ShantanuT01/DACTYL-Pretraining huggingface dataset:
Let G be a simple connected graph of order n with degree sequence d_1, d_2, ..., d_n in non-increasing order. The spectral radius rho(G) of G is the largest eigenvalue of its adjacency matrix. For each positive integer L at most n, we give a sharp upper bound for rho(G) by a function of d_1, d_2, ..., d_L, which generalizes a series of previous results.
The decoherence rate is a nonlinear channel parameter that describes quantitatively the decay of the off-diagonal elements of a density operator in the decoherence basis. We address the question of how to experimentally access such a nonlinear parameter directly without the need of complete process tomography. In particular, we design a simple experiment working with two copies of the channel, in which the registered mean value of a two-valued measurement directly determines the value of the average decoherence rate. No prior knowledge of the decoherence basis is required.
In glassy materials aging proceeds at large times via thermal activation. We show that this can lead to negative dynamical response functions and novel and well-defined violations of the fluctuation-dissipation theorem, in particular, negative fluctuation-dissipation ratios. Our analysis is based on detailed theoretical and numerical results for the activated aging regime of simple kinetically constrained models. The results are relevant to a variety of physical situations such as aging in glass-formers, thermally activated domain growth and granular compaction.
The key to unraveling intriguing phenomena observed in various Kitaev materials lies in understanding the interplay of Kitaev ($K$) interaction and a symmetric off-diagonal $\Gamma$ interaction. To provide insight into the challenging problems, we study the quantum phase diagram of a bond-alternating spin-$1/2$ $g_x$-$g_y$ $K$-$\Gamma$ chain by density-matrix renormalization group method where $g_x$ and $g_y$ are the bond strengths of the odd and even bonds, respectively. The phase diagram is dominated by even-Haldane ($g_x > g_y$) and odd-Haldane ($g_x < g_y$) phases where the former is topologically trivial while the latter is a symmetry-protected topological phase. Near the antiferromagnetic Kitaev limit, there are two gapped $A_x$ and $A_y$ phases characterized by distinct nonlocal string correlators. In contrast, the isotropic ferromagnetic (FM) Kitaev point serves as a multicritical point where two topological phase transitions meet. The remaining part of the phase diagram contains three symmetry-breaking magnetic phases. One is a six-fold degenerate FM$_{U_6}$ phase where all the spins are parallel to one of the $\pm \hat{x}$, $\pm \hat{y}$, and $\pm \hat{z}$ axes in a six-site spin rotated basis, while the other two have more complex spin structures with all the three spin components being finite. Existence of a rank-2 spin-nematic ordering in the latter is also discussed.
(Abridged) Spitzer data at 24, 70, and 160 micron and ground-based H-alpha images are analyzed for a sample of 189 nearby star-forming and starburst galaxies to investigate whether reliable star formation rate (SFR) indicators can be defined using the monochromatic infrared dust emission centered at 70 and 160 micron. We compare recently published recipes for SFR measures using combinations of the 24 micron and observed H-alpha luminosities with those using 24 micron luminosity alone. From these comparisons, we derive a reference SFR indicator for use in our analysis. Linear correlations between SFR and the 70 and 160 micron luminosity are found for L(70)>=1.4x10^{42} erg/s and L(160)>=2x10^{42} erg/s, corresponding to SFR>=0.1-0.3 M_sun/yr. Below those two luminosity limits, the relation between SFR and 70 micron (160 micron) luminosity is non-linear and SFR calibrations become problematic. The dispersion of the data around the mean trend increases for increasing wavelength, becoming about 25% (factor ~2) larger at 70 (160) micron than at 24 micron. The increasing dispersion is likely an effect of the increasing contribution to the infrared emission of dust heated by stellar populations not associated with the current star formation. The non-linear relation between SFR and the 70 and 160 micron emission at faint galaxy luminosities suggests that the increasing transparency of the interstellar medium, decreasing effective dust temperature, and decreasing filling factor of star forming regions across the galaxy become important factors for decreasing luminosity. The SFR calibrations are provided for galaxies with oxygen abundance 12+Log(O/H)>8.1. At lower metallicity the infrared luminosity no longer reliably traces the SFR because galaxies are less dusty and more transparent.
