Non-Hermitian Hamiltonians with unitary and antiunitary symmetries

We analyse several non-Hermitian Hamiltonians with antiunitary symmetry from the point of view of their point-group symmetry. It enables us to predict the degeneracy of the energy levels and to reduce the dimension of the matrices necessary for the diagonalization of the Hamiltonian in a given basis set. We can also classify the solutions according to the irreducible representations of the point group and thus analyse their properties separately. One of the main results of this paper is that some PT-symmetric Hamiltonians with point-group symmetry C_2v$C_{2v}$ exhibit complex eigenvalues for all values of a potential parameter. In such cases the PT phase transition takes place at the trivial Hermitian limit which suggests that the phenomenon is not robust. Point-group symmetry enables us to explain such anomalous behaviour and to choose a suitable antiunitary operator for the PT symmetry.     

On the Dirac equation with PT-symmetric potentials in the presence of position-dependent mass

The relativistic problem of fermions subject to a PT-symmetric potential in the presence of position-dependent mass is reinvestigated. The influence of the PT-symmetric potential in the continuity equation and in the orthonormalization condition are analyzed. In addition, a misconception diffused in the literature on the interaction of neutral fermions is clarified.     

Symmetric quadratic Hamiltonians with pseudo-Hermitian matrix representation

We prove that any symmetric Hamiltonian that is a quadratic function of the coordinates and momenta has a pseudo-Hermitian adjoint or regular matrix representation. The eigenvalues of the latter matrix are the natural frequencies of the Hamiltonian operator. When all the eigenvalues of the matrix are real, then the spectrum of the symmetric Hamiltonian is real and the operator is Hermitian. As illustrative examples we choose the quadratic Hamiltonians that model a pair of coupled resonators with balanced gain and loss, the electromagnetic self-force on an oscillating charged particle and an active LRC circuit.     

Solvable relativistic quantum dots with vibrational spectra

For Klein-Gordon equation a consistent physical interpretation of wave functions is reviewed as based on a proper modification of the scalar product in Hilbert space. Bound states are then studied in a deep-square-well model where the spectrum is roughly equidistant and where a fine-tuning of the levels is mediated by -symmetric interactions (composed of imaginary delta functions) which mimic creation/annihilation processes. Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22, 2005.     

引入Polyakov环路的手征模型中的涨落与相变

We explore the NJL model with Polyakov loops for a system of three colors and two flavors within the mean-field approximation, where both chiral symmetry and confinement are taken into account. We focus on the phase structure of the model and study the chiral and Polyakov loop susceptibilities.     

The nonequilibrium phase transition and the symmetry revival induced by time delay in an asymmetric bistable system with correlated noises

The nonequilibrium phase transition and the symmetry revival induced by time delay in a bistable system are investigated. The stationary probability distribution function (SPDF) of the bistable system with time delay and correlated noises are calculated by an analytical method and stochastic simulation respectively. The analytical and simulative results indicate that: (1) There is a certain value of λ (λ denotes the strength of correlations between the multiplicative and additive noises) to make the SPDF symmetric under some time delay; however, above or below the given value, the symmetry will be broken; (2) With the monotonic change of λ , the unimodal peak structure of SPDF becomes bimodal at the beginning, then it becomes unimodal again; this means that there is a reentrance phenomenon in the process; (3) There is a critical value of delay time, which makes the lower peak of SPDF equal to the higher one under the critical condition. This means that the symmetry revival phenomenon emerges.     

