ShantanuT01/DACTYL-Pretraining huggingface dataset:
We investigate the effects of long-ranged Coulomb interactions in a tilted Dirac semimetal in two dimensions by using the perturbative renormalization-group method. Depending on the magnitude of the tilting parameter, the undoped system can have either Fermi points (type-I) or Fermi lines (type-II). Previous studies usually performed the renormalization-group transformations by integrating out the modes with large momenta. This is problematic when the Fermi surface is open, like type-II Dirac fermions. In this work, we study the effects of Coulomb interactions, following the spirit of Shankar\cite{Shankar}, by introducing a cutoff in the energy scale around the Fermi surface and integrating out the high-energy modes. For type-I Dirac fermions, our result is consistent with that of the previous work. On the other hand, we find that for type-II Dirac fermions, the magnitude of the tilting parameter increases monotonically with lowering energies. This implies the stability of type-II Dirac fermions in the presence of Coulomb interactions, in contrast with previous results. Furthermore, for type-II Dirac fermions, the velocities in different directions acquire different renormalization even if they have the same bare values. By taking into account the renormalization of the tilting parameter and the velocities due to the Coulomb interactions, we show that while the presence of a charged impurity leads only to charge redistribution around the impurity for type-I Dirac fermions, for type-II Dirac fermions, the impurity charge is completely screened, albeit with a very long screening length. The latter indicates that the temperature dependence of physical observables are essentially determined by the RG equations we derived. We illustrate this by calculating the temperature dependence of the compressibility and specific heat of the interacting tilted Dirac fermions.
The antiferrodistortive (AFD) structural transitions of calcium titanate (CaTiO3) at ambient pressure have been extensively studied during the last few years. It is found none of the AFD polymorphs is polar or ferroelectric. However, it was recently shown theoretically and later experimentally confirmed that a ferroelectric transition in CaTiO3 can be induced by tensile strains. The ferroelectric instability is believed to be strongly coupled to the AFD soft modes. In this article, we present a complete thermodynamic potential for describing the coupling between the AFD and ferroelectric phase transitions. We analyzed the dependence of transition temperatures on stress and strain condition. Based on this potential, a (001) CaTiO3 thin film diagram was constructed. The results show good agreement with available experimental observations. The strong suppression of ferroelectric transition by the AFD transition is discussed.
This paper is an extended version of a talk at the conference Constrained Dynamics and Quantum Gravity QG99. It reviews some work on the quantum collapse of the spherically symmetric gravitating thin shell of zero rest mass. Recent results on Kucha\v{r} decomposition are applied. The constructed version of quantum mechanics is unitary, although the shell falls under its Schwarzschild radius if its energy is high enough. Rather that a permanent black hole, something like a transient black and white hole pair seems to be created in such a case.
We show that the previously predicted Fermion particle that has no analogue in the standard model of particle theory - the cubically dispersed Dirac semimetal (CDSM) - is realized in a specific, stable solid state system that has been made years ago, but was not appreciated to host such a unique Fermion, composed of six Weyl Fermions, 3 with left-handed and 3 with right-handed chirality. We identified the crystal symmetry constraints and found the space group P63/m as one of the two that can support a CDSM, of which the characteristic band crossing has linear dispersion along the principle axis but cubic dispersion in the plane perpendicular to it. We then conducted a material search using density functional theory identifying a group of quasi-one-dimensional molybdenum mono-chalcogenide compounds A(MoX)3 (A = Na, K, Rb, In, Tl, X = S, Se, Te) as ideal CDSM candidates. Studying the stability of the A(MoX)3 family reveals a few candidates such as Rb(MoTe)3 and Tl(MoTe)3 that are predicted to be resilient to Peierls distortion, thus retaining the metallic character. The combination of one-dimensionality and metallic nature in this family provides a platform for unusual optical signature - polarization dependent metallic vs insulating response.
