Lie-admissible perturbation methods for open quantum systems

✍ Scribed by A. Jannussis; R. Mignani; D. Skaltsas

• Publisher: Elsevier Science
• Year: 1992
• Tongue: English
• Weight: 408 KB
• Volume: 187
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/0378-4371(92)90011-e

✦ Synopsis

We consider open quantum systems described by a Hamiltonian of the type H 0 + AV, where A is a small parameter. For such systems, we develop perturbative methods of solution of the corresponding Liouville-von Neumann and Schr6dinger equations, by introducing "dissipation" operators which connect conservative to dissipative systems. In the case of the density matrix, the corresponding operator A is nothing but the non-unitary A-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 A. The matrix formulation of the above results is also given.