ShantanuT01/DACTYL-Pretraining huggingface dataset:
We propose the following conjecture: For every fixed $\alpha\in [0,\frac 13)$, each graph of minimum degree at least $(1+\alpha)\frac k2$ and maximum degree at least $2(1-\alpha)k$ contains each tree with $k$ edges as a subgraph. Our main result is an approximate version of the conjecture for bounded degree trees and large dense host graphs. We also show that our conjecture is asymptotically best possible. The proof of the approximate result relies on a second result, which we believe to be interesting on its own. Namely, we can embed any bounded degree tree into host graphs of minimum/maximum degree asymptotically exceeding $\frac k2$ and $\frac 43k$, respectively, as long as the host graph avoids a specific structure.
We use a nonperturbative variational method to investigate the phase transition of the Gross-Neveu model. It is shown that the variational procedure can be generalized to the finite temperature case. The large N result for the phase transition is correctly reproduced.
The detection of gravitational radiation raises some subtle issues having to do with the coordinate invariance of general relativity. This paper explains these issues and their resolution by using an analogy with the Aharonov-Bohm effect of quantum mechanics.
We use the S\'aez-Ballester (SB) theory on anisotropic Bianchi Class A cosmological model, with barotropic fluid and cosmological constant, using the Hamilton or Hamilton-Jacobi approach. Contrary to claims in the specialized literature, it is shown that the S\'aez-Ballester theory cannot provide a realistic solution to the dark matter problem of Cosmology for the dust epoch, without a fine tunning because the contribution of the scalar field in this theory is equivalent to a stiff fluid (as can be seen from the energy--momentum tensor for the scalar field), that evolves in a different way as the dust component. To have similar contributions of the scalar component and the dust component implies that their past values were fine tunned. So, we reinterpreting this null result as an indication that dark matter plays a central role in the formation of structures and galaxy evolution, having measureable effects in the cosmic microwave bound radiation, and than this formalism yield to this epoch as primigenius results. We do the mention that this formalism was used recently in the so called K-essence theory applied to dark energy problem, in place to the dark matter problem. Also, we include a quantization procedure of the theory which can be simplified by reinterpreting the theory in the Einstein frame, where the scalar field can be interpreted as part of the matter content of the theory, and exact solutions to the Wheeler-DeWitt equation are found, employing the Bianchi Class A cosmological models.
A theory of cyclic elements in semisimple Lie algebras is developed. It is applied to an explicit construction of regular elements in Weyl groups.
For a colloidal particle driven by a constant force across a periodic potential, we investigate the distribution of entropy production both experimentally and theoretically. For short trajectories, the fluctuation theorem holds experimentally. The mean entropy production rate shows two regimes as a function of the applied force. Theoretically, both mean and variance of the pronounced non-Gaussian distribution can be obtained from a differential equation in good agreement with the experimental data.
Computing polynomial form of the colored HOMFLY-PT for non-arborescent knots obtained from three or more strand braids is still an open problem. One of the efficient methods suggested for the three-strand braids relies on the eigenvalue hypothesis which uses the Yang-Baxter equation to express the answer through the eigenvalues of the ${\cal R}$-matrix. In this paper, we generalize the hypothesis to higher number of strands in the braid where commuting relations of non-neighbouring $\mathcal{R}$ matrices are also incorporated. By solving these equations, we determine the explicit form for $\mathcal{R}$-matrices and the inclusive Racah matrices in terms of braiding eigenvalues (for matrices of size up to 6 by 6). For comparison, we briefly discuss the highest weight method for four-strand braids carrying fundamental and symmetric rank two $SU_q(N)$ representation. Specifically, we present all the inclusive Racah matrices for representation $[2]$ and compare with the matrices obtained from eigenvalue hypothesis.
