ShantanuT01/DACTYL-Pretraining huggingface dataset:
The Berezinskii-Kosterlitz-Thouless (BKT) phase transition is considered in the condition of lowest temperatures, when thermal fluctuations give place to quantum ones. For this goal, the critical dynamic of the Sine-Gordon model near the quantum critical point is considered. The approach based on the Keldysh-Schwinger technique of non-equilibrium dynamics description is used, as well as the method of taking into account the crossover from the thermal fluctuation regime to the quantum one in the renormalization group technique. For the system with low vortex concentration, it is shown that the BKT transition unavoidably occurs at a temperature above the crossover temperature from the thermal fluctuation regime to quantum one. As a result at small temperatures the critical exponent of the BKT transition, $\eta=1/4$, remains unchanged, however, the universal relation of the superfluid density jump adjusts a little from the well-known relation by Nelson and Kosterlitz.
This work revisits the computation of six-gluon scattering amplitudes in the high energy limit of strongly coupled N=4 supersymmetric Yang-Mills theory. It is based on previous studies in which we showed that the amplitude simplifies in the Regge regime and outlined an efficient computational scheme. By exploiting a symmetry of the underlying equations we are now able to argue that a term we had seen in preliminary numerical studies must vanish identically. The derived formula for the Regge limit of the 6-gluon scattering amplitude at strong coupling differs from the one we had conjectured previously.
Skyrmion is a topologically protected spin texture excited in magnetic thin films. The radii of skyrmions are typically 10-100 nm. Because of the size, the skyrmion is expected to be a candidate for memory and novel-device usages. To realize the futuristic devices that will be using the skyrmion circuit, the tracks which guide the motion of skyrmions are needed. The tracks patterned with differences in the magnetic-anisotropy energy are well-paved without a potential pocket, whereas the tracks carved out of magnetic films have the potential pockets at corners due to the demagnetizing field. Therefore, the tracks patterned with the magnetic anisotropy plays a key role in making the skyrmion circuits. The experiment along this idea has been conducted for the hub and bent tracks. However, we have little known the motion of skyrmions in these tracks. This work aims to identify the forces acting between skyrmions and walls of the tracks. The static force on a skyrmion can be expressed as minus the gradient of the potential energy caused by the magnetic-anisotropy undulation. The potential can be estimated numerically, modeling the shape of skyrmions with their radii and domain wall widths. We find that the forces depend not only on the distance from the wall but also on the shape of skyrmions. We have also performed micromagnetic simulations where the Magnus force and the acceleration by the magnetic-anisotropy gradient are taken into account as well as the force by the walls. The simulation results show good agreement with those calculated from the modeled skyrmions.
In this work, we propose the N=2 and N=4 supersymmetric extensions of the Lorentz-breaking Abelian Chern-Simons term. We formulate the question of the Lorentz violation in 6 and 10 dimensions to obtain the bosonic sectors of N=2, and N=4, supersymmetries, respectively. From this, we carry out an analysis in N=1, D=4 superspace and, in terms of N=1, superfields, we are able to write down the N=2 and N=4 supersymmetric versions of the Lorentz-violating action term.