中子星内部强子-夸克相变的有限尺度效应研究

在致密星体内部极高密度条件下,强子物质可能发生退禁闭相变成为夸克物质,即强子-夸克相变。这种相变过程对于中子星的性质有着重要影响。考虑库仑能和表面能的影响,即有限尺度效应,相变过程中的混杂相包含了被称为pasta相的几何结构。强子-夸克共存相的平衡条件是通过求总能量的最小值得到的。采用相对论平均场（RMF）模型来描述强子物质相,采用Nambu-Jona-Lasinio（NJL）模型来描述夸克物质相。有限尺度效应一定程度上增加了中子星的最大质量,增加幅度取决于强子-夸克表面张力的大小。有限尺度效应能够降低混杂相的范围,其结果介于Gibbs结构和Maxwell结构的结果之间。研究结果表明,中子星中可能包含一个混杂相的核心部分,其大小受到表面张力等参数的影响。It is generally considered that hadron matter may undergo a deconfinement phase transition becoming quark matter at very high density in massive neutron stars. This hadron-quark phase transition has important impact on neutron stars, which has received much attention. We consider finite-size effect in this phase transition process, which contains the impact of Coulomb energy and surface energy. By including this effect, the mixed phase forms the pasta structures. The equilibrium conditions for coexisting hadronic and quark phases are derived by minimizing the total energy including the surface and Coulomb contributions. We employ the relativistic mean-field(RMF) model to describe the hadronic phase, while the Nambu-Jona-Lasinio(NJL) model is used for the quark phase. We conclude that the finite-size effect will raise the stiffness of EOS, and then increase the maximum mass of neutron stars, which depend on the value of surface tension. Our results show that finite-size effects can significantly reduce the region of the mixed phase, and the results lie between those from the Gibbs and Maxwell constructions. We show that a massive star may contain a mixed phase core and its size depends on the surface tension of the hadron-quark interface.     

高亏格膜泡形状的数值计算

通过对Willmore区域外,特别是中等及较小约化体积下的形状及其演化进行深入细致的研究,发现在这一区域的形状要远比原有的猜测丰富,亏格g=2的膜泡会展现出比已有结果更多迷人的形状并出现新的膜泡相变分支.同时,数值计算的结果更加期待实验验证,从而为曲率模型的正确性提供有力支持.     

Quantum Phase Transition and Magnetocaloric Effect in a Tetrameric Chain with Three-Spin Interaction

We investigate the quantum phase transition (QPT) and magnetocaloric effect (MCE) of a tetrameric chain with three-spin interaction using Green's function theory. The magnetization and gap analysis reveals a variety of quantum phases tuned by magnetic field and three-spin interaction, which can open up an energy gap, giving rise to the occurrence of zero magnetization plateau. However, strong three-spin couplings causing strong frustration will destroy the intermediate 1/2 plateau with emergence of a new gapless phase between two cusps. It favors achieving an enhanced MCE at the critical fields, where the minima of isoentropes as well as the valley-peak structure of Grüneisen ratio, signaling the accumulation of entropy, lead to cooling via adiabatic (de)magnetization processes. It is also found that the temperature dependence of specific heat combined with Grüneisen ratio can testify various quantum phases explicitly.     

Topological phase transition in cavity optomechanical system with periodical modulation

We investigate the topological phase transition and the enhanced topological effect in a cavity optomechanical system with periodical modulation. By calculating the steady-state equations of the system, the steady-state conditions of cavity fields and the restricted conditions of effective optomechanical couplings are demonstrated. It is found that the cavity optomechanical system can be modulated to different topological Su-Schrieffer-Heeger (SSH) phases via designing the optomechanical couplings legitimately. Meanwhile, combining the effective optomechanical couplings and the probability distributions of gap states, we reveal the topological phase transition between trivial SSH phase and nontrivial SSH phase via adjusting the decay rates of cavity fields. Moreover, we find that the enhanced topological effect of gap states can be achieved by enlarging the size of system and adjusting the decay rates of cavity fields.     