How to uses shared entanglement and forward classical communication to remotely prepare an arbitrary (mixed or pure) state has been fascinating quantum information scientists. A constructive scheme has been given by Berry for remotely preparing a general pure state with a pure entangled state and finite classical communication. Based on this scheme, for high-dimensional systems it is possible to use a coding of the target state to optimize the classical communication cost. Unfortunately, for low-dimensional systems such as a pure qubit the coding method is inapplicable. Because qubit plays a central role in quantum information theory, we propose an optimization procedure which can be used to minimize the classical communication cost in the remote preparation of a general pure qubit. Interestingly, our optimization procedure is linked to the uniform arrangement of $N$ points on the Bloch sphere, which provides a geometric description.
Refer to the literature of lung nodule classification, many studies adopt Convolutional Neural Networks (CNN) to directly predict the malignancy of lung nodules with original thoracic Computed Tomography (CT) and nodule location. However, these studies cannot tell how the CNN works in terms of predicting the malignancy of the given nodule, e.g., it's hard to conclude that whether the region within the nodule or the contextual information matters according to the output of the CNN. In this paper, we propose an interpretable and multi-task learning CNN -- Joint learning for \textbf{P}ulmonary \textbf{N}odule \textbf{S}egmentation \textbf{A}ttributes and \textbf{M}alignancy \textbf{P}rediction (PN-SAMP). It is able to not only accurately predict the malignancy of lung nodules, but also provide semantic high-level attributes as well as the areas of detected nodules. Moreover, the combination of nodule segmentation, attributes and malignancy prediction is helpful to improve the performance of each single task. In addition, inspired by the fact that radiologists often change window widths and window centers to help to make decision on uncertain nodules, PN-SAMP mixes multiple WW/WC together to gain information for the raw CT input images. To verify the effectiveness of the proposed method, the evaluation is implemented on the public LIDC-IDRI dataset, which is one of the largest dataset for lung nodule malignancy prediction. Experiments indicate that the proposed PN-SAMP achieves significant improvement with respect to lung nodule classification, and promising performance on lung nodule segmentation and attribute learning, compared with the-state-of-the-art methods.
The Letter is analyzing bulk spin (moment) currents and spin (moment) accumulation at edges of a 2D topological insulator taking into account reflection from edges. Accumulation occurs only at edge states, which distinguish topological insulators from conventional ones. The band continuum can support the transverse bulk spin (moment) current, but it does not governed by the topological Chern number and may exist in a conventional insulator. There is no edge accumulation related with bulk currents.
Two inequalities concerning the symmetry of the zeta-function and the Ramanujan $\tau$-function are improved through the use of some elementary considerations.
We study the binary fraction of the globular cluster M10 (NGC 6254) as a function of radius from the cluster core to the outskirts, by means of a quan- titative analysis of the color distribution of stars relative to the fiducial main sequence. By taking advantage of two data-sets, acquired with the Advanced Camera for Survey and the Wide Field Planetary Camera 2 on board the Hubble Space Telescope, we have studied both the core and the external regions of the cluster. The binary fraction is found to decrease from 14% within the core, to 1.5% in a region between 1 and 2 half-mass radii from the cluster centre. Such a trend and the derived values are in agreement with previous results ob- tained in clusters of comparable total magnitude. The estimated binary fraction is sufficient to account for the suppression of mass segregation observed in M10, without any need to invoke the presence of an intermediate-mass black hole in its centre.
The total luminosity of satellite galaxies around a central galaxy, L$_{sat}$, is a powerful metric for probing dark matter halos. In this paper we use data from the Sloan Digital Sky Survey and DESI Legacy Imaging Surveys to explore the relationship between L$_{sat}$ and various observable galaxy properties for a sample of 117,966 central galaxies out to $z = 0.15$. At fixed stellar mass, every galaxy property we explore shows a correlation with L$_{sat}$. This implies that dark matter halos play a possibly significant role in determining these secondary galaxy properties. We quantify these correlations by computing the mutual information between L$_{sat}$ and secondary properties and explore how this mutual information varies as a function of stellar mass and when separating the sample into star-forming and quiescent central galaxies. We find that absolute r-band magnitude correlates more strongly with L$_{sat}$ than stellar mass across all galaxy populations; and that effective radius, velocity dispersion, and S\'ersic index do so as well for star-forming and quiescent galaxies. L$_{sat}$ is sensitive to both the mass of the host halo as well as the halo formation history, with younger halos having higher L$_{sat}$. L$_{sat}$ by itself cannot distinguish between these two effects, but measurements of galaxy large-scale environment can break this degeneracy. For star-forming central galaxies, we find that r$_{\rm eff}$, $\sigma_v$, and S\'ersic index all correlate with large-scale density, implying that these halo age plays a role in determining these properties. For quiescent galaxies, we find that all secondary properties are independent of environment, implying that correlations with L$_{sat}$ are driven only by halo mass. These results are a significant step forward in quantifying the full extent of the galaxy-halo connection, and present a new test of galaxy formation models.
