ShantanuT01/DACTYL-Pretraining huggingface dataset:
Observations show that the surface brightness of disc galaxies can be well-described by a single exponential (TI), up-bending (TIII) or down-bending (TII) profiles in the outskirts. Here we characterize the mass surface densities of simulated late-type galaxies from the EAGLE project according to their distribution of mono-age stellar populations, the star formation activity and angular momentum content. We find a clear correlation between the inner scale-lengths and the stellar spin parameter, {\lambda}, for all three disc types with {\lambda} > 0.35. The outer scale-lengths of TII and TIII discs show a positive trend with {\lambda}, albeit weaker for the latter. TII discs prefer fast rotating galaxies. With regards to the stellar age distribution, negative and U-shape age profiles are the most common for all disc types. Positive age profiles are determined by a more significant contributions of young stars in the central regions, which decrease rapidly in the outer parts. TII discs prefer relative higher contributions of old stars compared to other mono-age populations across the discs whereas TIII discs become progressively more dominated by intermediate age (2-6 Gyrs) stars for increasing radius. The change in slope of the age profiles is located after the break of the mass surface density. We find evidence of larger flaring for the old stellar populations in TIII systems compared to TI and TII, which could indicate the action of other processes. Overall, the relative distributions of mono-age stellar populations and the dependence of the star formation activity on radius are found to shape the different disc types and age profiles.
The numerical emulation of quantum physics and quantum chemistry often involves an intractable number of degrees of freedom and admits no known approximation in general form. In practice, representing quantum-mechanical states using available numerical methods becomes exponentially more challenging with increasing system size. Recently quantum algorithms implemented as variational models, have been proposed to accelerate such simulations. Here we study the effect of noise on the quantum phase transition in the Schwinger model, within a variational framework. The experiments are built using a free space optical scheme to realize a pair of polarization qubits and enable any two-qubit state to be experimentally prepared up to machine tolerance. We specifically exploit the possibility to engineer noise and decoherence for polarization qubits to explore the limits of variational algorithms for NISQ architectures in identifying and quantifying quantum phase transitions with noisy qubits. We find that despite the presence of noise one can detect the phase transition of the Schwinger Hamiltonian even for a two-qubit system using variational quantum algorithms.
Dirac semimetals are expected to forbid the manifestation of the circular photogalvanic effect (CPGE) because of their crystal inversion symmetry. Here, we report the observation of the CPGE in Cd3As2 nanobelt field effect transistors, when the photoexcitation is focused in the vicinity of the metal contacts up to room temperature. We attribute the CPGE to the Schottky electric field induced symmetry breaking, which results in the photocurrent modulation by circularly polarized photoexcitation via spin-momentum locking. The hypothesis is supported by a suite of experiments including spatially and angularly resolved helicity dependent photocurrent, Kelvin probe force microscopy, and gate voltage dependence. First principles calculations confirmed a topological phase transition upon field induced structural distortion. This work provides key insights on the electrically controlled helicity dependent optoelectronics in Dirac materials.
For every $n\in\mathbb{N}$ and $k\geq2$, it is known that every $k$-edge-colouring of the complete graph on $n$ vertices contains a monochromatic connected component of order at least $\frac{n}{k-1}$. For $k\geq3$, it is known that the complete graph can be replaced by a graph $G$ with $\delta(G)\geq(1-\varepsilon_k)n$ for some constant $\varepsilon_k$. In this paper, we show that the maximum possible value of $\varepsilon_3$ is $\frac16$. This disproves a conjecture of Gy\'{a}rfas and S\'{a}rk\"{o}zy.
A square matrix is called stochastic (or row-stochastic) if it is non-negative and has each row sum equal to unity. Here, we constitute an eigenvalue localization theorem for a stochastic matrix, by using its principal submatrices. As an application, we provide a suitable bound for the eigenvalues, other than unity, of the Randi\'c matrix of a connected graph.