Given a closed, bounded convex set $\mathcal{W}\subset{\mathbb {R}}^d$ with nonempty interior, we consider a control problem in which the state process $W$ and the control process $U$ satisfy \[W_t= w_0+\int_0^t\vartheta(W_s) ds+\int_0^t\sigma(W_s) dZ_s+GU_t\in \mathcal{W},\qquad t\ge0,\] where $Z$ is a standard, multi-dimensional Brownian motion, $\vartheta,\sigma\in C^{0,1}(\mathcal{W})$, $G$ is a fixed matrix, and $w_0\in\mathcal{W}$. The process $U$ is locally of bounded variation and has increments in a given closed convex cone $\mathcal{U}\subset{\mathbb{R}}^p$. Given $g\in C(\mathcal{W})$, $\kappa\in{\mathbb{R}}^p$, and $\alpha>0$, consider the objective that is to minimize the cost \[J(w_0,U)\doteq\mathbb{E}\biggl[\int_0^{\infty}e^{-\alpha s}g(W_s) ds+\int_{[0,\infty)}e^{-\alpha s} d(\kappa\cdot U_s)\biggr]\] over the admissible controls $U$. Both $g$ and $\kappa\cdot u$ ($u\in\mathcal{U}$) may take positive and negative values. This paper studies the corresponding dynamic programming equation (DPE), a second-order degenerate elliptic partial differential equation of HJB-type with a state constraint boundary condition. Under the controllability condition $G\mathcal{U}={\mathbb{R}}^d$ and the finiteness of $\mathcal{H}(q)=\sup_{u\in\mathcal{U}_1}\{-Gu\cdot q-\kappa\cdot u\}$, $q\in {\mathbb{R}}^d$, where $\mathcal{U}_1=\{u\in\mathcal{U}:|Gu|=1\}$, we show that the cost, that involves an improper integral, is well defined. We establish the following: (i) the value function for the control problem satisfies the DPE (in the viscosity sense), and (ii) the condition $\inf_{q\in{\mathbb{R}}^d}\mathcal{H}(q)<0$ is necessary and sufficient for uniqueness of solutions to the DPE. The existence and uniqueness of solutions are shown to be connected to an intuitive ``no arbitrage'' condition. Our results apply to Brownian control problems that represent formal diffusion approximations to control problems associated with stochastic processing networks.
Pre-stellar cores are the basic unit for the formation of stars and stellar systems. The anatomy of the physical and chemical structures of pre-stellar cores is critical for understanding the star formation process. L1544 is a prototypical pre-stellar core, which shows significant chemical differentiation surrounding the dust peak. We aim to constrain the physical conditions at the different molecular emission peaks. This study allows us to compare the abundance profiles predicted from chemical models together with the classical density structure of Bonnor-Ebert (BE) sphere. We conducted multi-transition pointed observations of CH$_{3}$OH, c-C$_{3}$H$_{2}$ and HNCO with the IRAM 30m telescope, towards the dust peak and the respective molecular peaks of L1544. With non-LTE radiative transfer calculations and a 1-dimensional model, we revisit the physical structure of L1544, and benchmark with the abundance profiles from current chemical models. We find that the HNCO, c-C$_{3}$H$_{2}$ and CH$_{3}$OH lines in L1544 are tracing progressively higher density gas, from $\sim$10$^{4}$ to several times 10$^{5}$ cm$^{-3}$. Particularly, we find that to produce the observed intensities and ratios of the CH$_{3}$OH lines, a local gas density enhancement upon the BE sphere is required. This suggests that the physical structure of an early-stage core may not necessarily follow a smooth decrease of gas density profile locally, but can be intercepted by clumpy substructures surrounding the gravitational center. Multiple transitions of molecular lines from different molecular species can provide a tomographic view of the density structure of pre-stellar cores. The local gas density enhancement deviating from the BE sphere may reflect the impact of accretion flows that appear asymmetric and are enhanced at the meeting point of large-scale cloud structures.
The accretion of satellites onto central galaxies along vast cosmic filaments is an apparent outcome of the anisotropic collapse of structure in our Universe. Numerical work (based on gravitational dynamics of N-body simulations) indicates that satellites are beamed towards hosts along preferred directions imprinted by the velocity shear field. Here we use the Sloan Digital Sky Survey to observationally test this claim. We construct 3D filaments and sheets and examine the relative position of satellite galaxies. A statistically significant alignment between satellite galaxy position and filament axis in observations is confirmed. We find a qualitatively compatible alignments by examining satellites and filaments similarly identified in the Millennium simulation, semi-analytical galaxy catalogue. We also examine the dependence of the alignment strength on galaxy properties such as colour, magnitude and (relative) satellite magnitude, finding that the alignment is strongest for the reddest and brightest central and satellite galaxies. Our results confirm the theoretical picture and the role of the cosmic web in satellite accretion. Furthermore our results suggest that filaments identified on larger scales can be reflected in the positions of satellite galaxies that are quite close to their hosts.
