Convolution Theorem of Fractional Fourier Transformation Derived by Representation Transformation in Quantum Mechancis

Based on our previous paper （Commun. Theor. Phys. 39 （2003） 417） we derive the convolution theorem of fractional Fourier transformation in the context of quantum mechanics, which seems a convenient and neat way. Generalization of this method to the complex fractional Fourier transformation case is also possible.     

One Electron Atom in Special Relativity with de Sitter Space-Time Symmetry(Ⅱ): ——Higher Order Contributions

This is a follow of previous work entitled "One Electron Atom in Special Relativity with de Sitter SpaceTime Symmetry" [Commun. Theor. Phys. 57(2012) 930]. In this paper, we consider the higher order calculations and contributions in the previous framework to solve one electron atoms in de Sitter invariant relativistic quantum mechanics. The next-to-leading-order calculations in 1/R2-expansions show that the fine-structure constant α is variant with cosmologic time going by in the de Sitter invariant special relativistic quantum mechanics with standard FRW cosmologic model.     

A Note on Similarity Reductions of Barotropic and Quasi-geostrophic Potential Vorticity Equation

Applying the classical Lie symmetry approach to the barotropic and quasi-geostrophic potential vorticity equation without forcing and dissipation on a β-plane channel, we find a new symmetry, which is not presented in a previous work [F. Huang, Commun. Theor. Phys. （Beijing, China） 42 （2004） 903]. A general finite transformation group is obtained based on the full Lie point symmetry, Furthermore, two new types of similarity reduction solutions are obtained.     

Single-particle distribution function of a quantum dot system at finite temperature

In the present paper,we shall rigorously re-establish the result of the single-particle function of a quantum dot system at finite temperature.Unlike the proof given in our previous work(Phys.Rev.B 74 195414(2006)),we take a different approach,which does not exploit the explicit expression of the Gibbs distribution function.Instead,we only assume that the statistical distribution function of the quantum dot system is thermodynamically stable.As a result,we are able to show clearly that the electronic structure in the quantum dot system is completely determined by its thermodynamic stability.Furthermore,the weaker requirements on the statistical distribution function also make it possible to apply the same method to the quantum dot systems in non-equilibrium states.     

Representations and Classification of Traveling Wave Solutions to sinh-GSrdon Equation

Two concepts named atom solution and combinatory solution are defined. The classification of all single traveling wave atom solutions to sinh-Gordon equation is obtained, and qualitative properties of solutions are discussed. In particular, we point out that some qualitative properties derived intuitively from dynamic system method are not true. Finally, we prove that our solutions to sinh-Gordon equation include all solutions obtained in the paper [Z.T. Fu, et al., Commun. Theor. Phys. （Beijing, China） 45 （2006） 55]. Through an example, we show how to give some new identities on Jacobian elliptic functions.     

Entanglement and Quantity in Quantum Space —— About Quantum Measurement （II）

As a continuation and extension of “quantity in phase space“ “quantity in quantum space“ is introduced. With that, the disappearing of quantum interference discussed in a previous paper [S. Du^err, et al., Nature 395 (1998) 33] is explained in the same spirit as our recent papers [Ren De-Ming, Commun. Theor. Phys. (Beijing, China) 41(2004) 685, 833].     

Comment on ＂Approximate and Conditional Teleportation of an Unknown Atomic State Without Bell-State Measurement with Two-Photon Interaction＂

In a previous work [Commun. Theor. Phys. 45 （2006） 79] a scheme was presented for approximate and conditional teleportation of an unknown atomic state in a QED-cavity without Bell-state measurement via two-photon Jaynes-Cummings model in the effective Hamiltonian approach. This comment presents an alternative method, based on the so called ＂full two-photon Jaynes-Cummings Hamiltonian approach＂. Accordingly, it describes the evolution of the two-photon degenerate process for arbitrary average photon number inside the cavity, as the correct way to implement teleportation in this scenario.     

Recurrence spectra of Li atom in strong external fields

Based upon our previous work [Commun. Theor. Phys.. 40,702 (2003)], we developed the closed orbit theory from two degrees of freedom to three non-separable degrees of freedom and calculated the recurrence spectra of Li Rydberg atom in strong perpendicular electric and magnetic fields. The Fourier transformed spectra of Li atom has allowed direct comparison between the resonance peaks and the scaled action values of closed orbits, whereas the nonhydrogenic resonance can be explained in terms of the new orbits created by the core scattering. The semiclassical result is in good agreement with the quantum one, which suggests that our calculation is correct.     

Controlled Teleportation of Multi-qudit Quantum Information by Entanglement Swapping

In this paper, we present a scheme for teleporting multi-qudit quantum state, from the sender Alice to the receiver Charlie via many controllers Bobs, whose control parameters are obtained using entanglement swapping of maximally d-dimensional EPR pair. In our scheme, Yang＇s qutrit controlled teleportation protocol [Commun. Theor. Phys. 49 （2008） 338] based on Bell-state entanglement swapping is generalized to the qudit case. The scheme of multi-qudit owns the advantage of having higher code capacity and better security than that of multi-qutrit.     

Some Remarks on Exp-Function Method and Its Applications-A Supplement

Recently, the authors of [Commun. Theor. Phys. 56 （2011） 397] made a number of useful observations on Exp-function method. In this study, we focus on another vital issue, namely, the misleading results of double Exp-function method.     

Optical Operator Method in Two-Mode Case and Entangled Fresnel Operator＇s Decomposition

Based on the entangled Fresnel operator （EFO） proposed in [Commun. Theor. Phys. 46 （2006） 559], the optical operator method studied by the IWOP technique （Ma et al., Commun. Theor. Phys. 49 （2008） 1295） is extended to the two-mode case, which gives the decomposition of the entangled Fresnel operator, corresponding to the decomposition of ray transfer matrix [A, B, C, D]. The EFO can unify those optical operators in two-mode case. Various decompositions of EFO into the exponential canonical operators are obtained. The entangled state representation is useful in the research.     

