ShantanuT01/DACTYL-Pretraining huggingface dataset:
We have proposed in several recent papers a critical view of some parts of quantum mechanics (QM) that is methodologically unusual because it rests on analysing the language of QM by using some elementary but fundamental tools of mathematical logic. Our approach proves that some widespread beliefs about QM can be questioned and establishes new links with a classical view, which is significant in the debate on the interpretations of QM. We propose here a brief survey of our results, highlighting their common background. We firstly show how quantum logic (QL) can be embedded into classical logic (CL) if the embedding is required to preserve the logical order and not the algebraic structure, and also how QL can be interpreted as a pragmatic sublanguage within a pragmatic extension of CL. Both these results challenge the thesis that CL and QL formalize the properties of different and incompatible notions of truth. We then show that quantum probability admits an epistemic interpretation if contextuality is taken into account as a basic constituent of the language of QM, which overcomes the interpretation of quantum probability as ontic. Finally, we show that the proofs that QM is a contextual theory stand on a supplementary epistemological assumption that is usually unnoticed and left implicit. Dropping such assumption opens the way, at least in principle, to non-contextual interpretations of QM.
When the mass of one of the two bodies tends to zero, Weyl's definition of the gravitational force in an axially symmetric, static two-body solution can be given an invariant formulation in terms of a force four-vector. The norm of this force is calculated for Bach's two-body solution, that is known to be in one-to-one correspondence with Schwarzschild's original solution when one of the two masses l, l' is made to vanish. In the limit when, say, l' goes to zero, the norm of the force divided by l' and calculated at the position of the vanishing mass is found to coincide with the norm of the acceleration of a test body kept at rest in Schwarzschild's field. Both norms happen thus to grow without limit when the test body (respectively the vanishing mass l') is kept at rest in a position closer and closer to Schwarzschild's two-surface.
Under a standard set of assumptions for a hidden-variables model for quantum events, we show that all observables must commute simultaneously. And, despite Bell's complaint that a key condition of von Neumann's was quite unrealistic, we show these these conditions are entirely equivalent to those later introduced by Bell, Kochen and Specker. As is it known that these conditions are also equivalent to those under which the Bell-Clauser-Horne inequalities are derived, we see that any experimental violations of the inequalities demonstrate only that quantum observables do not commute.The same conclusion applies to the collection of elegant inequality-free no-go proofs of Greenberger-Horne-Zeilinger, Mermin and Peres. Otherwise expressed, the usual hidden-variable models have assumptions that are collectively too strong to be interesting, and hence need modification or deletion.
In contrast to the wellknown cases of large weights, Sturm's operator does not realize the holomorphic projection operator for lower weights. We prove its failure for arbitrary Siegel genus $m\geq 2$ and scalar weight $\kappa=m+1$. This generalizes a result for genus two in [4].
The finite-temperature magnetic properties of Fe$_x$Pd$_{1-x}$ and Co$_x$Pt$_{1-x}$ alloys have been investigated. It is shown that the temperature-dependent magnetic behaviour of alloys, composed of originally magnetic and non-magnetic elements, cannot be described properly unless the coupling between magnetic moments at magnetic atoms (Fe,Co) mediated through the interactions with induced magnetic moments of non-magnetic atoms (Pd,Pt) is included. A scheme for the calculation of the Curie temperature ($T_C$) for this type of systems is presented which is based on the extended Heisenberg Hamiltonian with the appropriate exchange parameters $J_{ij}$ obtained from {\em ab-initio} electronic structure calculations. Within the present study the KKR Green's function method has been used to calculate the $J_{ij}$ parameters. A comparison of the obtained Curie temperatures for Fe$_x$Pd$_{1-x}$ and Co$_x$Pt$_{1-x}$ alloys with experimental data shows rather good agreement.
