| In recent years,quantum mechanics has been widely applied in fields such as quantum computation and quantum information,among which chaos has attracted much attention.Quantum chaos is a kind of nonlinear dynamic process based on quantum mechanics,which has the complexity and randomness coexist.It has important applications in information encryption,random number generation,communication,computer simulation and so on.From condensed matter physics to quantum chaos,directional transport and quantum diffusion in real space and momentum space have aroused great interest in all fields of physics.The close connection between quantum diffusion and localization has become the starting point of this study.Among them,the kicked rotor model as a typical quantum mapping system has a wide range of applications in the study of basic problems such as quantum-classical transition and quantum irreversibility.Based on this,extending the periodic driven system to the non-Hermitian domain is a frontier research topic.In this paper,based on the non-Hermitian quantum kicked rotor model,the energy spectrum statistics and chaos dynamics characteristics of the model are studied from the perspective of quantum dynamics.In the level spectrum statistics,the relationship between random matrix theory and quantum chaos characteristics is introduced to introduce the use of level spacing distribution to describe quantum chaos.The statistical quantity of the nearest neighbor level spacing is used to study the rise and fall of the low level spectrum based on the statistical properties of the considered spectrum and the prediction of random matrix theory(RMT).Firstly,the Floquet operator matrix needs to be constructed and the eigenstates and eigenvalues are calculated by matrix diagonalization.Secondly,the flattening of the levels is more conducive to comparing with the predicted distribution of random matrix theory.The results show that in the transition from Hermitian to non-Hermitian,the nearest neighbor level spacing distribution presents a distinct distribution,thus reflecting the dynamical characteristics of the studied system.It was found that Wigner distribution is consistent in Hermitian conditions,and with the addition of non-Hermitian intensity,the distribution deviates from Hermitian conditions and approaches the Poisson distribution,which represents local states.In terms of dynamics,we investigate the dynamics of quantum irreversibility and quantum diffusion in a non-Hermitian kicked rotor model for which the kicking strength is complex.In the Hermitian case,the Loschmidt echo decays exponentially with time,and the rate of decay is proportional to the Lyapunov exponent of classical chaos.With the increase of the imaginary part of the non-Hermitian driving potential,the exponential attenuation of the Loschmidt echo gradually disappears,indicating that the non-Hermitian property inhibits the exponential instability.Moreover,we find that the exponential attenuation of the Loschmidt echo occurs only in the very weak non-Hermitian case.For sufficiently strong non-Hermiticity,the Loschmidt echo is consistent with the time evolution,demonstrating the disappearance of quantum irreversibility.Quantum diffusion exhibits dynamic localization in momentum space,that is,the mean square of momentum increases to saturation with time evolution.With the increase of the imaginary part strength of the non-Hermitian driving potential,it is found that the local platform is lower,which clearly reveals the enhancement of the non-Hermitian property on the localization of dynamics.In order to uncover the physical mechanism for the emergence of dynamical localization features,we numerically calculate the fidelity between quantum states and quasienergies by means of matrix exact diagonalization,and find that they almost completely overlap,with an exponential localization in momentum space.According to the Floquet theory,we predict that the quantum states will eventually evolve into the quasienergies with large imaginary parts of the quasienergies,which is verified by the numerical results of the fidelity between quantum states and quasienergies obtained through the time evolution.Interestingly,the mean value of the inverse participation ratio of the quasienergy state decreases with the increase of the imaginary part of the driving potential,which means that the characteristics of the quasienergy state determine the stability of the wave packet dynamics and the dynamic localization of the quantum diffusion.Finally,we prove the possibility of these states transition by means of the average energy level spacing ratio and the exponential index of the inverse participation rate. |
