单模激光Lorenz系统与Duffing系统缩阶反同步

 对于2阶Duffing系统与3阶单模激光Lorenz系统,用主动控制方法设计了一种同步控制器,实现二者之间的缩阶反同步。依据罗斯 霍维兹判据,给出误差系统在原点处渐进稳定的条件。数值试验证实：在控制器作用下,2阶Duffing系统的状态变量与3阶单模激光Lorenz投影子系统的状态变量振动的幅值相同但方向相反,且在随机噪声干扰下反同步仍能很好地实现。这表明所设计的控制器对于不同阶的Duffing系统与Lorenz系统的缩阶反同步的实现是可行的、有效的,而且具有很好的鲁棒性。     

Quantum phase transitions about parity breaking in matrix product systems

According to our scheme to construct quantum phase transitions (QPTs) in spin chain systems with matrix product ground states, we first successfully combine matrix product state (MPS) QPTs with spontaneous symmetry breaking. For a concrete model, we take into account a kind of MPS QPTs accompanied by spontaneous parity breaking, though for either side of the critical point the GS is typically unique, and show that the kind of MPS QPTs occur only in the thermodynamic limit and are accompanied by the appearance of singularities, diverging correlation length, vanishing energy gap and the entanglement entropy of a half-infinite chain not only staying finite but also whose first derivative discontinuous.     

Spin-glass behavior and magnetocaloric effect in melt-spun TbCuAl alloys

Magnetic properties and magnetocaloric effects of amorphous and crystalline TbCuAl ribbons are investigated by measuring their ac susceptibilities including a nonlinear term and dc magnetizations. The in-phase third harmonic ac susceptibility is found to be negative. It can be well fitted by the expression at high temperatures, indicating a spin-glass behavior in amorphous TbCuAl alloy. ΔT_f(ω)/[T_f(ω)Δlog₁₀ω], a possible distinguishing criterion to judge the presence of a spin-glass behavior is ∼0.011. The frequency-dependent data can be well fitted by the conventional critical slowing down law and the spin-glass transition temperature is obtained to be 20.1 K. The maximum of magnetic entropy change reaches 4.5 J kg⁻¹ K⁻¹ for a field change of 0-50 000 Oe, while the crystalline TbCuAl compound experiences a simple ferromagnetic-to-paramagnetic phase transition. The peak value of magnetic entropy change is obtained at the Curie temperature and reaches 14.4 J kg⁻¹ K⁻¹ for the same field change, which is much larger than that of amorphous TbCuAl alloy.     

Entropy of Partitions on Sequential Effect Algebras

By using the sequential effect algebra theory, we establish the partitions and refinements of quantum logics and study their entropies.     

Entanglement and localization of a two-mode Bose-Einstein condensate

A simple second quantization model is used to describe a two-mode Bose-Einstein condensate (BEC), which can be written in terms of the generators of a SU(2) algebra with three parameters. We study the behavior of the entanglement entropy and localization of the system in the parameter space of the model. The phase transitions in the parameter space are determined by means of the coherent state formalism and the catastrophe theory, which besides let us get the best variational state that reproduces the ground state energy. This semiclassical method let us organize the energy spectrum in regions where there are crossings and anticrossings. The ground state of the two-mode BEC, depending on the values of the interaction strengths, is dominated by a single Dicke state, a spin collective coherent state, or a superposition of two spin collective coherent states. The entanglement entropy is determined for two recently proposed partitions of the two-mode BEC that are called separation by boxes and separation by modes of the atoms. The entanglement entropy in the boxes partition is strongly correlated to the properties of localization in phase space of the model, which is given by the evaluation of the second moment of the Husimi function. To compare the fitness of the trial wavefunction its overlap with the exact quantum solution is evaluated. The entanglement entropy for both partitions, the overlap and localization properties of the system get singular values along the separatrix of the two-mode BEC, which indicates the phase transitions which remain in the thermodynamical limit, in the parameter space.     

Use of thermo‐Raman spectroscopy and chemometric analysis to identify dehydration steps of hydrated inorganic samples—application to copper sulfate pentahydrate

In situ thermo‐Raman spectroscopy (TRS) measurements were performed in order to investigate solid‐phase transformation of the copper sulfate pentahydrate from room temperature up to 300 °C. Band‐target entropy minimization (BTEM), a blind‐source separation algorithm, was employed in order to identify and reconstruct the pure component spectra of the species involved in the dehydration process. In spite of low signal‐to‐noise ratio and elevated baseline spectral data, BTEM was successfully utilized to identify and reconstruct four pure component spectra of copper sulfate pentahydrate, trihydrate, monohydrate, and anhydrate, which were formed during this thermally induced process. Subsequent mapping of these four pure component spectral estimates back onto the preprocessed spectra yielded the relative concentrations of each individual species. Finally, the transition temperatures of each dehydration step could be unambiguously deduced from the obtained concentration profile. The current study shows that combined thermo‐Raman spectroscopy and chemometric analysis provides an effective tool to determine the dehydration temperatures as well as to identify the structures of each individual species involved in a solid‐phase dehydration process. Copyright © 2009 John Wiley & Sons, Ltd.     

Mutual Information and Relative Entropy of Sequential Effect Algebras

In this paper, we introduce and investigate the mutual information and relative entropy on the sequential effect algebra, we also give a comparison of these mutual information and relative entropy with the classical ones by the venn diagrams. Finally, a nice example shows that the entropies of sequential effect algebra depend extremely on the order of its sequential product.     

Analytic solutions for degenerate Raman-coupled model

The Raman-coupled interaction between an atom and a single mode of a cavity field is studied. For the cases in which a light field is initially in a coherent state and in a thermal state separately, we have derived the analytic expressions for the time evolutions of atomic population difference W, modulus B of the Bloch vector, and entropy E. We find that the time evolutions of these quantities are periodic with a period of π. The maxima of W and B appear at the scaled interaction time points τ- = kπ（k = 0, 1, 2,...）. At these time points, E = 0, which shows that the atom and the field are not entangled. Between these time points, E ≠ 0, which means that the atom and the field are entangled. When the field is initially in a coherent state, near the maxima, the envelope of W is a Gaussian function with a variance of 1/（4n^-）（n^- is the mean number of photons）. Under the envelope, W oscillates at a frequency of n^-/π. When the field is initially in a thermal state, near the maxima, W is a Lorentz function with a width of 1/n^-.     

湍流信号分析中小波基的对比和选取

采用小波分析处理湍流脉动信号时,不同的小波基往往会带来不同的分析结果.为了尽可能准确地提取湍流流动的多尺度特征,研究并建立湍流信号处理中适宜小波基选取的合理方法是十分必要的.基于湍流时频特性,结合信息熵理论,建立了以品质因数和特征谱熵值为评价指标的小波基选取方法.以计算分析三组不同湍流信号的小波基为例,结果进一步验证了...     

Dynamical systems with relaxation time

We define mathematically a class of dynamical systems that exhibit relaxation corresponding to that observed in physical systems, and then show that this class is identical with the class ofK-mixing dynamical systems.