The coloured quantum plane

We study the quantum plane associated to the coloured quantum group GL_q^λ,μ(2) and solve the problem of constructing the corresponding differential geometric structure. This is achieved within the R-matrix framework generalising the Wess–Zumino formalism and leads to the concept of coloured quantum space. Both the coloured Manin plane as well as the bicovariant differential calculus exhibit the colour exchange symmetry. The coloured h-plane corresponding to the coloured Jordanian quantum group GL_h^λ,μ(2) is also obtained by contraction of the coloured q-plane.     

Geometric measure of quantum discord over two-sided projective measurements

The original definition of quantum discord of bipartite states was defined over one-sided projective measurements, it describes quantum correlations more extensively than entanglement. Dakic, Vedral, and Brukner [Phys. Rev. Lett. 105 (2010) 190502] introduced a geometric measure of quantum discord, Luo and Fu [Phys. Rev. A 82 (2010) 034302] simplified the variation expression of this geometric measure. In this Letter we introduce a geometric measure of quantum discord over two-sided projective measurements. A simplified expression and a lower bound of this two-sided geometric measure are derived and explicit expressions are obtained for some special cases.     

Intersubband optical absorptions of a two-electron quantum ring

In this Letter, the optical properties of a quantum ring with two electrons are studied. Its effective-mass Hamiltonian matrix was diagonalized with numerical methods, followed by the calculations of a number of optical quantities. We have found that the intersubband optical absorptions strongly depends on the ring radius, electron-electron interaction, and the incident optical intensity. We also found that the spin-singlet states are more sensitive to ring radius than the spin-triplet states.     

Optical absorptions of an exciton in a quantum ring: Effect of the repulsive core

We study the optical absorptions of an exciton in a quantum ring. The quantum ring is described as a circular quantum dot with a repulsive core. The advantage of our methodology is that one can investigate the influence of the repulsive core by varying two parameters in the confinement potential. The linear, third-order nonlinear and total optical absorption coefficients have been examined with the change of the confinement potential. The results show that the optical absorptions are strongly affected by the repulsive core. Moreover, the repulsive core can influence the oscillation in the resonant peak of the absorption coefficients.     

Effect of Rashba spin-orbit coupling on electron transport in asymmetrically coupled regular polygonal quantum ring

The effect of Rashba spin-orbit coupling (SOC) on electron transport in asymmetrically coupled regular polygonal quantum ring is investigated. In absence of SOC, two kinds of conductance zeros appear periodically. In presence of SOC, one kind of conductance zero can be lifted by the Rashba SOC, the others persist.     

Spatial correlation of two particles in semiconductor quantum ring

We analyze the effect of the spatial correlation on the ground state energy of two particles (two electrons and exciton–hole pair) confined in quantum ring (QR) with a soft-edge-barrier confinement potential. Starting from the Schrödinger variational principle we derive a one-dimensional differential equation for the spatial pair correlation function (SPCF), which we solve numerically by using the shooting method. The effect of the repulsive core in a self-assembled GaAs/InAs QR on the two-electron and exciton SPCF is analyzed. A comparative analysis of the dependencies of the two-particle ground state energies on the inner and outer radii of GaAs/InAs QRs with different confinement potential shapes is presented.     

Tuning of exciton states in a magnetic quantum ring

The exciton states in a CdTe quantum ring subjected to an external magnetic field containing a single magnetic impurity are investigated. We have used the multiband approximation which includes the heavy hole–light hole coupling effects. The electron–hole spin interactions and the s, p–d interactions between the electron, the hole and the magnetic impurity are also included. The exciton energy levels and optical transitions are evaluated using the exact diagonalization scheme. We show that due to the spin interactions it is possible to change the bright exciton state into the dark state and vice versa with the help of a magnetic field. We propose a new route to experimentally estimate the s, p–d spin interaction constants.     

Noncommutative geometry of the quantum clock

We introduce a model of noncommutative geometry that gives rise to the uncertainty relations recently derived from the discussion of a quantum clock. We investigate the dynamics of a free particle in this model from the point of view of doubly special relativity and discuss the geodesic motion in a Schwarzschild background.     

Effect of interdiffusion on electronic states in one-layer quantum ring superlattice

The effect of interdiffusion on band structure and Bloch amplitudes of two dimensional superlattice composed of initially cylindrical quantum rings is investigated in the framework of adiabatic approach and using transformation to in-plane momentum space. It is shown that the adiabatic approximation is applicable even if the ring’s height is equal to its radius, because of weak localization of electron in the superlattice plane comparing with the localization in perpendicular direction. The consideration of the dependence of effective mass on spatial coordinate and time leads to the energy correction up to 10 meV. It is shown that energy minibands rise and become wider due to interdiffusion and the dependence of Bloch amplitudes on quasimomentum direction is more pronounced in the case of diffused potential profile.     

