ShantanuT01/DACTYL-Pretraining huggingface dataset:
Elastic scattering of pions from finite nuclei is investigated utilizing a contemporary, momentum--space first--order optical potential combined with microscopic estimates of second--order corrections. The calculation of the first--order potential includes:\ \ (1)~full Fermi--averaging integration including both the delta propagation and the intrinsic nonlocalities in the $\pi$-$N$ amplitude, (2)~fully covariant kinematics, (3)~use of invariant amplitudes which do not contain kinematic singularities, and (4)~a finite--range off--shell pion--nucleon model which contains the nucleon pole term. The effect of the delta--nucleus interaction is included via the mean spectral--energy approximation. It is demonstrated that this produces a convergent perturbation theory in which the Pauli corrections (here treated as a second--order term) cancel remarkably against the pion true absorption terms. Parameter--free results, including the delta--nucleus shell--model potential, Pauli corrections, pion true absorption, and short--range correlations are presented. (2 figures available from authors)
GRB 090417B was an unusually long burst with a T_90 duration of at least 2130 s and a multi-peaked light curve at energies of 15-150 keV. It was optically dark and has been associated with a bright star-forming galaxy at a redshift of 0.345 that is broadly similar to the Milky Way. This is one of the few cases where a host galaxy has been clearly identified for a dark gamma-ray burst and thus an ideal candidate for studying the origin of dark bursts. We find that the dark nature of GRB 090417B cannot be explained by high redshift, incomplete observations, or unusual physics in the production of the afterglow. Assuming the standard relativistic fireball model for the afterglow we find that the optical flux is at least 2.5 mag fainter than predicted by the X-ray flux. The Swift/XRT X -ray data are consistent with the afterglow being obscured by a dense, localized sheet of dust approximately 30-80 pc from the burst along the line of sight. Our results suggest that this dust sheet imparts an extinction of A_V >~ 12 mag, which is sufficient to explain the missing optical flux. GRB 090417B is an example of a gamma-ray burst that is dark due to the localized dust structure in its host galaxy.
The entanglement entropy of two gapless non-interacting fermion subsystems is computed approximately in a way that avoids the introduction of replicas and a geometric interpretation of the reduced density matrix. We exploit the similarity between the Schmidt basis wavefunction and superfluid BCS wavefunction and compute the entropy using the BCS approximation. Within this analogy, the Cooper pairs are particle-hole pairs straddling the boundary and the effective interaction between them is induced by the projection of the Hilbert space onto the incomplete Schmidt basis. The resulting singular interaction may be thought of as "lifting" the degeneracy of the single particle distribution function. For two coupled fermion systems of linear size $L$, we solve the BCS gap equation approximately to find the entropy $S \approx (w^2/t^2)\log{L}$ where $w$ is the hopping amplitude at the boundary of the subsystem and $2t$ is the bandwidth. We further interpret this result based upon the relationship between entanglement spectrum, entropy and number fluctuations.
We present a detailed study of the field-dependent specific heat of the bimetallic ferromagnetically coupled chain compound MnNi(NO$_2$)$_4$(en)$_2$, en = ethylenediamine. For this material, which in zero field orders antiferromagnetically below $T_N=2.45$ K, small fields suppress magnetic order. Instead, in such fields a double-peak like structure in the temperature dependence of the specific heat is observed. We attribute this behavior to the existence of an acoustic and an optical mode in the spin wave dispersion as result of the existence of two different spins per unit cell. We compare our experimental data to numerical results for the specific heat obtained by exact diagonalization and Quantum-Monte-Carlo simulations for the alternating spin chain model, using parameters that have been derived from the high-temperature behavior of the magnetic susceptibility. The interchain coupling is included in the numerical treatment at the mean-field level. We observe remarkable agreement between experiment and theory, including the ordering transition, using previously determined parameters. Furthermore, the observed strong effect of an applied magnetic field on the ordered state of MnNi(NO$_2$)$_4$(en)$_2$ promises interesting magnetocaloric properties.