We study the entanglement effect of beam splitter on the temporally stable phase states. Specifically, we consider the eigenstates (phase states) of an unitary phase operator resulting from the polar decomposition of ladder operators of generalized Weyl--Heisenberg algebras possessing finite dimensional representation space. The linear entropy that measures the degree of entanglement at the output of the beam splitter is analytically obtained. We find that the entanglement is not only strongly dependent on the Hilbert space dimension but also quite related to strength the parameter ensuring the temporal stability of the phase states. Finally, we discuss the evolution of the entangled phase states.
In the context of communication networks, the framework of stochastic event graphs allows a modeling of control mechanisms induced by the communication protocol and an analysis of its performances. We concentrate on the logarithmic tail asymptotics of the stationary response time for a class of networks that admit a representation as (max,plus)-linear systems in a random medium. We are able to derive analytic results when the distribution of the holding times are light-tailed. We show that the lack of independence may lead in dimension bigger than one to non-trivial effects in the asymptotics of the sojourn time. We also study in detail a simple queueing network with multipath routing.
We propose analogs of the classical Generalized Riemann Hypothesis and the Generalized Simplicity Conjecture for the characteristic p L-series associated to function fields over a finite field. These analogs are based on the use of absolute values. Further we use absolute values to give similar reformulations of the classical conjectures (with, perhaps, finitely many exceptional zeroes). We show how both sets of conjectures behave in remarkably similar ways.
We study the zero-temperature magnetization process (M-H curve) of one-dimensional quantum antiferromagnets using a variant of the density-matrix renormalization group method. For both the S=1/2 zig-zag spin ladder and the S=1 bilinear-biquadratic chain, we find clear cusp-type singularities in the middle-field region of the M-H curve. These singularities are successfully explained in terms of the double-minimum shape of the energy dispersion of the low-lying excitations. For the S=1/2 zig-zag spin ladder, we find that the cusp formation accompanies the Fermi-liquid to non-Fermi-liquid transition.
A new numerical framework, based on the use of a simple first order strongly hyperbolic evolution equations, is introduced and tested in case of 4-dimensional spherically symmetric gravitating systems. The analytic setup is chosen such that our numerical method is capable to follow the time evolution even after the appearance of trapped surfaces, more importantly, until the true physical singularities are reached. Using this framework, the gravitational collapse of various gravity-matter systems are investigated, with distinguished attention to the evolution in trapped regions. It is justified that in advance to the formation of these curvature singularities, trapped regions develop in all cases, thereby supporting the validity of the weak cosmic censor hypothesis of Penrose. Various upper bounds on the rate of blow-up of the Ricci and Kretschmann scalars and the Misner-Sharp mass are provided. In spite of the unboundedness of the Ricci scalar, the Einstein-Hilbert action was found to remain finite in all the investigated cases. In addition, important conceptual issues related to the phenomenon of topology changes are also discussed.
Learning rich and compact representations is an open topic in many fields such as object recognition or image retrieval. Deep neural networks have made a major breakthrough during the last few years for these tasks but their representations are not necessary as rich as needed nor as compact as expected. To build richer representations, high order statistics have been exploited and have shown excellent performances, but they produce higher dimensional features. While this drawback has been partially addressed with factorization schemes, the original compactness of first order models has never been retrieved, or at the cost of a strong performance decrease. Our method, by jointly integrating codebook strategy to factorization scheme, is able to produce compact representations while keeping the second order performances with few additional parameters. This formulation leads to state-of-the-art results on three image retrieval datasets.
We revise the sequences of SUSY for a cyclic adiabatic evolution governed by the supersymmetric quantum mechanical Hamiltonian. The condition (supersymmetric adiabatic evolution) under which the supersymmetric reductions of Berry (nondegenerated case) or Wilczek-Zee (degenerated case) phases of superpartners are taking place is pointed out. The analogue of Witten index (supersymmetric Berry index) is determined. As the examples of suggested concept of supersymmetric adiabatic evolution the Holomorphic quantum mechanics on complex plane and Meromorphic quantum mechanics on Riemann surface are considered. The supersymmetric Berry indexes for the models are calculated.
