20,907 research outputs found
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.
The Role of Crystal Symmetry in the Magnetic Instabilities of -YbAlB and -YbAlB
Density functional theory methods are applied to investigate the properties
of the new superconductor -YbAlB and its polymorph
-YbAlB. We utilize the generalized gradient approximation + Hubbard
U (GGA+U) approach with spin-orbit(SO) coupling to approximate the effects of
the strong correlations due to the open shell of Yb. We examine closely
the differences in crystal bonding and symmetry of -YbAlB and
-YbAlB. The in-plane bonding structure amongst the dominant
itinerant electrons in the boron sheets is shown to differ significantly. Our
calculations indicate that, in both polymorphs, the localized 4 electrons
hybridize strongly with the conduction sea when compared to the related
materials YbRhSi and YbB. Comparing -YbAlB to the
electronic structure of related crystal structures indicates a key role of the
7-member boron coordination of the Yb ion in -YbAlB in producing its
enhanced Kondo scale and superconductivity. The Kondo scale is shown to depend
strongly on the angle between the B neighbors and the Yb ion, relative to the
plane, which relates some of the physical behavior to structural
characteristics.Comment: 9 pages, 9 figures, 2 table
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