Rashba自旋轨道耦合下square-octagon晶格的拓扑相变

本文研究了各向同性square-octagon晶格在内禀自旋轨道耦合、Rashba自旋轨道耦合和交换场作用下的拓扑相变,同时引入陈数和自旋陈数对系统进行拓扑分类.系统在自旋轨道耦合和交换场的影响下会出现许多拓扑非平庸态,包括时间反演对称破缺的量子自旋霍尔态和量子反常霍尔态.特别的是,在时间反演对称破缺的量子自旋霍尔效应中,无能隙螺旋边缘态依然能够完好存在.调节交换场或者填充因子的大小会导致系统发生从时间反演对称破缺的量子自旋霍尔态到自旋过滤的量子反常霍尔态的拓扑相变.边缘态能谱和自旋谱的性质与陈数和自旋陈数的拓扑刻画完全一致.这些研究成果为自旋量子操控提供了一个有趣的途径.     

窗口声阻抗对锆相变动力学的影响

基于磁驱动加载装置CQ-4开展了锆的斜波压缩相变实验,研究了锆样品后表面窗口声阻抗对相变波形的影响.实验结果显示,锆后表面为较低声阻抗窗口(自由面和LiF窗口)时,相变起始对应的特征粒子速度约331.0 m/s,而高阻抗蓝宝石窗口时,特征粒子速度约301.9 m/s,特征速度对应的压力从约9.14 GPa下降到8.27 GPa.相变对应的速度特征拐点是与多种因素相关的实验信息,因此它对应的压力并不是材料属性参数相变压力.结合基于热力学Helmholtz自由能的多相状态方程和非平衡相变动力学方程开展了锆的相变动力学数值模拟研究,相变弛豫时间为30 ns,计算结果与三种情况的实验结果符合良好,可以较好地模拟斜波压缩下锆的弹塑性转变、相变等物理过程.在压力-比容和温度-压力热力学平面,相变前锆的准等熵线与冲击绝热线差异很小,相变后准等熵线都位于冲击绝热线下方,随着压力的增加准等熵线和冲击绝线偏差越来越大,温度-压力平面中在20 GPa时相差约100 K.相变开始后,由于相变引起比容的间断,导致锆的拉氏声速迅速下降约7%,相变完成后拉氏声速恢复到体波声速.     

利用两种响应时间不同的光折变晶体实现仅对物体变化部分成像

用两种响应时间相差很大的光折变晶体Ce:SBN和Fe:LiNbO_3作为相位共轭麦克尔逊干涉仪的两个相位共轭镜,得到同一物体的两个有时间差的相位共轭像,再对这两个像做实时“异或”运算,就能实现仅对物体随时间变化部分的成像.这种方法可以大大增加两相位共轭镜的响应时间差,具有最小可探测速度低,输出信号强、输出保持时间长的优点.文中对此作了理论分析,并提供了该系统对真实物体成像的实验结果.     

Martensitic phase transition with magnetocaloric effect and double-shifted exchange bias in the martensitic phase for Ni48Mn39Sn13-xGex alloys

Ni₄₈Mn₃₉Sn_13-xGe_x (x?=?1, 2) Heusler alloys have been prepared, and the martensitic phase transition (MPT), magnetocaloric effect and exchange bias (EB) have been explored. At room temperature, the structure of both samples presents L2₁ type, and the MPT shifts to a higher temperature, while the Curie temperature (T_C) of the austenitic phase decreases with the increase of the Ge content. The maximum magnetic entropy change of Ni₄₈Mn₃₉Sn_13-xGe_x with x?=?2 reaches about 14.67?J/kg?K under the magnetic field of 5?T during reverse MPT. In addition, an interesting phenomenon is the enhancement of EB with the increase of the Ge content, especially the abnormal presence of the double-shifted hysteresis loop has been realized in Ni₄₈Mn₃₉Sn_13-xGe_x with x?=?2, which can be interpreted by the fact that the antiferromagnetic (AFM) regions couple with proximal ferromagnetic (FM) regions in the opposite way at low temperature.     

Shape phase transition in neutron-rich even-even light nuclei with Z=20-28

The E-Gamma Over Spin (E-GOS) analysis method is applied to the study of the shape phase transition of neutron-rich even-even light nuclei with Z=20-28. Some valuable results are gained through analysing E-GOS curves of Ca, Ti, Cr, Fe and Ni nuclei.     