Direct measurements of the magnetocaloric effect (MCE) in different materials (Gd, Fe48Rh52, Ni43Mn37.9In12.1Co7 and Ni2.07Co0.09Mn0.84Ga) in alternating magnetic fields with frequencies f < 22 Hz and an amplitude deltaH = 6.2 kOe are carried out. The MCE in Gd shows inconsiderable changes with field frequency. Near paramagnetic-ferromagnetic phase transition in Ni43Mn37.9In12.1Co7 Heusler alloy a slight reduction of MCE with frequency is observed. In weak alternating fields in materials with AFM-FM magneto-structural phase transitions (Fe48Rh52, Ni43Mn37.9In12.1Co7) it is not possible to get a structural contribution to overall MCE because of irreversibility of the transitions in these fields. Near magneto-structural phase transitions the MCE in these alloys has only magnetic contribution, and does not show a significant dependence on the magnetic field frequency. In Ni2.07Co0.09Mn0.84Ga Heusler alloy the MCE vanishes at frequencies about 20 Hz. The obtained results show the increase of frequencies of operating cycles is one of the powerful methods to improve the efficiency of magnetic refrigerators in case of Gd as a refrigerant.
We compute that the growth of the origin occupation-time variance up to time t in dimension d=2 with respect to asymmetric simple exclusion in equilibrium with density 1/2 is in a certain sense at least t(log(log t)) for general rates, and at least t(log t)^{1/2} for rates which are asymmetric only in the direction of one of the axes. These estimates are consistent with conjectures with respect to the transition function and variance of 'second-class' particles.
Long-distance quantum optical communications usually require efficient wave-mixing processes to convert the wavelengths of single photons. Many quantum applications based on electromagnetically induced transparency (EIT) have been proposed and demonstrated at the single-photon level, such as quantum memories, all-optical transistors, and cross-phase modulations. However, EIT-based four-wave mixing (FWM) in a resonant double-$\Lambda$ configuration has a maximum conversion efficiency (CE) of 25% because of absorptive loss due to spontaneous emission. An improved scheme using spatially modulated intensities of two control fields has been theoretically proposed to overcome this conversion limit. In this study, we first demonstrate wavelength conversion from 780 to 795 nm with a 43% CE by using this scheme at an optical density (OD) of 19 in cold $^{87}$Rb atoms. According to the theoretical model, the CE in the proposed scheme can further increase to 96% at an OD of 240 under ideal conditions, thereby attaining an identical CE to that of the previous non resonant double-$\Lambda$ scheme at half the OD. This spatial-light-modulation-based FWM scheme can achieve a near-unity CE, thus providing an easy method of implementing an efficient quantum wavelength converter for all-optical quantum information processing.
The Euclid space telescope will measure the shapes and redshifts of galaxies to reconstruct the expansion history of the Universe and the growth of cosmic structures. Estimation of the expected performance of the experiment, in terms of predicted constraints on cosmological parameters, has so far relied on different methodologies and numerical implementations, developed for different observational probes and for their combination. In this paper we present validated forecasts, that combine both theoretical and observational expertise for different cosmological probes. This is presented to provide the community with reliable numerical codes and methods for Euclid cosmological forecasts. We describe in detail the methodology adopted for Fisher matrix forecasts, applied to galaxy clustering, weak lensing and their combination. We estimate the required accuracy for Euclid forecasts and outline a methodology for their development. We then compare and improve different numerical implementations, reaching uncertainties on the errors of cosmological parameters that are less than the required precision in all cases. Furthermore, we provide details on the validated implementations that can be used by the reader to validate their own codes if required. We present new cosmological forecasts for Euclid. We find that results depend on the specific cosmological model and remaining freedom in each setup, i.e. flat or non-flat spatial cosmologies, or different cuts at nonlinear scales. The validated numerical implementations can now be reliably used for any setup. We present results for an optimistic and a pessimistic choice of such settings. We demonstrate that the impact of cross-correlations is particularly relevant for models beyond a cosmological constant and may allow us to increase the dark energy Figure of Merit by at least a factor of three.