We present UBVI surface photometry for 20.'5 X 20.'5 area of a late-type spiral galaxy NGC 300. In order to understand the morphological properties and luminosity distribution characteristics of NGC 300, we have derived isophotal maps, surface brightness profiles, ellipticity profiles, position angle profiles, and color profiles. By merging the I-band data of our surface brightness measurements with those of Boeker et al. (2002) based on Hubble Space Telescope observations, we have made combined I-band surface brightness profiles for the region of 0."02 < r < 500" and decomposed the profiles into three components: a nucleus, a bulge, and an exponential disk.
By two different methods, we show that LHS 4033 is an extremely massive white dwarf near its likely upper mass limit for destruction by unstable electron captures. From the accurate trigonometric parallax reported herein, the effective temperature (T=10,900 K) and the stellar radius (R=0.00368 R_sun) are directly determined from the broad-band spectral energy distribution -- the parallax method. The effective temperature and surface gravity are also estimated independently from the simultaneous fitting of the observed Balmer line profiles with those predicted from pure-hydrogen model atmospheres -- the spectroscopic method (T=10,760 K, log g=9.46). The mass of LHS 4033 is then inferred from theoretical mass-radius relations appropriate for white dwarfs. The parallax method yields a mass estimate of 1.310--1.330 M_sun, for interior compositions ranging from pure magnesium to pure carbon, respectively, while the spectroscopic method yields an estimate of 1.318--1.335 M_sun for the same core compositions. This star is the most massive white dwarf for which a robust comparison of the two techniques has been made.
It is von Neumann who opened the window for today's Information epoch. He defined quantum entropy including Shannon's information more than 20 years ahead of Shannon, and he introduced a concept what computation means mathematically. In this paper I will report two works that we have recently done, one of which is on quantum algorithum in generalized sense solving the SAT problem (one of NP complete problems) and another is on quantum mutual entropy properly describing quantum communication processes.
Let $x_1,\ldots,x_n$ be a fixed sequence of real numbers. At each stage, pick two indices $I$ and $J$ uniformly at random and replace $x_I$, $x_J$ by $(x_I+x_J)/2$, $(x_I+x_J)/2$. Clearly all the coordinates converge to $(x_1+\cdots+x_n)/n$. We determine the rate of convergence, establishing a sharp "cutoff" transition, answering a question of Jean Bourgain.
Transport coefficients are obtained by incorporating a gauge principle into thermo field dynamics of inhomogeneous systems. In contrast to previous derivations, neither imaginary time arguments nor perturbation theory in powers of a coupling constant are used in the calculation. Numerical values are calculated for the pion component in hot nuclear matter.
Given a function field $K$ and $\phi \in K[x]$, we study two finiteness questions related to iteration of $\phi$: whether all but finitely many terms of an orbit of $\phi$ must possess a primitive prime divisor, and whether the Galois groups of iterates of $\phi$ must have finite index in their natural overgroup $\text{Aut}(T_d)$, where $T_d$ is the infinite tree of iterated preimages of $0$ under $\phi$. We focus particularly on the case where $K$ has characteristic $p$, where far less is known. We resolve the first question in the affirmative under relatively weak hypotheses; interestingly, the main step in our proof is to rule out "Riccati differential equations" in backwards orbits. We then apply our result on primitive prime divisors and adapt a method of Looper to produce a family of polynomials for which the second question has an affirmative answer; these are the first non-isotrivial examples of such polynomials. We also prove that almost all quadratic polynomials over $\mathbb{Q}(t)$ have iterates whose Galois group is all of $\text{Aut}(T_d)$.
