Dynamics Of The Dissipative Two-state System

Macroscopic quantum effects have been an advanced research hotspot in recent years. Oneimportant and basic issue in macroscopic quantum effects is the decoherence resulting from envi-ronment, and the most famous paradigm is the so-called dissipative two-state system, namely spinboson model, which is the most basic model in the dissipative quantum systems. The dynamics ofa two-state system coupled to the dissipative degrees of freedom of the environment has been stud-ied by various methods. Firstly this thesis investigate dissipative two-state system in the long-timelimit by perturbation theory. Secondly we map the spin-boson model onto the Ising model with along-range interaction∝r^-s-1 [24, 25] and exploit variational approach to calculate the dynamicsof the spin-boson model. The effective tunneling matrix element is renormalized by the interactionwith the bath, which denotes the quantum transition from a delocalized to localized phases whenthe splitting decline to zero with the dissipation increasing. A general formulation of the problemwas given and the mechanism of this quantum transition was studied by analyzing the evolutionof the solutions of the self-consistent equation derived from the variational approach around thecritical point. Our conclusion is in agreement with the result of numerical renormalization groupcalculation. We also compare two different phase transitions according to Landau theory, whichinduced by different types of dissipative environment (mainly about two cases of Ohmic, sub-Ohmic) where at zero temperature or at finite temperature. Finally we study the factors exert onthe splitting in the biased two-state system coupled to a single-mode phonon. These works will behelpful to apprehend the mechanism of this phase transition in physics.