We establish a smoothed asymptotic formula for the third moment of quadratic {D}irichlet $L$-functions at the central value. In addition to the main term, which is known, we prove the existence of a secondary term of size $x^{\frac{3}{4}}$. The error term in the asymptotic formula is on the order of $O(x^{\frac{2}{3}+\delta})$ for every $\delta > 0.$
We study the asymptotic behavior of solutions to a monostable integro-differential Fisher-KPP equation , that is where the standard Laplacian is replaced by a convolution term, when the dispersal kernel is fat-tailed. We focus on two different regimes. Firstly, we study the long time/long range scaling limit by introducing a relevant rescaling in space and time and prove a sharp bound on the (super-linear) spreading rate in the Hamilton-Jacobi sense by means of sub-and super-solutions. Secondly, we investigate a long time/small mutation regime for which, after identifying a relevant rescaling for the size of mutations, we derive a Hamilton-Jacobi limit.
NGC604 is the largest HII-region in M33, second only within the Local Group to 30 Dor, and is important as a laboratory for understanding how massive young stellar clusters interact with the surrounding interstellar medium. Here, we present deep (300ks) X-ray imagery of NGC604 obtained as part of the Chandra ACIS Survey of M33 (ChASeM33), which show highly structured X-ray emission covering ~70% of the full Halpha extent of NGC604. The main bubbles and cavities in NGC604 are filled with hot (kT=0.5keV) X-ray emitting gas and X-ray spectra extracted from these regions indicate that the gas is thermal. For the western part of NGC604 we derive an X-ray gas mass of ~4300M_sol and an unabsorbed (0.35-2.5keV) X-ray luminosity of L_X = 9.3E35 erg/s. These values are onsistent with a stellar mass loss bubble entirely powered by about 200 OB-stars. This result is remarkable because the standard bubble model tends to underpredict the luminosity of X-ray bright bubbles and usually requires additional heating from SNRs. Given a cluster age of ~3Myr it is likely that the massive stars have not yet evolved into SNe. We detect two discrete spots of enhanced and harder X-ray emission, which we consider to be fingerprints from a reverse shock produced by a supersonic wind after it collided with the shell wall. In the eastern part of NGC604 the X-ray gas mass amounts to ~1750M_sol. However, mass loss from young stars cannot account for the unabsorbed X-ray luminosity of L_X = 4.8E35 erg/s. Off-center SNRs could produce the additional luminosity. The bubbles in the east seem to be much older and were most likely formed and powered by stars and SNe in the past.
With motivation from K. D\c{e}bicki and P. Kisowski (2007), in this paper we derive the exact tail asymptotics of $\alpha(t)$-locally stationary Gaussian processes with non-constant variance functions. We show that some certain variance functions lead to qualitatively new results.
We study theoretically the full distribution of transferred charge in a tunnel junction (or quantum point contact) coupled to a nanomechanical oscillator, as well as the conditional evolution of the oscillator. Even if the oscillator is very weakly coupled to the tunnel junction, it can strongly affect the tunneling statistics and lead to a highly non-Gaussian distribution. Conversely, given a particular measurement history of the current, the oscillator energy distribution may be localized and highly non-thermal. We also discuss non-Gaussian correlations between the oscillator motion and tunneling electrons; these show that the tunneling back-action cannot be fully described as an effective thermal bath coupled to the oscillator.