Three types of reciprocity laws for arithmetic surfaces are established. For these around a point or along a vertical curve, we first construct $K_2$ type central extensions, then introduce reciprocity symbols, and finally prove the law as an application of Parshin-Beilinson's theory of adelic complex. For reciprocity law along a horizontal curve, we first introduce a new type of arithmetic central extensions, then apply our arithmetic adelic cohomology theory and arithmetic intersection theory to prove the related reciprocity law.   All this can be interpreted within the framework of arithmetic central extensions. We add an appendix to deal with some basic structures of such extensions.
We investigate the role of dust in star formation activity of extremely metal-poor blue compact dwarf galaxies (BCDs). Observations suggest that star formation in BCDs occurs in two different regimes: "active" and "passive". The "active" BCDs host super star clusters (SSCs), and are characterised by compact size, rich H2 content, large dust optical depth, and high dust temperature; the "passive" BCDs are more diffuse with cooler dust, and lack SSCs and large amounts of H2. By treating physical processes concerning formation of stars and dust, we are able to simultaneously reproduce all the above properties of both modes of star formation (active and passive). We find that the difference between the two regimes can be understood through the variation of the "compactness" of the star-forming region: an "active" mode emerges if the region is compact (with radius $\la 50$ pc) and dense (with gas number density $\ga 500$ cm$^{-3}$). The dust, supplied from Type II supernovae in a compact star-forming region, effectively reprocesses the heating photons into the infrared and induces a rapid H2 formation over a period of several Myr. This explains the high infrared luminosity, high dust temperature, and large H2 content of active BCDs. Moreover, the gas in "active" galaxies cools ($\la 300$ K) on a few dynamical timescales, producing a "run-away" star formation episode because of the favourable (cool) conditions. The mild extinction and relatively low molecular content of passive BCDs can also be explained by the same model if we assume a diffuse region (with radius $\ga 100$ pc and gas number density $\la 100$ cm$^{-3}$). We finally discuss primordial star formation in high-redshift galaxies in the context of the "active" and "passive" star formation scenario.
We study the spectral structure of the complex linearized operator for a class of nonlinear Schr\"odinger systems, obtaining as byproduct some interesting properties of non-degenerate ground state of the associated elliptic system, such as being isolated and orbitally stable.
The transresistance and the Hall transresistance of dirty two-dimensional bi-layer systems in the presence of tunneling bridges (pinholes) are studied theoretically. We find, at weak magnetic field, a non-zero Hall transresistance. In a geometry where the pinholes are concentrated in the middle of the sample, a quantum process gives the dominant contribution to both the ordinary transresistance and the Hall transresistance. Arising from the interplay between Coulomb repulsion, disorder and tunneling, the quantum contribution increases in a singular way as the temperature decreases.
Quantum spin liquid is an elusive state that display strong many-body entanglement with potential applications in future quantum computing. This study reports muon spin relaxation ($\mu^+$SR) measurements on a novel high-pressure synthesized material, the Hollandite K$_{2}$V$_8$O$_{16}$. In this quasi-one-dimensional compound, charge ordering (CO) at $T_{\rm MIT}\approx160$~K effectively isolates half of the vanadium chains and model-like Heisenberg spin-1/2 chains are realized. Our zero field $\mu^+$SR measurements show exponential like relaxation down to the lowest temperature $T=100$~mK and the absence of long range ordering is confirmed. The relaxation rate is found to be temperature independent below $T_{\rm QSL}\approx2$~K and measurements in longitudinal field confirms a highly dynamic ground state. These results represents the first confirmation of quantum spin liquid (QSL) behavior within the Hollandite family, stabilized by the CO. Finally, the presence of strong local electron correlation and one dimensional Fermi surface suggest this QSL to be a gapless Tomonaga-Luttinger liquid (TLL), which here uniquely presents itself in a stoichiometric compound under zero applied magnetic field and at ambient pressure.
