  Based on the non-autonomous quantum master equation, we investigate the
dissipative and decoherence properties of the two-level atom system interacting
with the environment of thermal quantum radiation fields. For this system, by a
novel algebraic dynamic method, the dynamical symmetry of the system is found,
the quantum master equation is converted into a Schr\"{o}dinger-like equation
and the non-Hermitian rate (quantum Liouville) operator of the master equation
is expressed as a linear function of the dynamical u(2) generators.
Furthermore, the integrability of the non-autonomous master equation has been
proved for the first time. Based on the time-dependent analytical solutions,
the asymptotic behavior of the solution has been examined and the approach to
the equilibrium state has been proved. Finally, we have studied the decoherence
property of the multiple two-level atom system coupled to the thermal radiation
fields, which are related to the quantum register.
