ShantanuT01/DACTYL-Pretraining huggingface dataset:
We investigate the influence on the density of states and the density of spin polarization for a two-dimensional hole gas with Rashba spin-orbit coupling under intense terahertz laser fields. Via Floquet theorem, we solve the time-dependent Schr\"{o}dinger equation and calculate these densities. It is shown that a terahertz magnetic moment can be induced for low hole concentration. Different from the electron case, the induced magnetic moment is quite anisotropic due to the anisotropic spin-orbit coupling. Both the amplitude and the direction of the magnetic moment depend on the direction of the terahertz field. We further point out that for high hole concentration, the magnetic moment becomes very small due to the interference caused by the momentum dependence of the spin-orbit coupling. This effect also appears in two-dimensional electron systems.
Let $k$ be a field containing $\mathbb{F}_q$. Let $\psi$ be a rank $r$ Drinfeld $\mathbb{F}_q[t]$-module determined by $\psi_t(X) = tX+a_1X^q+\cdots+a_{r-1}X^{q^{r-1}}+X^{q^r}$, where $t,a_1,\ldots,a_{r-1}$ are algebraically independent over $k$. Let $n\in\mathbb{F}_q[T]$ be a monic polynomial. We show that the Galois group of $\psi_n(X)$ over $k(t,a_1,\ldots,a_{r-1})$ is isomorphic to $\mathrm{GL}_r(\mathbb{F}_q[t]/n\mathbb{F}_q[t])$, settling a conjecture of Abhyankar. Along the way we obtain an explicit construction of Drinfeld moduli schemes of level $tn$.
We report the discovery of new Herbig-Haro (HH) jets in the Carina Nebula, and we discuss the protostellar outflow activity of a young OB association. These are the first results of an HST/ACS H-alpha imaging survey of Carina. Adding to the one previously known example (HH666), we detect 21 new HH jets, plus 17 new candidate jets, ranging in length from 0.005 to 3 pc. We derive jet mass-loss rates ranging from 8e-9 to 1e-6 Msun/yr, but a comparison to the distribution of jet mass-loss rates in Orion suggests that we may be missing a large fraction of the jets below 1e-8 Msun/yr. A key qualitative result is that even some of the smallest dark globules with sizes of 0.01pc are active sites of ongoing star formation because we see HH jets emerging from them, and that these offer potential analogs to the cradle of our Solar System because of their proximity to dozens of imminent supernovae that will enrich them with radioactive nuclides like 60Fe. HST images reveal proplyd structures in the core of the Tr14 cluster, only 0.1-0.2 pc from several O-type stars. Many examples of bent jets serve as "wind socks"; strong photoevaporative flows can shape the jets, competing with the direct winds and radiation from massive stars. Finally, even allowing for a large number of jets that may escape detection, we find that HH jets are negligible to the global turbulence of the surrounding region, which is driven by massive star feedback.
We report the crystal structure and highly-anisotropic magnetic, transport and thermal properties of an exceptionally good single crystal of U(Ru0.92Rh0.08)2Si2 prepared using a modified Czochralski method. Our study, that also includes neutron diffraction results, shows all the heavy-fermion signatures of pristine URu2Si2 , however, the superconductivity, hidden order and remanent weak antiferromagnetic orders are absent. Instead, the ground state of the doped system can be classified as a spin liquid that preserves the heavy-fermion character. U(Ru0.92Rh0.08)2Si2 exhibits a short-range magnetic order distinguished by reflections of a Lorentzian profile at qIII = (1/2 1/2 1/2) positions that disappear above approx. 15 K. The short-range order seems to be a precursor of a long-range magnetic order that occurs with higher Rh concentration. We indicate that these short-range fluctuations involve, at least partially, inelastic scattering processes.
