The proton imaging system is composed of four quadrupole magnetic lenses and a collimator. The quadrupole magnetic lenses can realize point-to-point imaging, and the collimator can improve image quality by controlling proton flux and realize material diagnosis. The magnetic field gradient of an ideal quadrupole lens becomes zero at the edge. Inside the lens, the magnetic field gradient is constant along the axis, while the magnetic field boundary of the actual lens extends outward. In the proton imaging system, the fringing field will affect the proton transport state and the performance of the imaging system as well. In this paper, a method to optimize the system is presented when the fringe field is considered. A proton imaging system of 1.6 GeV is established with the Geant 4 program, in which the magnetic field gradient distribution of the actual lens is approximated by the Bell function. In an ideal imaging system, the external drift length is 1.2 m, the internal drift length is 0.5 m, the length of the magnet is 0.8 m, and the magnetic field gradient is 8.09 T/m. The parameters of the practical imaging system can be obtained by using the optimization method: when the integral difference in magnetic field gradient distribution between the actual lens and the ideal lens is equal to zero, the outer drift length of the imaging system is 1.203 m and the inner drift length is 0.506 m; when the integral difference in the magnetic field gradient distribution between the actual lens and the ideal lens is equal to 1%, the outer drift length is 1.208 m and the inner drift length is 0.516 m. In the numerical simulation, a 1mm-thick copper plate and a concentric ball are chosen as the objects, and the influence of the fringing field on the collimator aperture and that on the proton flux error are studied. The results show that the optimized imaging system can reduce the flux error of protons passing through the object, and the difference in the aperture of collimator is on the order of 10^–2 when the integral difference is on the order of 10^–2 in magnitude.

With the recent development of experimental technology, the ability to control the dissipation in quantum many-body system is greatly enhanced. Meanwhile, many new breakthroughs are achieved in detecting the quantum states and others. All these advances make it necessary to establish a new theory for calculating the dissipative dynamics in strongly correlated sstems. Very recently, we found that by taking the interactions between the system and the bath as a perturbation, a systematic dissipative response theory can be established. In this new approach, the calculation of dissipative dynamics for any physical observables and the entropies can be converted into the calculation of certain correlation functions in initial states. Then we discuss how Markovian approximation at low temperature limit and at high temperature limit can be reached Also, we review the progress of the dissipative dynamics in open Bose-Hubbard model. In the fourth section, we review recent progress of entropy dynamics of quench dynamics of an open quantum system. Finally, we draw a conclusion and discuss possible development in the future.

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