We study electron transport through a multi-level quantum dot with Rashba spin-orbit interaction in the presence of local Coulomb repulsion. Motivated by recent experiments, we compute the level splitting induced by the spin-orbit interaction at finite Zeeman fields $B$, which provides a measure of the renormalized spin-orbit energy. This level splitting is responsible for the suppression of the Kondo ridges at finite $B$ characteristic for the multi-level structure. In addition, the dependence of renormalized $g$-factors on the relative orientation of the applied $B$ field and the spin-orbit direction following two different protocols used in experiments is investigated.
We present Karl G. Jansky Very Large Array radio frequency observations of the new accreting millisecond X-ray pulsar (AMXP), IGR J16597$-$3704, located in the globular cluster NGC 6256. With these data, we detect a radio counterpart to IGR J16597$-$3704, and determine an improved source position. Pairing our radio observations with quasi-simultaneous Swift/XRT X-ray observations, we place IGR J16597$-$3704 on the radio -- X-ray luminosity plane, where we find that IGR J16597$-$3704 is one of the more radio-quiet neutron star low-mass X-ray binaries known to date. We discuss the mechanisms that may govern radio luminosity (and in turn jet production and evolution) in AMXPs. Further, we use our derived radio position to search for a counterpart in archival Hubble Space Telescope and Chandra X-ray Observatory data, and estimate an upper limit on the X-ray luminosity of IGR J16597$-$3704 during quiescence.
By electron and X-ray diffraction we establish that the CrB$_4$ compound discovered over 40 years ago crystallizes in the $oP10$ (\emph{Pnnm}) structure, in disagreement with previous experiments but in agreement with a recent first-principles prediction. The 3D boron network in the new structure is a distorted version of the rigid carbon $sp^3$ network proposed recently for the high-pressure C$_4$ allotrope. According to our density functional theory calculations and the analysis of the bonding, CrB$_4$ is a potentially superhard material. In fact, the calculated weakest shear and tensile stresses exceed 50 GPa and its Vickers hardness is estimated to be 48 GPa.
Let $E_1$ and $E_2$ be elliptic curves in Legendre form with integer parameters. We show there exists a constant $C$ such that for almost all primes, for all but at most $C$ pairs of points on the reduction of $E_1 \times E_2$ modulo $p$ having equal $x$ coordinate, at least one among $P_1$ and $P_2$ has a large group order. We also show similar abundance over finite fields of elements whose images under the reduction modulo $p$ of a finite set of rational functions have large multiplicative orders
In Phys. Rev. D 102, 024057 (2020), the authors studied energy conditions in $f(Q)$ theory following the same path as researchers handled the energy conditions in the curvature-based modified gravity theories, like $f(R)$ or $f(R,G)$ theories. However, the field equations in the $f(Q)$ theory was not expressed as an effective theory in the literature earlier and in the above mentioned paper [1], the authors claimed that the pressure and energy density follow a set of energy condition criteria without showing how they came to this conclusion. In this comment, we express $f(Q)$ theory as an effective theory in Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) universe. And from there, the correct energy conditions are obtained in the traditional (general relativistic) way. Unfortunately, some missing terms in the published work [1] are noticed.
We complement the PARSEC data base of stellar evolutionary tracks with new models of massive stars, from the pre-main sequence phase to the central carbon ignition. We consider a broad range of metallicities, 0.0001$\leq Z \leq$0.04 and initial masses up to $M_{\rm ini}=350\,M_\odot$. The main difference with respect to our previous models of massive stars is the adoption of a recent formalism accounting for the mass-loss enhancement when the ratio of the stellar to the Eddington luminosity, $\Gamma_e$, approaches unity. With this new formalism, the models are able to reproduce the Humphreys-Davidson limit observed in the Galactic and Large Magellanic Cloud colour-magnitude diagrams, without an ad hoc mass-loss enhancement. We also follow the predictions of recent wind models indicating that the metallicity dependence of the mass-loss rates becomes shallower when $\Gamma_e$ approaches unity. We thus find that the more massive stars may suffer from substantial mass-loss even at low metallicity. We also predict that the Humphreys-Davidson limit should become brighter at decreasing metallicity. We supplement the evolutionary tracks with new tables of theoretical bolometric corrections, useful to compare tracks and isochrones with the observations. For this purpose, we homogenize existing stellar atmosphere libraries of hot and cool stars (PoWR, ATLAS9 and Phoenix) and we add, where needed, new atmosphere models computed with WM-basic. The mass, age and metallicity grids are fully adequate to perform detailed investigations of the properties of very young stellar systems, both in local and distant galaxies. The new tracks supersede the previous old Padova models of massive stars.