The effects of substrate on electronic and optical properties of triangular and hexagonal graphene nanoflakes with armchair edges are investigated by using a configuration interaction approach beyond double excitation scheme. The quasiparticle correction to the energy gap and exciton binding energy are found to be dominated by the long-range Coulomb interactions and exhibit similar dependence on the dielectric constant of the substrate, which leads to a cancellation of their contributions to the optical gap. As a result, the optical gaps are shown to be insensitive to the dielectric environment and unexpectedly close to the single-particle gaps.
We investigate definitions of and protocols for multi-party quantum computing in the scenario where the secret data are quantum systems. We work in the quantum information-theoretic model, where no assumptions are made on the computational power of the adversary. For the slightly weaker task of verifiable quantum secret sharing, we give a protocol which tolerates any t < n/4 cheating parties (out of n). This is shown to be optimal. We use this new tool to establish that any multi-party quantum computation can be securely performed as long as the number of dishonest players is less than n/6.
We investigate quasi-periodic pulsations (QPPs) of high-energy nonthermal emissions from an X9.3 flare (SOL2017-Sep-06T11:53), the most powerful flare since the beginning of solar cycle 24. The QPPs are identified as a series of regular and repeating peaks in the light curves in the gamma- and hard X-ray (HXR) channels recorded by the Konus-Wind, as well as the radio and microwave fluxes measured by the CALLISTO radio spectrograph during the impulsive phase. The periods are determined from the global wavelet and Fourier power spectra, as 24-30 s in the HXR and microwave channels which are associated with nonthermal electrons, and ~20 s in the gamma-ray band related to nonthermal ions. Both nonthermal electrons and ions may be accelerated by repetitive magnetic reconnection during the impulsive phase. However, we could not rule out other mechanisms such as the MHD oscillation in a sausage mode. The QPP detected in this study is useful for understanding the particle acceleration and dynamic process in solar flares and also bridging the gap between stellar and solar flares since the energy realm of the X9.3 solar flare is almost compared with a typical stellar flare.
Distribution of the positive and negative photospheric fields is studied on the base of synoptic maps of the photospheric magnetic field produced by the National Solar Observatory Kitt Peak (NSO Kitt Peak) for 1976-2016. In the analysis only the sign of the field irrespective of its strength is taken into account, emphasizing the role of the fields with average and weak strengths.   Time changes in the positive and negative magnetic fields for two hemispheres, for the high latitudes and for the sunspot zone as well as their imbalances are considered. Distributions of fields of opposite polarities, which are defined mostly by the fields of the high latitudes, change with a 22-year cycle. The polarity imbalance in each hemisphere is closely connected with the dipole moment $g_{10}$.   The imbalance of high latitudes for two hemispheres changes with the 22-year period and coincides with the sign of both the polar field in the southern hemisphere, and the quadrupole moment $g_{20}$. For the magnetic fields of the sunspot zone during ~75% of time a connection of the magnetic field imbalance with the quadrupole moment taken with the reversed sign $- g_{20}$ and with the sign of the polar field in the northern hemisphere is observed. The received results testify to cyclic changes in the polarity imbalance.
