ShantanuT01/DACTYL-Pretraining huggingface dataset:
While calculations and measurements of single-particle spectral properties often offer the most direct route to study correlated electron systems, the underlying physics may remain quite elusive, if information at higher particle levels is not explicitly included. Here, we present a comprehensive overview of the different approaches which have been recently developed and applied to identify the dominant two-particle scattering processes controlling the shape of the one-particle spectral functions and, in some cases, of the physical response of the system. In particular, we will discuss the underlying general idea, the common threads and the specific peculiarities of all the proposed approaches. While all of them rely on a selective analysis of the Schwinger-Dyson (or the Bethe-Salpeter) equation, the methodological differences originate from the specific two-particle vertex functions to be computed and decomposed. Finally, we illustrate the potential strength of these methodologies by means of their applications the two-dimensional Hubbard model, and we provide an outlook over the future perspective and developments of this route for understanding the physics of correlated electrons.
We present a one-shot method for preparing pure entangled states between a sender and a receiver at a minimal cost of entanglement and quantum communication. In the case of preparing unentangled states, an earlier paper showed that a 2n-qubit quantum state could be communicated to a receiver by physically transmitting only n+o(n) qubits in addition to consuming n ebits of entanglement and some shared randomness. When the states to be prepared are entangled, we find that there is a reduction in the number of qubits that need to be transmitted, interpolating between no communication at all for maximally entangled states and the earlier two-for-one result of the unentangled case, all without the use of any shared randomness. We also present two applications of our result: a direct proof of the achievability of the optimal superdense coding protocol for entangled states produced by a memoryless source, and a demonstration that the quantum identification capacity of an ebit is two qubits.
We give a short proof of It\^o's formula for stochastic Hilbert-space valued processes in the setting $V\subset H\subset V^{*}$ based on the possibility to lift the stochastic differentials, which are originally in $V^{*}$, into $H$. Using this result we also prove the maximum principle for second-order SPDEs in arbitrary domains.
Forward shocks caused by the interaction between a relativistic blast wave and the circum-burst medium are thought to be responsible for the afterglow emission in Gamma-Ray Bursts (GRBs). We consider the hydrodynamics of a spherical relativistic blast wave expanding into the surrounding medium and we generalize the standard theory in order to account for several effects that are generally ignored. In particular, we consider the role of adiabatic and radiative losses on the hydrodynamical evolution of the shock, under the assumption that the cooling losses are fast. Our model can describe adiabatic, fully radiative and semi-radiative blast waves, and can describe the effects of a time-varying radiative efficiency. The equations we present are valid for arbitrary density profiles, and also for a circum-burst medium enriched with electron-positron pairs. The presence of pairs enhances the fraction of shock energy gained by the leptons, thus increasing the importance of radiative losses. Our model allows to study whether the high-energy (>0.1 GeV) emission in GRBs may originate from afterglow radiation. In particular, it is suitable to test whether the fast decay of the high-energy light curve observed in several Fermi LAT GRBs can be ascribed to an initial radiative phase, followed by the standard adiabatic evolution.
The Numerical INJection Analysis (NINJA) project is a collaborative effort between members of the numerical relativity and gravitational-wave data analysis communities. The purpose of NINJA is to study the sensitivity of existing gravitational-wave search algorithms using numerically generated waveforms and to foster closer collaboration between the numerical relativity and data analysis communities. We describe the results of the first NINJA analysis which focused on gravitational waveforms from binary black hole coalescence. Ten numerical relativity groups contributed numerical data which were used to generate a set of gravitational-wave signals. These signals were injected into a simulated data set, designed to mimic the response of the Initial LIGO and Virgo gravitational-wave detectors. Nine groups analysed this data using search and parameter-estimation pipelines. Matched filter algorithms, un-modelled-burst searches and Bayesian parameter-estimation and model-selection algorithms were applied to the data. We report the efficiency of these search methods in detecting the numerical waveforms and measuring their parameters. We describe preliminary comparisons between the different search methods and suggest improvements for future NINJA analyses.
Massive high-redshift quiescent compact galaxies (nicknamed red nuggets) have been traditionally connected to present-day elliptical galaxies, often overlooking the relationships that they may have with other galaxy types. We use large bulge-disk decomposition catalogues based on the Sloan Digital Sky Survey (SDSS) to check the hypothesis that red nuggets have survived as compact cores embedded inside the haloes or disks of present-day massive galaxies. In this study, we designate a "compact core" as the bulge component that satisfies a prescribed compactness criterion. Photometric and dynamic mass-size and mass-density relations are used to show that, in the inner regions of galaxies at z ~ 0.1, there are "abundant" compact cores matching the peculiar properties of the red nuggets, an abundance comparable to that of red nuggets at z ~ 1.5. Furthermore, the morphology distribution of the present-day galaxies hosting compact cores is used to demonstrate that, in addition to the standard channel connecting red nuggets with elliptical galaxies, a comparable fraction of red nuggets might have ended up embedded in disks. This result generalises the inside-out formation scenario; present-day massive galaxies can begin as dense spheroidal cores (red nuggets), around which either a spheroidal halo or a disk are formed later.
