ShantanuT01/DACTYL-Pretraining huggingface dataset:
Queueing networks are notoriously difficult to analyze sans both Markovian and stationarity assumptions. Much of the theoretical contribution towards performance analysis of time-inhomogeneous single class queueing networks has focused on Markovian networks, with the recent exception of work in Liu and Whitt (2011) and Mandelbaum and Ramanan (2010). In this paper, we introduce transitory queueing networks as a model of inhomogeneous queueing networks, where a large, but finite, number of jobs arrive at queues in the network over a fixed time horizon. The queues offer FIFO service, and we assume that the service rate can be time-varying. The non-Markovian dynamics of this model complicate the analysis of network performance metrics, necessitating approximations. In this paper we develop fluid and diffusion approximations to the number-in-system performance metric by scaling up the number of external arrivals to each queue, following Honnappa et al. (2014). We also discuss the implications for bottleneck detection in tandem queueing networks.
The assumption of measurement independence is required for a local deterministic model to conduct a Bell test. The violation of a Bell inequality by such a model implies that this assumption must be relaxed. The degree to which the assumption needs to be relaxed to achieve violation of some bipartite Bell inequalities, has been investigated recently in [Phys. Rev. Lett. 105, 250404(2010), Phys. Rev. A 99, 012121(2019)]. In this work, we study the minimum degree of relaxation required to simulate violations of various well-known tripartite Bell inequalities and opens the possibility of relaxation in multipartite scenario. Local deterministic models are also provided to achieve the violations of these Bell inequalities.
The magnetic susceptibility $\chi$, the magnetization $M$, and the specific heat $C$ were measured for the caged cubic compound NdRu$_2$Zn$_{20}$ at temperatures down to 0.5 K in the magnetic field $H$ along the three crystallographic principal axes, [100], [110], and [111]. The ferromagnetic phase transition was observed at the Curie temperature $T_{\rm C}=1.9$ K in both the temperature dependence of $\chi(T)$ and $C(T)$. Below $T_{\rm C}$, the magnetization curves $M(H)$ show very weak magnetic anisotropy, and the $C(T)$ curves in the fields along the three principal axes show no magnetic anisotropy both below and above $T_{\rm C}$. The easy direction of magnetization at 0.5 K changes from the [111] direction in 0 T to the [110] diretion in 7 T. We analyzed these characteristic behaviors theoretically taking into account the crystalline-electric-field energy, the magnetic exchange interaction, and the Zeeman energy. It was found that these features are originated from the isotropic $\Gamma_6$ ground state mixing with the magnetic $\Gamma_8^{(1)}$ excited state. The temperature and the magnetic field dependences of $M(T,H)$ and $C(T,H)$ are quantitatively well analyzed by this theoretical calculation.
We find exact solutions in five dimensional inhomogeneous matter dominated model with a varying cosmological constant. Adjusting arbitrary constants of integration one can also achieve acceleration in our model. Aside from an initial singularity our spacetime is regular everywhere including the centre of the inhomogeneous distribution. We also study the analogous homogeneous universe in (4+d) dimensions. Here an initially decelerating model is found to give late acceleration in conformity with the current observational demands. We also find that both anisotropy and number of dimensions have a role to play in determining the time of flip, in fact the flip is delayed in multidimensional models. Some astrophysical parameters like the age, luminosity distance etc are also calculated and the influence of extra dimensions is briefly discussed. Interestingly our model yields a larger age of the universe compared to many other quintessential models.
We infer stellar metallicity and abundance ratio gradients for a sample of red galaxies in the Sloan Digital Sky Survey (SDSS) Main galaxy sample. Because this sample does not have multiple spectra at various radii in a single galaxy, we measure these gradients statistically. We separate galaxies into stellar mass bins, stack their spectra in redshift bins, and calculate the measured absorption line indices in projected annuli by differencing spectra in neighboring redshift bins. After determining the line indices, we use stellar population modeling from the EZ\_Ages software to calculate ages, metallicities, and abundance ratios within each annulus. Our data covers the central regions of these galaxies, out to slightly higher than $1 R_{e}$. We find detectable gradients in metallicity and relatively shallow gradients in abundance ratios, similar to results found for direct measurements of individual galaxies. The gradients are only weakly dependent on stellar mass, and this dependence is well-correlated with the change of $R_e$ with mass. Based on this data, we report mean equivalent widths, metallicities, and abundance ratios as a function of mass and velocity dispersion for SDSS early-type galaxies, for fixed apertures of 2.5 kpc and of 0.5 $R_e$.
