ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper, we use multi-frequency angular size measurements of 58 intermediate-luminosity quasars reaching the redshifts $z\sim 3$ and demonstrate that they can be used as standard rulers for cosmological inference. Our results indicate that, for the majority of radio-sources in our sample their angular sizes are inversely proportional to the observing frequency. From the physical point of view it means that opacity of the jet is governed by pure synchrotron self-absorption, i.e. external absorption does not play any significant role in the observed angular sizes at least up to 43 GHz. Therefore, we use the value of the intrinsic metric size of compact milliarcsecond radio quasars derived in a cosmology independent manner from survey conducted at 2 GHz and rescale it properly according to predictions of the conical jet model. This approach turns out to work well and produce quite stringent constraints on the matter density parameter $\Omega_m$ in the flat $\Lambda$CDM model and Dvali-Gabadadze-Porrati braneworld model. The results presented in this paper pave the way for the follow up engaging multi-frequency VLBI observations of more compact radio quasars with higher sensitivity and angular resolution.
We establish a formula of the large N factorization of the modular S-matrix for the coupled representations in U(N) Chern-Simons theory. The formula was proposed by Aganagic, Neitzke and Vafa, based on computations involving the conifold transition. We present a more rigorous proof that relies on the universal character for rational representations and an expression of the modular S-matrix in terms of the specialization of characters.
We study the weak antilocalization (WAL) effect in the magnetoresistance of narrow HgTe wires fabricated in quantum wells (QWs) with normal and inverted band ordering. Measurements at different gate voltages indicate that the WAL is only weakly affected by Rashba spin-orbit splitting and persists when the Rashba splitting is about zero. The WAL signal in wires with normal band ordering is an order of magnitude smaller than for inverted ones. These observations are attributed to a Dirac-like topology of the energy bands in HgTe QWs. From the magnetic-field and temperature dependencies we extract the dephasing lengths and band Berry phases. The weaker WAL for samples with a normal band structure can be explained by a non-universal Berry phase which always exceeds \pi, the characteristic value for gapless Dirac fermions.
The Brownian motion of a particle immersed in a medium of charged particles is considered when the system is placed in magnetic or electric fields. Coming from the Zwanzig-Caldeira-Legget particle-bath model, we modify it so that not only the charged Brownian particle (BP) but also the bath particles respond to the external fields. For stationary systems the generalized Langevin equations are derived. Arbitrarily time-dependent electric fields do not affect the memory functions, the thermal noise force, and the BP velocity correlation functions. In the case of a constant magnetic field two equations with different memory functions are obtained for the BP motion in the plane perpendicular to the field. As distinct from the previous theories, the random thermal force depends on the field magnitude. Its time correlation function is connected with one of the found memory functions through the familiar second fluctuation-dissipation theorem.
We construct curves of each genus $g\geq 2$ for which Coleman's effective Chabauty bound is sharp and Coleman's theorem can be applied to determine rational points if the rank condition is satisfied. We give numerous examples of genus two and rank one curves for which Coleman's bound is sharp. Based on one of those curves, we construct an example of a curve of genus five whose rational points are determined using the descent method together with Coleman's theorem.
In this paper we calculate the cardinality of the set S_n(T,tau) of all permutations in S_n that avoid one pattern from S_4 and a nonempty set of patterns from S_3.
Transfer mechanism of orbital angular moment(OAM) of light to trapped ground-state atoms under paraxial approximation is well known. Here we show how optical OAM of a Laguerre-Gaussian(LG) beam under paraxial approximation can be transferred to trapped Rydberg atoms. Optical OAM is shown to be transferable to a Rydberg electronic state in dipole transition. The Gaussian part of the profile of the LG beam, which is generally neglected , is found to have an important effect on the OAM transfer to the Rydberg atoms. Numerical calculations are calculated based on this theory for Rubidium Rydberg atoms trapped in a harmonic potential. Our results exhibit the mixing of final states of different parities.
The circulant graph $C_n(S)$ with connection set $S\subseteq \{1,2,\cdots,n\}$ is the graph with vertex set $V=\{1,\ldots, n\}$ and two vertices $x,y$ are adjacent if $|x-y|\in S$. In this paper, we will calculate the total dominator chromatic number of the circulant graph $C_n(\{a,b\})$ when $n\geq 6$, $gcd(a,n)=1$ and $ a^{-1}b\equiv 3 \pmod{n}$.