It is widely accepted that the large obliquity of Uranus is the result of a great tangential collision (GC) with an Earth size proto-planet at the end of the accretion. We attempt to constraint the GC scenario as the cause of Uranus' obliquity as well as on the mechanisms able to give origin to the Uranian irregulars. Different capture mechanisms for irregulars operate at different stages on the giant planets formation process. The mechanisms able to capture the uranian irregulars before and after the GC are analysed. Assuming that they were captured before the GC, we calculate the orbital transfer of the nine irregulars by the impulse imparted by the GC. If their orbital transfer results dynamically implausible, they should have originated after the GC. We investigate and discuss the dissipative mechanisms able to operate later. In particular Prospero could not exist at the time of the GC. Different capture mechanisms for Prospero after the GC are investigated. Gas drag by Uranus'envelope and pull-down capture are not plausible mechanisms. Capture of Prospero through a collisionless interaction seems to be difficult. The GC itself provides a mechanism of permanent capture. However, the capture of Prospero by the GC is a low probable event. Catastrophic collisions could be a possible mechanism for the birth of Prospero and the other irregulars after the GC. Orbital and physical clusterings should then be expected. Either Prospero had to originate after the GC or the GC did not occur. In the former case, the mechanism for the origin of Prospero after the GC remains an open question. In the latter case, another theory to account for Uranus' obliquity and the formation of the Uranian regular satellites on the equatorial plane of the planet would be needed.
We report HST NICMOS observations of the central region of NGC 5128 at 2.2mic and in Paschen Alpha (PA). The continuum images show extended emission typical of an elliptical galaxy and a strong unresolved central source we identify as the nucleus of the galaxy. Its position is consistent with ground-based IR and radio data, and with the peak of reddening found with WF/PC-1. In PA, we detect a prominent elongated structure, centered on the nucleus, extended by ~2" at a position angle of 33deg, and with a major to minor axis ratio of ~2. We interpret this as an inclined, ~40 parsec diameter, thin nuclear disk of ionized gas rather than a jet-gas cloud interaction. We do see several weaker PA features, some of which may be circumnuclear gas clouds shocked by the X-ray/radio jet. The disk is one of the smallest ever observed at the nucleus of an AGN. It is not perpendicular to the jet, but consistent with being oriented along the major axis of the bulge. If it represents the warped outer portion of an accretion disk around a black hole, we conclude that even on the scale of a few parsecs, the disk is dominated by the galaxy gravitational potential and not directly related to the symmetry axis of the AGN.
The two-fermion relativistic wave equations of Constraint Theory are reduced, after expressing the components of the $4\times 4$ matrix wave function in terms of one of the $2\times 2$ components, to a single equation of the Pauli-Schr\"odinger type, valid for all sectors of quantum numbers. The potentials that are present belong to the general classes of scalar, pseudoscalar and vector interactions and are calculable in perturbation theory from Feynman diagrams. In the limit when one of the masses becomes infinite, the equation reduces to the two-component form of the one-particle Dirac equation with external static potentials. The Hamiltonian, to order $1/c^2$, reproduces most of the known theoretical results obtained by other methods. The gauge invariance of the wave equation is checked, to that order, in the case of QED. The role of the c.m. energy dependence of the relativistic interquark confining potential is emphasized and the structure of the Hamiltonian, to order $1/c^2$, corresponding to confining scalar potentials, is displayed.
Although the leading-order scaling of entanglement entropy is non-universal at a quantum critical point (QCP), sub-leading scaling can contain universal behaviour. Such universal quantities are commonly studied in non-interacting field theories, however it typically requires numerical calculation to access them in interacting theories. In this paper, we use large-scale T=0 quantum Monte Carlo simulations to examine in detail the second R\'enyi entropy of entangled regions at the QCP in the transverse-field Ising model in 2+1 space-time dimensions -- a fixed point for which there is no exact result for the scaling of entanglement entropy. We calculate a universal coefficient of a vertex-induced logarithmic scaling for a polygonal entangled subregion, and compare the result to interacting and non-interacting theories. We also examine the shape-dependence of the R\'enyi entropy for finite-size toroidal lattices divided into two entangled cylinders by smooth boundaries. Remarkably, we find that the dependence on cylinder length follows a shape-dependent function calculated previously by Stephan {\it et al.} [New J. Phys., 15, 015004, (2013)] at the QCP corresponding to the 2+1 dimensional quantum Lifshitz free scalar field theory. The quality of the fit of our data to this scaling function, as well as the apparent cutoff-independent coefficient that results, presents tantalizing evidence that this function may reflect universal behaviour across these and other very disparate QCPs in 2+1 dimensional systems.
