Painlevé analysis and integrability of the damped anharmonic oscillator equation

The Painlevé analysis is applied to the anharmonic oscillator equation . The following three integrable cases are identified: (i)C=0,d ²=25A/6,A>0,B arbitrary, (ii)d ²=9A/2,B=0,A>0,C arbitrary and (iii)d ²=−9A/4,C=2B ²/(9A),A<0,C<0,B arbitrary. The first two integrable choices are already reported in the literature. For the third integrable case the general solution is found involving elliptic function with exponential amplitude and argument.     

Chemical chaos in novel iodate-driven oscillator-thiophenol-iodate-H2SO4 system

Chaotic oscillations in redox potential have been observed in thiophenol-KIO₃-H₂SO₄ system in batch reactors. These occur in a concentration and temperature range. Bifurcation from a stable regime to a chaotic regime occurs in a straight way in the entire concentration and temperature range. Oscillations were also studied in continuously stirred tank reactors. These oscillations are deterministic chaos. It is tentatively suggested that chaos in the system is due to a time delay caused by a large number of intermediates.     

Visualization of aerosol particles generated by near infrared nano- and femtosecond laser ablation

The expansion of aerosols generated by near infrared (NIR) nanosecond (ns) and femtosecond (fs) laser ablation (LA) of metals at atmospheric pressures was explored by laser-induced scattering. In order to achieve adequate temporal and spatial resolution a pulsed laser source was utilized for illuminating a 0.5 mm-wide cross section of the expanding aerosol. It could, for instance, be shown that NIR-ns-LA under quiescent argon atmosphere provokes the formation of a dense aerosol confined within a radially propagating vortex ring. The expansion dynamics achieved under these conditions were found to be fairly slow whereas the degree of aerosol dispersion for NIR-ns-LA using helium drastically increased due to its lower viscosity. As a consequence, the maximum diameter of expansion differed by a factor of approximately four. The trajectories of aerosol particles generated by NIR-ns-LA using argon could, furthermore, be simulated on the basis of computational fluid dynamics (CFD). For this purpose, a model inspired by the thermal character of NIR-ns-LA taking into account a sudden temperature build-up of 10,000 K at the position of the laser focus was implemented.     

光场算符n次幂叠加激发混沌场的量子特性

构造了光场算符n次幂叠加激发混沌场,采用数值计算方法研究了该量子态的压缩效应、反聚束效应和统计性质,讨论了混沌场平均光子数、算符叠加系数及其幂次n对量子特性的影响.研究结果表明:光场算符n次幂叠加激发混沌场不呈现压缩效应,但呈现出反聚束效应和亚泊松分布性质,并且随平均光子数增大,它的反聚束效应和亚泊松分布性质减弱;随着算符组合部分中产生算符的比重增大,光场反聚束效应和亚泊松分布性质增强;随着算符幂次增大,亚泊松分布性质加强.     

Quantum theory with an energy operator defined as a quartic form of the momentum

Quantum theory of the non-harmonic oscillator defined by the energy operator proposed by Yurke and Buks (2006) is presented. Although these authors considered a specific problem related to a model of transmission lines in a Kerr medium, our ambition is not to discuss the physical substantiation of their model. Instead, we consider the problem from an abstract, logically deductive, viewpoint. Using the Yurke–Buks energy operator, we focus attention on the imaginary-time propagator. We derive it as a functional of the Mehler kernel and, alternatively, as an exact series involving Hermite polynomials. For a statistical ensemble of identical oscillators defined by the Yurke–Buks energy operator, we calculate the partition function, average energy, free energy and entropy. Using the diagonal element of the canonical density matrix of this ensemble in the coordinate representation, we define a probability density, which appears to be a deformed Gaussian distribution. A peculiarity of this probability density is that it may reveal, when plotted as a function of the position variable, a shape with two peaks located symmetrically with respect to the central point.     

A novel hybrid color image encryption algorithm using two complex chaotic systems

Based on complex Chen and complex Lorenz systems, a novel color image encryption algorithm is proposed. The larger chaotic ranges and more complex behaviors of complex chaotic systems, which compared with real chaotic systems could additionally enhance the security and enlarge key space of color image encryption. The encryption algorithm is comprised of three step processes. In the permutation process, the pixels of plain image are scrambled via two-dimensional and one-dimensional permutation processes among RGB channels individually. In the diffusion process, the exclusive-or (XOR for short) operation is employed to conceal pixels information. Finally, the mixing RGB channels are used to achieve a multilevel encryption. The security analysis and experimental simulations demonstrate that the proposed algorithm is large enough to resist the brute-force attack and has excellent encryption performance.     

Solvable potentials with exceptional orthogonal polynomials

Classes of solvable potentials are presented within an standard application of supersymmetric quantum mechanics. Sets of exceptional orthogonal polynomials generated by these solvable potentials are introduced and examined in detail. Several properties of these polynomials including orthogonality conditions, weight functions, differential equations, the Wronskains, possible recurrence relations are also investigated.

     

Spin–orbit interaction for the double ring-shaped oscillator

The spin–orbit interactions (SOI) for the single and double ring-shaped oscillator potentials are studied as an energy correction to the Schrödinger equation. We find that the degeneracy for the energy levels with angular quantum number m=0$m=0$ keeps invariant in the case of the SOI. The degeneracy is still 2 for single ring-shaped potential and 4 for double ring-shaped potential. However, for the energy levels with angular quantum number m≠0$m\ne 0$ the degeneracy is reduced from original 4 for the single ring-shaped potential and 8 for the double ring-shaped potential to 2. That is, their energy levels in the case of the SOI are split to 2 (single) and 4 (double) sublevels. There exists an accidental degeneracy for the cases |m|=2,3,4,…$\left|m\right|=2,3,4,\dots$. We note that around the critical value b₀$b_0$, the energy levels are reversed.   We also discuss some special cases for η=2,3,4,5,6,…$\eta =2,3,4,5,6,\dots$, and the b=0,c>0$b=0,c>0$. It should be pointed out that the parameter b₀$b_0$ is relevant for the angular part parameter b$b$ in the single and double ring-shaped potentials and it makes the energy levels changed from positive to negative, but the parameter c$c$ corresponds to the angular part parameter in double ring-shaped potential and the η$\eta$ is related to it. This model can be useful for investigations of axial symmetric subjects like the ring-shaped molecules or related problems and may also be easily extended to a many-electron theory.