A (minimal) transversal of a partition is a set which contains exactly one element from each member of the partition and nothing else. A coloring of a graph is a partition of its vertex set into anticliques, that is, sets of pairwise nonadjacent vertices. We study the following problem: Given a transversal $T$ of a proper coloring $\mathfrak{C}$ of some graph $G$, is there a partition $\mathfrak{H}$ of a subset of $V(G)$ into connected sets such that $T$ is a transversal of $\mathfrak{H}$ and such that two sets of $\mathfrak{H}$ are adjacent if their corresponding vertices from $T$ are connected by a path in $G$ using only two colors?   It has been suggested by the first author to study the following question: for any transversal $T$ of a coloring $\mathfrak{C}$ of order $k$ of some graph $G$ such that any pair of color classes induces a connected graph, does there exist such a partition $\mathfrak{H}$ with pairwise adjacent sets (which would prove Hadwiger's Conjecture for the class of uniquely optimally colorable graphs)? This is open for small $k \geq 5$, here we give a proof for the case that $k=5$ and the subgraph induced by $T$ is connected. Moreover, we show that for $k\geq 7$, it is not sufficient for the existence of $\mathfrak{H}$ as above just to force any two transversal vertices to be connected by a 2-colored path.
In this paper, we analyze the dependence of elastic constants c_ij on composition for random wurtzite quater- nary AlGayInN alloy in the whole concentration range. The study takes as its starting point the c_ij parameters for zinc blende phase calculated earlier by the authors on the basis of valence force field model. To obtain the wurtzite constants from cubic material parameters the Martin transformation is used. The de- viations from linear Vegard-like dependence of c_ij on composition are analyzed and accurate quadratic fits to calculated moduli are presented. The influence of nonlinear internal strain term in the Martin transformation is also investigated. Our general results for quaternary AlGaInN alloys are compared with the recent ab initio calculations for ternaries GaInN and AlInN (Gorczyca and Lepkowski, Phys. Rev. B 83 203201, 2011) and good qualitative agreement is found.
We determine the quantum phase diagram of a two-dimensional bosonic t-Jz model as a function of the lattice anisotropy gamma, using a quantum Monte Carlo loop algorithm. We show analytically that the low-energy sectors of the bosonic and the fermionic t-Jz models become equivalent in the limit of small gamma. In this limit, the ground state represents a static stripe phase characterized by a non-zero value of a topological order parameter. This phase remains up to intermediate values of gamma, where there is a quantum phase transition to a phase-segregated state or a homogeneous superfluid with dynamic stripe fluctuations depending on the ratio Jz/t.
We study the extremal behavior of a stochastic integral driven by a multivariate L\'{e}vy process that is regularly varying with index $\alpha>0$. For predictable integrands with a finite $(\alpha+\delta)$-moment, for some $\delta>0$, we show that the extremal behavior of the stochastic integral is due to one big jump of the driving L\'{e}vy process and we determine its limit measure associated with regular variation on the space of c\`{a}dl\`{a}g functions.
We study short-range ferromagnetic models residing on planar manifolds with global negative curvature. We show that the local metric properties of the embedding surface induce droplet formation from the boundary, resulting in the stability of a Griffiths phase at a temperature lower than that of the bulk transition. We propose that this behavior is independent of order parameter and hyperlattice specifics, and thus is universal for such non-Euclidean spin models. Their temperature-curvature phase diagrams are characterized by two distinct bulk and boundary transitions; each has mean-field critical behavior and a finite correlation length related to the curvature of the embedding surface. The implications for experiments on superconducting hyperlattice networks are also discussed.
We obtain a local estimate for the gradient of solutions to a second-order elliptic equation in divergence form with bounded measurable coefficients that are square-Dini continuous at the single point x=0. In particular, we treat the case of solutions that are not Lipschitz continuous at x=0. We show that our estimate is sharp.
