described in terms of the canonical equations of motion in the classical mechanics. Then, it is shown that the su(1, 1)-algebra plays an essential role in treating this model. An exact solution with appropriate initial conditions is obtained in terms of Jacobi's elliptic function. The implications for the dissipative process are discussed.