Exact Solution of the Bloch Equation with Time- Dependent Coefficients and Aharonov-Anandan Phase

In this letter, the matrix invariant of the Bloch equation with time-dependent coefficients is found, the time evolution of the system is discussed and the exact solution of the system is obtained. We then proceed to study the cyclic evolution of the system, obtaining the Aharonov-Anandan phase Finally, it is shown that the study of noncyclic evolution of the system can be reduced to the cyclic evolution.