Taking the Ising chain as a reference model we have derived a perturbative expression for the free energy density of the Heisenberg-Ising chain with strong easy-axis anisotropy. All calculations are performed on the ground of the Quantum Transfer Matrix approach. The obtained result agrees with the direct high-temperature expansion. It also agrees with the low-temperature cluster expansion in the special subregime when quantum fluctuations are weak against thermodynamical ones.
We present a study of the cavity system in the galaxy cluster RBS 797 based on Chandra and VLA data. RBS 797 (z = 0.35), is one of the most distant galaxy clusters in which two pronounced X-ray cavities have been discovered. The Chandra data confirm the presence of a cool core and indicate an higher metallicity along the cavity directions. This is likely due to the AGN outburst, which lifts cool metal-rich gas from the center along the cavities, as seen in other systems. We find indications that the cavities are hotter than the surrounding gas. Moreover, the new Chandra images show bright rims contrasting with the deep, X-ray deficient cavities. The likely cause is that the expanding 1.4 GHz radio lobes have displaced the gas, compressing it into a shell that appears as bright cool arms. Finally we show that the large-scale radio emission detected with our VLA observations may be classified as a radio mini-halo, powered by the cooling flow (CF), as it nicely follows the trend P_radio vs. P_CF predicted by the re-acceleration model.
In this paper, we investigate the impact of gating potential and magnetic field on phonon induced spin relaxation rate and the speed of the electrically driven single-qubit operations inside the InSb nanowire spin qubit. We show that a strong $g$ factor and high magnetic field strength lead to the prevailing influence of electron-phonon scattering due to deformation potential, considered irrelevant for materials with a weak $g$ factor, like GaAs or Si/SiGe. In this regime, we find that spin relaxation between qubit states is significantly suppressed due to the confinement perpendicular to the nanowire axis. We also find that maximization of the number of single-qubit operations that can be performed during the lifetime of the spin qubit requires single quantum dot gating potential.
We construct an estimator of the unknown drift parameter $\theta\in {\mathbb{R}}$ in the linear model \[X_t=\theta t+\sigma_1B^{H_1}(t)+\sigma_2B^{H_2}(t),\;t\in[0,T],\] where $B^{H_1}$ and $B^{H_2}$ are two independent fractional Brownian motions with Hurst indices $H_1$ and $H_2$ satisfying the condition $\frac{1}{2}\leq H_1<H_2<1.$ Actually, we reduce the problem to the solution of the integral Fredholm equation of the 2nd kind with a specific weakly singular kernel depending on two power exponents. It is proved that the kernel can be presented as the product of a bounded continuous multiplier and weak singular one, and this representation allows us to prove the compactness of the corresponding integral operator. This, in turn, allows us to establish an existence--uniqueness result for the sequence of the equations on the increasing intervals, to construct accordingly a sequence of statistical estimators, and to establish asymptotic consistency.
Heavy-ion collisions at the BNL-RHIC collider can probe whether gluon saturation effects in nuclei at small x have set in, or whether leading-twist perturbative estimates of particle production are still applicable. I discuss that soon to come data from pA collisions at RHIC may provide more systematic insight into this problem than present data on the energy and centrality dependence of hadron production from Au+Au collisions. Results from pA collisions at RHIC could also help to understand some controversial and puzzling results from ion-ion collisions, for example the large azimuthal asymmetry at high p_t, as measured by the STAR collaboration.
Beta-decay properties of proton-rich odd-A and even-even Krypton isotopes are studied in the framework of a deformed selfconsistent Hartree-Fock calculation with density-dependent Skyrme forces, including pairing correlations between like nucleons in BCS approximation. Residual spin-isospin interactions are consistently included in the particle-hole and particle-particle channels and treated in Quasiparticle Random Phase Approximation. The similarities and differences in the treatment of even-even and odd-A nuclei are stressed. Comparison to available experimental information is done for Gamow-Teller strength distributions, summed strengths, and half-lives. The dependence of these observables on deformation is particularly emphasized in a search for signatures of the shape of the parent nucleus.