We use the Millennium Simulation series to study the relation between the accretion history (MAH) and mass profile of cold dark matter halos. We find that the mean density within the scale radius, r_{-2} (where the halo density profile has isothermal slope), is directly proportional to the critical density of the Universe at the time when the main progenitor's virial mass equals the mass enclosed within r_{-2}. Scaled to these characteristic values of mass and density, the mean MAH, expressed in terms of the critical density of the Universe, M(\rho_{crit}(z)), resembles that of the enclosed density profile, M(<\rho >), at z=0. Both follow closely the NFW profile, suggesting that the similarity of halo mass profiles originates from the mass-independence of halo MAHs. Support for this interpretation is provided by outlier halos whose accretion histories deviate from the NFW shape; their mass profiles show correlated deviations from NFW and are better approximated by Einasto profiles. Fitting both M(<\rho >) and M(\rho_{crit}) with either NFW or Einasto profiles yield concentration and shape parameters that are correlated, confirming and extending earlier work linking the concentration of a halo with its accretion history. These correlations also confirm that halo structure is insensitive to initial conditions: only halos whose accretion histories differ greatly from the NFW shape show noticeable deviations from NFW in their mass profiles. As a result, the NFW profile provides acceptable fits to hot dark matter halos, which do not form hierarchically, and for fluctuation power spectra other than CDM. Our findings, however, predict a subtle but systematic dependence of mass profile shape on accretion history which, if confirmed, would provide strong support for the link between accretion history and halo structure we propose here.
In this paper, we formulate a generalised photon Boltzmann hierarchy that allows us to model the evolution and creation of spectral distortion anisotropies in the early Universe. We directly build on our first paper in this series, extending the thermalisation Green's function treatment to the anisotropic case. We show that the problem can be described with the common Boltzmann hierarchy for the photon field extended by new spectral parameters -- a step that reduces the complexity of the calculation by at least two orders of magnitude. Our formalism describes the effects of i) Doppler and potential driving, ii) spectral evolution by Compton scattering, iii) perturbed thermalisation and iv) anisotropic heating on the distortion anisotropies. We highlight some of the main physical properties of the equations and also outline the steps for computing CMB power spectra including distortion anisotropies. Limitations and extensions of the formulation are also briefly discussed. The novel Boltzmann hierarchy given here is the basis for a series of companion papers studying how distortion anisotropies evolve in the perturbed Universe and which physical processes could be constrained using future CMB imaging techniques.
I describe an empirical-yet-rigorous, algorithm, based on Riordan's rook polynomials and the so-called C-finite ansatz, fully implemented in the accompanying Maple package (http://www.math.rutgers.edu/~zeilberg/tokhniot/MENAGES ), MENAGES, that reproduces in a few seconds, rigorously-proved enumeration theorems on permutations with restricted positions, previously proved by quite a few illustrious human mathematicians, and that can go far beyond any human attempts.
A study of the high angular momentum particles 'atmosphere' near the Schwarzschild black hole horizon suggested that strong gravitational interactions occur at invariant distance of the order of $\sqrt[3]{M}$ (A. Casher et. al). We present a generalization of this result to the Kerr-Newman black hole case. It is shown that the larger charge and angular momentum black hole bears, the larger invariant distance at which strong gravitational interactions occur becomes. This invariant distance is of order $\sqrt[3]{r_+^2/\hh}.$ This implies, that the Planckian structure of the Hawking radiation of extreme black holes is completely broken.
Exponential tightness of a family of Skorohod integrals is studied in this paper. We first provide a counterexample to illustrate that in general the exponential tightness with speed $\epsilon$ similar to It\^o integral does not hold, even for any speed $\epsilon^\alpha$ with $\alpha > 0$. Then, some characterizations of this subject are given. Application is also provided to illustrate the proposed results.
Given $2k-1$ convex sets in $R^2$ such that no point of the plane is covered by more than $k$ of the sets, is it true that there are two among the convex sets whose union contains all $k$-covered points of the plane? This question due to Gy. Petruska has an obvious affirmative answer for $k=1,2,3$; we show here that the claim is also true for $k=4$, and we present a counterexample for $k=5$. We explain how Petruska's geometry question fits into the classical hypergraph extremal problems, called arrow problems, proposed by P. Erd\H{o}s.
Let K/F be a finite Galois extension of global fields with Galois group G and let M be a 1-motive over F. We discuss the kernel and cokernel of the restriction map Sha^{i}(F,M) --> Sha^{i}(K,M)^{G} for i=1 and 2, independently of any finiteness hypotheses. We show that these groups are finite and obtain, in particular, formulas for the corresponding quotient of group orders.