We give an $O(n)$ time and space algorithm for constructing a diagonal matrix congruent to A+xI, where A is the adjacency matrix of a cograph and $x\in \mathbb{R}$. Applications include determining the number of eigenvalues of a cograph's adjacency matrix that lie in any interval, obtaining a formula for the inertia of a cograph, and exhibiting infinitely many pairs of equienergetic cographs with integer energy.
We present an analysis of the energy and frequency dependence of the Fourier time lags of the hectoHertz quasi-periodic oscillations (QPOs) and of the QPOs at the frequency at which the power density spectrum shows a break in the neutron-star low-mass X-ray binary 4U 1636-53, using a large data set obtained with the Rossi X-ray Timing Explorer. We found that: (i) For the break frequency QPO: for low frequencies, in general the time lag is positive, but it is decreasing with increasing frequency, reaching zero lag at 20 Hz. Between 20 and 35 Hz there is a small fluctuation around zero, from where the time lags become positive again and increase slightly above zero up to 65 Hz. (ii) For the hHz QPO: we see that when the frequency is 100 Hz the time lag is negative, but it increases to zero already at 110 Hz, being consistent with this value up to 130 Hz from where it increases to 0.5 msec at around 140 Hz. From 140 Hz the time lag decreases sharply, being strongly negative for hHz greater than 220 Hz. We compare these lags with our previous results for the lags of the kiloHertz QPOs in this same source and discuss possible scenarios for producing the lags in this system in the context of reflection off the accretion disc or (up-)down-scattering in a hot medium close to the neutron star.
We apply a cross-correlation technique to infer the $S>3$mJy radio luminosity function (RLF) from the NRAO VLA sky survey (NVSS) to $z\sim3.5$. We measure $\Sigma$ the over density of radio sources around spectroscopically confirmed quasars. $\Sigma$ is related to the space density of radio sources at the distance of the quasars and the clustering strength between the two samples, hence knowledge of one constrains the other. Under simple assumptions we find $\Phi\propto (1+z)^{3.7\pm0.7}$ out to $z\sim2$. Above this redshift the evolution slows and we constrain the evolution exponent to $<1.01$ ($2\sigma$). This behaviour is almost identical to that found by previous authors for the bright end of the RLF potentially indicating that we are looking at the same population. This suggests that the NVSS is dominated by a single population; most likely radio sources associated with high-excitation cold-mode accretion. Inversely, by adopting a previously modelled RLF we can constrain the clustering of high-redshift radio sources and find a clustering strength consistent with $r_0=15.0\pm 2.5$ Mpc up to $z\sim3.5$. This is inconsistent with quasars at low redshift and some measurements of the clustering of bright FRII sources. This behaviour is more consistent with the clustering of lower luminosity radio galaxies in the local universe. Our results indicate that the high-excitation systems dominating our sample are hosted in the most massive galaxies at all redshifts sampled.
A graph G is H-free if it has no induced subgraph isomorphic to H. We prove that a $P_5$-free graph with clique number $\omega\ge 3$ has chromatic number at most $\omega^{\log_2(\omega)}$. The best previous result was an exponential upper bound $(5/27)3^{\omega}$, due to Esperet, Lemoine, Maffray, and Morel. A polynomial bound would imply that the celebrated Erdos-Hajnal conjecture holds for $P_5$, which is the smallest open case. Thus there is great interest in whether there is a polynomial bound for $P_5$-free graphs, and our result is an attempt to approach that.
We present a comprehensive study of the spectral and transport properties in the Anderson--Holstein model both in and out of equilibrium using the functional renormalization group (FRG). We show how the previously established machinery of Matsubara and Keldysh FRG can be extended to include the local phonon mode. Based on the analysis of spectral properties in equilibrium we identify different regimes depending on the strength of the electron--phonon interaction and the frequency of the phonon mode. We supplement these considerations with analytical results from the Kondo model. We also calculate the non-linear differential conductance through the Anderson--Holstein quantum dot and find clear signatures of the presence of the phonon mode.