In this paper, a systematic analysis of hourly wind speed data obtained from four potential wind generation sites in North Dakota is conducted. The power spectra of the data exhibited a power law decay characteristic of $1/f^{\alpha}$ processes with possible long range correlations. The temporal scaling properties of the records were studied using multifractal detrended fluctuation analysis {\em MFDFA}. It is seen that the records at all four locations exhibit similar scaling behavior which is also reflected in the multifractal spectrum determined under the assumption of a binomial multiplicative cascade model.
We investigate electric and magnetic properties of graphene with rotationally symmetric strain. The strain generates large pseudo magnetic field with alternating sign in space, which forms a strongly confined quantum dot connected to six chiral channels. The orbital magnetism, degeneracy, and channel opening can be understood from the interplay between real and pseudo magnetic field which have different parities under time reversal and mirror reflection.   While the orbital magnetic response of the confined state is diamagnetic, it can be paramagnetic if there is an accidental degeneracy with opposite mirror reflection parity.
With decades of years development, although important progresses have been made by the pioneers of this field, providing a sophisticated truncation scheme is still a great challenge up to now if the Dyson-Schwinger Equations(DSEs) of both quark and gluon propagators (or including even more DSEs) remain after truncation. In this work we view the coupled reminiscent DSEs of the gluon and quark propagators after truncation as a system with feedback. Then studying the stability of this equation array gives useful results. Our calculation shows that the sum of the gluon and ghost loops plays the most important role in keeping this system stable and having reasonable solutions. The quark-gluon vertex plays a relative smaller but also important role. Our method also could give constraints and inspirations on fabricating a more sophisticated model of the quark-gluon vertex.
The problem of the hierarchy of lifetimes of charmed hadrons is reviewed. The QCD-based theory of preasymptotic effects in inclusive weak decays dating back to the beginning of the eighties is now entering its mature phase. Combining recent and old results we argue that the observed hierarchy reflects most intimate features of the hadronic structure. The problem of a wide spread of lifetimes of charmed hadrons is addressed.   We speculate on what is to be expected from QCD to provide the observed pattern. A number of predictions is given for the hierarchy of lifetimes in the family of the beautiful hadrons.
Within the superfield formalism, we study the dynamical generation of mass to the gauge superfield in the noncommutative two-dimensional supersymmetric Schwinger model. We show that the radiatively generated mass does not depend on the noncommutative parameter up to one-loop order.
We use the shell model Monte Carlo approach to study thermal properties and pair correlations in $^{54,56,58}$Fe and in $^{56}$Cr. The calculations are performed with the modified Kuo-Brown interaction in the complete $1p0f$ model space. We find generally that the proton-proton and neutron-neutron $J=0$ pairing correlations, which dominate the ground state properties of even-even nuclei, vanish at temperatures around 1 MeV. This pairing phase transition is accompanied by a rapid increase in the moment of inertia and a partial unquenching of the M1 strength. We find that the M1 strength totally unquenches at higher temperatures, related to the vanishing of isoscalar proton-neutron correlations, which persist to higher temperatures than the pairing between like nucleons. The Gamow-Teller strength is also correlated to the isoscalar proton-neutron pairing and hence also unquenches at a temperature larger than that of the pairing phase transition.
Within the matrix product state framework, we study the non-Markovian feedback dynamics of a two-level system interacting with the electromagnetic field inside a semi-infinite waveguide where the excitation of an atom-photon bound state is possible. Taking the steady-state excitation of the emitter as a figure of merit, we compare the trapped excitation for an initially excited quantum emitter and an emitter prepared via quantized pulses containing up to four photons. In the latter case, we find that for large feedback delay times, multi-photon pulses can yield a significantly higher steady-state excitation than possible with an initially excited emitter since the stimulated emission process can enhance the trapping probability in comparison to the spontaneous decay of an initially excited emitter.
