LIE-ADMISSIBLE PERTURBATION-METHODS FOR OPEN QUANTUM-SYSTEMS

We consider open quantum systems described by a Hamiltonian of the type H0 + lambdaV, where lambda is a small parameter. For such systems, we develop perturbative methods of solution of the corresponding Liouville-von Neumann and Schrodinger equations, by introducing "dissipation" operators which connect conservative to dissipative systems. In the case of the density matrix, the corresponding operator LAMBDA is nothing but the non-unitary LAMBDA-transformation of Misra, Prigogine and Courbage. Our perturbative approach possesses a Lie-admissible structure, since the "dissipation" operators obey time-evolution equations whose brackets are the product of a Lie-admissible algebra. Explicit solutions for such operators are found in the form of series expansions in lambda. The matrix formulation of the above results is also given.