We discuss the properties of atom-photon bound states in waveguide QED systems consisting of single or multiple atoms coupled strongly to a finite-bandwidth photonic channel. Such bound states are formed by an atom and a localized photonic excitation and represent the continuum analog of the familiar dressed states in single-mode cavity QED. Here we present a detailed analysis of the linear and nonlinear spectral features associated with single- and multi-photon dressed states and show how the formation of bound states affects the waveguide-mediated dipole-dipole interactions between separated atoms. Our results provide a both qualitative and quantitative description of the essential strong-coupling processes in waveguide QED systems, which are currently being developed in the optical and the microwave regime.
The deviation of the electron density around the nuclei from spherical symmetry determines the electric field gradient (EFG), which can be measured by various types of spectroscopy. Nuclear Quadrupole Resonance (NQR) is particularly sensitive to the EFG. The EFGs, and by implication NQR frequencies, vary dramatically across materials. Consequently, searching for NQR spectral lines in previously uninvestigated materials represents a major challenge. Calculated EFGs can significantly aid at the search inception. To facilitate this task, we have applied high-throughput density functional theory calculations to predict EFGs for 15187 materials in the JARVIS-DFT database. This database, which will include EFG as a standard entry, is continuously increasing. Given the large scope of the database, it is impractical to verify each calculation. However, we assess accuracy by singling out cases for which reliable experimental information is readily available and compare them to the calculations. We further present a statistical analysis of the results. The database and tools associated with our work are made publicly available by JARVIS-DFT ( https://www.ctcms.nist.gov/~knc6/JVASP.html ) and NIST-JARVIS API ( http://jarvis.nist.gov ).
Electroproduction of neutral pions in exclusive reaction $p(e,e'\pi^0)p$ is studied above the resonance region, $\sqrt{s}>2$ GeV. The reaction amplitude is described by exchanges of vector $\omega(782)$, $\rho(770)$ and axial-vector $h_1(1170)$ and $b_1(1235)$ Regge trajectories. The residual effect of $s$- and $u$-channel nucleon resonances is taken into account using a dual connection between the exclusive form factors and inclusive deep inelastic structure functions. In photoproduction at forward angles the exchange of Regge trajectories dominates and the dip region is filled by the resonances. In electroproduction the excitation of nucleon resonances explains the high $Q^2$ data from JLAB. The results for the beam spin azimuthal asymmetry measured at CLAS/JLAB are presented. Model calculations in the deep inelastic region at HERMES/DESY are given.
We study the dynamics of ordering of the nonconserved and conserved Heisenberg magnet. The dynamics consists of two parts - an irreversible dissipation into a heat bath and a reversible precession induced by a torque due to the local molecular field. For quenches both to T=0 and T=T_c, we show that the torque is irrelevant when the dynamics is nonconserved but relevant when the dynamics is conserved and is governed by a new nontrivial fixed point.
The annihilation of antiprotons on deuterons at rest are investigated for the case when pion-nucleon and pion-delta-isobar pairs are produced. The two-step mechanism is investigated by analysing these processes when either neutral particles and charged ones are produced. Some predictions for the branching ratios are presented.
We study heat conduction in one dimensional lattice dynamical systems far from equilibrium. The Fermi-Pasta-Ulam model and the $\phi^4$ model are numerically compared to elucidate differences between momentum-conserving and nonconserving systems. As a results, it is found that the heat flux in the $\phi^4$ model does not increase monotonically as the temperature differences at the ends of the lattice is increased, while it does in the FPU chain.
We study the propagation of sound-like perturbations created by a jet moving with supersonic velocity through the quark-gluon-plasma created in heavy-ion reactions within the model MACE (MAch Cone Evolution). Predictions for heavy-ion reactions at RHIC energies (Au+Au-collisions) and for Pb+Pb reactions at the LHC ($\sqrt s=5.5A$ TeV) are presented and potential observations by the STAR, PHENIX and ALICE experiments are discussed.