We use the Matsubara functional renormalization group (FRG) to describe electronic correlations within the single impurity Anderson model. In contrast to standard FRG calculations, we account for the frequency-dependence of the two-particle vertex in order to address finite-energy properties (e.g, spectral functions). By comparing with data obtained from the numerical renormalization group (NRG) framework, the FRG approximation is shown to work well for arbitrary parameters (particularly finite temperatures) provided that the electron-electron interaction U is not too large. We demonstrate that aspects of (large U) Kondo physics which are described well by a simpler frequency-independent truncation scheme are no longer captured by the 'higher-order' frequency-dependent approximation. In contrast, at small to intermediate U the results obtained by the more elaborate scheme agree better with NRG data. We suggest to parametrize the two-particle vertex not by three independent energy variables but by introducing three functions each of a single frequency. This considerably reduces the numerical effort to integrate the FRG flow equations.
We review our results for the dynamics of isolated many-body quantum systems described by one-dimensional spin-1/2 models. We explain how the evolution of these systems depends on the initial state and the strength of the perturbation that takes them out of equilibrium; on the Hamiltonian, whether it is integrable or chaotic; and on the onset of multifractal eigenstates that occurs in the vicinity of the transition to a many-body localized phase. We unveil different behaviors at different time scales. We also discuss how information about the spectrum of a many-body quantum system can be extracted by the sole analysis of its time evolution, giving particular attention to the so-called correlation hole. This approach is useful for experiments that routinely study dynamics, but have limited or no direct access to spectroscopy, as experiments with cold atoms and trapped ions.
While it is well known that constant rotation induces linear dispersive effects in various fluid models, we study here its effect on long time nonlinear dynamics in the inviscid setting. More precisely, we investigate stability in the 3d rotating Euler equations in $\mathbb{R}^3$ with a fixed speed of rotation. We show that for any $M>0$, axisymmetric initial data of sufficiently small size $\varepsilon$ lead to solutions that exist for a long time at least $\varepsilon^{-M}$ and disperse. This is a manifestation of the stabilizing effect of rotation, regardless of its speed.   To achieve this we develop an anisotropic framework that naturally builds on the available symmetries. This allows for a precise quantification and control of the geometry of nonlinear interactions, while at the same time giving enough information to obtain dispersive decay via adapted linear dispersive estimates.
Let $p$ and $\ell$ be distinct primes, and $\rho$ be an orthogonal or symplectic representation of the absolute Galois group of an $\ell$-adic field over a finite field of characteristic $p$. We define and study a liftable deformation condition of lifts of $\rho$ "ramified no worse than $\rho$", generalizing the minimally ramified deformation condition for $GL_n$ studied in \cite{cht08}. The key insight is to restrict to deformations where an associated unipotent element does not change type when deforming. This requires an understanding of nilpotent orbits and centralizers of nilpotent elements in the relative situation, not just over fields.
The Michelson Doppler Imager (MDI) aboard the Solar and Heliospheric Observatory observed the transits of Mercury on 2003 May 7 and 2006 November 8. Contact times between Mercury and the solar limb have been used since the 17th century to derive the Sun's size but this is the first time that high-quality imagery from space, above the Earth's atmosphere, has been available. Unlike other measurements this technique is largely independent of optical distortion. The true solar radius is still a matter of debate in the literature as measured differences of several tenths of an arcsecond (i.e., about 500 km) are apparent. This is due mainly to systematic errors from different instruments and observers since the claimed uncertainties for a single instrument are typically an order of magnitude smaller. From the MDI transit data we find the solar radius to be 960".12 +/- 0".09 (696,342 +/- 65 km). This value is consistent between the transits and consistent between different MDI focus settings after accounting for systematic effects.