I explore the form of the effective interaction in harmonic-oscillator-based effective theory (HOBET) in next-to-next-to-next-to-leading order (N3LO). As the included space in a HOBET (as in the shell model) is defined by the oscillator energy, both long-distance (low-momentum) and short-distance (high-momentum) degrees of freedom reside in the high-energy excluded space. A HOBET effective interaction is developed in which a short-range contact-gradient expansion is combined with an exact summation of the relative kinetic energy. By this means the very strong coupling of the included (P) and excluded (Q) spaces by the kinetic energy is removed. One finds that the interplay of QT and QV is governed by a single parameter kappa, the ratio of an observable, the binding energy |E|, to a parameter in the effective theory, the oscillator energy. Once the functional dependence on kappa is identified, the remaining order-by-order subtraction of the short-range physics residing in Q becomes systematic and rapidly converging. Numerical calculations are used to demonstrate how well the resulting expansion reproduces the running of Heff from high scales to a typical shell-model scale of 8 hbar omega. At N3LO various global properties of Heff are reproduced to a typical accuracy of 0.01%, or about 1 keV.   The state-dependence of the effective interaction has been a troubling problem in nuclear physics, and is embodied in the energy dependence of Heff(|E|) in the Bloch-Horowitz formalism. It is shown that almost all of this state dependence is also extracted in the procedures followed here, isolated in the analytic dependence of Heff on kappa. Thus there exists a simple, Hermitian Heff that can be use in spectral calculations.
Total mass is arguably the most fundamental property for cosmological studies with galaxy clusters. We investigate the present differences in the mass estimates obtained through independent X-ray, weak-lensing, and dynamical studies. We quantify the differences as the mean ratio 1-$b$=M$_{\rm HE}$/M$_{\rm WL,dyn}$, where HE refers to hydrostatic masses obtained from X-ray observations, WL refers to the results of weak-lensing measurements, and dyn refers to the mass estimates either from velocity dispersion or from the caustic technique. Recent X-ray masses reported by independent groups show average differences smaller than $\sim$10$\%$, posing a strong limit on the systematics that can be ascribed to the differences in the X-ray analysis when studying the hydrostatic bias. The mean ratio between our X-ray masses and the weak-lensing masses in the LC$^2$-single catalog is 1-$b$=0.74$\pm$0.06. However, the mean mass ratios inferred from the WL masses of different projects vary by a large amount, with APEX-SZ showing a bias consistent with zero (1-$b$=1.02$\pm$0.12), LoCuSS and CCCP/MENeaCS showing a significant difference (1-$b$=0.76$\pm$0.09 and 1-$b$=0.77$\pm$0.10, respectively), and WtG pointing to the largest deviation (1-$b$=0.61$\pm$0.12). At odds with the WL results, the dynamical mass measurements show better agreement with the X-ray hydrostatic masses, although there are significant differences when relaxed or disturbed clusters are used. The different ratios obtained using different mass estimators suggest that there are still systematics that are not accounted for in all the techniques used to recover cluster masses. This prevents the determination of firm constraints on the level of hydrostatic mass bias in galaxy clusters.
One of the outstanding mysteries surrounding the rich diversity found in supernova remnants (SNRs) is the recent discovery of over-ionized or recombining plasma from a number of dynamically evolved objects. To help decipher its formation mechanism, we have developed a new simulation framework capable of modeling the time evolution of the ionization state of the plasma in an SNR. The platform is based on a one-dimensional hydrodynamics code coupled to a fully time-dependent non-equilibrium ionization calculation, accompanied by a spectral synthesis code to generate space-resolved broadband X-ray spectra for SNRs at arbitrary ages. We perform a comprehensive parametric survey to investigate the effects of different circumstellar environments on the ionization state evolution in SNRs up to a few 10,000 years. A two-dimensional parameter space, spanned by arrays of interstellar medium (ISM) densities and mass-loss rates of the progenitor, is used to create a grid of models for the surrounding environment, in which a core-collapse explosion is triggered. Our results show that a recombining plasma can be successfully reproduced in the case of a young SNR (a few 100 to 1,000 years old) expanding fast in a spatially extended low-density wind, an old SNR (> a few 1,000 years) expanding in a dense ISM, or an old SNR broken out from a confined dense wind region into a tenuous ISM. Finally, our models are confronted with observations of evolved SNRs, and an overall good agreement is found except for a couple of outliers.
We consider systems of particles coupled with fluids. The particles are described by the evolution of their density, and the fluid is described by the Navier-Stokes equations. The particles add stress to the fluid and the fluid carries and deforms the particles. Because the particles perform rapid random motion, we assume that the density of particles is carried by a time average of the fluid velocity. The resulting coupled system is shown to have smooth solutions at all values of parameters, in two spatial dimensions.