Critical dynamics associated with dynamic disordering near the depinning transition in different vortex phases

We study a depinning transition based on transient dynamics of vortices driven by a suddenly applied dc current, focusing on whether a difference in the equilibrium vortex phase that can lead to a different vortex flow will change the critical behavior. After preparing an ordered initial vortex configuration, we measure the time evolution of voltage associated with dynamic disordering in three magnetic fields, corresponding to the ordered phase (OP), disordered phase (DP), and coexistence phase. The critical behavior of the depinning transition is commonly observed in these phases, pointing to the universality of the transition. However, the critical behavior is most marked in the coexistence phase, while the suppression of the critical region and that of dynamic disordering are observed in OP and DP, respectively, whose origin is attributed to the different flow states among these phases.     

Absorption and luminescence spectra of KHo(WO<Subscript>4</Subscript>)<Subscript>2</Subscript> and KEr(WO<Subscript>4</Subscript>)<Subscript>2</Subscript> single crystals

The optical absorption and luminescence properties of potassium-holmium and potassium-erbium double tungstates have been studied. It is established that the potassium-holmium double tungstate belongs to a group of biaxial and pleochromic crystals. The emission and excitation spectra of the KHo(WO₄)₂ and KEr(WO₄)₂ single crystals were measured at room temperature.Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 71, No. 6, pp. 810–814, November–December, 2004.This revised version was published online in April 2005 with a corrected cover date.     

Symmetry Restoring Phase Transitions at High Density in a 4D Nambu-Jona-Lasinio Model with a Single Order Parameter

High density phase transitions in a 4-dimensional Nambu-Jona-Lasinio model containing a single symmetry breaking order parameter coming from the fermion-antifermion condensates are researched and expounded by means of both the gap equation and the effective potential approach. The phase transitions are proven to be second-order at a high temperature T; however at T = 0 they are first- or second-order, depending on whether A/m(0), the ratio of the momentum cutoff A in the fermion-loop integrals to the dynamicalfermion mass m(0) at zero temperature, is less than 3.387 or not. The former condition cannot be satisfied in some models. The discussions further show complete effectiveness of the critical analysis based on the gap equation for second order phase transitions including determination of the condition of their occurrence.     

Comparative first-principles analysis of the absorption spectra of ZnAl2S4 and ZnGa2O4 crystals doped with Cr3+

Systematic first-principles analysis of the energy level schemes and ground state absorption spectra of trivalent chromium in ZnAl₂S₄ and ZnGa₂O₄ crystals has been performed in the present paper. The recently developed first-principles approach to the analysis of the absorption spectra of impurity ions in crystals based on the discrete variational multi-electron (DV-ME) method [K. Ogasawara et al., Phys. Rev. B 64, 115413 (2001)] was used in the calculations. The method is based on the numerical solution of the Dirac equation; no phenomenological parameters are used in the calculations. As a result, complete energy level schemes of the Cr³⁺ ion and its absorption spectra in both crystals were calculated, assigned and compared with experimental data. By performing analysis of the molecular orbital (MO) population, it was shown that the covalency of the chemical bonds between the Cr³⁺ and S^2- ions is more significant than that one between the Cr³⁺ and O^2- ions.     

不等长相移效应滤波器的快速调试方法

提出一种基于渐进空间映射算法（ASM）与遗传算法（GA）相结合的I/O端口不等长相移效应的滤波器快速调试方法。渐进空间映射算法能够准确预测精细模型的调试方向与幅度,遗传算法能够准确快速得到I/O端口的相移效应,并且通过柯西法提取粗糙模型。基于有限元的全波电磁仿真软件HFSS, 建立精细模型,粗糙模型参数即等效电路参数, 则由去除I/O端口处相移效应后的S参数获得。利用该方法对六阶交叉耦合滤波器进行调试,经过几步迭代即可使滤波器满足所要求的响应指标,验证了该调试方法的正确性和有效性。