Multi-messenger astronomy is a powerful tool to study the physical processes driving the non-thermal Universe. A combination of observations in cosmic rays, neutrinos, photons of all wavelengths and gravitational waves is expected. The alert system of the Baikal-GVD detector under construction will allow for a fast, on-line reconstruction of neutrino events recorded by the Baikal-GVD telescope and - if predefined conditions are satisfied - for the formation of an alert message to other communities. The preliminary results of searches for high-energy neutrinos in coincidence with GW170817/GRB170817A using the cascade mode of neutrino detection are discussed. Two Baikal-GVD clusters were operating during 2017. The zenith angle of NGC 4993 at the detection time of the GW170817 was 93.3 degrees. No events spatially coincident with GRB170817A were found. Given the non-detection of neutrino events associated with GW170817, upper limits on the neutrino fluence were established.
Using $^{63,65}$Cu nuclear magnetic resonance (NMR) in magnetic fields up to 30 T we study the microscopic properties of the 12-site valence-bond-solid ground state in the "pinwheel" kagome compound Rb$_2$Cu$_3$SnF$_{12}$. We find that the ground state is characterized by a strong transverse staggered spin polarization whose temperature and field dependence points to a mixing of the singlet and triplet states. This is further corroborated by the field dependence of the gap $\Delta (H)$, which has a level anticrossing with a large minimum gap value of $\approx \Delta (0)/2$, with no evidence of a phase transition down to 1.5\,K. By the exact diagonalization of small clusters, we show that the observed anticrossing is mainly due to staggered tilts of the $g$-tensors defined by the crystal structure, and reveal symmetry properties of the low-energy excitation spectrum compatible with the absence of level crossing.
The intrinsic structure of binary fields poses a challenging complexity problem from both hardware and software point of view. Motivated by applications to modern cryptography, we describe some simple techniques aimed at performing computations over binary fields using systems with limited resources. This is particularly important when such computations must be carried out by means of very small and simple machines. The algorithms described in the present paper provide an increased efficiency in computations, when compared to the previously known algorithms for the arithmetic over prime fields.
Precision modeling of M dwarfs has become worthwhile in recent years due to the increasingly precise values of masses and radii which can be obtained from eclipsing binary studies. Torres (2013) has identified 4 prime M dwarf pairs with the most precise empirical determinations of masses and radii. The measured radii are consistently larger than standard stellar models predict. We have previously modeled M dwarfs in the context of a criterion due to Gough & Tayler in which magnetic fields inhibit the onset of convection according to a physics-based prescription. New constraints on the models of M dwarfs are now provided by measurements of lithium abundances. The key aspect of Li in terms of setting constraints on magnetic modeling is that Li burning starts at T = 2.5 MK, and temperatures of just such magnitude are associated with the base of the convection zone: magnetic inhibition of convective onset can shift this base slightly closer to the surface, i.e. to slightly lower temperatures, thereby reducing the amount of Li depletion compared to a non-magnetic model. In the present paper, we consider how our magneto-convection models handle the new test of stellar structure provided by Li measurements. Among the prime systems listed by Torres, we find that plausible magnetic models work well for CM Dra and YY Gem but not for CU Cnc. (The fourth system in Torres's list does not yet have enough information to warrant magnetic modeling.) For CU Cnc, we suggest that the observed lithium may have been accreted from a circumstellar disk. We find that our magneto-convection models of CM Dra, YY Gem and CU Cnc yield results which are consistent with the observed correlation between magnetic flux and X-ray luminosity.
Long lifetimes of spatially indirect excitons (IXs), also known as interlayer excitons, make possible long-range IX propagation. Van der Waals heterostructures composed of atomically thin layers of transition-metal dichalcogenides (TMDs) give an opportunity to realize excitons with high binding energies and provide a materials platform for the realization of both excitonic quantum phenomena and excitonic devices. Propagation of IXs in TMD heterostructures is intensively studied. However, in spite of long IX lifetimes, orders of magnitude longer than lifetimes of spatially direct excitons (DXs), a relatively short-range IX propagation with the $1/e$ decay distances $d_{1/e}$ up to few $\mu$m was reported in the studies of TMD heterostructures. The short-range of IX propagation originates from in-plane potentials, which localize excitons and suppress exciton transport. In particular, significant in-plane moir\'e potentials predicted in TMD heterostructures can cause an obstacle for IX propagation. In this work, we realize in a MoSe$_2$/WSe$_2$ heterostructure a macroscopically long-range IX propagation with $d_{1/e}$ reaching $\sim 100$ $\mu$m. The strong enhancement of IX propagation is realized using an optical excitation resonant to DXs in the heterostructure. The strong enhancement of IX propagation originates from the suppression of IX localization and scattering and is observed in the quantum regime.
