Relational Hidden Variables and Non-Locality

We use a simple relational framework to develop the key notions and results on hidden variables and non-locality. The extensive literature on these topics in the foundations of quantum mechanics is couched in terms of probabilistic models, and properties such as locality and no-signalling are formulated probabilistically. We show that to a remarkable extent, the main structure of the theory, through the major No-Go theorems and beyond, survives intact under the replacement of probability distributions by mere relations.Comment: 42 pages in journal style. To appear in Studia Logic

Phonon Hall effect in ionic crystals in the presence of static magnetic field

We study phonon Hall effect (PHE) for ionic crystals in the presence of static magnetic field. Using Green-Kubo formula, we present an exact calculation of thermal conductivity tensor by considering both positive and negative frequency phonons. Numerical results are shown for some lattices such as hexagonal lattices, triangular lattices, and square lattices. We find that the PHE occurs on the nonmagnetic ionic crystal NaCl, although the magnitude is very small which is due to the tiny charge-to-mass ratio of the ions. The off-diagonal thermal conductivity is finite for nonzero magnetic field and changes sign for high value of magnetic field at high temperature. We also found that the off-diagonal thermal conductivity diverges as $\pm{1/T}$ at low temperature

Pairing symmetry and long range pair potential in a weak coupling theory of superconductivity

We study the superconducting phase with two component order parameter scenario, such as, $d_{x^2-y^2} + e^{i\theta}s_{\alpha}$, where $\alpha = xy, x^2+y^2$. We show, that in absence of orthorhombocity, the usual $d_{x^2-y^2}$ does not mix with usual $s_{x^2+y^2}$ symmetry gap in an anisotropic band structure. But the $s_{xy}$ symmetry does mix with the usual d-wave for $\theta =0$. The d-wave symmetry with higher harmonics present in it also mixes with higher order extended $s$ wave symmetry. The required pair potential to obtain higher anisotropic $d_{x^2-y^2}$ and extended s-wave symmetries, is derived by considering longer ranged two-body attractive potential in the spirit of tight binding lattice. We demonstrate that the dominant pairing symmetry changes drastically from $d$ to $s$ like as the attractive pair potential is obtained from longer ranged interaction. More specifically, a typical length scale of interaction $\xi$, which could be even/odd multiples of lattice spacing leads to predominant $s/d$ wave symmetry. The role of long range interaction on pairing symmetry has further been emphasized by studying the typical interplay in the temperature dependencies of these higher order $d$ and $s$ wave pairing symmetries.Comment: Revtex 8 pages, 7 figures embeded in the text, To appear in PR

Mergelyan sets and the modulus of continuity of analytic functions

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/21993/1/0000405.pd

Cornerstones of Sampling of Operator Theory

This paper reviews some results on the identifiability of classes of operators whose Kohn-Nirenberg symbols are band-limited (called band-limited operators), which we refer to as sampling of operators. We trace the motivation and history of the subject back to the original work of the third-named author in the late 1950s and early 1960s, and to the innovations in spread-spectrum communications that preceded that work. We give a brief overview of the NOMAC (Noise Modulation and Correlation) and Rake receivers, which were early implementations of spread-spectrum multi-path wireless communication systems. We examine in detail the original proof of the third-named author characterizing identifiability of channels in terms of the maximum time and Doppler spread of the channel, and do the same for the subsequent generalization of that work by Bello. The mathematical limitations inherent in the proofs of Bello and the third author are removed by using mathematical tools unavailable at the time. We survey more recent advances in sampling of operators and discuss the implications of the use of periodically-weighted delta-trains as identifiers for operator classes that satisfy Bello's criterion for identifiability, leading to new insights into the theory of finite-dimensional Gabor systems. We present novel results on operator sampling in higher dimensions, and review implications and generalizations of the results to stochastic operators, MIMO systems, and operators with unknown spreading domains

Entangled-Photon Generation from Parametric Down-Conversion in Media with Inhomogeneous Nonlinearity

