Density of integers which are discriminants of cyclic fields of odd prime degree

An asymptotic formula is given for the number of integers x which are discriminants of cyclic fields of odd prime degree.Received: 17 February 2004     

First-principles study of the local structure and crystal field of Yb2＋ in sodium and potassium halides

The local coordination structures around the doping Yb 2+ ions in sodium and potassium halides were calculated by using the first-principles supercell model.Both the cases with and without the charge compensation vacancy in the local environment of the doping Yb 2+ were calculated to study the effect of the doping on the local coordination structures of Yb 2+.Using the calculated local structures,we obtained the crystal-field parameters for the Yb 2+ ions doped in sodium and potassium halides by a method based on the combination of the quantum-chemical calculations and the effective Hamiltonian method.The calculated crystal-field parameters were analyzed and compared with the fitted results.     

The optimal thickness of a transmission-mode GaN photocathode

A 150-nm-thick GaN photocathode with a Mg doping concentration of 1.6×1017cm-3 is activated by Cs/O in an ultrahigh vacuum chamber,and a quantum efficiency(QE) curve of the negative electron affinity transmission-mode(t-mode) of the GaN photocathode is obtained.The maximum QE reaches 13.0% at 290 nm.According to the t-mode QE equation solved from the diffusion equation,the QE curve is fitted.From the fitting results,the electron escape probability is 0.32,the back-interface recombination velocity is 5×104 cm·s-1,and the electron diffusion length is 116 nm.Based on these parameters,the influence of GaN thickness on t-mode QE is simulated.The simulation shows that the optimal thickness of GaN is 90 nm,which is better than the 150-nm GaN.     

Efficient generation of two-dimensional cluster states in a cavity QED

We propose a scheme to achieve a kind of nontrivial multipartite pair-wise controlled phase operation in a cavity QED setup. The operation implemented is of geometrical nature and is not sensitive to the thermal state of the cavity. In particular, we have managed to avoid the conventional dispersive coupling so that high speed gate operation is achieved which is very important in view of decoherence. We show that this multipartite pair-wise controlled phase operation makes the generation of two-dimensional cluster states very efficient.     

Chaos suppression of uncertain gyros in a given finite time

The gyro is one of the most interesting and everlasting nonlinear dynamical systems,which displays very rich and complex dynamics,such as sub-harmonic and chaotic behaviors.We study the chaos suppression of the chaotic gyros in a given finite time.Considering the effects of model uncertainties,external disturbances,and fully unknown parameters,we design a robust adaptive finite-time controller to suppress the chaotic vibration of the uncertain gyro as quickly as possible.Using the finite-time control technique,we give the exact value of the chaos suppression time.A mathematical theorem is presented to prove the finite-time stability of the proposed scheme.The numerical simulation shows the efficiency and usefulness of the proposed finite-time chaos suppression strategy.     

The effect of electron initial longitudinal velocity on the non-sequential double ionization process in an elliptically polarized laser field

The effect of initial longitudinal velocity of the tunnelled electron on the non-sequential double ionization(NSDI) process in an elliptically polarized laser field is studied by a semiclassical model.We find that the non-zero initial longitudinal velocity has a suppressing effect on single-return collision(SRC) events in the double ionization process,more specifically,it results in an obvious reduction in the center part of the correlation momentum distributions in the direction of the major polarization axis(z axis) and makes the distribution of single-return collision in the minor polarization axis(x axis) become narrower.     

Fano resonance and wave transmission through a chain structure with an isolated ring composed of defects

We consider a discrete model that describes a linear chain of particles coupled to an isolated ring composed of N defects.This simple system can be regarded as a generalization of the familiar Fano-Anderson model.It can be used to model discrete networks of coupled defect modes in photonic crystals and simple waveguide arrays in two-dimensional lattices.The analytical result of the transmission coefficient is obtained,along with the conditions for perfect reflections and transmissions due to either destructive or constructive interferences.Using a simple example,we further investigate the relationship between the resonant frequencies and the number of defects N,and study how to affect the numbers of perfect reflections and transmissions.In addition,we demonstrate how these resonance transmissions and refections can be tuned by one nonlinear defect of the network that possesses a nonlinear Kerr-like response.     

First-principles study of mechanical stability and thermal properties of MNNi₃ （M=Zn,Mg,Al） under pressure

The mechanical stability,elastic,and thermodynamic properties of the anti-perovskite superconductors MNNi 3(M=Zn,Mg,Al) are investigated by means of the first-principles calculations.The calculated structural parameters and elastic properties of MNNi 3 are in good agreement with the experimental and the other theoretical results.From the elastic constants under high pressure,we predict that ZnNNi 3,MgNNi 3,and AlNNi 3 are not stable at the pressures above 61.2 GPa,113.3 GPa,and 122.4 GPa,respectively.By employing the Debye model,the thermodynamic properties,such as the heat capacity and the thermal expansion coefficient,under pressures and at finite temperatures are also obtained successfully.