Solving the time-dependent Schrödinger equation by combining smooth exterior complex scaling and Arnoldi propagator

Abstract We develop a highly efficient scheme for numerically solving the three-dimensional time-dependent Schrödinger equation of the single-active-electron atom in the field of laser pulses by combining smooth exterior complex scaling(SECS)absorbing method and Arnoldi propagation method.Such combination has not been reported in the literature.The proposed scheme is particularly useful in the applications involving long-time wave propagation.The SECS is a wonderful absorber,but its application results in a non-Hermitian Hamiltonian,invalidating propagators utilizing the Hermitian symmetry of the Hamiltonian.We demonstrate that the routine Arnoldi propagator can be modified to treat the non-Hermitian Hamiltonian.The efficiency of the proposed scheme is checked by tracking the time-dependent electron wave packet in the case of both weak extreme ultraviolet(XUV)and strong infrared(IR)laser pulses.Both perfect absorption and stable propagation are observed.

Modified projective synchronization with complex scaling factors of uncertain real chaos and complex chaos

To increase the variety and security of communication, we present the definitions of modified projective synchronization with complex scaling factors （CMPS） of real chaotic systems and complex chaotic systems, where complex scaling factors establish a link between real chaos and complex chaos. Considering all situations of unknown parameters and pseudo-gradient condition, we design adaptive CMPS schemes based on the speed-gradient method for the real drive chaotic system and complex response chaotic system and for the complex drive chaotic system and the real response chaotic system, respectively. The convergence factors and dynamical control strength are added to regulate the convergence speed and increase robustness. Numerical simulations verify the feasibility and effectiveness of the presented schemes.

Resonances of a hydrogen atom in strong parallel electric and magnetic fields using B-spline basis sets

The B-spline basis set plus complex scaling method is applied to the numerical calculation of the exact resonance parameters Er and Г/2 of a hydrogen atom in parallel electric and magnetic fields. The method can calculate the ground and higher excited resonances accurately and efficiently. The resonance parameters with accuracies of 10^-9 - 10^-12 for hydrogen atom in parallel fields with different field strengths and symmetries are presented and compared with previous ones. Extension to the calculation of Rydberg atom in crossed electric and magnetic fields and of atomic double excited states in external electric fields is discussed.

Resonances with triaxial deformation in the complex scaled Green's function method

We extend the complex scaled Green＇s function （CGF） method to describe resonances with triaxial deformation and present a theoretical formalism. Taking 43S as an example, we elaborate numerical details and demonstrate how to determine the resonance parameters. With changes in the deformation parameters, we study the influence of the triaxial deformation parameter γ on single-particle levels. In particular, the present scheme focuses on the advantages of the complex scaling method （CSM） and the Green＇s function method, and is suitable for the exploration of resonances.

Explanation of Y(4630) as a hadronic resonant state

Theorists have given various explanations for the discovery of Y(4630).We find that if Y(4630)is inter-preted as the D-wave resonant state of the ∧_(c)∧_(c)。system,the particle mass,decay width,and all quantum numbers are consistent with experimental observations.We use the Bonn approximation to obtain the interaction potential of the one boson exchange model.Then,we extend the complex scaling method to calculate the bound and resonant states.The results indicate that the ∧_(c)∧_(c) system can form not only the bound state of the S wave but also the reson-ant state of the high angular momentum,and the ^(3)D_(1) wave resonant state can explain the structure of Y(4630)very Well.