The Stationary Optomechanical Entanglement Between an Optical Cavity Field and a Cubic Anharmonic Oscillator

International Journal of Theoretical Physics - Currently, the creation of the quantum entanglement is still one of the most challenging goals. Here, we theoretically investigate the stationary...     

Normal Mode Splitting in a Cavity Optomechanical System with a Cubic Anharmonic Oscillator

The strong coupling between a macroscopic mechanical oscillator and a cavity field is essential for many quantum phenomena in a cavity optomechanical system. In this work, we discuss the normal mode splitting in a cavity optomechanical system with a cubic nonlinear movable mirror. We study how the mechanical nonlinearity affects the normal-mode splitting behavior of the movable mirror and the output field. We find that the mechanical nonlinearity can increase the peak separation in the spectra of the movable mirror and the output field. We also find that the heights and linewidths of the two peaks are very sensitive to the mechanical nonlinearity.

     

Electron Spectrum Topology and Giant Singularities of the Electron Density of States in Cubic Lattices

The topology of energy surfaces in reciprocal space is studied in detail for simple cubic (sc), body-centered cubic (bcc), and face-centered cubic (fcc) lattices in the tight-binding approximation, taking into account hopping integrals t and t′ between the nearest and next-nearest neighbor sites, respectively. It is shown that lines and surfaces formed by van Hove k points can arise at values τ = t′/t = τ* corresponding to a change in the surface topology. At a small deviation of τ from these special values, the spectrum near the van Hove line (surface) only slightly depends on k. This corresponds to a giant effective mass proportional to |τ - τ*|⁻¹ near several van Hove points. Singular contributions to the density of states near these special t values are analyzed and explicit expressions are obtained for the density of states in terms of elliptic integrals. It is shown that, in some cases, the maximum density of states is achieved at energies corresponding to k points in high-symmetry directions inside the Brillouin zone rather than at its edges. The corresponding contributions to electronic and magnetic characteristics are discussed, in particular, in application to itinerant weak magnets.

     

The Relations Between q-Deformed Oscillator and Fermionic Oscillator

We study the relevance between the statistical property of q-deformed oscillator and thevalue of q. It is shown that there is the consistency condition |q| = 1. When q is not a realnumber. The q-Fock space is reconstructed so that it is applicable to the case in which q is extended to the complex number. And the general expression of q-deformed oscillator b_q and b_q⁺ in the new g-Fock space is given. It is found that q = ±i correspond to fermionic oscillator(the mix of the ordinary proper and improper one). This conclusion implies that q-deformedoscillator relates naturally and inherently the fermionic oscillator with the bosonic oscillatorby choosing the value of q. Actually, the bosonization structure of the single mode of fermioncan also be obtained in the way. Of course, the solution of the fermionic oscillator given inthis paper is a representation of quantum algebra SU_q(2).     

Pure Point Spectrum of the Floquet Hamiltonian for the Quantum Harmonic Oscillator Under Time Quasi-Periodic Perturbations

We prove that the 1-d quantum harmonic oscillator is stable under spatially localized, time quasi-periodic perturbations on a set of Diophantine frequencies of positive measure. This proves a conjecture raised by Enss-Veselic in their 1983 paper [EV] in the general quasi-periodic setting. The motivation of the present paper also comes from construction of quasi-periodic solutions for the corresponding nonlinear equation. Partially supported by NSF grant DMS-05-03563.     

微小尺寸立方氮化硼晶体蓝紫光发射光谱的测量与分析

对于微小尺寸的N型宽禁带立方氮化硼(CBN)半导体晶体,在施加恒稳电场的情况下,观察到电致发光现象。通过置CBN单晶样品于光栅单色仪抛物面反射镜焦点的方法,对于CBN的蓝紫光辐射获得了测试系统的最大入射光通量和理想的信噪比。在350～450 nm波长范围内,CBN加上4.7×106 V·cm-1恒稳电场条件下,测量出立方氮化硼的蓝紫光发射光谱。同时,结合基于第一性原理的GGA方法计算出的立方氮化硼能带结构和电子态密度,以及测量得到的非线性j-E关系和电击穿特性,讨论了发光机理。提出了在雪崩击穿前的缺陷偶极子极化和击穿后,产生大量的激发态电子,电子在Γ能谷和X能谷间迁移的发光机制。     

The Singular Kane Oscillator

The energy spectrum of carriers in narrow band gap semiconductor nanocrystals are studied theoretically taking into account the nonparabolicity of charge carriers dispersion laws. The confinement potential of nanocrystals is approximated to be λγ^2 ＋ λ1γ^-2, and the dispersion laws are considered within the framework of the three-band Kane model.     

The Representation of Bosonic Oscillator

The bosonic oscillator is discussed in quite a different method compared with the conventional one. We first strictly deduce an algebraic identity. After introducing an important,boundary condition, we deduce the characteristic equation of number operator N. From this equation,we discuss some properties of bosonic oscillator including its Hilbert space.     

用超对称性和形不变性方法求解环形振子的能谱和波函数

运用超对称性和形不变性方法计算环形振子的能量本征值和本征波函数.所得到的能谱公式与用费曼路径积分方法得到的严格解完全一致.     

On the Spectrum of a (p,q)-Deformed Oscillator with a Kind of Nonlinear Interaction

Spectrum of a (p,q)-deformed oscillator interacting with a classical current via intensity-dependent field operator is investigated by means of the factorization method. It is shown that the spectrum in this case is similar to the one ofq-oscillator with a linear interaction; but the discrete spectrum consisting of a finite number of levels with infinite multiplicity may appear only when the parameters still satisfy a couple of additional conditions.     

用超对称性和形不变性方法求解环形振子的能谱和波函适

运用超对称性和形不变性方法计算环形振子的能量本征值和本征波函数. 所得到的能谱公式与用费曼路径积分方法得到的严格解完全一致.     

The Quantum Harmonic Oscillator in the ESR Model

The ESR model proposes a new theoretical perspective which incorporates the mathematical formalism of standard (Hilbert space) quantum mechanics (QM) in a noncontextual framework, reinterpreting quantum probabilities as conditional on detection instead of absolute. We have provided in some previous papers mathematical representations of the physical entities introduced by the ESR model, namely observables, properties, pure states, proper and improper mixtures, together with rules for calculating conditional and overall probabilities, and for describing transformations of states induced by measurements. We study in this paper the relevant physical case of the quantum harmonic oscillator in our mathematical formalism. We reinterpret the standard quantum rules for probabilities, provide new expressions for absolute probabilities, and show how the standard state transformations must be modified according to the ESR model.     

混合光谱中已知组分光谱的自加强方法研究

通过数学变换手段将混合物光谱中某待测组分（已知纯光谱组分）所包含的信息集中于原点,使得待分析组分光谱在变换结果曲线的原点处贡献最大,称之为纯光谱组分的自加强作用;在杂质光谱所包含谱带中心位置与待分析组分纯光谱差别较大的假设基础之上,通过理论分析可认为杂质光谱在变换结果曲线原点处贡献最小,因而可选择变换结果曲线原点处的小波变换系数作为待测组分定量分析的依据,降低了分析位置选择的人为性,增强了分析手段的可靠性与适应性。模拟对比了理想曲线与含加性高斯白噪声信号的变换结果,证明该方法具有好的抗噪特性。模拟分析结果表明,该方法相比以往文献报道的单纯利用小波系数作为定量分析依据的做法在分析误差方面有很大改善。