蓝宝石(α-Al_2O_3:Fe~(3+))体系基态分裂与局域晶格畸变的研究

2002年Scholz和Buzaré对蓝宝石晶体中Fe3+离子的基态分裂重新进行了EPR实验测量和研究,他们的初步分析表明在蓝宝石晶体中Fe3+离子的6A1基态分裂有可能同时与两个方向的畸变角(θ和φ)有关.本文采用对角化d5组态在C3点群对称下的252×252完全能量矩阵的方法,对蓝宝石晶体中Fe3+离子的光谱和EPR谱进行了系统的研究.计算结果表明蓝宝石体系中Fe3+离子的6A1基态分裂确实将明显依赖于两个方向的畸变角θ和φ,这一理论结果与Scholz和Buzaré等的实验相符合.同时,通过拟合Fe3+离子在蓝宝石体系中的实验光谱和EPR参量,确定了蓝宝石晶体中(FeO6)9团簇局域晶格畸变角θi的范围.     

Limiting values of large deviation probabilities of quadratic statistics

Application of exact Bahadur efficiencies in testing theory or exact inaccuracy rates in estimation theory needs evaluation of large deviation probabilities. Because of the complexity of the expressions, frequently a local limit of the nonlocal measure is considered. Local limits of large deviation probabilities of general quadratic statistics are obtained by relating them to large deviation probabilities of sums of k-dimensional random vectors. The results are applied, e.g., to generalized Cramér-von Mises statistics, including the Anderson-Darling statistic, Neyman's smooth tests, and likelihood ratio tests.     

Echo spectroscopy and atom optics billiards

We discuss a recently demonstrated type of microwave spectroscopy of trapped ultra-cold atoms known as “echo spectroscopy” [Phys. Rev. Lett., 2003;90:023001[1]–[4]]. Echo spectroscopy can serve as an extremely sensitive experimental tool for investigating quantum dynamics of trapped atoms even when a large number of states are thermally populated. We show numerical results for the stability of eigenstates of an atom-optics billiard of the Bunimovich type, and discuss its behavior under different types of perturbations. Finally, we propose to use special geometrical constructions to make a dephasing free dipole trap.     

Darboux transformations of the Supersymmetric BKP hierarchy

In this paper, we construct Darboux transformations of the supersymmetric BKP(SBKP) hierarchy. These Darboux transformations can generate new solutions from seed solutions by using bosonic eigenfunctions.     

Quantum coherence and ground-state phase transition in a four-chain Bose–Hubbard model

We study the quantum coherence and ground-state phase transition of a four-chain Bose–Hubbard model with the long-range interaction. In a special four-chain Bose–Hubbard model,i.e., each chain only has one optical potential, four types of the ground-state phases are discovered. The effects of the disorder, the on-site interaction and the long-range interaction on the quantum coherence are studied. For the system without the long-range interaction, the quantum coherence changes from one periodic oscillation to two periodic oscillations as the onsite interaction increases. By considering the long-range interaction, the quantum coherence goes back to one periodic oscillation again. The on-site interaction itself suppresses the quantum coherence, both the on-site interaction and long-range interaction together enhance the quantum coherence with the weak disorder. If the disorder strength is increased beyond a critical value,they start to suppress the quantum coherence. In a regular four-chain Bose–Hubbard model, i.e.,each chain has many optical potentials, the ground-state phase transitions are obtained by using the cluster Gutzwiller mean-field method. Exotic ground-state phases are found, i.e., superfluid phase, integer Mott insulator phase, supersolid phase and loophole insulator phase. The combination of the loophole insulator phase and the supersolid phase expands the lobes with the half-integer filling per site for the small ratio β = t_■/t_⊥.     

Spectral theory for Maxwell’s equations at the interface of a metamaterial. Part I: Generalized Fourier transform

We explore the spectral properties of the time-dependent Maxwell’s equations for a plane interface between a metamaterial represented by the Drude model and the vacuum, which fill, respectively, complementary half-spaces. We construct explicitly a generalized Fourier transform which diagonalizes the Hamiltonian that describes the propagation of transverse electric waves. This transform appears as an operator of decomposition on a family of generalized eigenfunctions of the problem. It will be used in a forthcoming paper to prove both limiting absorption and limiting amplitude principles.     

The spin-one Duffin Kemmer Petiau equation in the presence of pseudo-harmonic oscillatory ring-shaped potential

The Duffin-Kemmer-Petiau equation （DKP） is studied in the presence of a pseudo-harmonic oscillatory ring-shaped potential in （1 ＋ 3）-dimensional space-time for spin-one particles. The exact energy eigenvalues and the eigenfunctions are obtained using the Nikiforov-Uvarov method.     

Structures, stabilities and electronic properties of FePbn (n=1-14) clusters: Density-functional theory investigations

The structures, stabilities and electronic properties of FePb_n (n=1-14) clusters have been studied using the density-functional theory (DFT). Extensive search of the ground-state structures has been carried out by considering a larger number of structural isomers for each cluster size. The Fe atom gradually falls into the interior of the Pb framework as the number of Pb atom increases from 1 to 14. The FePb_n clusters at n=3, 5, 10, 12 have relatively higher stability by analyzing the averaged binding energy and the second-order energy difference. Especially, FePb₁₂ is more stable, owing to its highest symmetrical icosahedron structure. The magnetic moments of FePb_n clusters do not quench when Fe atom is encapsulated in the Pb framework and mostly originate from 3d state of Fe atom.     

Suppression of Stokes heating processes and improved optomechanical cooling with frequency modulation

Ground-state cooling of mesoscopic mechanical objects is still a major challenge in the unresolved-sideband regime. We present a frequency modulation (FM) scheme to achieve cooling of the mechanical resonator to its ground-state in a double-cavity optomechanical system containing a mechanical resonator. The mean phonon number is determined by numerically solving a set of differential equations derived from the quantum master equations. Due to efficient suppression of Stokes heating processes in the presence of FM, the ground-state cooling, indicated by numerical calculations, is significantly achievable, regardless of whether in the resolved-sideband regime or the unresolved-sideband regime. Furthermore, by choosing parameters reasonably, the improvement of the quantum cooling limit is found to be capable of being positively correlated with the modulation frequency. This method provides new insight into quantum manipulation and creates more possibilities for applications of quantum devices.