This is a draft of a monograph to appear in the Springer series "Encyclopaedia of Mathematical Sciences", subseries "Invariant Theory and Algebraic Transformation Groups". The subject is homogeneous spaces of algebraic groups and their equivariant embeddings. The style of exposition is intermediate between survey and detailed monograph: some results are supplied with detailed proofs, while the other are cited without proofs but with references to the original papers.   The content is briefly as follows. Starting with basic properties of algebraic homogeneous spaces and related objects, such as induced representations, we focus the attention on homogeneous spaces of reductive groups and introduce two important invariants, called complexity and rank. For the embedding theory it is important that homogeneous spaces of small complexity admit a transparent combinatorial description of their equivariant embeddings. We consider the Luna-Vust theory of equivariant embeddings, paying special attention to the case of complexity not greater than one. A special chapter is devoted to spherical varieties (= embeddings of homogeneous spaces of complexity zero), due to their particular importance and ubiquity. A relation between equivariant embedding theory and equivariant symplectic geometry is also discussed. The book contains several classification results (homogeneous spaces of small complexity, etc).   The text presented here is not in a final form, and the author will be very grateful to any interested reader for his comments and/or remarks, which may be sent to the author by email.
Simulations of the magnetorotational instability (MRI) in 'unstratified' shearing boxes exhibit powerful coherent flows, whereby the fluid vertically splits into countermoving planar jets or `channels'. Channel flows correspond to certain axisymmetric linear MRI modes, and their preponderance follows from the remarkable fact that they are approximate nonlinear solutions of the MHD equations in the limit of weak magnetic fields. We show in this paper, analytically and with one-dimensional numerical simulations, that this property is also shared by certain axisymmetric MRI modes in vertically-stratified shearing boxes. These channel flows rapidly capture significant amounts of magnetic and kinetic energy, and thus are vulnerable to secondary shear instabilities. We examine these parasites in the vertically stratified context, and estimate the maximum amplitudes that channels attain before they are destroyed. These estimates suggest that a dominant channel flow will usually drive the disk's magnetic field to thermal strengths. The prominence of these flows and their destruction place enormous demands on simulations, but channels in their initial stages also offer a useful check on numerical codes. These benchmarks are especially valuable given the increasing interest in the saturation of the stratified MRI. Lastly we speculate on the potential connection between 'run-away' channel flows and outburst behaviour in protostellar and dwarf nova disks.
During its performance verification phase, the soft X-ray instrument eROSITA aboard the Spektrum-Roentgen-Gamma(SRG) spacecraft observed large regions in the Magellanic Clouds, where almost 40 known high-mass X-ray binaries (HMXBs, including candidates) are located. We looked for new HMXBs in the eROSITA data, searched for pulsations in HMXB candidates and investigated the long-term behaviour of the full sample using archival X-ray and optical data. For sources sufficiently bright, a detailed spectral and temporal analysis of their eROSITA data was performed. A source detection analysis of the eROSITA images in different energy bands provided count rates and upper limits for the remaining sources. We report the discovery of a new Be/X-ray binary in the Large Magellanic Cloud. The transient SRGEt J052829.5-690345 was detected with a 0.2-8.0 keV luminosity of ~10^35 erg/s and exhibits a hard X-ray spectrum, typical for this class of HMXBs. The OGLE I-band light curve of the V~15.7 mag counterpart shows large variations by up to 0.75 mag, which occur quasi periodically with ~511 days. The eROSITA observations of the Small Magellanic Cloud covered 16 Be/X-ray binary pulsars, five of them were bright enough to accurately determine their current pulse period. The pulse periods for SXP 726 and SXP 1323 measured from eROSITA data are ~800 s and ~1006 s, respectively, far away from their discovery periods. Including archival XMM-Newton observations we update the spin-period history of the two long-period pulsars which show nearly linear trends in their period evolution since more than 15 years. The corresponding average spin-down rate for SXP 726 is 4.3 s/yr while SXP 1323 shows spin-up with a rate of -23.2 s/yr. We discuss the spin evolution of the two pulsars in the framework of quasi-spherical accretion.