We study the correspondence that connects the space of solutions of General Relativity (GR) with that of Ricci-based Gravity theories (RBGs) of the $f(R,Q)$ type in the metric-affine formulation, where $Q=R_{(\mu\nu)}R^{(\mu\nu)}$. We focus on the case of scalar matter and show that when one considers a free massless scalar in the GR frame, important simplifications arise that allow to establish the correspondence for arbitrary $f(R,Q)$ Lagrangian. We particularize the analysis to a quadratic $f(R,Q)$ theory and use the spherically symmetric, static solution of Jannis-Newman-Winicour as seed to generate new compact objects in our target theory. We find that two different types of solutions emerge, one representing naked singularities and another corresponding to asymmetric wormholes with bounded curvature scalars everywhere. The latter solutions, nonetheless, are geodesically incomplete.
We study photoproduction of rho mesons in a model of hidden local symmetry. The rho meson is introduced as a hidden gauge boson and a phenomenological rho meson-nucleon Lagrangian is constructed respecting chiral symmetry. It is shown that the sigma exchange interaction is needed for neutral rho meson photoproduction to reproduce the experimental cross sections. For charged rho meson photoproduction, the model takes into account the rho meson magnetic moments from the three-point vertex in the kinetic terms. We show that the magnetic moment of the charged rho meson has a significant effect on the total cross sections through the rho meson exchange process, which is proportional to the energy of the photon. The t-channel dominance may be used for the study of structures of various unstable particles.
In this work we present a formal solution of the extended version of the Friedrichs Model. The Hamiltonian consists of discrete and continuum bosonic states, which are coupled to fermions. The simultaneous treatment of the couplings of the fermions with the discrete and continuous sectors of the bosonic degrees of freedom leads to a system of coupled equations, whose solutions are found by applying standard methods of representation of bound and resonant states.
We report Hubble Space Telescope Cosmic Origins Spectrograph far-ultraviolet and Arecibo Telescope H{\sc i} 21cm spectroscopic studies of six damped and sub-damped Lyman-$\alpha$ absorbers (DLAs and sub-DLAs, respectively) at $z \lesssim 0.1$, that have yielded estimates of their H{\sc i} column density, metallicity and atomic gas mass. This significantly increases the number of DLAs with gas mass estimates, allowing the first comparison between the gas masses of DLAs and local galaxies. Including three absorbers from the literature, we obtain H{\sc i} masses $\approx (0.24 - 5.2) \times 10^9 \: {\rm M}_\odot$, lower than the knee of the local H{\sc i} mass function. This implies that massive galaxies do not dominate the absorption cross-section for low-$z$ DLAs. We use Sloan Digital Sky Survey photometry and spectroscopy to identify the likely hosts of four absorbers, obtaining low stellar masses, $\approx 10^7-10^{8.7} M_\odot$, in all cases, consistent with the hosts being dwarf galaxies. We obtain high H{\sc i} 21\,cm or CO emission line widths, $\Delta V_{20} \approx 100-290$~km~s$^{-1}$, and high gas fractions, $f_{\rm HI} \approx 5-100$, suggesting that the absorber hosts are gas-rich galaxies with low star formation efficiencies. However, the H{\sc i} 21\,cm velocity spreads ($\gtrsim 100$~km~s$^{-1}$) appear systematically larger than the velocity spreads in typical dwarf galaxies.
Zeeman effect has been an invaluable tool for the detection and measurement of the effects of a magnetic field on the internal behavior of atoms and nuclei. Along with M\"{o}ssbauer effect, it has been used to determine the magnitude of the magnetic field present in nuclei of atoms but has not been detected inside nucleons so far. In this work, we present a possible signature of the Zeeman-like effect in nucleons that one can extract from the parton distributions with the use of statistical models and Fermi-Dirac distribution. These effects in turn---if electromagnetically dominated---predict the presence of magnetic fields of an unprecedented magnitude inside protons.