In this paper we present a detailed calculation of an Ansatz that allows to obtain spherically symmetric Einstein-Dirac configurations in $d$-dimensions. We show that this is possible by combining $2^{\lfloor \frac{d-2}{2} \rfloor}$ Dirac fields, making use of the properties of the angular dependence of the spinors in a spherical background. By applying this Ansatz, we investigate some simple analytical solutions. One of them is a regular wormhole supported by the Dirac fields. Other solutions include a pathological black hole and a naked singularity. We analyze the domain of existence and properties of all these solutions.
We use ~88 arcmin**2 of deep (>~26.5 mag at 5 sigma) NICMOS data over the two GOODS fields and the HDF South to conduct a search for bright z>~7 galaxy candidates. This search takes advantage of an efficient preselection over 58 arcmin**2 of NICMOS H-band data where only plausible z>~7 candidates are followed up with NICMOS J-band observations. ~248 arcmin**2 of deep ground-based near-infrared data (>~25.5 mag, 5 sigma) is also considered in the search. In total, we report 15 z-dropout candidates over this area -- 7 of which are new to these search fields. Two possible z~9 J-dropout candidates are also found, but seem unlikely to correspond to z~9 galaxies. The present z~9 search is used to set upper limits on the prevalence of such sources. Rigorous testing is undertaken to establish the level of contamination of our selections by photometric scatter, low mass stars, supernovae (SNe), and spurious sources. The estimated contamination rate of our z~7 selection is ~24%. Through careful simulations, the effective volume available to our z>~7 selections is estimated and used to establish constraints on the volume density of luminous (L*(z=3), or -21 mag) galaxies from these searches. We find that the volume density of luminous star-forming galaxies at z~7 is 13_{-5}^{+8}x lower than at z~4 and >25x lower (1 sigma) at z~9 than at z~4. This is the most stringent constraint yet available on the volume density of >~L* galaxies at z~9. The present wide-area, multi-field search limits cosmic variance to <20%. The evolution we find at the bright end of the UV LF is similar to that found from recent Subaru Suprime-Cam, HAWK-I or ERS WFC3/IR searches. The present paper also includes a complete summary of our final z~7 z-dropout sample (18 candidates) identified from all NICMOS observations to date (over the two GOODS fields, the HUDF, galaxy clusters).
Based on the Wigner function in local equilibrium, we derive hydrodynamical quantities for a system of polarized spin-1/2 particles: the particle number current density, the energy-momentum tensor, the spin tensor, and the dipole moment tensor. Comparing with ideal hydrodynamics without spin, additional terms at first and second order in the Knudsen number $\text{Kn}$ and the average spin polarization $\chi_s$ have been derived. The Wigner function can be expressed in terms of matrix-valued distributions, whose equilibrium forms are characterized by thermodynamical parameters in quantum statistics. The equations of motions for these parameters are derived by conservation laws at the leading and next-to-leading order $\text{Kn}$ and $\chi_s$.
We report a spectral-line survey of the extreme carbon star IRC+10216 carried out between 293.9 and 354.8 GHz with the Submillimeter Array. A total of 442 lines were detected, more than 200 for the first time; 149 are unassigned. Maps at an angular resolution of ~3" were obtained for each line. A substantial new population of narrow lines with an expansion velocity of ~4 km/s (i.e. ~ 30% of the terminal velocity) was detected. Most of these are attributed to rotational transitions within vibrationally excited states, emitted from energy levels above the v=0, J=0 ground state with excitation energy of 1000-3000 K. Emission from these lines appears to be centered on the star with an angular extent of <1". We use multiple transitions detected in several molecules to derive physical conditions in this inner envelope of IRC+10216.
Muon spin relaxation measurements around the 25 K metal-insulator transition in Li$_{0.9}$Mo$_6$O$_{17}$ elucidate a profound role of disorder as a possible mechanism for this transition. The relaxation rate $1/T_1$ and the muon Knight shift are incompatible with the transition to a SDW state and thus exclude it.