We study the supersymmetric free energy of three dimensional Chern-Simons-matter theories holographically dual to AdS$_4$ times toric Sasaki-Einstein seven-manifolds. In the large $N$ limit, we argue that the square of the free energy can be written as a quartic polynomial of trial R-charges. The coefficients of the polynomial are determined geometrically from the toric diagrams. We present the coefficients of the quartic polynomial explicitly for generic toric diagrams with up to 6 vertices, and some particular diagrams with 8 vertices. Decomposing the trial R-charges into mesonic and baryonic variables, and eliminating the baryonic ones, we show that the quartic polynomial reproduces the inverse of the Martelli-Sparks-Yau volume function. On the gravity side, we explore the possibility of using the same quartic polynomial as the prepotential in the AdS gauged supergravity. Comparing Kaluza-Klein gravity and gauged supergravity descriptions, we find perfect agreement in the mesonic sector but some discrepancy in the baryonic sector.
The critical properties of the Ziff-Gulari-Barshad (ZGB) model with the addition of long-range reactivity [C.H. Chan and P.A. Rikvold, Phys. Rev. E 91, 012103 (2015)] are further investigated. The scaling behaviors of the order parameter, susceptibility, and correlation length provide addi- tional evidence that the universality class of the ZGB system changes from the two-dimensional Ising class to the mean-field class with the addition of even a weak long-range reactivity mechanism.
Fractional Brownian motion belongs to a class of long memory Gaussian processes that can be represented as linear functionals of an infinite dimensional Markov process. This representation leads naturally to: - An efficient algorithm to approximate the process. - An infinite dimensional ergodic theorem which applies to functionals of the type $integral_0^t phi(V_h(s)) ds $ where $V_h(s)=integral_0^t h(t-u) dB_u$ and $B$ is a standard Brownian motion.
Cosmic microwave background (CMB) temperature anisotropies follow a Gaussian statistical distribution in the standard inflationary model, but there are non-Gaussian contributions due to astrophysical foregrounds. The detection of the non-Gaussian signal due to extragalactic point sources and its distinction from the possible intrinsic non-Gaussianity is an issue of great importance in CMB analysis. The Mexican Hat Wavelet Family (MHWF), which has been proved very useful for the detection of extragalactic point sources, is applied here to the study of non-Gaussianity due to point sources in CMB maps. We carry out simulations of CMB maps with the characteristics of the forthcoming Planck mission at 70 and 100 GHz and filter them with the MHWF. By comparing the skewness and kurtosis of simulated maps with and without point sources, we are able to detect clearly the non-Gaussian signal due to point sources for flux limits as low as 0.4 Jy (70 GHz) and 0.3 Jy (100 GHz). The second and third members of the MHWF perform better in this respect than the Mexican Hat Wavelet (MHW1) and much better than the Daubechies 4 wavelet. We have also estimated the third order, $K_3$, and fourth order, $K_4$, cumulants produced by point sources at these Planck channels by means of a fit with the MHWF. The average relative errors with respect to the real values are below 12% for fluxes down to 0.6 Jy (70 GHz) and 0.4 Jy (100 GHz). The values of these cumulants allow us to distinguish between different source counts models.