Much of modern condensed matter physics is understood in terms of elementary excitations, or quasiparticles - fundamental quanta of energy and momentum. Various strongly-interacting atomic systems are successfully treated as a collection of quasiparticles with weak or no interactions. However, there are interesting limitations to this description: the very existence of quasiparticles cannot be taken for granted in some systems. Like unstable elementary particles, quasiparticles cannot survive beyond a threshold where certain decay channels become allowed by conservation laws - their spectrum terminates at this threshold. This regime of quasiparticle failure was first predicted for an exotic state of matter, super-fluid helium-4 at temperatures close to absolute zero - a quantum Bose-liquid where zero-point atomic motion precludes crystallization. Using neutron scattering, here we show that it can also occur in a quantum magnet and, by implication, in other systems with Bose-quasiparticles. We have measured spin excitations in a two dimensional (2D) quantum-magnet, piperazinium hexachlorodicuprate (PHCC) in which spin-1/2 copper ions form a non-magnetic quantum spin liquid (QSL), and find remarkable similarities with excitations measured in superfluid 4He. There is a threshold momentum beyond which the quasiparticle peak merges with the two-quasiparticle continuum. It then acquires a finite energy width and becomes indistinguishable from a leading-edge singularity, so that lowest excited states occupy a wide band of energy. Our findings have important ramifications for understanding phenomena involving excitations with gapped spectra in many condensed matter systems, including high-transition-temperature superconductors.
The boundary of any observer's spacetime is the boundary that divides what the observer can see from what they cannot see. The boundary of an observer's spacetime in the presence of a black hole is not the true (future event) horizon of the black hole, but rather the illusory horizon, the dimming, redshifting surface of the star that collapsed to the black hole long ago. The illusory horizon is the source of Hawking radiation seen by observers both outside and inside the true horizon. The perceived acceleration (gravity) on the illusory horizon sets the characteristic frequency scale of Hawking radiation, even if that acceleration varies dynamically, as it must do from the perspective of an infalling observer. The acceleration seen by a non-rotating free-faller both on the illusory horizon below and in the sky above is calculated for a Schwarzschild black hole. Remarkably, as an infaller approaches the singularity, the acceleration becomes isotropic, and diverging as a power law. The isotropic, power-law character of the Hawking radiation, coupled with conservation of energy-momentum, the trace anomaly, and the familiar behavior of Hawking radiation far from the black hole, leads to a complete description of the quantum energy-momentum inside a Schwarzschild black hole. The quantum energy-momentum near the singularity diverges as $r^{-6}$, and consists of relativistic Hawking radiation and negative energy vacuum in the ratio $3 : -2$. The classical back reaction of the quantum energy-momentum on the geometry, calculated using the Einstein equations, serves merely to exacerbate the singularity. All the results are consistent with traditional calculations of the quantum energy-momentum in 1+1 spacetime dimensions.
We assess the most plausible scenarios for generating large amounts of dust in high-z quasars (QSOs) on the basis of observationally derived physical properties of QSOs at z > 6. We use a chemical evolution model to compute the temporal progression of quantities, such as the amount of dust and gas, stellar masses, star formation rates (SFRs) and the metallicity for various combinations of the initial mass function (IMF), the mass of the galaxy, dust production efficiencies, and the degree of dust destruction in the ISM. We investigate the influence of the SFR on the evolution of these quantities, and determine the earliest epochs at which agreement with observations can be achieved. We apply the obtained results to individual QSOs at z > 6. We find that large quantities of dust can be generated rapidly as early as 30 Myr after the onset of the starburst when the SFR of the starburst is > 10^3 M_sun yr^(-1). The amount of dust and several other physical quantities of individual QSOs at z > 6 are satisfactorily reproduced by models at epochs 30, 70, 100, and 170 Myr for galaxies with initial gas masses of 1-3 x 10^11 M_sun. The best agreement with observations is obtained with top-heavy IMFs. A sizable dust contribution from supernovae (SNe) is however required, while at these epochs dust production by asymptotic giant branch (AGB) stars is negligible. Moderate dust destruction in the ISM can be accommodated.