This paper introduces stochastic processes that describe the evolution of systems of particles in which particles immigrate according to a Poisson measure and split according to a self-similar fragmentation. Criteria for existence and absence of stationary distributions are established and uniqueness is proved. Also, convergence rates to the stationary distribution are given. Linear equations which are the deterministic counterparts of fragmentation with immigration processes are next considered. As in the stochastic case, existence and uniqueness of solutions, as well as existence and uniqueness of stationary solutions, are investigated.
We study phase structure of mass-deformed ABJM theory which is a three dimensional $\mathcal{N}=6$ superconformal theory deformed by mass parameters and has the gauge group $\text{U}(N)\times \text{U}(N)$ with Chern-Simons levels $(k,-k)$ which may have a gravity dual. We discuss that the mass deformed ABJM theory on $S^3$ breaks supersymmetry in a large-$N$ limit if the mass is larger than a critical value. To see some evidence for this conjecture, we compute the partition function exactly, and numerically by using the Monte Carlo Simulation for small $N$. We discover that the partition function has zeroes as a function of the mass deformation parameters if $N\ge k$, which supports the large-$N$ supersymmetry breaking. We also find a solution to the large-$N$ saddle point equations, where the free energy is consistent with the finite $N$ result.
We discuss a new algorithm to generate multi-scale initial conditions with multiple levels of refinements for cosmological "zoom-in" simulations. The method uses an adaptive convolution of Gaussian white noise with a real space transfer function kernel together with an adaptive multi-grid Poisson solver to generate displacements and velocities following first (1LPT) or second order Lagrangian perturbation theory (2LPT). The new algorithm achieves RMS relative errors of order 10^(-4) for displacements and velocities in the refinement region and thus improves in terms of errors by about two orders of magnitude over previous approaches. In addition, errors are localized at coarse-fine boundaries and do not suffer from Fourier-space induced interference ringing. An optional hybrid multi-grid and Fast Fourier Transform (FFT) based scheme is introduced which has identical Fourier space behaviour as traditional approaches. Using a suite of re-simulations of a galaxy cluster halo our real space based approach is found to reproduce correlation functions, density profiles, key halo properties and subhalo abundances with per cent level accuracy. Finally, we generalize our approach for two-component baryon and dark-matter simulations and demonstrate that the power spectrum evolution is in excellent agreement with linear perturbation theory. For initial baryon density fields, it is suggested to use the local Lagrangian approximation in order to generate a density field for mesh based codes that is consistent with Lagrangian perturbation theory instead of the current practice of using the Eulerian linearly scaled densities.
A set of edges $\Gamma$ of a graph $G$ is an edge dominating set if every edge of $G$ intersects at least one edge of $\Gamma$, and the edge domination number $\gamma_e(G)$ is the smallest size of an edge dominating set. Expanding on work of Laskar and Wallis, we study $\gamma_e(G)$ for graphs $G$ which are the incidence graph of some incidence structure $D$, with an emphasis on the case when $D$ is a symmetric design. In particular, we show in this latter case that determining $\gamma_e(G)$ is equivalent to determining the largest size of certain incidence-free sets of $D$. Throughout, we employ a variety of combinatorial, probabilistic and geometric techniques, supplemented with tools from spectral graph theory.
Let $p$ be an odd prime. For field extensions $L/\mathbb{Q}_p$ with Galois group isomorphic to the dihedral group $D_{2p}$ of order $2p$, we consider the problem of computing a basis of the associated order in each Hopf Galois structure and the module structure of the ring of integers $\mathcal{O}_L$. We solve the case in which $L/\mathbb{Q}_p$ is not totally ramified and present a practical method which provides a complete answer for the cases $p=3$ and $p=5$. We see that within this family of dihedral extensions, the ring of integers is always free over the associated orders in the different Hopf Galois structures.
We compute the magnetic profile of spin Peierls solitons in a simple Heisenberg model with magneto elastic couplings, using independently the DMRG method and the Hartree Fock approximation. Our results agree qualitatively with published NMR data provided we average over the spin profiles. We conclude that he dynamics of the spin plus lattice system must be included in a more detailed theory of the spin Peierls transition in CuGeO.
