We study the entanglement between the internal(coin)and the external(position)degrees of freedom in the dynamic and the static deterministic aperiodic quantum walks(QWs).For the dynamic(static)aperiodic QWs,the coin depends on the time(position)and takes two coins C(α)and C(β)arranged in the two classes of generalized Fibonacci(GF)and the Thue–Morse(TM)sequences.We found that for the dynamic QWs,the entanglement of three kinds of the aperiodic QWs are close to the maximal value,which are all much larger than that of the homogeneous QWs.Further,the first class of GF(1st GF)QWs can achieve the maximum entangled state,which is similar to that of the dynamic disordered QWs.And the entanglement of 1st GF QWs is greater than that of the TM QWs,being followed closely by the entanglement of the second class of GF(2nd GF)QWs.For the static QWs,the entanglement of three kinds of the aperiodic QWs are also close to the maximal value and 1st GF QWs can achieve the maximum entangled state.The entanglement of the TM QWs is between1st GF QWs and 2nd GF QWs.However,the entanglement of the static disordered QWs is less than that of three kinds of the aperiodic QWs.This is different from those of the dynamic QWs.From these results,we can conclude that the dynamic and static 1st GF QWs can also be considered as maximal entanglement generators.
The structural and elastic properties of multiferroic Ca3Mn2O7 with ferroelectric orthorhombic(O-phase) and paraelectric tetragonal structures(T-phase) have been studied by first-principles calculations within the generalized gradient approximation(GGA) and the GGA plus Hubbard U approaches(GGA+U).The calculated theoretical structures are in good agreement with the experimental values.The T-phase is found to be antiferromagnetic(AFM) and the AFM O-phase is more stable than the T-phase,which also agree with the experiments.On these bases,the single-crystal elastic constants(Cij s) and elastic properties of polycrystalline aggregates are investigated for the two phases.Our elasticity calculations indicate Ca3Mn2O7 is mechanically stable against volume expansions.The AFM O-phase is found to be a ductile material,while the AFM T-phase shows brittle nature and tends to be elastically isotropic.We also investigate the influence of strong correlation effects on the elastic properties,qualitatively consistent results are obtained in a reasonable range of values of U.Finally,the ionicity is discussed by Bader analysis.Our work provides useful guidance for the experimental elasticity measurements of Ca3Mn2O7,and makes the strain energy calculation in multiferroic Ca3Mn2O7 thin films possible.
本文通过数值计算的方法研究了一维离散时间准周期量子行走的动力学特性,主要研究了两个自旋空间C 算符按照广义Fibonacci准周期排列的量子行走,发现对两类广义Fibonacci准周期序列,波包扩散都是超扩散（即标准方差σ约为tγ,0.5〈γ〈1）,而且在给定的两个 C 算符下,第二类广义Fibonacci准周期序列的幂指数γ大于第一类广义Fibonacci准周期序列.通过对波包扩散的概率分布情形和标准方差的研究发现,第一类广义Fibonacci准周期序列的波包扩散更接近于经典随机行走（γ=0.5）,而第二类广义Fibonacci准周期序列的波包扩散更接近于均匀量子行走（γ=1）,这与两类广义Fibonacci准周期量子自旋链中量子相变时的特性相反.
The effects of the Dzyaloshinski-Moriya (DM) interaction on the ground-state properties of the anisotropic XY chain in a transverse field have been studied by means of correlation functions and entanglement. Different from the case without the DM interaction, the excitation spectra εk of this model are not symmetrical in the momentum space and are not always positive. As a result, besides the ferromagnetic (FM) and the paramagnetic (PM) phases, a gapless chiral phase is induced. In the chiral phase, the von Neumann entropy is proportional to log2L (L is the length of a subchain) with the coefficient A ≈ 1/3, which is the same as that of the XY chain in a transverse field without the DM interaction for γ = 0 and 0 < h ≤ 1. And in the vicinity of the critical point between the chiral phase and the FM (or PM) phase, the behaviors of the nearest-neighbor concurrence and its derivative are like those for the anisotropy transition.