We prove new upper bounds for the number of representations of an arbitrary rational number as a sum of three unit fractions. In particular, for fixed $m$ there are at most $\mathcal{O}_{\epsilon}(n^{3/5+\epsilon})$ solutions of $\frac{m}{n}=\frac{1}{a_1}+\frac{1}{a_2}+\frac{1}{a_3}$. This improves upon a result of Browning and Elsholtz (2011) and extends a result of Elsholtz and Tao (2013) who proved this when $m=4$ and $n$ is a prime. Moreover there exists an algorithm finding all solutions in expected running time $\mathcal{O}_{\epsilon}\left(n^{\epsilon}\left(\frac{n^3}{m^2}\right)^{1/5}\right)$, for any $\epsilon >0$. We also improve a bound on the maximum number of representations of a rational number as a sum of $k$ unit fractions. Furthermore, we also improve lower bounds. In particular we prove that for given $m\in \mathbb{N}$ in every reduced residue class $e \bmod f$ there exist infinitely many primes $p$ such that the number of solutions of the equation $\frac{m}{p}=\frac{1}{a_1}+\frac{1}{a_2}+\frac{1}{a_3}$ is $\gg_{f,m} \exp\left(\left(\frac{5\log 2}{12 \mathrm{lcm}(m,f)}+o_{f,m}(1)\right)\frac{\log p}{\log \log p}\right)$. Previously the best known lower bound of this type was of order $(\log p)^{0.549}$.
We present a technique for constructing equilibrium triaxial N-body haloes with nearly arbitrary density profiles, axial ratios and spin parameters. The method is based on the way in which structures form in hierarchical cosmological simulations, where prolate and oblate haloes form via mergers with low and high angular momentum, respectively. We show that major mergers between equilibrium spherical cuspy haloes produce similarly cuspy triaxial remnants and higher angular-momentum mergers produce systems with lower concentrations. Triaxial haloes orbiting within deeper potentials become more spherical and their velocity dispersion tensors more isotropic. The rate of mass loss depends sensitively on the halo shape: a prolate halo can lose mass at a rate several times higher than an isotropic spherical halo with the same density profile. Subhaloes within cosmological simulations are significantly rounder than field haloes with axial ratios that are ~ 30% larger.
We study the physics of the solar tachocline and related MHD instabilities. We have performed 3-D MHD simulations of the solar radiative interior to check whether a fossil magnetic field is able to prevent the spread of the tachocline. Starting with a purely poloidal magnetic field and a latitudinal shear meant to be imposed by the convection zone at the top of the radiation zone, we have investigated the interactions between magnetic fields, rotation and shear, using the spectral code ASH on massive parallel supercomputers. In all cases we have explored, the fossil field diffuses outward and ends up connecting with the convection zone, whose differential rotation is then imprinted at latitudes above 40 deg throughout the radiative interior, according to Ferraro's law of isorotation. Rotation remains uniform in the lower latitude region which is contained within closed field lines. We find that the meridional flow cannot stop the inward progression of the differential rotation. Further, we observe the development of non-axisymmetric magnetohydrodynamic instabilities, first due to the initial poloidal configuration of the fossil field, and later to the toroidal field produced by shearing the poloidal field through the differential rotation. We do not find dynamo action as such in the radiative interior, since the mean poloidal field is not regenerated. But the instability persists during the whole evolution, while slowly decaying with the mean poloidal field. According to our numerical simulations, a fossil magnetic field cannot prevent the radiative spread of the tachocline, and thus it is unable to enforce uniform rotation in the radiation zone. Neither can the observed thinness of that layer be invoked as a proof for such an internal fossil magnetic field.
A 1977 theorem of T. Harris states that an attractive spin system preserves the class of associated probability measures. We study analogues of this result for measures that satisfy various conditional positive correlations properties. In particular, we show that a spin system preserves measures satisfying the FKG lattice condition (essentially) if and only if distinct spins flip independently. The downward FKG property, which has been useful recently in the study of the contact process, lies between the properties of lattice FKG and association. We prove that this property is preserved by a spin system if the death rates are constant and the birth rates are additive (e.g., the contact process), and prove a partial converse to this statement. Finally, we introduce a new property, which we call downward conditional association, which lies between the FKG lattice condition and downward FKG, and find essentially necessary and sufficient conditions for this property to be preserved by a spin system. This suggests that the latter property may be more natural than the downward FKG property.