We develop and experimentally verify a theory of Type-II spontaneous parametric down-conversion (SPDC) in media with inhomogeneous distributions of second-order nonlinearity. As a special case, we explore interference effects from SPDC generated in a cascade of two bulk crystals separated by an air gap. The polarization quantum-interference pattern is found to vary strongly with the spacing between the two crystals. This is found to be a cooperative effect due to two mechanisms: the chromatic dispersion of the medium separating the crystals and spatiotemporal effects which arise from the inclusion of transverse wave vectors. These effects provide two concomitant avenues for controlling the quantum state generated in SPDC. We expect these results to be of interest for the development of quantum technologies and the generation of SPDC in periodically varying nonlinear materials.Comment: submitted to Physical Review

Fibulin-3 is necessary to prevent cardiac rupture following myocardial infarction

Published online: 11 September 2023Despite the high prevalence of heart failure in the western world, there are few effective treatments. Fibulin-3 is a protein involved in extracellular matrix (ECM) structural integrity, however its role in the heart is unknown. We have demonstrated, using single cell RNA-seq, that fibulin-3 was highly expressed in quiescent murine cardiac fibroblasts, with expression highest prior to injury and late post-infarct (from ~ day-28 to week-8). In humans, fibulin-3 was upregulated in left ventricular tissue and plasma of heart failure patients. Fibulin-3 knockout (Efemp1-/-) and wildtype mice were subjected to experimental myocardial infarction. Fibulin-3 deletion resulted in significantly higher rate of cardiac rupture days 3-6 post-infarct, indicating a weak and poorly formed scar, with severe ventricular remodelling in surviving mice at day-28 post-infarct. Fibulin-3 knockout mice demonstrated less collagen deposition at day-3 post-infarct, with abnormal collagen fibre-alignment. RNA-seq on day-3 infarct tissue revealed upregulation of ECM degradation and inflammatory genes, but downregulation of ECM assembly/structure/organisation genes in fibulin-3 knockout mice. GSEA pathway analysis showed enrichment of inflammatory pathways and a depletion of ECM organisation pathways. Fibulin-3 originates from cardiac fibroblasts, is upregulated in human heart failure, and is necessary for correct ECM organisation/structural integrity of fibrotic tissue to prevent cardiac rupture post-infarct.Lucy A. Murtha, Sean A. Hardy, Nishani S. Mabotuwana, Mark J. Bigland, Taleah Bailey, Kalyan Raguram, Saifei Liu, Doan T. Ngo, Aaron L. Sverdlov, Tamara Tomin, Ruth Birner, Gruenberger, Robert D. Hume, Siiri E. Iismaa, David T. Humphreys, Ralph Patrick, James J. H. Chong, Randall J. Lee, Richard P. Harvey, Robert M. Graham, Peter P. Rainer and Andrew J. Boyl

On the Effect of Nb on the Microstructure and Properties of Next Generation Polycrystalline Powder Metallurgy Ni-Based Superalloys

Abstract The effect of Nb on the properties and microstructure of two novel powder metallurgy (P/M) Ni-based superalloys was evaluated, and the results critically compared with the Rolls-Royce alloy RR1000. The Nb-containing alloy was found to exhibit improved tensile and creep properties as well as superior oxidation resistance compared with both RR1000 and the Nb-free variant tested. The beneficial effect of Nb on the tensile and creep properties was due to the microstructures obtained following the post-solution heat treatments, which led to a higher γ′ volume fraction and a finer tertiary γ′ distribution. In addition, an increase in the anti-phase-boundary energy of the γ′ phase is also expected with the addition of Nb, further contributing to the strength of the material. However, these modifications in the γ′ distribution detrimentally affect the dwell fatigue crack-growth behavior of the material, although this behavior can be improved through modified heat treatments. The oxidation resistance of the Nb-containing alloy was also enhanced as Nb is believed to accelerate the formation of a defect-free Cr2O3 scale. Overall, both developmental alloys, with and without the addition of Nb, were found to exhibit superior properties than RR1000.This work was supported by the Rolls-Royce/EPSRC Strategic Partnership under EP/H022309/1, EP/H500375/1 and EP/ M005607/1