Dynamics of Quantum State and Effective Hamiltonian with Vector Differential Form of Motion Method

Effective Hamiltonians in periodically driven systems have received widespread attention for realization of novel quantum phases, non-equilibrium phase transition, and Majorana mode. Recently, the study of effective Hamiltonian using various methods has gained great interest. We consider a vector differential equation of motion to derive the effective Hamiltonian for any periodically driven two-level system, and the dynamics of the spin vector are an evolution under the Bloch sphere. Here, we investigate the properties of this equation and show that a sudden change of the effective Hamiltonian is expected. Furthermore, we present several exact relations, whose expressions are independent of the different starting points. Moreover, we deduce the effective Hamiltonian from the high-frequency limit, which approximately equals the results in previous studies. Our results show that the vector differential equation of motion is not affected by a convergence problem, and thus, can be used to numerically investigate the effective models in any periodic modulating system. Finally, we anticipate that the proposed method can be applied to experimental platforms that require time-periodic modulation, such as ultracold atoms and optical lattices.

Application of a Discrete Phase-Randomized Coherent State Source in Round-Robin Differential Phase-Shift Quantum Key Distribution

Recently, a novel kind of quantum key distribution called the round-robin differential phase-shift （RRDPS） protocol was proposed, which bounds the amount of leakage without monitoring signal disturbance. The protocol can be implemented by a weak coherent source. The security of this protocol with a simply characterized source has been proved. The application of a common phase shift can improve the secret key rate of the protocol. In practice, the randomized phase is discrete and the secret key rate is deviated from the continuous case. In this study, we analyze security of the RRDPS protocol with discrete-phase-randomized coherent state source and bound the secret key rate. We fix the length of each packet at 32 and 64, then simulate the secret key rates of the RRDPS protocol with discrete-phase randomization and continuous-phase randomization. Our simulation results show that the performance of the discrete-phase randomization case is close to the continuous counterpart with only a small number of discrete phases. The research is practically valuable for experimental implementation.

Study on the Phenotypic Mutation Generated from ^(60)Coγ-ray Irradiated Oxlias triangularis Purpurea Regeneration System

Mutations induced from tissue culture are easily to be separated,which might be propagated in the same medium,especially for the color-leaf ornamental grass,Oxalis triaggularis purpurea.Mutations of the ornamental traits in the tissue culture bottle could be investigated easily.The 35 d regeneration system group showed the lowest adventitious bud number and adventitious root number among 4 inoculation dates by 50 Gy dose of ^(60)Coγ radiation.More studies were carried out based on the 35d differentiation state of O.triangularis purpurea regeneration system.The 35 d regeneration system was then irradiated by 10,25 and 50 Gy doses of ^(60)Coγ rays.Numbers of adventitious buds and roots induced from the regeneration system were cut down with the increment of radiation doses.Seedling length was not distinctly reduced at the absorbed doses of 10 and 25 Gy,but reduced distinctly under 50 Gy of ^(60)Coγ irradiation.The optimal irradiation dose for 35 d O.triangularis regeneration system survival and mutation induction was approximately 25 Gy.The M_2 phenotypic mutation rate was 2.9%,especially,and the leaf number mutation accounted for 76%of the total mutation.The phenotypic mutations,especially in the 10 Gy group,on 0.1 m M Vc containing MS medium were recovered,which indicated that ROS plays a key role in the phenotypic mutation induced by ^(60)Coγ -rays.

Stochastic maximum principle for mean-field forward-backward stochastic control system with terminal state constraints

In this paper,we consider an optimal control problem with state constraints,where the control system is described by a mean-field forward-backward stochastic differential equation(MFFBSDE,for short)and the admissible control is mean-field type.Making full use of the backward stochastic differential equation theory,we transform the original control system into an equivalent backward form,i.e.,the equations in the control system are all backward.In addition,Ekeland's variational principle helps us deal with the state constraints so that we get a stochastic maximum principle which characterizes the necessary condition of the optimal control.We also study a stochastic linear quadratic control problem with state constraints.