Thermodynamic limit of the XXZ central spin model with an arbitrary central magnetic field

The U(1)symmetry of the X X Z central spin model with an arbitrary central magnetic field B is broken,since its total spin in the z-direction is not conserved.We obtain the exact solutions of the system by using the off-diagonal Bethe ansatz method.The thermodynamic limit is investigated based on the solutions.We find that the contribution of the inhomogeneous term in the associated T-Q relation to the ground state energy satisfies an N^(-1)scaling law,where N is the total number of spins.This result makes it possible to investigate the properties of the system in the thermodynamic limit.By assuming the structural form of the Bethe roots in the thermodynamic limit,we obtain the contribution of the direction of B to the ground state energy.It is shown that the contribution of the direction of the central magnetic field is a finite value in the thermodynamic limit.This is the phenomenon caused by the U(1)symmetry breaking of the system.

A commutation analytical model for quench protection of the CFETR central solenoid model coil

A central solenoid model coil will be set up to develop and verify the technique for the full-size central solenoid coil of the China Fusion Engineering Test Reactor.In case of quench and failures of superconducting coils,the quench protection(QP)system,which employs fuse-based commutation technology,is designed.This paper presents an analytical model to investigate the commutation process in the QP circuit.The model consists of the QP circuit equations,the breaker arc model,the fuse pre-arc model,and the fuse arc model.The model is employed in the whole commutation process including current transfer from breaker branch to the fuse branch model,then from fuse branch to the discharge resistor branch,and current decrease to zero in the discharge resistor.The experiment result verified the effectiveness of the presented model.The model might be helpful for design of the fuse and optimization of the commutation circuit.

Effect of Silicon Content on Thermodynamics of Austenite Decomposition in C-Si-Mn TRIP Steels

Some numerical models such as central atoms model （CAM） and superelement model were used to simulate the thermodynamics of austenite decomposition in the Fe-C-Mn-Si TRIP （transformation induced plasticity） steels. Thermodynamic calculations were carried out under a para-equilibrium （PE） condition. The results show that certain silicon content can accelerate the polygonal ferritic transformation and increase the volume fraction and stability of retained austenite by retarding the precipitation of carbides during the bainitic transformation.

EFFICIENCY DECOMPOSITION WITH SHARED INPUTS AND OUTPUTS IN TWO-STAGE DEA

Data envelopment analysis （DEA） is an effective non-parametric method for measuring the relative efficiencies of decision making units （DMUs） with multiple inputs and outputs. In many real situations, the internal structure of DMUs is a two-stage network process with shared inputs used in both stages and common outputs produced by the both stages. For example, hospitals have a two-stage network structure. Stage 1 consumes resources such as information technology system, plant, equipment and admin personnel to generate outputs such as medical records, laundry and housekeeping. Stage 2 consumes the same set of resources used by stage 1 （named shared inputs） and the outputs generated by stage 1 （named intermediate measures） to provide patient services. Besides, some of outputs, for instance, patient satisfaction degrees, are generated by the two individual stages together （named shared outputs）. Since some of shared inputs and outputs are hard split up and allocated to each individual stage, it needs to develop two-stage DEA methods for evaluating the performance of two-stage network processes in such problems. This paper extends the centralized model to measure the DEA efficiency of the two-stage process with non split-table shared inputs and outputs. A weighted additive approach is used to combine the two individual stages. Moreover, additive efficiency decomposition models are developed to simultaneously evaluate the maximal and the minimal achievable efficiencies for the individual stages. Finally, an example of 17 city branches of China Construction Bank in Anhui Province is employed to illustrate the proposed approach.

Quantum dynamics of Gaudin magnets

Quantum dynamics of many-body systems is a fascinating and significant subject for both theory and experiment.The question of how an isolated many-body system evolves to its steady state after a sudden perturbation or quench still remains challenging.In this paper,using the Bethe ansatz wave function,we study the quantum dynamics of an inhomogeneous Gaudin magnet.We derive explicit analytical expressions for various local dynamic quantities with an arbitrary number of flipped bath spins,such as:the spin distribution function,the spin-spin correlation function,and the Loschmidt echo.We also numerically study the relaxation behavior of these dynamic properties,gaining considerable insight into coherence and entanglement between the central spin and the bath.In particular,we find that the spin-spin correlations relax to their steady value via a nearly logarithmic scaling,whereas the Loschmidt echo shows an exponential relaxation to its steady value.Our results advance the understanding of relaxation dynamics and quantum correlations of long-range interacting models of the Gaudin type.

Ground-state and dynamical properties of a spin-S Heisenberg star

We generalize the Heisenberg star consisting of a spin-1/2 central spin and a homogeneously coupled spin bath modeled by the XXX ring[Richter J and Voigt A 1994 J.Phys.A:Math.Gen.271139-1149]to the case of arbitrary central-spin size S<N/2,where N is the number of bath spins.We describe how to block-diagonalize the model based on the Bethe ansatz solution of the XXX ring,with the dimension of each block Hamiltonian≤2 S+1.We obtain all the eigenenergies and explicit expressions of the sub-ground states in each l-subspace with l being the total angular momentum of the bath.Both the eigenenergies and the sub-ground states have distinct structures depending whether S≤l or l<S.The absolute ground-state energy and the corresponding l as functions of the intrabath coupling are numerically calculated for N=16 and S=1,2,…,7 and their behaviors are quantitatively explained in the weak and strong intrabath coupling limits.We then study the dynamics of the antiferromagnetic order within an XXX bath prepared in the Néel state.Effects of the initial state of the central spin,the value of S,and the system-bath coupling strength on the staggered magnetization dynamics are investigated.By including a Zeeman term for the central spin and the anisotropy in the intrabath coupling,we also study the polarization dynamics of the central spin for a bath prepared in the spin coherent state.Under the resonant condition and at the isotropic point of the bath,the polarization dynamics for S>1/2 exhibit collapse-revival behaviors with fine structures.However,the collapserevival phenomena are found to be fragile with respect to the anisotropy of the intrabath coupling.