Random and free observables saturate the Tsirelson bound for CHSH inequality

Maximal violation of the CHSH-Bell inequality is usually said to be a feature of anticommuting observables. In this work we show that even random observables exhibit near-maximal violations of the CHSH-Bell inequality. To do this, we use the tools of free probability theory to analyze the commutators of large random matrices. Along the way, we introduce the notion of "free observables" which can be thought of as infinite-dimensional operators that reproduce the statistics of random matrices as their dimension tends towards infinity. We also study the fine-grained uncertainty of a sequence of free or random observables, and use this to construct a steering inequality with a large violation

Competing Phases, Strong Electron-Phonon Interaction and Superconductivity in Elemental Calcium under High Pressure

The observed "simple cubic" (sc) phase of elemental Ca at room temperature in the 32-109 GPa range is, from linear response calculations, dynamically unstable. By comparing first principle calculations of the enthalpy for five sc-related (non-close-packed) structures, we find that all five structures compete energetically at room temperature in the 40-90 GPa range, and three do so in the 100-130 GPa range. Some competing structures below 90 GPa are dynamically stable, i.e., no imaginary frequency, suggesting that these sc-derived short-range-order local structures exist locally and can account for the observed (average) "sc" diffraction pattern. In the dynamically stable phases below 90 GPa, some low frequency phonon modes are present, contributing to strong electron-phonon (EP) coupling as well as arising from the strong coupling. Linear response calculations for two of the structures over 120 GPa lead to critical temperatures in the 20-25 K range as is observed, and do so without unusually soft modes.Comment: 8 pages, 6 figures, 1 table, accepted for publication in Phys. Rev.

Seismic performance analysis of blast furnace shell structure

In this paper, the finite element software ANSYS is used to establish a three-dimensional space model of the blast furnace shell, and the static analysis of the space steel structure system of the blast furnace is carried out. The seismic response of the outer shell system of the blast furnace is analyzed by response spectrum method and linear time history analysis method, so as to explore the seismic response of the blast furnace shell