Solitons on a Periodic Wave Background of the Modified KdV-Sine-Gordon Equation

The B?cklund transformation(BT) of the m Kd V-s G equation is constructed by introducing a new transformation. Infinitely many nonlocal symmetries are obtained in terms of its BT. The soliton-periodic wave interaction solutions are explicitly derived by the classical Lie-group reduction method. Particularly, some special concrete soliton and periodic wave interaction solutions and their behaviours are discussed both in analytical and graphical ways.     

Majorana zero modes,unconventional real-complex transition,and mobility edges in a one-dimensional non-Hermitian quasi-periodic lattice

A one-dimensional non-Hermitian quasiperiodic p-wave superconductor without PT-symmetry is studied.By analyzing the spectrum,we discovered that there still exists real-complex energy transition even if the inexistence of PT-symmetry breaking.By the inverse participation ratio,we constructed such a correspondence that pure real energies correspond to the extended states and complex energies correspond to the localized states,and this correspondence is precise and effective to detect the mobility edges.After investigating the topological properties,we arrived at a fact that the Majorana zero modes in this system are immune to the non-Hermiticity.     

量子体系的相空间规范变换

外尔于1918年引入的规范变换实际上是相位变换而非真正的尺度变换,但规范不变性、规范理论等概念都沿袭了下来.我们发现,针对由量子化条件[x,p]=i(h)而来的量子体系之本征值问题存在规范变换,或者说尺度变换,x→x/α,p→αp,该变换保体系的能量谱不变.量子谐振子、氢原子问题及一类多体问题的精确解析解证实了这一点....     

点缺陷扶手型石墨烯量子点的电子性质研究

基于有限差分方法, 数值求解了Dirac方程, 研究了垂直磁场下的点缺陷扶手型 石墨烯 量子点的能谱结构, 分析了尺寸大小对带隙的影响. 与无磁场时具有一定带隙 (带隙的大小与半径成反比) 的量子点相比, 在外加有限磁场下, 能谱中出现朗道能级, 最低朗道能级能量为零并与磁场强度无关, 并且朗道能级的简并度随着磁场的增加而增加. 进一步的计算表明, 最低朗道能级的简并度与磁场成线性关系, 与半径的平方成线性关系. 本文工作对基于石墨烯量子点的器件设计具有一定的指导意义.     

Spectrum Density Factor of Photons and Its Application in the Casimir Force

The observables of continuous eigenvalues are de?ned in an in?nite-dimensional ket space. The complete set of such eigenstates demands a spectrum density factor, for example, for the photons in the free space and electrons in the vacuum. From the derivation of the Casimir force without an arti?cial regulator we determine the explicit expression of the spectrum density factor for the photon ?eld to be an exponential function. The undetermined constant in the function is ?xed by the experimental data for the Lamb shift. With that, we predict that there exists a correction to the Casimir force.     

Metal–insulator phase transition and topology in a three-component system

Due to the topology, insulators become non-trivial, particularly those with large Chern numbers which support multiple edge channels, catching our attention. In the framework of the tight binding approximation, we study a non-interacting Chern insulator model on the three-component dice lattice with real nearest-neighbor and complex next-nearest-neighbor hopping subjected to Λ-or V-type sublattice potentials. By analyzing the dispersions of corresponding energy bands, we find that the system undergoes a metal–insulator transition which can be modulated not only by the Fermi energy but also the tunable extra parameters. Furthermore, rich topological phases, including the ones with high Hall plateau, are uncovered by calculating the associated band’s Chern number. Besides, we also analyze the edge-state spectra and discuss the correspondence between Chern numbers and the edge states by the principle of bulk-edge correspondence. In general, our results suggest that there are large Chern number phases with C = ±3 and the work enriches the research about large Chern numbers in multiband systems.     

完备Buck-Sukumar模型的光子阻塞效应

Buck-Sukumar (BS)模型在一定的耦合强度处会出现能级塌缩现象.通过引入一个非线性光子项,定义了一个完备的BS模型,消除了能级塌缩.进一步通过计算二阶关联函数等物理量理解了非线性光子项与失谐量对该模型的影响.结果表明,在共振情况下,非线性光子项破坏了BS模型的能谱简谐性,可以在更大的耦合强度范围内产生单光子投影态,形成光子阻塞;而在非共振情况下,非线性光子项使非简谐的能谱在整个耦合区间都有定义,且正失谐促进光子阻塞,负失谐抑制光子阻塞.     

具有p波超流的一维非公度晶格中迁移率边研究

研究了具有p波超流的一维非公度晶格中迁移率边的性质. 发现适当的p波超流可以增加体系中的迁移率边的数目, 并且通过多分形分析确定了迁移率边所在的位置.     

有限温度下一维Hubbard模型的化学势泛函理论研究

通过数值方法求解了有限温度下一维均匀Hubbard模型的热力学Bethe-ansatz方程组,得到了在给定温度和相互作用强度情况下,比热c、磁化率χ和压缩比κ随化学势μ的变化图像.基于有限温度下一维均匀Hubbard模型的精确解,利用化学势(μ)-泛函理论研究了一维谐振势下的非均匀Hubbard模型,给出了金属态和Mott绝缘态下不同温度情况时局域粒子密度n_i和局域压缩比_κi随格点的变化情况.     

受限一维无自旋费米子系统的性质研究

本文借助于一维自旋1/2-XXZ模型的Bethe-ansatz精确解, 利用局域密度近似(LDA), 讨论了谐振势中一维无自旋费米子的密度分布, 得出了ρ-u相图(这里的ρ为无量纲的粒子数密度 变量u为相互作用强度)对相图的分析表明, 随着原子密度和近邻相互作用的变化, 系统出现五个不同的混合量子相通过对热力学硬度S_ρ的计算, 发现其可作为体系的序参量, 其奇异点可用以度量受限体系中量子相变的发生