We analyze the Vavilov-Cherenkov radiation (VCR) in a dispersive nontransparent dielectric air-like medium both below and above the Cherenkov threshold, in the framework of classical electrodynamics. It is shown that the transition to the subthreshold energies leads to the destruction of electromagnetic shock waves and to the sharp reduction of the frequency domain where VCR is emitted. The fine wake-like structure of the Vavilov-Cherenkov radiation survives and manifests the existence of the subthreshold radiation in the domain of anomalous dispersion. These domains can approximately be defined by the two phenomenological parameters of the medium, namely, the effective frequency of oscillators and the damping describing an interaction with the other degrees of freedom.
The aim of this tutorial is to analyze the equilibrium properties of some simple but widely used quantum systems. The canonical ensemble is used to evaluate the required properties here.
We prove that the arboreal Galois representations attached to certain unicritical polynomials have finite index in an infinite wreath product of cyclic groups, and we prove surjectivity for some small degree examples, including a new family of quadratic polynomials. To do this, we use a combination of local techniques including the Chabauty-Coleman method and the Mordell-Weil sieve.
We consider the lattice version of the free field in two dimensions and study the fractal structure of the sets where the field is unusually high (or low). We then extend some of our computations to the case of the free field conditioned on being everywhere nonnegative. For example, we compute the width of the largest downward spike of a given length. Through the prism of these results, we find that the extrema of the free field under entropic repulsion (minus its mean) and those of the unconditioned free field are identical. Finally, when compared to previous results these findings reveal a suggestive analogy between the square of the free field and the two-dimensional simple random walk on the discrete torus.
We investigate nonequilibrium relaxations of Ising models at the critical point by using a cluster update. While preceding studies imply that nonequilibrium cluster-flip dynamics at the critical point are universally described by the stretched-exponential function, we find that the dynamics changes from the stretched-exponential to the power function as the dimensionality is increased: The two-, three-, four-, and infinite-dimensional Ising models are numerically studied, and the four- and infinite-dimensional Ising models exhibit the power-law relaxation. We also show that the finite-size scaling analysis using the normalized correlation length is markedly effective for the analysis of relaxational processes rather than the direct use of the Monte Carlo step.
The stability is analyzed of the magnetic junction collinear configurations against small fluctuations under amplitude-modulated current with CPP mode. High spin injection is assumed. Under parametric resonance conditions, with the modulation frequency twice the precession frequency, instability is possible of one, or another, or both the collinear configurations. When the dc component of the current density exceeds the instability threshold of the antiparallel configuration, the parametric instability is suppressed by nonparametric one which is induced by the dc current. The parametric instability manifests itself as lowering the threshold of the dc current density in presence of the high-frequency current, such an effect has been observed in experiments repeatedly.
We investigate the interaction of magnetohydrodynamic waves with plasma density inhomogeneities. Our numerical study of the full MHD equations shows that: (A) Plasma density inhomogeneities are a source of non-linear generation of transverse compressive waves by a plane Alfven wave, and substantially enhance (by about a factor of 2) the generation of the longitudinal compressive waves. (B) Attained maximal values of the generated transverse compressive waves are insensitive to the strength of the plasma density inhomogeneity and the initial amplitude of the Alfven wave. (C) Efficiency of the generation depends weakly upon the plasma beta parameter. The maximum generated amplitude of transverse compressive wave, up to 32% of the initial Alfven wave amplitude, is reached for about beta=0.5. The results obtained demonstrate that plasma inhomogeneities enhance the efficiency of the non-linear wave coupling.
Ever since J.M. Hammersley showed the existence of phase-transitions regarding independent bond percolation on general $d \geq 2$ dimensional integer-lattices in the late 50's, the continuity (or discontinuity) of which is perhaps the most prominent and long-standing basic open problem in the subsequently extensively developed theory of percolation.