Electron and hole states in a quantum ring grown by droplet epitaxy: Influence of the layer inside the ring opening

The electronic structure of the conduction and valence bands of a quantum ring containing a layer inside the ring opening is modeled. This structure (nanocup) consists of a GaAs nanodisk (the cup’s bottom) and a GaAs nanoring (the cup’s rim) which encircles the disk. The whole system is embedded in an (Al,Ga)As matrix, and its shape resembles realistic ring structures grown by the droplet epitaxy technique. The conduction-band states in the structure are modeled by the single-band effective-mass theory, while the 4-band Luttinger–Kohn model is adopted to compute the valence-band states. We analyze how the electronic structure of the nanocup evolves from the one of a quantum ring when the size of either the nanodisk or the nanoring is changed. For that purpose, (1) the width of the ring, (2) the disk radius, and (3) the disk height are separately varied. For dimensions typical for experimentally realized structures, we find that the electron wavefunctions are mainly localized inside the ring, even when the thickness of the inner layer is 90% of the ring thickness. These calculations indicate that topological phenomena, like the excitonic Aharonov–Bohm effect, are negligibly affected by the presence of the layer inside the ring.     

The local geometry of compact homogeneous Lorentz spaces

In 1995, S. Adams and G. Stuck as well as A. Zeghib independently provided a classification of non-compact Lie groups which can act isometrically and locally effectively on compact Lorentzian manifolds. In the case that the corresponding Lie algebra contains a direct summand isomorphic to the two-dimensional special linear algebra or to a twisted Heisenberg algebra, Zeghib also described the geometric structure of the manifolds. Using these results, we investigate the local geometry of compact homogeneous Lorentz spaces whose isometry groups have non-compact connected components. It turns out that they all are reductive. We investigate the isotropy representation and curvatures. In particular, we obtain that any Ricci-flat compact homogeneous Lorentz space is flat or has compact isometry group.     

量子环中量子比特的声子效应

在量子环中电子与体纵光学声子强耦合的情况下,通过求解能量本征方程,得出了电子的基态和第一激发态的本征能量及其波函数,进而以电子-声子系的基态与第一激发态构造了一个量子比特.数值计算结果表明量子比特内电子的空间概率密度分布随时间和空间角坐标作周期性振荡,且振荡周期随耦合强度的增大而减小,说明声子将导致量子比特相干性降低;还表明振荡周期随量子环内径（或外径）的增大而增大,因此适当改变量子环的尺度,可以提高量子比特的相干性. 关键词： 量子环 量子信息 量子比特     

Aharonov–Bohm oscillation of photoionization cross section in a quantum ring with a repulsive scattering center

The photoionization cross section (PCS) associated with intersubband transitions in quantum rings which include a repulsive scattering centre is investigated for the case with the presence of an external magnetic field. Calculations are carried out by using the matrix diagonalization method of the Hamiltonian matrix within the effective-mass approximation. Our results show that both the magnetic field, the ring radius and the impurity can affect the PCS of quantum rings. In addition, we found that the resonant peak of the PCS shows the Aharonov–Bohm oscillation with changing the magnetic field and the ring radius. Moreover, the width of the ring can influence the Aharonov–Bohm oscillation in peak while the resonant peak value of the PCS decreases as the ring width increases in the same ring geometry.     

四氢呋喃的糖环不是平面而是螺旋面

基于分子的群理论和量子力学计算，本文首次证明：四氢呋喃[THF]的平衡构型是C1 对称性，其糖环不是平面而是螺旋面。     

量子环中量子比特的消相干时间

在量子环中电子与体纵光学声子强耦合的情况下,通过求解能量本征方程,得出了电子的基态和第一激发态的本征能量及其波函数,进而以电子-声子体系的基态与第一激发态构造一个量子比特.结果讨论了消相干时间与耦合强度,色散系数以及量子环内径、外径的变化关系.     

Commutator representations of differential calculi on the quantum group SUq(2)

Let (Γ, d) be the 3D-calculus or the 4D_±-calculus on the quantum group SU_q (2). We describe all pairs (π, F) of a ^*-representation π of (SU_q(2)) and of a symmetric operator F on the representation space satisfying a technical condition concerning its domain such that there exist a homomorphism of first order differential calculi which maps dx into the commutator [iF, π(x)] for x ε (SU_q (2)). As an application commutator representations of the two-dimensional left-covariant calculus on Podles quantum 2-sphere S_qc² with c = 0 are given.     

Observables in a noncommutative approach to the unification of quanta and gravity: a finite model

We further develop a noncommutative model unifying quantum mechanics and general relativity proposed in Gen. Rel. Grav. (36, 111–126 (2004)). Generalized symmetries of the model are defined by a groupoid given by the action of a finite group on a space E. The geometry of the model is constructed in terms of suitable (noncommutative) algebras on . We investigate observables of the model, especially its position and momentum observables. This is not a trivial thing since the model is based on a noncommutative geometry and has strong nonlocal properties. We show that, in the position representation of the model, the position observable is a coderivation of a corresponding coalgebra, coparallelly to the well-known fact that the momentum observable is a derivation of the algebra. We also study the momentum representation of the model. It turns out that, in the case of the algebra of smooth, quickly decreasing functions on , the model in its quantum sector is nonlocal, i.e., there are no nontrivial coderivations of the corresponding coalgebra, whereas in its gravity sector such coderivations do exist. They are investigated.This revised version was published online in April 2005. The publishing date was inserted.     

Electron spectral properties of the InAs/GaAs quantum ring

A 3D model of semiconductor quantum ring (QR) based on the single sub-band approach with an energy-dependent electron effective mass is considered. The non-linear energy confinement problem is numerically solved iteratively by using the finite elements method. We calculate the energy spectrum of the electron states for the InAs/GaAs QR using the geometrical parameters obtained in the fabrication of such rings by A. Lorke, et al. (Phys. Rev. Lett. 84 (2000) 2223). The calculated energies are compared with the experimental data.