The Dynamics Of Nonlinear Landau-Zener-Coulomb Transition

Quantum nonadiabatic transition is a fundamental physical phenomenon in quantum mechanics.It has important applications in various fields such as atomicmolecular physics,quantum information,quantum optics.With the development of nonadiabatic transition theory,some nonadiabatic transition models have been proposed.Exactly solvable Landau-Zener-Coulomb model is a nonadiabatic transition model which has been used in many linear systems.However,due to the existence of various complex coupling effects,realistic physical systems are always nonlinear,thus,the study of nonlinear Landau-Zener-Coulomb model is very important.This paper mainly investigates the Landau-Zener-Coulomb transition dynamics in nonlinear two-level and multi-level systems with the particle interaction.In the first chapter,this chapter briefly introduces the background and significance of nonadiabatic transition,the theoretical basis of nonlinear dynamics.Then it briefly summarizes several typical nonlinear quantum transition models,such as the nonlinear Landau-Zener transition model,the nonlinear Rosen-Zener transition model,the nonlinear Demkov-Kunike transition model.Finally,the Landau-Zener-Coulomb model is introduced..In the second chapter,this chapter investigates the Landau-Zener-Coulomb transition dynamics in a nonlinear two-level system and analyzes the influence of the particle interaction on the transition dynamics of the system.By the analysis of the classical Hamiltonian,the law of the fixed point changing with the interaction is obtained.The variation of the transition probability for different particle interactions with coupling strengths,the slope of the energy level,and the curvature of the energy level are investigated.By analyzing the energy level structure of the system and the analytical expression of the transition probability is obtained by the stationary phase approximation in special cases.The results show that when the slope of the energy level is positive or negative.the particle interaction has different effects on the transition dynamics of the system.When the slope of energy levels is positive,the particle interaction always suppresses nonadiabatic transitions between energy levels.As the interaction increases,the nonadiabatic transition between energy levels becomes more difficult to happen.When the slope of energy levels is negative,in the case of weak interaction,the nonlinearity can promote the nonadiabatic transition between energy levels.In the case of strong interaction,the transition probability can oscillate.As the interaction increases,the amplitude of oscillation can gradually decrease and the nonadiabatic transition between energy levels is suppressed.In the third chapter,this chapter investigates the Landau-Zener-Coulomb transition dynamics in a nonlinear three-level system and a nonlinear multi-level system.It mainly investigates the influence of the coupling strength and the slope of the energy level on the transition probability for different particle interactions and analyzes the energy level structure of the system.The results show that due to the existence of the particle interaction,the coupling strength between energy levels can affect the nonadiabatic transition between energy levels.When the slope of the energy level is positive,the transition probability can oscillate,with the interaction strength continues to increase,the transition probability of oscillation amplitude can gradually decrease,and the nonadiabatic transition between energy levels can be suppressed.When the energy level slope is negative,the probability of transition to upper energy levels is no longer independent of the coupling strength between lower energy levels and the counterintuitive behavior is destroyed.The particle interaction always suppresses the nonadiabatic transition between energy levels.The fourth chapter summarizes the results of this article and looks forward to the research in this field.