Kinetic equation, non-perturbative approach and decoherence free subspace for quantum open system

A Schrödinger (Liouville) type of equation for an quantum open system is presented. The equation has a correlated part and many Master equations can be derived from it as special cases. Most significantly, it can be applied to construct a decoherence-free subspace for quantum computing. The original Schrödinger (Liouville) equation for the total system is related to it by a non-unitary similarity transformation, which enables us to propose a non-perturbative method for solving the eigenvalue problem for the total Hamiltonian. In addition, it also enables one to uncover a simple procedure to treat the eigenvalue problem of an open system under strong interaction. The correlated part of the equation is not necessarily self-adjoint, so that there exists a complex spectrum for the corresponding Hamiltonian (Liouvillian) which enables the time evolution of states to be asymmetric. This then exposes just the correlation required to produce evolution, which coincides with the second law of thermodynamics.