We have investigated the optical and transport properties of MBE grown short-period superlattices of InAs/GaAs with different numbers of periods (3 <= N <= 24) and a total thickness 14 nm. Bandstructure calculations show that these superlattices represent a quantum well with average composition In_0.16Ga_0.84As. The electron wave functions are only slightly modulated by the superlattice potential as compared to a single quantum well with the same composition, which was grown as a reference sample. The photoluminescence, the resistance, the Shubnikov-de Haas effect and the Hall effect have been measured as a function of the InAs layer thickness Q in the range 0.33 <= Q <= 2.7 monolayers (ML). The electron densities range from 6.8 to 11.5x10^11 cm^-2 for Q <= 2.0 ML. The photoluminescence and magnetotransport data show that only one subband is occupied. When Q >= 2.7 ML quantum dots are formed and the metallic type of conductivity changes to variable range hopping conductivity.
In this paper we construct $q$-Genocchi numbers and polynomials.   By using these numbers and polynomials, we investigate the   $q$-analogue of alternating sums of powers of consecutive   integers due to Euler.
We determine the number of functionally independent components of tensors involving higher-order derivatives of a Riemannian metric.
Blazar spectral models generally have numerous unconstrained parameters, leading to ambiguous values for physical properties like Doppler factor delta or fluid magnetic field B'. To help remedy this problem, a few modifications of the standard leptonic blazar jet scenario are considered. First, a log-parabola function for the electron distribution is used. Second, analytic expressions relating energy loss and kinematics to blazar luminosity and variability, written in terms of equipartition parameters, imply delta, B', and the principal electron Lorentz factor gamma'_pk. The external radiation field in a blazar is approximated by Ly alpha radiation from the broad line region (BLR) and ~0.1 eV infrared radiation from a dusty torus. When used to model 3C 279 SEDs from 2008 and 2009 reported by Hayashida et al. (2012), we derive delta ~ 20-30, B' ~ few G, and total (IR + BLR) external radiation field energy densities u ~ 0.01 - 0.001 erg/cm^3, implying an origin of the gamma-ray emission site in 3C 279 at the outer edges of the BLR. This is consistent with the gamma-ray emission site being located at a distance R <~ Gamma^2 c t_{var} ~ 0.1 (\Gamma/30)^2 (t_{var}/10^4 s) pc from the black hole powering 3C 279's jets, where t_{var} is the variability time scale of the radiation in the source frame, and at farther distances for narrow-jet and magnetic_reconnection models. Excess >~ 5 GeV gamma-ray emission observed with Fermi LAT from 3C 279 challenge the model, opening the possibility of hadronic origins of the emission. For low hadronic content, absolute jet powers of ~10% of the Eddington luminosity are calculated.
Let $L$ be a nonnegative, self-adjoint operator satisfying Gaussian estimates on $L^2(\RR^n)$. In this article we give an atomic decomposition for the Hardy spaces $ H^p_{L,max}(\R)$ in terms of the nontangential maximal functions associated with the heat semigroup of $L$, and this leads eventually to characterizations of Hardy spaces associated to $L$, via atomic decomposition or the nontangential maximal functions. The proofs are based on a modification of technique due to A. Calder\'on \cite{C}.
We consider the Klein-Gordon equation on two half-axes connected at their origins. We add a potential that is constant but different on each branch. In a previous paper, we studied the L-infinity-time decay via H\"ormander's version of the stationary phase method. Here we apply these results to show that for initial conditions in an energy band above the threshold of the tunnel effect a fixed portion of the energy propagates between group lines. Further we consider the situation that the potential difference tends to infinity while the energy band of the initial condition is shifted upwards such that the particle stays above the threshold of tunnel effect. We show that the total transmitted energy as well as the portion between the group lines tend to zero like the inverse of the square root of the higher potential in the corresponding branch if this potential tends to infinity. At the same time the cone formed by the group lines inclines to the t-axis while its aperture tends to zero.
The graph of overlapping permutations is defined in a way analogous to the De Bruijn graph on strings of symbols. That is, for every permutation $\pi = \pi_{1} \pi_{2} ... \pi_{n+1}$ there is a directed edge from the standardization of $\pi_{1} \pi_{2} ... \pi_{n}$ to the standardization of $\pi_{2} \pi_{3} ... \pi_{n+1}$. We give a formula for the number of cycles of length $d$ in the subgraph of overlapping 312-avoiding permutations. Using this we also give a refinement of the enumeration of 312-avoiding affine permutations and point out some open problems on this graph, which so far has been little studied.