Let T be an ergodic automorphism of the d-dimensional torus T^d, and f be a continuous function from T^d to R^l. On the probability space T^d equipped with the Lebesgue-Haar measure, we prove the weak convergence of the sequential empirical process of the sequence (f o T^i)_{i \geq 1} under some mild conditions on the modulus of continuity of f. The proofs are based on new limit theorems and new inequalities for non-adapted sequences, and on new estimates of the conditional expectations of f with respect to a natural filtration.
Loebl, Komlos, and Sos conjectured that if at least half of the vertices of a graph G have degree at least some natural number k, then every tree with at most k edges is a subgraph of G. Our main result is an approximate version of this conjecture for large enough n=|V(G)|, assumed that n=O(k). Our result implies an asymptotic bound for the Ramsey number of trees. We prove that r(T_k,T_m)\leq k+m+o(k+m),as k+m tends to infinity.
Recent advances in experimental control of colloidal systems have spurred a revolution in the production of mesoscale thermodynamic devices. Functional "textbook" engines, such as the Stirling and Carnot cycles, have been produced in colloidal systems where they operate far from equilibrium. Simultaneously, significant theoretical advances have been made in the design and analysis of such devices. Here, we use methods from thermodynamic geometry to characterize the optimal finite-time, nonequilibrium cyclic operation of the parametric harmonic oscillator contact with a time-varying heat bath, with particular focus on the Brownian Carnot cycle. We derive the optimally parametrized Carnot cycle, along with two other new cycles and compare their dissipated energy, efficiency, and steady-state power production against each other and a previously tested experimental protocol for the Carnot cycle. We demonstrate a 20\% improvement in dissipated energy over previous experimentally tested protocols and a $\sim$50\% improvement under other conditions for one of our engines, while our final engine is more efficient and powerful than the others we considered. Our results provide the means for experimentally realizing optimal mesoscale heat engines.
The discovery of frame-dragging effects in binary pulsar timing experiments requires a compact companion with sufficiently large spin. A pulsar orbiting a fast rotating black hole could provide an appropriate test system. In this paper we address questions concerning the identification of a black hole companion in such a system, the measurability of the frame dragging caused by the rotation of the black hole, and the measurability of the quadrupole moment, which would prove the presence of a Kerr black hole.
We prove that all subclasses of the separable permutations not containing Av(231) or a symmetry of this class have rational generating functions. Our principal tools are partial well-order, atomicity, and the theory of strongly rational permutation classes introduced here for the first time.
We discuss certain representations of GL 2 Fq[T] in equal characteristic and associated vectorial modular forms
I stress that [PRL 111,240402(2013)] contains no result that need to be explained by so-called Two State Vector Formalism, and closely inspected data are in disagreement with claims of Danan, Farfurnik, Bar-Ad, and Vaidman
We prove the existence of infinite energy global solutions of the cubic wave equation in dimension greater than 3. The data is a typical element on the support of suitable probability measures.
A recently observed bump in the cosmic ray (CR) spectrum from 0.3--30 TV is likely caused by a stellar bow shock that reaccelerates \emph{preexisting} CRs, which further propagate to the Sun along the magnetic field lines. Along their way, these particles generate an Iroshnikov-Kraichnan (I-K) turbulence that controls their propagation and sustains the bump. {\it Ad hoc} fitting of the bump shape requires six adjustable parameters. Our model requires none, merely depending on \emph{three physical unknowns that we constrain using the fit.} These are the shock Mach number, $M$, its size, $l_{\perp}$, and the distance to it, $\zeta_{\text{obs}}$. Altogether, they define the bump rigidity $R_{0}$. With $M$$\approx$1.5--1.6 and $R_{0}$$\approx$4.4 TV, the model fits the data with $\approx$$0.08\%$ accuracy. The fit critically requires the I-K spectrum predicted by the model and rules out the alternatives. These fit's attributes make an accidental agreement highly unlikely. In turn, $R_{0}$ and $M$ derived from the fit impose the distance-size %($\zeta_{{\rm obs}}$$-$$l_{\perp}$) relation on the shock: $\zeta_{{\rm obs}}$(pc)$\sim$$10^{2}\sqrt{l_{\perp}(\text{pc})}$. For sufficiently large bow shocks, $l_{\perp}$$=$$10^{-3}$$-$$10^{-2}$ pc, we find the distance of $\zeta_{{\rm obs}}$$=$3--10 pc. Three promising stars in this range are: Scholz's Star at 6.8 pc, Epsilon Indi at 3.6 pc, and Epsilon Eridani at 3.2 pc. Based on their current positions and velocities, we propose that Epsilon Indi and Epsilon Eridani can produce the observed spectral bump. Moreover, Epsilon Eridani's position is only $\sim$$6.7^{\circ}$ off of the magnetic field direction in the solar neighborhood, which also changes the CR arrival direction distribution. Given the proximity of these stars, the bump appearance may change in a relatively short time.