We measure a triple quantum dot in the regime where three addition lines, corresponding to the addition of an electron to each of three dots, pass through each other. In particular, we probe the interplay between transport and the tridimensional nature of the stability diagram. We choose the regime most pertinent for spin qubit applications. We find that at low bias transport through the triple quantum dot circuit is only possible at six quadruple point locations. The results are consistent with an equivalent circuit model.
Laves-phase Nb{1+c}Fe_{2-c} is a rare itinerant intermetallic compound exhibiting magnetic quantum criticality at c_{cr}=1.5%Nb excess; its origin, and how alloying mediates it, remains an enigma. For NbFe_2, we show that an unconventional band critical point (uBCP) above the Fermi level E_F explains most observations, and that chemical alloying mediates access to this uBCP by an increase in E_F with decreasing electrons (increasing %Nb), counter to rigid-band concepts. We calculate that E_F enters the uBCP region for c_{cr} > 1.5%Nb and by 1.74%Nb there is no Nb site-occupation preference between symmetry-distinct Fe sites, i.e., no electron-hopping disorder, making resistivity near constant as observed. At larger Nb (Fe) excess, the ferromagnetic Stoner criterion is satisfied.
Recently, analytical solutions of a nonlinear Fokker-Planck equation describing anomalous diffusion with an external linear force were found using a non extensive thermostatistical Ansatz. We have extended these solutions to the case when an homogeneous absorption process is also present. Some peculiar aspects of the interrelation between the deterministic force, the nonlinear diffusion and the absorption process are discussed.
We provide an analogue of the Dulmage-Mendelsohn decomposition for a class of grafts known as comb-bipartite grafts. The Dulmage-Mendelsohn decomposition in matching theory is a classical canonical structure theorem for bipartite graphs. The substantial part of this classical theorem resides in bipartite graphs that are factorizable, that is, those with a perfect matching. Minimum joins in grafts, also known as minimum $T$-joins in graphs,   is a generalization of perfect matchings in factorizable graphs. Seb\"o revealed in his paper that comb-bipartite grafts form one of the two fundamental classes of grafts that serve as skeletons or building blocks of any grafts. Particularly, any bipartite grafts, that is, bipartite counterpart of grafts, can be considered as a recursive combination of comb-bipartite grafts. In this paper, we generalize the Dulmage-Mendelsohn decomposition for comb-bipartite grafts. We also show for this decomposition a property that is characteristics to grafts using the general Kotzig-Lov\'asz decomposition for grafts, which is a known graft analogue of another canonical structure theorem from matching theory. This paper is the first from a series of studies regarding bipartite grafts.
We report on a heretofore unnoted giant negative magnetocapacitance (>20%) in non-magnetic Au/GaAs:Si Schottky barriers that we attribute to a magnetic field in-duced increase in the binding energy of the shallow donor Si impurity atoms. Depletion capacitance (Cdep) dispersion identifies the impurity ionization and capture processes that give rise to a magnetic field dependent density of ionized impurities. Internal photoemission experiments confirm that the large field-induced shifts in the built-in potential, inferred from 1/Cdep^2 vs voltage measurements, are not due to a field-dependent Schottky barrier height, thus requiring a modification of the abrupt junction approximation that accounts for the observed magnetodielectric coupling.
The self--energy of the strange baryon $\Lambda$ in $^{17}$O is calculated using a microscopic many--body approach which accounts for correlations beyond the mean--field or Hartree--Fock approximation. The non-locality and energy-dependence of the $\Lambda$ self--energy is discussed and the effects on the bound and scattering states are investigated. For the nucleon--hyperon interaction, we use the potential models of the J\"{u}lich and Nijmegen groups.
We report on the polarization properties of two fast radio bursts (FRBs): 151230 and 160102 discovered in the SUrvey for Pulsars and Extragalactic Radio Bursts (SUPERB) at the Parkes radio telescope. FRB 151230 is observed to be 6 $\pm$ 11% circularly polarized and 35 $\pm$ 13 % linearly polarized with a rotation measure (RM) consistent with zero. Conversely, FRB 160102 is observed to have a circular polarization fraction of 30 $\pm$ 11 %, linear polarization fraction of 84 $\pm$ 15 % for RM = -221(6) rad m$^{-2}$ and the highest measured DM (2596.1 $\pm$ 0.3 pc cm$^{-3}$) for an FRB to date. We examine possible progenitor models for FRB 160102 in extragalactic, non-cosmological and cosmological scenarios. After accounting for the Galactic foreground contribution, we estimate the intrinsic RM to be -256(9) rad m$^{-2}$ in the low-redshift case and $\sim 2.4 \times 10^{2}$ rad m$^{-2}$ in the high-redshift case. We assess the relative likeliness of these scenarios and how each can be tested. We also place constraints on the scattering measure and study the impact of scattering on the signal's polarization position angle.
