Quantum theory as a description of robust experiments: Derivation of the Pauli equation

It is shown that the Pauli equation and the concept of spin naturally emerge from logical inference applied to experiments on a charged particle under the conditions that (i) space is homogeneous (ii) the observed events are logically independent, and (iii) the observed frequency distributions are robust with respect to small changes in the conditions under which the experiment is carried out. The derivation does not take recourse to concepts of quantum theory and is based on the same principles which have already been shown to lead to e.g. the Schrödinger equation and the probability distributions of pairs of particles in the singlet or triplet state. Application to Stern–Gerlach experiments with chargeless, magnetic particles, provides additional support for the thesis that quantum theory follows from logical inference applied to a well-defined class of experiments.     

From Quantum Probabilities to Quantum Amplitudes

The task of reconstructing the system’s state from the measurements results, known as the Pauli problem, usually requires repetition of two successive steps. Preparation in an initial state to be determined is followed by an accurate measurement of one of the several chosen operators in order to provide the necessary “Pauli data”. We consider a similar yet more general problem of recovering Feynman’s transition (path) amplitudes from the results of at least three consecutive measurements. The three-step histories of a pre- and post-selected quantum system are subjected to a type of interference not available to their two-step counterparts. We show that this interference can be exploited, and if the intermediate measurement is “fuzzy”, the path amplitudes can be successfully recovered. The simplest case of a two-level system is analysed in detail. The “weak measurement” limit and the usefulness of the path amplitudes are also discussed.     

Delocalized \begin{document}$\pi_3^6$\end{document} Bond in OX\begin{document}$_2$\end{document} (X=Halogen) Molecules

OX\begin{document}$_2$\end{document} (X=halogen) molecules was studied theoretically. Calculation results show that delocalized \begin{document}$\pi_3^6$\end{document} bonds exist in their electronic structures and O atoms adopt the sp\begin{document}$^2$\end{document} type of hybridization, which violates the prediction of the valence shell electron pair repulsion theory of sp\begin{document}$^3$\end{document} type. Delocalization stabilization energy is proposed to measure the contribution of delocalized \begin{document}$\pi_3^6$\end{document} bond to energy decrease and proves to bring extra-stability to the molecule. These phenomena can be summarized as a kind of coordinating effect.     

Experimental and mechanistic study of mudstone volumetric swelling at the bottom of salt cavern gas storage

Salt cavern gas storage is one of the vital strategic natural gas reserves and emergency peak shaving facilities all over the world. However, rock salt in China is primarily bedded salt, usually composed of many thin salt layers and interlayers (e.g., anhydrite, mudstone, and glauberite). During the water solution mining process of the cavern, the insoluble mudstones fall to the bottom and account for 1/3 up to 2/3 of the storage capacity. The bulk volume of the insoluble mudstones is almost twice its in-suit volume. It is of great urgency to investigate the swelling mechanisms of the bottom insoluble mudstones. Given this, we first analyzed the mineral composition of salt rock and insoluble mudstones by using XRD and SEM methods. Then, experimental studies were carried out considering both clay swelling and physical packing. At last, the zeta potential tests were conducted to reveal the swelling mechanisms of the bottom mudstones. Results show that the volumetric expansion of mudstones is made up of three parts: clay swelling, particle surface bound water volume, and pore space free water volume increase. Because the content of expansive clay in the bottom mudstones is less than 2%, and the high salinity brine in the cavern has excellent clay stability performance, clay swelling is not the main contributor to the volumetric expansion of the bottom mudstones. Measurement results show that the surface of the mudstones is negatively charged after hydration. Electrostatic repulsion can increase the spacing between small rock particles and creates approximately 47.6% of the pore space, which is the main factor in the volumetric expansion of mudstones. This study provides a theoretical basis for the mining solution and capacity enlargement during the construction of bedded salt cavern gas storage in China.     

About the compatibility between ansatzes and constraints for a local formulation of orbital‐free density functional theory

Functional properties that are exact for the Hohenberg–Kohn functional may turn into mutually exclusive constraints at a given level of ansatz. This is exemplarily shown for the local density approximation. Nevertheless, it is possible to reach exactly the Kohn–Sham data from an orbital‐free density functional framework based on simple one‐point functionals by starting from the Levy–Perdew–Sahni formulation. The energy value is obtained from the density‐potential pair, and therefore does not refer to the functional dependence of the potential expression. Consequently, the potential expression can be obtained from any suitable model and is not required to follow proper scaling behavior.     

Crystal Structure,Magnetism, 89Y Solid State NMR,and 121Sb Mössbauer Spectroscopic Investigations of YIrSb

The ternary antimonide YIrSb was synthesized from the binary precursor YIr and elemental antimony by a diffusion controlled solid‐state reaction. Single crystals were obtained by a flux technique with elemental bismuth as an inert solvent. The YIrSb structure (TiNiSi type, space group Pnma) was refined from single‐crystal X‐ray diffractometer data: a = 711.06(9), b = 447.74(5), c = 784.20(8) pm, wR₂ = 0.0455, 535 F² values, 20 variables. ⁸⁹Y solid state MAS NMR and ¹²¹Sb Mössbauer spectra show single resonance lines in agreement with single‐crystal X‐ray data. YIrSb is a Pauli paramagnet.     

A full‐pivoting algorithm for the Cholesky decomposition of two‐electron repulsion and spin‐orbit coupling integrals

A significant reduction in the computational effort for the evaluation of the electronic repulsion integrals (ERI) in ab initio quantum chemistry calculations is obtained by using Cholesky decomposition (CD), a numerical procedure that can remove the zero or small eigenvalues of the ERI positive (semi)definite matrix, while avoiding the calculation of the entire matrix. Conversely, due to its antisymmetric character, CD cannot be directly applied to the matrix representation of the spatial part of the two‐electron spin‐orbit coupling (2e‐SOC) integrals. Here, we present a computational strategy to achieve a Cholesky representation of the spatial part of the 2e‐SOC integrals, and propose a new efficient CD algorithm for both ERI and 2e‐SOC integrals. The proposed algorithm differs from previous CD implementations by the extensive use of a full‐pivoting design, which allows a univocal definition of the Cholesky basis, once the CD δ threshold is made explicit. We show that is the upper limit for the errors affecting the reconstructed 2e‐SOC integrals. The proposed strategy was implemented in the ab initio program Computational Emulator of Rare Earth Systems (CERES), and tested for computational performance on both the ERI and 2e‐SOC integrals evaluation. © 2017 Wiley Periodicals, Inc.