Informative recent measurements on the heavy-fermion metal $\rm \beta-YbAlB_4$ performed with applied magnetic field and pressure as control parameters are analyzed with the goal of establishing a sound theoretical explanation for the inferred scaling laws and non-Fermi-liquid (NFL) behavior, which demonstrate some unexpected features. Most notably, the robustness of the NFL behavior of the thermodynamic properties and of the anomalous $T^{3/2}$ temperature dependence of the electrical resistivity under applied pressure $P$ in zero magnetic field $B$ is at variance with the fragility of the NFL phase under application of a field. We show that a consistent topological basis for this combination of observations, as well as the empirical scaling laws, may be found within fermion-condensation theory in the emergence and destruction of a flat band, and explain that the paramagnetic NFL phase takes place without magnetic criticality, thus not from quantum critical fluctuations. Schematic $T-B$ and $T-P$ phase diagrams are presented to illuminate this scenario.
The group delay time of Dirac fermions subjected to a tilting barrier potential along the $ x $-axis is investigated in graphene. We start by finding the eigenspinor solution of the Dirac equation and then relating it to incident, reflected, and transmitted beam waves. This relationship allows us to compute the group delay time in transmission and reflection by obtaining the corresponding phase shifts. We discovered that the barrier width, incident energy, and incident angle can all be used to modify the group delay time, and that the particles travel through the barrier at the Fermi velocity $ v_F $. Our findings also show that the transmission group delay might be controlled, and that gate voltage control could be useful in graphene-based tilting barriers.
Let $G$ be a compact Lie group, $N\geq 1$ and $L>0$. The random geometric graph on $G$ is the random graph $\Gamma(N,L)$ whose vertices are $N$ random points $g_1,\ldots,g_N$ chosen under the Haar measure of $G$, and whose edges are the pairs $\{g_i,g_j\}$ with $d(g_i,g_j)\leq L$, $d$ being the distance associated to the standard Riemannian structure on $G$. In this paper, we describe the asymptotic behavior of the spectrum of the adjacency matrix of $\Gamma(N,L)$, when $N$ goes to infinity. If $L$ is fixed and $N \to + \infty$ (Gaussian regime), then the largest eigenvalues of $\Gamma(N,L)$ converge after an appropriate renormalisation towards certain explicit linear combinations of values of Bessel functions. If $L = O(N^{-\frac{1}{\dim G}})$ and $N \to +\infty$ (Poissonian regime), then the random geometric graph $\Gamma(N,L)$ converges in the local Benjamini-Schramm sense, which implies the weak convergence in probability of the spectral measure of $\Gamma(N,L)$. In both situations, the representation theory of the group $G$ provides us with informations on the limit of the spectrum, and conversely, the computation of this limiting spectrum involves many classical tools from representation theory: Weyl's character formula and the weight lattice in the Gaussian regime, and a degeneration of these objects in the Poissonian regime. The representation theoretic approach allows one to understand precisely how the degeneration from the Gaussian to the Poissonian regime occurs, and the article is written so as to highlight this degeneration phenomenon. In the Poissonian regime, this approach leads us to an algebraic conjecture on certain functionals of the irreducible representations of $G$.