Improvement on Quantum Secure Direct Communication with W State in Noisy Channel

An improvement （Y-protocol） [Commun. Theor. Phys. 49 （2008） 103] on the quantum secure direct communication with W state （C-protocol） [Chin. Phys. Lett. 23 （2006） 290] is proposed by Yuan et al. The quantum bit error rate induced by eavesdropper is 4.17% in C-protocol and 6.25% in Y-protocoL In this paper, another improvement on C-protocol is given. The quantum bit error rate of the eavesdropping will increase to 8.75%, which is 1.1 times larger than that in C-protocol and 0.4 times larger than that in Y-protocol.     

Faithful Teleportation of an Unknown Atomic-Entangled State Without Bell-State Measurement

An alternative scheme is proposed for teleportation of an unknown atomic-entangled state. The scheme is based on the resonant interaction of a two-mode cavity field with a A-type three-level atom. In contrast with the previously proposed scheme of [Commun. Theor. Phys. 47 （2007） 253], the present scheme is ascendant, since the fidelity is 1.0 in principle similarly without the Bell-state measurement. The scheme may be generalized to not only the teleportation of the cavity-mode-entangled-state but also the teleportation of the multi-atomic entangled states included in generalized GHZ states. And the scheme is experimentally feasible based on the current cavity QED technique.     

Influence of Different Connectivity Topologies in Small World Networks Modeling Earthquakes

We introduce the Olami-Feder-Christensen (OFC) model on a square lattice with some “rewired“ longrange connections having the properties of small world networks. We find that our model displays the power-law behavior, and connectivity topologies are very important to model‘s avalanche dynamical behaviors. Our model has some behaviors different from the OFC model on a small world network with “added“ long-range connections in our previous work [LIN Min, ZHAO Xiao-Wei, and CHEN Tian-Lun, Commun. Theor. Phys. (Beijing, China) 41 (2004) 557.].     

Controlled Teleportation of Multi-qutrit Quantum Information by Swapping Entanglement

We present a scheme for teleporting multi-qutrit quantum information from a sender to a receiver via the control of many agents in a network. Agents＇s control parameters are obtained via quantum entanglement swapping. In our scheme, Zhang and Man＇s QSS protocol [Phys. Rev. A 72 （2005） 022303] based on Bell-state entanglement swapping is generalized to a qutrit case. Our scheme owns the advantage of having higher code capacity and better security than the work [Commun. Theor. Phys. 44 （2005） 847] on controlled teleportation for multi-qubit.     

The influence of surface effects on Frederiks transition in nematic liquid crystal doped with ferroelectric nanoparticles

Motivated by our recent work,in this work,we present the numerical study of the anchoring effect on the Frederiks threshold field in a nematic liquid crystal doped with ferroelectric colloidal nanoparticles.Assuming weak anchoring conditions,we employ the relaxation method and Maxwell construction to numerically solve the Euler–Lagrangian differential equation for the total free energy together the Rapini–Papoular surface energy to take into account anchoring of nematic liquid crystal molecules at the substrates.In this study,we focus our attention on obtaining the phase diagrams of Frederiks transition for different values of anchoring strength which have been not computed in our previous work.In this way,the effect of nanoparticle radius,nanoparticle volume fraction,nanoparticle polarization,and cell thickness on the Frederiks transition for different values of anchoring conditions are summarized in the phase diagrams.The numerical results show that by increasing the nanoparticles size and nanoparticle volume fraction in the ferronematic system,the Frederiks threshold field is strongly reduced.     

Complex Behaviors of a Simple Traffic Model

In this paper, we propose a modified traffic model in which a single car moves through a sequence of traffic lights controlled by a step function instead of a sine function. In contrast to the previous work [Phys. Rev. E 70 (2004)016107], we have investigated in detail the dependence of the behavior on four parameters, ω, α, η, and a1, and given three kinds of bifurcation diagrams, which show three kinds of complex behaviors. We have found that in this model there are chaotic and complex periodic motions, as well as special singularities. We have also analyzed the characteristic of the complex period motion and the essential feature of the singularity.     

Manipulation of Nanoparticles Using Dark-Field-Illumination Optical Tweezers with Compensating Spherical Aberration

Based on our previous investigation of optical tweezers with dark field illumination [Chin. Phys. Left. 25（2008）329] nanoparticles at large trap depth are better viewed in wide field and real time for a long time, but with poor forces. Here we present the mismatched tube length to compensate for spherical aberration of an oil-immersion objective in a glass-water interface in an optical tweezers system for manipulating nanoparticles. In this way, the critical power of stable trapping particles is measured at different trap depths. It is found that trap depth is enlarged for trapping nanoparticles and trapping forces are enhanced at large trap depth. According to the measurement, 70-nm particles are manipulated in three dimensions and observed clearly at large appropriate depth. This will expand applications of optical tweezers in a nanometre-scale colloidal system.     

A Note on ＂Global Exponential Convergence Analysis of Hopfield Neural Networks with Continuously Distributed Delays＂

In this note, we would like to point out that （i） of Corollary 1 given by Zhang et al. （cf Commun. Theor. Phys. 39 （2003） 381） is incorrect in general.     

Comment on ＂Vortex of Fluid Field as Viewed from Curvature＂ [Commun. Theor. Phys. 43 （2005） 604]

Here, we make comments to the conclusions of the paper： LIU Shi-Da, Sill Shao-Ying, LIU Shi-Kuo, et al., ＂Vortex of Fluid Field as Viewed from Curvature＂ [Commun. Theor. Phys. 43 （2005） 604].