The purpose of this short note is to give a proof of the following identity between (logarithmic) Mahler measures m(y^2+2xy+y-x^3-2x^2-x)=5/7*m(y^2+4xy+y-x^3+x^2) which is one of many examples that arise from the comparison of Mahler measures and special values of L-functions.
For every fixed graph $H$ and every fixed $0 < \alpha < 1$, we show that if a graph $G$ has the property that all subsets of size $\alpha n$ contain the ``correct'' number of copies of $H$ one would expect to find in the random graph $G(n,p)$ then $G$ behaves like the random graph $G(n,p)$; that is, it is $p$-quasi-random in the sense of Chung, Graham, and Wilson. This solves a conjecture raised by Shapira and solves in a strong sense an open problem of Simonovits and S\'os.
Understanding various phenomena in non-equilibrium dynamics of closed quantum many-body systems, such as quantum thermalization, information scrambling, and nonergodic dynamics, is a crucial for modern physics. Using a ladder-type superconducting quantum processor, we perform analog quantum simulations of both the $XX$ ladder and one-dimensional (1D) $XX$ model. By measuring the dynamics of local observables, entanglement entropy and tripartite mutual information, we signal quantum thermalization and information scrambling in the $XX$ ladder. In contrast, we show that the $XX$ chain, as free fermions on a 1D lattice, fails to thermalize, and local information does not scramble in the integrable channel. Our experiments reveal ergodicity and scrambling in the controllable qubit ladder, and opens the door to further investigations on the thermodynamics and chaos in quantum many-body systems.
We study the redshift evolution of the X-ray and Sunyaev-Zel'dovich (SZ) scaling relations for galaxy groups and clusters in the FABLE suite of cosmological hydrodynamical simulations. Using an expanded sample of $27$ high-resolution zoom-in simulations, together with a uniformly-sampled cosmological volume to sample low-mass systems, we find very good agreement with the majority of observational constraints up to $z \sim 1$. We predict significant deviations of all examined scaling relations from the simple self-similar expectations. While the slopes are approximately independent of redshift, the normalisations evolve positively with respect to self-similarity, even for commonly-used mass proxies such as the $Y_{\mathrm{X}}$ parameter. These deviations are due to a combination of factors, including more effective AGN feedback in lower mass haloes, larger binding energy of gas at a given halo mass at higher redshifts and larger non-thermal pressure support from kinetic motions at higher redshifts. Our results have important implications for cluster cosmology from upcoming SZ surveys such as SPT-3G, ACTpol and CMB-S4, as relatively small changes in the observable--mass scaling relations (within theoretical uncertainties) have a large impact on the predicted number of high-redshift clusters and hence on our ability to constrain cosmology using cluster abundances. In addition, we find that the intrinsic scatter of the relations, which agrees well with most observational constraints, increases at lower redshifts and for lower mass systems. This calls for a more complex parametrization than adopted in current observational studies to be able to accurately account for selection biases.
We compare two different approaches to the control of the dynamics of a continuously monitored open quantum system. The first is Markovian feedback as introduced in quantum optics by Wiseman and Milburn [Phys. Rev. Lett. {\bf 70}, 548 (1993)]. The second is feedback based on an estimate of the system state, developed recently by Doherty {\em et al.} [Phys. Rev. A {\bf 62}, 012105 (2000)]. Here we choose to call it, for brevity, {\em Bayesian feedback}. For systems with nonlinear dynamics, we expect these two methods of feedback control to give markedly different results. The simplest possible nonlinear system is a driven and damped two-level atom, so we choose this as our model system. The monitoring is taken to be homodyne detection of the atomic fluorescence, and the control is by modulating the driving. The aim of the feedback in both cases is to stabilize the internal state of the atom as close as possible to an arbitrarily chosen pure state, in the presence of inefficient detection and other forms of decoherence. Our results (obtain without recourse to stochastic simulations) prove that Bayesian feedback is never inferior, and is usually superior, to Markovian feedback. However it would be far more difficult to implement than Markovian feedback and it loses its superiority when obvious simplifying approximations are made. It is thus not clear which form of feedback would be better in the face of inevitable experimental imperfections.