We have used the AMR hydrodynamic code, MG, to perform 3D hydrodynamic simulations with self-gravity of stellar feedback in a spherical clumpy molecular cloud formed through the action of thermal instability. We simulate the interaction of the mechanical energy input from 15 Msun, 40 Msun, 60 Msun and 120 Msun stars into a 100 pc-diameter 16,500 Msun cloud with a roughly spherical morphology with randomly distributed high density condensations. The stellar winds are introduced using appropriate non-rotating Geneva stellar evolution models. In the 15 Msun star case, the wind has very little effect, spreading around a few neighbouring clumps before becoming overwhelmed by the cloud collapse. In contrast, in the 40 Msun, 60 Msun and 120 Msun star cases, the more powerful stellar winds create large cavities and carve channels through the cloud, breaking out into the surrounding tenuous medium during the wind phase and considerably altering the cloud structure. After 4.97 Myrs, 3.97 Myrs and 3.01 Myrs respectively, the massive stars explode as supernovae (SNe). The wind-sculpted surroundings considerably affect the evolution of these SN events as they both escape the cloud along wind-carved channels and sweep up remaining clumps of cloud/wind material. The `cloud' as a coherent structure does not survive the SN from any of these stars, but only in the 120 Msun case is the cold molecular material completely destabilised and returned to the unstable thermal phase. In the 40 Msun and 60 Msun cases, coherent clumps of cold material are ejected from the cloud by the SN, potentially capable of further star formation.
In spontaneous parametric down conversion (SPDC) based quantum information processing (QIP) experiments, there is a tradeoff between the coincide count rates (i.e. the pumping power of the SPDC), which limits the rate of the protocol, and the visibility of the quantum interference, which limits the quality of the protocol. This tradeoff is mainly caused by the multi-photon pair emissions from the SPDCs. In theory, the problem is how to model the experiments without truncating these multi-photon emissions while including practical imperfections.   In this paper, we establish a method to theoretically simulate SPDC based QIPs which fully incorporates the effect of multi-photon emissions and various practical imperfections. The key ingredient in our method is the application of the characteristic function formalism which has been used in continuous variable QIPs. We apply our method to three examples, the Hong-Ou-Mandel interference and the Einstein-Podolsky-Rosen interference experiments, and the concatenated entanglement swapping protocol. For the first two examples, we show that our theoretical results quantitatively agree with the recent experimental results. Also we provide the closed expressions for these the interference visibilities with the full multi-photon components and various imperfections. For the last example, we provide the general theoretical form of the concatenated entanglement swapping protocol in our method and show the numerical results up to 5 concatenations. Our method requires only a small computation resource (few minutes by a commercially available computer) which was not possible by the previous theoretical approach. Our method will have applications in a wide range of SPDC based QIP protocols with high accuracy and a reasonable computation resource.
We consider Mn-doped bulk zinc-blende semiconductors described by the 4 $ \times$ 4 Luttinger Hamiltonian. In these semiconductors, Mn atom acts as an acceptor providing the system a mobile hole, and also acts like a magnetic impurity of spin $S=5/2$. We obtain exact analytical expressions of the hole mediated Ruderman-Kittel-Kasuya-Yoshida (RKKY) exchange interaction between two Mn${}^{2+}$ ions. The RKKY interaction of the Luttinger system consists of collinear Heisenberg-like and Ising-like interactions. The characteristic beating patterns appear in the range functions of the RKKY interaction owing to the presence of multiple Fermi wave-vectors of the underlying $j=3/2$ states. As an application of the analytical form of the range function, from the finite temperature evaluation of the correlation functions, we calculate the contribution of RKKY interaction to the Curie-Weiss temperatures of a particular dilute magnetic semiconductor ZnMnTe where $4\times4$ Luttinger Hamiltonian is valid.
