Analytical approach to dynamical behavior and phase diagrams in dissipative two-state systems

An analytical approach is developed to investigate the phase transitions and the dynamical behaviors in dissipative two-state systems in a unified method for different bath indices with the view of understanding the effects of environments and tunneling on the systems. Analytic expressions of the current correlation function, the nonequilibrium correlation function, and the critical points of coherent-incoherent and delocalized-localized transitions for various bath indices are obtained by implementing perturbation treatment and employing the Green’s function method. The phase boundaries can be precisely determined at both the scaling limit and the finite bare tunneling. The results of the dynamical behaviors of the correlation functions are consistent well with those of previous works and some well-established values are reproduced exactly. This theory is quite simple and may be applied as a potential method to study absorption spectra and photoluminescence in quantum dots and other confined quantum systems.