Direct hyperlogarithmic integration offers a strong alternative to differential equation methods for Feynman integration, particularly for multi-particle diagrams. We review a variety of results by the authors in which this method, employed with some care, can compute diagrams of up to eight particles and four loops. We also highlight situations in which this method fails due to an algebraic obstruction. In a large number of cases the obstruction can be associated with a Calabi-Yau manifold.
The orbital angular momentum of individual stars in galactic discs can be permanently changed through torques from transient spiral patterns. Interactions at the corotation resonance dominate these changes and have the further property of conserving orbital circularity. We derived in an earlier paper an analytic criterion that an unperturbed stellar orbit must satisfy in order for such an interaction to occur i.e. for it to be in a trapped orbit around corotation. We here use this criterion in an investigation of how the efficiency of induced radial migration for a population of disc stars varies with the angular momentum distribution of that population. We frame our results in terms of the velocity dispersion of the population, this being an easier observable than is the angular momentum distribution. Specifically, we investigate how the fraction of stars in trapped orbits at corotation varies with the velocity dispersion of the population, for a system with an assumed flat rotation curve. Our analytic results agree with the finding from simulations that radial migration is less effective in populations with 'hotter' kinematics. We further quantify the dependence of this trapped fraction on the strength of the spiral pattern, finding a higher trapped fraction for higher amplitude perturbations.
The macroscopic quantum states of a condensed neutral Bose gas in one-dimensional power-law traps are obtained by solving the Gross-Pitaevskii equation numerically. A suitable candidate for a trial wave function for the variational calculation of ground state energy is suggested, and shown that the suggested function produces a lower ground state energy than the conventional Gaussian trial wave function.
Thermodynamic properties are presented for four magnetic impurity models describing delocalized fermions scattering from a localized orbital at an energy-dependent rate $\Gamma(\epsilon)$ which vanishes precisely at the Fermi level, $\epsilon = 0$. Specifically, it is assumed that for small $|\epsilon|$, $\Gamma(\epsilon)\propto|\epsilon|^r$ with $r>0$. The cases $r=1$ and $r=2$ describe dilute magnetic impurities in unconventional superconductors, ``flux phases'' of the two-dimensional electron gas, and zero-gap semiconductors. For the nondegenerate Anderson model, the depression of the low-energy scattering rate suppresses mixed valence in favor of local-moment behavior, and leads to a marked reduction in the exchange coupling on entry to the local-moment regime, with a consequent narrowing of the range of parameters within which the impurity spin becomes Kondo-screened. The relationship between the Anderson model and the exactly screened Kondo model with power-law exchange is examined. The intermediate-coupling fixed point identified in the latter model by Withoff and Fradkin (WF) has clear signatures in the thermodynamic properties and in the local magnetic response of the impurity. The underscreened, impurity-spin-one Kondo model and the overscreened, two-channel Kondo model both exhibit a conditionally stable intermediate-coupling fixed point in addition to unstable fixed points of the WF type. In all four models, the presence or absence of particle-hole symmetry plays a crucial role.
This paper has been withdrawn by Christino Tamon and Tomoyuki Yamakami because of errors of the main theorems. An erratum appeared in the Proceedings of the UMC 2000 Conference published by Springer.
We consider the restrictions of Shi arrangements to Weyl cones, their relations to antichains in the root poset, and their intersection posets. For any Weyl cone, we provide bijections between regions, flats intersecting the cone, and antichains of a naturally-defined subposet of the root poset. This gives a refinement of the parking function numbers via the Poincar\'e polynomials of the intersection posets of all Weyl cones. Finally, we interpret these Poincar\'e polynomials as the Hilbert series of two isomorphic graded rings, one arising from the Varchenko-Gel'fand ring and another, which we call the order ring since it turns out to be naturally associated to the order polytope.
We construct a new supermatrix model which represents a manifestly supersymmetric noncommutative regularisation of the $UOSp(2\vert 1)$ supersymmetric Schwinger model on the supersphere. Our construction is much simpler than those already existing in the literature and it was found by using Poisson geometry in a substantial way.