Quantum Kinetic Expansion In The Two-State System Model

Quantum dissipative dynamics is widely applied in many physical,chemical,and biological processes.The influence from the surrounding bath induces dissipation of the system dynamics.It is difficult to provide an analytical solution for the system dynamics,even for the simple two-state system model.Instead,a variety of numerical methods are developed to describe the quantum dissipative dynamics.Among these methods,perturbation methods are computational inexpensive,less constrained,and reliable in specific parameter regime.The second-order expansion over the system-bath coupling and the state-state coupling of system are respectively often used in literature.However,both second-order perturbation methods break down in the regime that the system-bath coupling is comparable to the state-state coupling.To improve the second-order expansion methods,the quantum kinetic expansion(QKE)in-cludes correction from higher-order expansions to provide reliable results of time evolution.In the QKE methods,a systematical resummation technique is lacking;There is few comprehensive discussions about the influence of initial system-bath entanglement;There is no application in the anharmonic bath.Towards these issues of QKE methods,The main research contents in this thesis are as following:(1)We develop the continued fraction resummation technique to systematically include all the QKE rate kernels to improve the estimation of second-order expansion.Numerical calculations for both Markovian and non-Markovian QKE predictions are provided in the harmonic bath.Compar-ing with a benchmark of numerical exact results,we verify the reliability of the continued fraction resummation technique.(2)With an inherent assumption of local equilibrium initial state in QKE methods,we extend the formation to the system-bath factorized initial state in the framework of hierarchical equa-tions of motion(HEOM).A modification expansion is introduced to describe the influence from changing the initial state to the dynamics.The Markovian and non-Markovian QKE results for different initial state are compared.We verify that the modification terms are capable to describe the influence of the initial system-bath entanglement to the dynamics.(3)In the framework of the quantum-classical Liouville equation(QCLE),we extend the QKE methods to an arbitrary combination of the bath potential and the system-bath interaction.In the QCLE-QKE methods,The calculation of the QKE rate kernels and modification functions are transformed into averages of classical trajectories over Wigner initial distribution.For the standard two-state system bilinearly interacted with a harmonic bath,QCLE-QKE can produces exactly the same results of full quantum dynamics.For an anharmonic bath with a quartic potential,the QCLE-QKE and Ehrenfest calculations are performed in different conditions.The QCLE-QKE can provide a better description effect of the anharmonicity to the dynamics.