Thermodynamic and transport properties of a two dimensional circular quantum dot are studied theoretically at zero magnetic field. In the limit of a large confining potential, where the dot spectrum exhibits a shell structure, it is argued that both spectral and transport properties should exhibit Luttinger liquid behavior. These predictions are verified by direct numerical diagonalization. The experimental implications of such Luttinger liquid characteristics are discussed.
In this paper, the null geodesics and gravitational lensing in a nonsingular spacetime are investigated. According to the nature of the null geodesics, the spacetime is divided into several cases. In the weak deflection limit, we find the influence of the nonsingularity parameter $q$ on the positions and magnifications of the images is negligible. In the strong deflection limit, the coefficients and observables for the gravitational lensing in a nonsingular black hole background and a weakly nonsingular spacetime are obtained. Comparing these results, we find that, in a weakly nonsingular spacetime, the relativistic images have smaller angular position and relative magnification, but larger angular separation than that of a nonsingular black hole. These results might offer a way to probe the spacetime nonsingularity parameter and put a bound on it by the astronomical instruments in the near future.
Electroweak production of single top quarks is an as-yet-unverified prediction of the Standard model, potentially sensitive to new physics. Two of the single top quark productions channels have significant charge asymmetries at the LHC, while the much larger background from $t\bar{t}$ is nearly charge-symmetric. This can be used to reduce systematic uncertainties and make precision measurements of single top quark production.
We examine closed geodesics in the quotient of hyperbolic three space by the discrete group of isometries SL(2,Z[i]). There is a correspondence between closed geodesics in the manifold, the complex continued fractions originally studied by Hurwitz, and binary quadratic forms over the Gaussian integers. According to this correspondence, a geodesic is called fundamental if the associated binary quadratic form is. Using techniques from sieve theory, symbolic dynamics, and the theory of expander graphs, we show the existence of a compact set in the manifold containing infinitely many fundamental geodesics.
We prove a new variant of comparison principle for logarithmic $L_2$-small ball probabilities of Gaussian processes. As an application, we obtain logarithmic small ball asymptotics for some well-known processes with smooth covariances.
The paper proposes and motivates a conjecture on the invariance of cohomological support loci under derived equivalence. It contains a proof in the case of surfaces, and explains further developments and consequences.
The hat guessing number is a graph invariant based on a hat guessing game introduced by Winkler. Using a new vertex decomposition argument involving an edge density theorem of Erd\H{o}s for hypergraphs, we show that the hat guessing number of all outerplanar graphs is less than $2^{125000}$. We also define the class of layered planar graphs, which contains outerplanar graphs, and we show that every layered planar graph has bounded hat guessing number.
According to the AdS/CFT correspondence, the maximally supersymmetric SU(N) Yang-Mills theory in 4 dimensions is dual to the type IIB string theory compactified on AdS_5 x S^5. Most of the tests performed so far are confined to the leading order at large N or equivalently string tree-level. To probe the correspondence beyond this leading order and obtain 1/N^2 corrections is difficult since string one-loop computations on an AdS_5 x S^5 background generally are beyond feasibility. However, we will show that the chiral SU(4)_R anomaly of the super YM theory provides an ideal testing ground to go beyond leading order in N. We review and develop further our previous results that the 1/N^2 corrections to the chiral anomaly on the super YM side can be exactly accounted for by the supergravity/string effective action induced at one loop.
We obtain a formal characterization of the compatibility or otherwise of a set of positive-operator-valued measures (POVMs) via their Naimark extensions. We show that a set of POVMs is jointly measurable if and only if there exists a single Naimark extension, specified by a fixed ancilla state on the same ancilla Hilbert space, that maps them to a set of commuting projective measurements (PVMs). We use our result to obtain an easily checkable sufficient condition for the compatibility of a pair of dichotomic observables in any dimension. This in turn leads to a characterization of the compatibility regions for some important classes of observables including a pair of unsharp qubit observables. Finally, we also outline as to how our result provides an alternate approach to quantifying the incompatibility of a general set of quantum measurements.
