Algebraic Structure of a Master Equation with Generalized Lindblad Form

The quantum damped harmonic oscillator is described by the master equation with usual Lindblad form. The equation has been solved completely by us in arXiv : 0710.2724 [quant-ph]. To construct the general solution a few facts of representation theory based on the Lie algebra su(1, 1) were used. In this paper we treat a general model described by a master equation with generalized Lindblad form. Then we examine the algebraic structure related to some Lie algebras and construct the interesting approximate solution. Quantum Computation (Computer) is one of main subjects in Quantum Physics. To realize it we must overcome severe problems arising from Decoherence, so we need to study Quantum Open System to control decoherence (if possible). This paper is a series of [1] and [2], and we study dynamics of a quantum open system. First we explain our purpose in a short manner. See [3] as a general introduction to this subject. ∗E-mail address : [email protected]