The Legendre transformation method, applied in 1987 to deal with purely metric gravitational Lagrangians with nonlinear dependence on the Ricci tensor, is extended to metric-affine models and is shown to provide a concise and insightful comparison of the dynamical content of the two variational frameworks.
As one of the most violent eruptions on the Sun, flares are believed to be powered by magnetic reconnection. The fundamental physics involving the release, transfer and deposition of energy have been studied extensively. Taking advantage of the unprecedented resolution provided by the 1.6-m Goode Solar Telescope, here we show a sudden rotation of vector magnetic fields, about 12$^{\circ}$-20$^{\circ}$ counterclockwise, associated with a flare. Unlike the permanent changes reported previously, the azimuth-angle change is transient and co-spatial/temporal with H$\alpha$ emission. The measured azimuth angle becomes closer to that in potential fields suggesting untwist of flare loops. The magnetograms were obtained in the near infrared at 1.56~$\mu$m, which is minimally affected by flare emission and no intensity profile change was detected. We believe that these transient changes are real and discuss the possible explanations in which the high energy electron beams or $Alfv\acute{e}n$ waves play a crucial role.
In this paper, we establish two different results. The first result is a characterization theorem saying that if the stationary state probabilities for originally described Markovian discriminatory processor sharing (DPS) system have a closed product geometric form (the exact definition is given in the paper), then the system must only be Egalitarian, i.e. all flows in this system must have equal priorities. The second result is the tail asymptotics for the stationary probabilities. We provide a detailed asymptotic analysis of the system, and obtain the exact asymptotic form of the stationary probabilities in DPS systems when the number of flows in the system is large.
v2: We improved a little bit according to the referee's wishes.   v1: On $X$ projective smooth over a field $k$, Pink and Roessler conjecture that the dimension of the Hodge cohomology of an invertible $n$-torsion sheaf $L$ is the same as the one of its $a$-th power $L^a$ if $a$ is prime to $n$, under the assumptions that $X$ lifts to $W_2(k)$ and $dim X\le p$, if $k$ has characteristic $p>0$. They show this if $k$ has characteristic 0 and if $n$ is prime to $p$ in characteristic $p>0$. We show the conjecture in characteristic $p>0$ if $n=p$ assuming in addition that $X$ is ordinary (in the sense of Bloch-Kato).
We demonstrate tuning of the Fermi contour anisotropy of two-dimensional (2D) holes in a symmetric GaAs (001) quantum well via the application of in-plane strain. The ballistic transport of high-mobility hole carriers allows us to measure the Fermi wavevector of 2D holes via commensurability oscillations as a function of strain. Our results show that a small amount of in-plane strain, on the order of $10^{-4}$, can induce significant Fermi wavevector anisotropy as large as 3.3, equivalent to a mass anisotropy of 11 in a parabolic band. Our method to tune the anisotropy \textit{in situ} provides a platform to study the role of anisotropy on phenomena such as the fractional quantum Hall effect and composite fermions in interacting 2D systems.
We analyze observations of the quadruple lensed quasar Q2237+0305, taken with the WFPC2 camera in the F336W and F300W bands. 25 exposures were performed within 15 hours real time on 3 November 1995. On a timescale of 3--4 hours, we observe no variation in component A of greater than 0.02 mag. The other components are constant over a period of 10 hours to within about 0.05 mag. In the final 5 hours there is some evidence (not conclusive) for variation of component D by about 0.1 mag. Component A was brighter than component B by about 0.3 mag. Components C and D were fainter than component A by about 1.3 and 1.4 mag. Any fifth (central) component was at least 6.5 mag fainter than component A. Using the PC chip, we measure the relative distances of the four components with high accuracy. Our values are systematically larger than other investigators' (by 0.1% to 2.0%). The F336W filter had been chosen for the observations because it could have allowed us to see extended Ly-alpha emission from the Broad-Line Region (BLR). However, the quasar components are consistent with a point source. We conclude that there cannot be a Ly-alpha feature in the image plane brighter than about 23.5 mag in F336W and further from the quasar core than 100 mas. According to a lensing model by Rix, Scheider & Bahcall (1992), this would preclude any such features in the source plane further than 20 mas (~ 100 h^{-1} pc, assuming q_0 = 0.5) from the quasar core and brighter than 25 mag before magnification.