We study a $(3+1)$-dimensional $U(N)$ gauge theory with $N$-flavor fundamental scalar fields, whose color-flavor locked (CFL) phase has topologically stable non-Abelian vortices. The $U(1)$ charge of the scalar fields must be $Nk+1$ for some integer $k$ in order for them to be in the representation of $U(N)$ gauge group. This theory has a $\mathbb{Z}_{Nk+1}$ one-form symmetry, and it is spontaneously broken in the CFL phase, i.e., the CFL phase is topologically ordered if $k\not=0$. We also find that the world sheet of topologically stable vortices in CFL phase can generate this one-form symmetry.
We study the asymptotic behavior of the solutions to a family of discounted Hamilton Jacobi equations, posed in the Euclidean N dimensional space, when the discount factor goes to zero. The ambient space being noncompact, we introduce an assumption implying that the Aubry set is compact and there is no degeneracy at infinity. Our approach is to deal not with a single Hamiltonian and Lagrangian but with the whole space of generalized Lagrangians, and then to define via duality minimizing measures associated to both the corresponding ergodic and discounted equations. The asymptotic result follows from convergence properties of these measures with respect to the narrow topology. We use as duality tool a separation theorem in locally convex Hausdorff spaces, we use the strict topology in the space of the bounded generalized Lagrangians as well.
Aims:To obtain insight into the physical structure of the warm gas in the inner envelope of protostars and the interaction with the outflow. Methods: Sub-millimeter observations of 12CO, 13CO and/or C18O in J=3-2, J=4-3 and J=7-6 were obtained with the APEX Telescope towards IRAS 12496-7650, an intermediate mass young stellar object. The data are compared to ISO-LWS observations of CO J=14-13 up to J=19-18 lines to test the different proposed origins of the CO lines. Results: The outflow is prominently detected in the 3-2 and 4-3 lines, but not seen at similar velocities in the 7-6 line, constraining the temperature in the high-velocity (> 5 km/s from line center) gas to less than 50 K, much lower than inferred from the analysis of the ISO-LWS data. In addition, no isothermal gas model can reproduce the emission in both the 7-6 and the higher-J ISO-LWS lines.The 7-6 line probably originates in the inner (<250 AU) region of the envelope at ~150 K. Detailed radiative transfer calculations suggest that the ISO-LWS lines are excited by a different mechanism, possibly related to the larger-scale outflow. All possible mechanisms on scales smaller than 8 " are excluded. High-resolution continuum as well as high-J 12CO and isotopic line mapping are needed to better constrain the structure of the warm gas in the inner envelope and the interaction with the outflow.
The recent coincident detection of gravitational waves (GW) from a binary neutron star merger with aLIGO/Virgo and short-lived gamma-ray emission with Fermi/GBM (called GW 170817) is a milestone for the establishment of multi-messenger astronomy. Merging neutron stars (NS) represent the standard scenario for short-duration (< 2 sec) gamma-ray bursts (GRBs) which are produced in a collimated, relativistically expanding jet with an opening angle of a few degrees and a bulk Lorentz factor of 300-1000. While the present aLIGO detection is consistent with predictions, the measured faint gamma-ray emission from GW 170817A, if associated to the merger event at a distance of 40 Mpc, is about 1000x less luminous than known short-duration GRBs (sGRBs). Hence, the presence of this sGRB in the local Universe is either a very rare event, or points to a dramatic ignorance of the emission properties of sGRBs outside their narrow jets. Here we show that the majority of previously detected faint sGRBs are local, at redshift smaller than 0.1, seen off-axis. In contrast, the brighter sGRBs are seen on-axis, and therefore out to larger distances, consistent with the measured redshift distribution. Examining the observer-frame parameter space of all Fermi/GBM sGRBs shows that the sGRB associated with GW 170817A is extreme in its combination of flux, spectral softness and temporal structure. We identify a group of similar GRBs, one of which has been associated to a bright galaxy at 75 Mpc. We incorporate off-axis emission in the estimate of the rates of sGRBs, and predict that the majority of future GW-detections of NS-NS mergers will be accompanied by faint gamma-ray emission, contrary to previous thinking. The much more frequent off-axis emission of sGRBs also implies a much higher deadly rate of gamma-rays for extraterrestrial life in the Universe.