Whether the Cygnus X complex consists of one physically connected region of star formation or of multiple independent regions projected close together on the sky has been debated for decades. The main reason for this puzzling scenario is the lack of trustworthy distance measurements. We aim to understand the structure and dynamics of the star-forming regions toward Cygnus X by accurate distance and proper motion measurements. To measure trigonometric parallaxes, we observed 6.7 GHz methanol and 22 GHz water masers with the European VLBI Network and the Very Long Baseline Array. We measured the trigonometric parallaxes and proper motions of five massive star-forming regions toward the Cygnus X complex and report the following distances within a 10% accuracy: 1.30+-0.07 kpc for W 75N, 1.46^{+0.09}_{-0.08} kpc for DR 20, 1.50^{+0.08}_{-0.07} kpc for DR 21, 1.36^{+0.12}_{-0.11} kpc for IRAS20290+4052, and 3.33+-0.11kpc for AFGL 2591. While the distances of W 75N, DR 20, DR 21, and IRAS 20290+4052 are consistent with a single distance of 1.40+-0.08 kpc for the Cygnus X complex, AFGL 2591 is located at a much greater distance than previously assumed. The space velocities of the four star-forming regions in the Cygnus X complex do not suggest an expanding Stroemgren sphere.
Ammonium DiNitramide (ADN) is one of the most promising green energetic oxidizers for future rocket propellant formulations. In the present work, we report a detailed theoretical study on structural, elastic, and vibrational properties of the emerging oxidizer under hydrostatic compression using various dispersion correction methods to capture weak intermolecular (van der Waals and hydrogen bonding) interactions. The calculated ground state lattice parameters, axial compressibilities, and equation of state are in good accord with the available experimental results. Strength of intermolecular interactions has been correlated using the calculated compressibility curves and elastic moduli. Apart from this, we also observe discontinuities in the structural parameters and elastic constants as a function of pressure. Pictorial representation and quantification of intermolecular interactions are described by the 3D Hirshfeld surfaces and 2D finger print maps. In addition, the computed infra-red (IR) spectra at ambient pressure reveal that ADN is found to have more hygroscopic nature over Ammonium Perchlorate (AP) due to the presence of strong hydrogen bonding. Pressure dependent IR spectra show blue- and red-shift of bending and stretching frequencies which leads to weakening and strengthening of the hydrogen bonding below and above 5 GPa, respectively. The abrupt changes in the calculated structural, mechanical, and IR spectra suggest that ADN might undergo a first order structural transformation to a high pressure phase around 5-6 GPa. From the predicted detonation properties, ADN is found to have high and low performance characteristics when compared with ammonium based energetic oxidizers and well-known secondary explosives, respectively.
In this paper we present a superspace formulation of $N = 1, D = 6$ supergravity with one tensor-multiplet and an arbitrary number of vector- and hypermultiplets, in which the bosonic abelian superforms of the theory, the dilaton, the abelian gauge fields and the two-form are replaced by their S-duals i.e. four, three and two-superforms respectively, in compatibility with supersymmetry. As usual this replacement interchanges Bianchi identities with equations of motion. This formulation holds in the presence of one tensor multiplet and arbitrary numbers of hypermultiplets and abelian super-Maxwell multiplets if all couplings are minimal. We determine the consistency conditions for non-minimal couplings in $N = 1$, $D = 6$ supergravity, for which we present a particularly significant solution, namely the one associated with the Chern-Simons-Lorentz three-form which entails the Green-Schwarz anomaly cancellation mechanism. In the case of non minimal couplings it is found that the gauge fields and the two-form can still be dualized while the dilaton has to remain a zero-form.
This is (hopefully) a Latexable version of a talk given at the XXX Winter School in Theoretical Physics at Karpacz in February 1994. It discusses the use of non-commutative differential calculus to construct a Lie algebra of a quantum group. Usually the result has a different dimension from the classical Lie algebra. This is illustrated by menas of the orthogonal quantum group, and various other possible ways of constructing an orthogonal Lie algebra are described.