Water masers have been observed in several high redshift active galactic nuclei, including the gravitationally lensed quasar MG 0414+0534. This quasar is lensed into four images, and the water maser is detected in two of them. The broadening of the maser emission line and its velocity offset are consistent with a group of masers associated with a quasar jet. If the maser group is microlensed we can probe its structure and size by observing its microlensing behaviour over time. We present results of a high resolution numerical analysis of microlensing of the maser in MG 0414+0534, using several physically motivated maser models covering a range of sizes and emission profiles. Time-varying spectra of the microlensed maser are generated, displayed, and analysed, and the behaviour of the different models compared. The observed maser line in MG 0414+0534 is consistent with maser spots as in other quasar jets, provided substructure is de-magnified or currently lost in noise; otherwise smooth extended maser models are also candidates to generate the observed spectrum. Using measures of spectral variability we find that if the maser has small substructure of ~ 0.002 pc then a variation of 0.12 mag in flux and 2.0 km/s in velocity centroid of the maser line could be observed within 2 decades. For the smallest maser model in this study a magnification of > 35 is possible 22% of the time, which is of significance in the search for other lensed masers.
We performed spin-polarized scanning tunneling spectroscopy on biatomic-layer-high Co nanoislands grown on Cu(111) in magnetic fields oriented normal to the sample surface, with Fe-coated W tips. Increasing the temperature from 10 to 30 K, we observe a reduced slope of the differential conductance around zero field. A quantitative analysis of the field- and temperature-dependent differential conductance data in the framework of superparamagnetism as described by a Langevin function gives an excellent description of the experimental results. The analysis suggests that a Fe nano-apex at the W tip, which is composed of 220-300 Fe atoms, determines the magnetic response of the tip.
Context. The Kepler mission has recently discovered a brown dwarf companion transiting one member of the M4V+M5V visual binary system LHS 6343 AB with an orbital period of 12.71 days. Aims. The particular interest of this transiting system lies in the synchronicity between the transits of the brown dwarf C component and the main modulation observed in the light curve, which is assumed to be caused by rotating starspots on the A component. We model the activity of this star by deriving maps of the active regions that allow us to study stellar rotation and the possible interaction with the brown dwarf companion. Methods. An average transit profile was derived, and the photometric perturbations due to spots occulted during transits are removed to derive more precise transit parameters. We applied a maximum entropy spot model to fit the out-of-transit optical modulation as observed by Kepler during an uninterrupted interval of 500 days. It assumes that stellar active regions consist of cool spots and bright faculae whose visibility is modulated by stellar rotation. Results. Thanks to the extended photometric time series, we refine the determination of the transit parameters and find evidence of spots that are occulted by the brown dwarf during its transits. The modelling of the out-of-transit light curve of LHS 6343 A reveals several starspots rotating with a slightly longer period than the orbital period of the brown dwarf, i.e., 13.13 +- 0.02 days. No signature attributable to differential rotation is observed. We find evidence of a persistent active longitude on the M dwarf preceding the sub- companion point by 100 deg and lasting for at least 500 days. This can be relevant for understanding how magnetic interaction works in low-mass binary and star-planet systems.
For active galactic nuclei (AGNs) we study the role of the mechanism of quasi-linear diffusion (QLD) in producing the high energy emission in the MeV-GeV domains strongly connected with the submillimeter/infrared radiation. Considering the kinetic equation governing the stationary regime of the QLD we investigate the feedback of the diffusion on electrons. We show that this process leads to the distribution of particles by the pitch angles, implying that the synchrotron mechanism is no longer prevented by energy losses. Examining a reasonable interval of physical parameters, we show that it is possible to produce MeV-GeV gamma-rays, strongly correlated with submillimeter/infrared bands.
We present a follow-up analysis examining the dynamics and structures of 41 massive, large star-forming galaxies at z~0.67-2.45 using both ionized and molecular gas kinematics. We fit the galaxy dynamics with models consisting of a bulge, a thick, turbulent disk, and a NFW dark matter halo, using code that fully forward models the kinematics, including all observational and instrumental effects. We explore the parameter space using Markov Chain Monte Carlo (MCMC) sampling, including priors based on stellar and gas masses and disk sizes. We fit the full sample using extracted 1D kinematic profiles. For a subset of 14 well-resolved galaxies, we also fit the 2D kinematics. The MCMC approach robustly confirms the results from least-squares fitting presented in Paper I (Genzel et al. 2020): the sample galaxies tend to be baryon-rich on galactic scales (within one effective radius). The 1D and 2D MCMC results are also in good agreement for the subset, demonstrating that much of the galaxy dynamical information is captured along the major axis. The 2D kinematics are more affected by the presence of non-circular motions, which we illustrate by constructing a toy model with constant inflow for one galaxy that exhibits residual signatures consistent with radial motions. This analysis, together with results from Paper I and other studies, strengthens the finding that massive, star-forming galaxies at z~1-2 are baryon-dominated on galactic scales, with lower dark matter fractions towards higher baryonic surface densities. Finally, we present details of the kinematic fitting code used in this analysis.
