Dynamics Research In One-Dimensional Quantum Scattering Systems

In recent years,with the rapid development of applied research on quantum mechanics,people have been able to simulate the quantum system to be studied by means of quantum simulation that use artificially tunable quantum systems to explore physical phenomena that are difficult to observe and calculate under current experimental conditions,such as the strongly correlated system in traditional condensed matter physics is simulated by systems such as optical lattices and coupled cavity arrays,and finally the purpose of preparation,transmission and controlling quantum states is achieved in these controllable systems.In the process of preparation,transmission and controlling quantum states,basic calculations and analyses have been done on the dynamic behavior of particles in Hermitian systems under the effect of chemical potentials.However,when Bender et al.proposed that Dirac Hermitian is not a necessary condition for the real number spectrum and the time evolution of unitary,it was found that the interaction potential in the system Hamiltonian can be extended from real to complex domain,which is still not change the reality of its energy spectrum.Therefore,non-Hermitian systems have attracted widespread attention and interest.As we all know,the Hermitian system often describes a closed independent system that has no connection with the outside world,and it is an ideal physical model.But for the real world in which everything is interconnected and interacts with each other,the introduction of an equivalent nonHermitian Hamiltonian can more simply and directly describe the impact of the external environment on the system that researchers care about.Among them,there are various special introduction plan for the non-Hermitian property in the system,including the introduction of imaginary potentials and asymmetric coupling terms.With the maturity of technical means,people have been able to successfully simulate non-Hermitian Hamiltonians in the laboratory.Therefore,the exploration and development of non-Hermitian quantum systems provides the possibility for the diversification and controllability of quantum information transport equipment.Based on this,this paper aims to study the dynamic properties and simulation of single-particle tight-binding models in Hermitian and non-Hermitian systems under the framework of quantum mechanics,which is mainly composed of the following three parts:1.The characteristics of the single-particle tight-binding model are the preconditions for the realization of the relevant calculation in this paper.Introduce the potential to the tight-binding chain and tight-binding ring models in the Hermitian system,and study the dynamics behavior of the single-particle tight-binding model under the effect of the potential by calculating the eigenenergy of the single-particle wave packet and its eigenstates.2.Based on the characteristics of the tight-binding ring and the tight-binding chain model,the conversion between the ring and the chain is realized through the symmetric and anti-symmetric transformation of the basis vector in the matrix,and the understanding of the tight-binding model is deepened.3.Under the effect of the non-Hermitian Hamiltonian,the dynamic characteristics of the singleparticle tight-binding model are determined by the transmittance and reflectivity of the wave packet,and can be analyzed and discussed through numerical simulation.Based on the infinite single chain,through the regulation of the imaginary potential in the asymmetric coupling cavity and the unequal amplitude jump between the lattice points in the cavity,we can observe and analyze the unidirectional transport of information under specific parameters after single-particle wave packets incident on non-Hermitian scattering centers.Further research found that the non-Hermitian scattering center of the asymmetric coupling structure can induce the resonance transmission of the particle wave packet under different conditions.The unidirectional nality of this particle wave packet provides a scheme for the transportation of quantum information.