Corrections to the phenomenological relaxation models for open quantum systems

The accurate description of dissipative effects in quantum systems is needed for the development of modern quantum information and metrology techniques. We find a simple method for considerably improving the accuracy of phenomenological relaxation models. This method can be applied for both Von Neumann and Heisenberg-Langevin equations. It is based on some general properties of the relaxation operator which follow from initial exact equations for the unreduced system but can be lost due to various approximations (for example rotating-wave approximation) used in popular models. In particular, we show that use of simple relaxation rate model violates the fundamental relation between the macroscopic current and polarization in the dielectric and can lead to unphysical instabilities. We show that the relaxation rate dependence of resonance line of two-level system with the modified relaxation operator differs from that obtained from the standard optical Bloch equation and corresponds strictly to the classical oscillator with friction. This result is important for improving the quantum frequency standards. The analogous result is obtained for the damped three-dimensional quantum oscillator in arbitrary oriented magnetic field, which is a robust model for the theory of quantum dots.