Based on a canonical approach and functional-integration techniques, a series expansion of Green's function of a scalar field, in the presence of a medium, is obtained. A series expansion for Lifshitz-energy, in finite-temperature, in terms of the susceptibility of the medium is derived and the whole formalism is generalized to the case of electromagnetic field in the presence of some dielectrics. A covariant formulation of the problem is presented.
We Show that pair hopping through a Kondo singlet give rise to a negative Josephson coupling. Thus, our calculation supports the existance of staggered pair correlations in the strong coupling limit of a one dimensional Kondo lattice.
In the gift exchange game there are n players and n wrapped gifts. When a player's number is called, that person can either choose one of the remaining wrapped gifts, or can "steal" a gift from someone who has already unwrapped it, subject to the restriction that no gift can be stolen more than a total of sigma times. The problem is to determine the number of ways that the game can be played out, for given values of sigma and n. Formulas and asymptotic expansions are given for these numbers. This work was inspired in part by a 2005 remark by Robert A. Proctor in the On-Line Encyclopedia of Integer Sequences.
In this paper we consider two natural notions of connectivity for hypergraphs: weak and strong. We prove that the strong vertex connectivity of a connected hypergraph is bounded by its weak edge connectivity, thereby extending a theorem of Whitney from graphs to hypergraphs. We find that while determining a minimum weak vertex cut can be done in polynomial time and is equivalent to finding a minimum vertex cut in the 2-section of the hypergraph in question, determining a minimum strong vertex cut is NP-hard for general hypergraphs. Moreover, the problem of finding minimum strong vertex cuts remains NP-hard when restricted to hypergraphs with maximum edge size at most 3. We also discuss the relationship between strong vertex connectivity and the minimum transversal problem for hypergraphs, showing that there are classes of hypergraphs for which one of the problems is NP-hard while the other can be solved in polynomial time.
Stochastic motion of particles in a highly unstable potential generates a number of diverging trajectories leading to undefined statistical moments of the particle position. This makes experiments challenging and breaks down a standard statistical analysis of unstable mechanical processes and their applications. A newly proposed approach takes advantage of the local characteristics of the most probable particle motion instead of the divergent averages. We experimentally verify its theoretical predictions for a Brownian particle moving near an inflection in a highly unstable cubic optical potential. The most-likely position of the particle atypically shifts against the force despite the trajectories diverge in the opposite direction. The local uncertainty around the most-likely position saturates even for strong diffusion and enables well-resolved position detection. Remarkably, the measured particle distribution quickly converges to the quasi-stationary one with the same atypical shift for different initial particle positions. The demonstrated experimental confirmation of the theoretical predictions approves the utility of local characteristics for highly unstable systems which can be exploited in thermodynamic processes to uncover energetics of unstable systems.
We present broadband X-ray spectral study of two ultraluminous X-ray sources (ULXs), M81 X-6 and Holmberg IX X-1 based on Suzaku & XMM-Newton observations. We perform joint broadband spectral analysis of the brightest sources in the field, i.e. the two ULXs and the active galactic nucleus (AGN) in M81, and demonstrate that the X-ray spectra of the ULXs cut off at energies more than about 3keV with negligible contribution at high energies in the Suzaku HXD/PIN band. The 90% upper limit on the 10-30keV band luminosity of an underlying broadband power-law component is 3.5e38 ergs/s for M81 X-6 and 1.2e39ergs/s for Holmberg IX X-1. These limits are more than an order of magnitude lower than the bolometric (0.1-30 keV) luminosity of 6.8e39ergs/s for M81 X-6 and 1.9e40 ergs/s for Holmberg IX X-1. Our results confirm earlier indications of spectral cut-offs inferred from the XMM-Newton observations of bright ULXs and show that there isn't an additional high energy power-law component contributing significantly to the X-ray emission. The spectral form of the two ULXs are very different from those of Galactic black hole X-ray binaries (BHBs) or AGNs. This implies that the ULXs are neither simply scaled-up versions of stellar mass BHBs or scaled-down versions of AGNs.
A closed virial equation-of-state for the low density fluid phase of hard disks is obtained from the known virial coefficients. The equation exhibits 6-figure accuracy for the thermodynamic (MD) pressure up to the reduced number density ~ 0.4 Interpolation of the discrepancy at higher densities indicates a higher-order thermodynamic phase transition at the extensive-intensive free-volume percolation transition previously located by Hoover et al. (JCP 70 1837 1979)