Three PT-symmetric Hamiltonians with completely different spectra

We discuss three Hamiltonians, each with a central-field part H₀$H_0$ and a PT-symmetric perturbation igz$igz$. When H₀$H_0$ is the isotropic Harmonic oscillator the spectrum is real for all g$g$ because H$H$ is isospectral to H₀+g²/2$H_0+g^2/2$. When H₀$H_0$ is the Hydrogen atom then infinitely many eigenvalues are complex for all g$g$. If the potential in H₀$H_0$ is linear in the radial variable r$r$ then the spectrum of H$H$ exhibits real eigenvalues for 0<g<g_c$0<g<g_c$ and a PT phase transition at g_c$g_c$.     

基于铂电阻的温度测量仪的设计与实现

针对大亚湾中微子实验中,需要精确测量掺钆液闪温度的问题,设计并实现了一种基于铂电阻的分布式温度测量仪。该测量仪可以同时测量多点的温度,并将测量结果通过网络传输到数据服务器中,从而实现远程在线监测。为解决器件温漂带来的误差问题,该文采用了3电阻测量法的自校正技术,通过比较3组测量信号的相对大小来求得被测热电阻的电阻值,进而计算出温度值。通过计量炉的实测的数据比较,测量误差小于0.059℃, 满足测量精度需求。     

On some meaningful inner product for real Klein—Gordon fields with positive semi-definite norm

A simple derivation of a meaningful, manifestly covariant inner product for real Klein—Gordon (KG) fields with positive semi-definite norm is provided, which turns out — assuming a symmetric bilinear form — to be the real-KG-field limit of the inner product for complex KG fields reviewed by A. Mostafazadeh and F. Zamani in December 2003, and February 2006 (quant-ph/0312078, quant-ph/0602151, quant-ph/0602161). It is explicitly shown that the positive semi-definite norm associated with the derived inner product for real KG fields measures the number of active positive and negative energy Fourier-modes of the real KG field on the relativistic mass shell. The very existence of an inner product with positive semi-definite norm for the considered real, i.e. neutral, KG fields shows that the metric operator entering the inner product does not contain the charge-conjugation operator. This observation sheds some additional light on the meaning of the C operator in the CPT inner product of PT-symmetric quantum mechanics defined by C.M. Bender, D.C. Brody and H.F. Jones.     

High pyroelectric power generation of 0.7Pb(Mg1/3Nb2/3)O3–0.3PbTiO3 single crystal

We report the pyroelectric power generation of a relaxor ferroelectric 0.7Pb(Mg_1/3Nb_2/3)O₃–0.3PbTiO₃ (PMN–PT) single crystal. For a temperature variation rate of 0.5 K/s, the PMN–PT generated a closed-circuit current of 10 nA and an open-circuit voltage of 1.1 V at room temperature. The pyroelectric current and voltage of the PMN–PT single crystal were proportional to the temperature variation rate and were sharply enhanced near the structural phase-transition temperature. Additionally, the PMN–PT pyroelectric generator produced stable power for excessive thermal cycling and was highly sensitive to random thermal fluctuations. Our results indicate the potential importance of PMN–PT for high-power pyroelectric generator applications.     

Gaussian-Random Ensembles of Pseudo-Hermitian Matrices

Attention has been brought to the possibility that statistical fluctuation properties of several complex spectra, or well-known number sequences, may display strong signatures that the Hamiltonian yielding them as eigenvalues is PT-symmetric (pseudo-Hermitian). We find that the random matrix theory of pseudo-Hermitian Hamiltonians gives rise to new universalities of level-spacing distributions other than those of GOE, GUE and GSE of Wigner and Dyson. We call the new proposals as Gaussian Pseudo-Orthogonal Ensemble and Gaussian Pseudo-Unitary Ensemble. We are also led to speculate that the enigmatic Riemann-zeros (1/2±it _n would rather correspond to some PT-symmetric (pseudo-Hermitian) Hamiltonian.     

泛系哲学与泛系数学和应用：事理，物理，技理，医理与战理（Ⅰ）

这里从泛系观引入一种的哲学与数学研究，包括在乏系框架下 发展哲学七论与数学和一些第二第三哲学以及对事理、物理、技理、医理与战理的某些应用。     

Elastic–plastic deformation of Pb(Zn1/3Nb2/3)O3–(6–7)% PbTiO3 single crystals during nanoindentation

The elastic–plastic deformation behavior of (001)- and (011)-oriented single crystal solid solutions of Pb(Zn_1/3Nb_2/3)O₃–(6–7)% PbTiO₃ (PZN–PT) have been studied using a nanoindentation technique. A procedure is presented here to isolate the elastic, elastic–plastic and plastic contributions to the deformation using the unloading data, and a parameter, referred to as relaxation, is defined to characterize the elastic–plastic deformation during nanoindentations. This relaxation parameter increases with the maximum indentation load due to the higher indentation stress induced, and it also causes less recovery of the material upon indentation unloading compared to predicted pure elastic recovery. For a (001) surface, the relaxation value remains virtually unchanged within the range of the maximum indentation load of 10–50 mN, possibly due to a complete localized depoling of the non-180° domain switching. It is also found that the unpoled surface is more prone to stress-induced depolarization compared to the poled surfaces. Furthermore, by applying the continuous stiffness measurement (CSM) technique, the effects of multiple loading/unloading are studied for both (001)- and (011)-oriented PZN–PTs using the maximum indentation loads of 20 and 50 mN. With more loading/unloading cycles at higher CSM frequencies, stress-induced depolarization becomes prevalent and the contribution of the domain reorientation towards elastic recovery is significantly reduced. As a consequence, the relaxation value is increased, indicating more elastic–plastic deformation. This CSM effect is especially pronounced for poled (011) surfaces.     

对称量子理论的计算

根据[WTHX]PT 对称量子系统中PT 内积和原内积之间的关系, 给出PT 对称量子理论中纯态的刻画以及PT 对称量子系统中混合态的一个刻画, 研究PT对称量子系统中态的演化, 并给出其为酉演化的充要条件.     

Challenges in preparing water-matrix reference materials for PAHs and pesticides: examples from SWIFT-WFD proficiency-testing schemes

In accordance with Article 8 of the European Union (EU) Water Framework Directive (WFD), EU Member States are required to establish monitoring programs for the quality of the surface water and the groundwater within each river-basin district. As such data are the basis for regulatory decisions and measures required to achieve WFD environmental objectives, appropriate analytical quality-assurance and quality-control tools have to be implemented by the monitoring laboratories. In this respect, reference materials (RMs) play a key role. Within the framework of the SWIFT-WFD project (Screening methods for Water data InFormation in support of the WFD), several approaches to the preparation of matrix RMs for the analysis of polycyclic aromatic hydrocarbons and pesticides in water have been used in wide-scale proficiency-testing (PT) schemes. We present the different strategies employed in preparing water-matrix RMs for organic analytes. By reviewing the results from the SWIFT-WFD PT schemes, we reflect on the applicability and the suitability of the different approaches.