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

The su(2)-algebraic model interacting with an environment is investigated f rom the viewpoint of treating a dissipative system. By using a time-depende nt variational approach with a coherent state and with the help of the cano nicity condition, the time-evolution of this quantum many-body system is de scribed in terms of the canonical equations of motion in the classical mech anics. Then, it is shown that the su(1, 1)-algebra plays an essential role in treating this model. An exact solution with appropriate initial conditio ns is obtained in terms of Jacobi's elliptic function. The implications for the dissipative process are discussed.