Optical Bloch Equations (OBE) describe the coherent exchange of energy between a quantum bit (qubit) and a quasi-resonant driving field in the presence of a thermal bath. Despite it being an ubiquitous process in quantum technologies, a sound thermodynamic analysis is still missing. We hereby provide such an analysis, by deriving the relevant framework from first principles. Building on a microscopic model of the bath, we first express heat, work and entropy production for the closed qubit-bath system where these definitions are unambiguous. We coarse-grain the obtained expressions, using a methodology similar to the derivation of the dynamical master equation and giving rise to consistent expressions of the First and Second Law. We verify that long coarse graining times yield the Floquet Master Equation and its already known thermodynamic description. Conversely, short coarse-graining times yield the OBE and its consistent thermodynamic framework, whose variables explicitly depend on the quantum coherences in the qubit's energy basis. These quantum signatures in the heat and in the entropy production flows allow us to characterize a genuinely quantum non-equilibrium situation, where the coherences created by the driving field are continuously erased by the bath. Our findings can be readily extended to larger open quantum systems. They carry the seeds for future thermodynamic analyses of quantum gates and the design of quantum engines in the strong coherent driving regime.
We prove some analogues of the central point theorem and Tverberg's theorem, where instead of points, we consider hyperplanes or affine flats of given dimension.
A tight-binding model for eg electrons coupled to Jahn-Teller lattice distortions is studied via unbiased Monte- Carlo simulations. By focusing on the periodicity of the Jahn Teller distortions, and the one-particle spectral function, our results clarify the physical origin of the Fermi-arcs phase observed in layered manganites. In a range of parameters where no broken symmetry phase exists, the nearly nested Fermi surface favors certain correlations between Jahn Teller distortions. The spectral weight near the Brillouin zone edge is suppressed, leading to the pseudogap in the density of states. We discuss the stability of this phase as a function of temperature and coupling strength for different hole dopings.
We consider linear statistics of the scaled zeros of Dirichlet $L$--functions, and show that the first few moments converge to the Gaussian moments. The number of Gaussian moments depends on the particular statistic considered. The same phenomenon is found in Random Matrix Theory, where we consider linear statistics of scaled eigenphases for matrices in the unitary group. In that case the higher moments are no longer Gaussian. We conjecture that this also happens for Dirichlet $L$--functions.
In the last years different studies have revealed the usefulness of a microcanonical analysis of finite systems when dealing with phase transitions. In this approach the quantities of interest are exclusively expressed as derivatives of the entropy $S = \ln \Omega$ where $\Omega$ is the density of states. Obviously, the density of states has to be known with very high accuracy for this kind of analysis. Important progress has been achieved recently in the computation of the density of states of classical systems, as new types of algorithms have been developed. Here we extend one of these methods, originally formulated for systems with discrete degrees of freedom, to systems with continuous degrees of freedoms. As an application we compute the density of states of the three-dimensional XY model and demonstrate that critical quantities can directly be determined from the density of states of finite systems in cases where the degrees of freedom take continuous values.
The mechanism of the evolution of the deformed microstructure at the earliest stage of annealing where the existence of the lowest length scale substructure paves the way to the formation of the so-called subgrains, has been studied for the first time. The study has been performed at high temperature on heavily deformed Ti-modified austenitic stainless steel using X-ray diffraction technique. Significant changes were observed in the values of the domain size, both with time and temperature. Two different types of mechanism have been proposed to be involved during the microstructural evolution at the earliest stages of annealing. The nature of the growth of domains with time at different temperatures has been modelled using these mechanisms. High-resolution transmission electron microscopy has been used to view the microstructure of the deformed and annealed sample and the results have been corroborated successfully with those found from the X-ray diffraction techniques.
Classical ergodicity retains its meaning in the quantum realm when the employed measurement is protective. This unique measuring technique is reexamined in the case of post-selection, giving rise to novel insights studied in the Heisenberg representation. Quantum statistical mechanics is then briefly described in terms of two-state density operators.