The LIT method has allowed ab initio calculations of electroweak cross sections in light nuclear systems. This review presents a description of the method from both a general and a more technical point of view, as well as a summary of the results obtained by its application. The remarkable features of the LIT approach, which make it particularly efficient in dealing with a general reaction involving continuum states, are underlined. Emphasis is given on the results obtained for electroweak cross sections of few--nucleon systems. Their implications for the present understanding of microscopic nuclear dynamics are discussed.
A promising material for hydrogen storage at room temperature-Al doped graphene was proposed theoretically by using density functional theory calculation. Hydrogen storage capacity of 5.13 wt% was predicted at T = 300 K and P = 0.1 Gpa with adsorption energy Eb = -0.260 eV/H2. This is close to the target of 6 wt% and satisfies the requirement of immobilization hydrogen with Eb of -0.2 ~ -0.4 eV/H2 at ambient temperature and modest pressure for commercial applications specified by U.S. Department of Energy. It is believed that the doped Al varies the electronic structures of both C and H2. The bands of H2 overlapping with those of Al and C synchronously are the underlying mechanism of hydrogen storage capacity enhancement.
To determine whether the Shapiro time delay of light passing near a moving object depends on the ``speed of gravity'' or the ``speed of light,'' one must analyze observations in a bimetric framework in which these two speeds can be different. In a recent comment (gr-qc/0510048), Kopeikin has argued that such a computation -- described in gr-qc/0403060 -- missed a hidden dependence on the speed of gravity. By analyzing the observables in the relevant bimetric model, I show that this claim is incorrect, and that the conclusions of gr-qc/0403060 stand.
We present a fiber-based source of polarization-entangled photon pairs that is well suited for quantum communication applications in the 1.5$\mu$m band of standard telecommunication fiber. Quantum-correlated signal and idler photon pairs are produced when a nonlinear-fiber Sagnac interferometer is pumped in the anomalous-dispersion region of the fiber. Recently, we have demonstrated nonclassical properties of such photon pairs by using Geiger-mode InGaAs/InP avalanche photodiodes. Polarization entanglement in the photon pairs can be created by pumping the Sagnac interferometer with two orthogonally polarized pulses. In this case the parametrically scattered signal-idler photons yield biphoton interference with $>$90% visibility in coincidence detection, while no interference is observed in direct detection of either the signal or the idler photons.
Precision measurements of the Hall effect have been carried out for both archetypal heavy fermion compound - CeCu6 and exemplary solid solutions CeCu6-xAux (x= 0.1 and 0.2) with quantum critical behavior. The experimental results have been obtained by technique with a sample rotation in magnetic field in the temperature range 1.8-300K. The experiment revealed a complex activation type dependence of the Hall coefficient RH(T) in CeCu6 with activation energies Ea1/kB = 110K and Ea2/kB = 1.5K in temperature ranges 50-300K and 3-10K, respectively. Microscopic parameters of charge carriers transport (effective masses, relaxation time) and localization radii ap1,2* of heavy fermions (ap1*(T>50K)= 1.7 A and ap2*(T<20K)= 14 A) were estimated for CeCu6. The second angular harmonic contribution has been established in the Hall voltage of CeCu5.9Au0.1 and CeCu6 at temperatures below T*=24K. A hyperbolic type divergence of the second harmonic term in Hall effect RH2(T)= C(1/T-1/T*) at low temperatures is found to be accompanied with a power-law behavior RH(T)= T -0.4 of the main contribution in the Hall coefficient for CeCu5.9Au0.1 compound with quantum critical behavior.
We present a method for quantum state tomography that enables the efficient estimation, with fixed precision, of any of the matrix elements of the density matrix of a state, provided that the states from the basis in which the matrix is written can be efficiently prepared in a controlled manner. Furthermore, we show how this algorithm is well suited for quantum process tomography, enabling to perform selective and efficient quantum process tomography.
We study the formation of antiferromagnetic correlations induced by impurity doping in anisotropic two-dimensional spin-Peierls systems. Using a mean-field approximation to deal with the inter-chain magnetic coupling, the intra-chain correlations are treated exactly by numerical techniques. The magnetic coupling between impurities is computed for both adiabatic and dynamical lattices and is shown to have an alternating sign as a function of the impurity-impurity distance, hence suppressing magnetic frustration. An effective model based on our numerical results supports the coexistence of antiferromagnetism and dimerization in this system.
The identifiability of parameters in a probabilistic model is a crucial notion in statistical inference. We prove that a general tensor of rank 8 in C^3\otimes C^6\otimes C^6 has at least 6 decompositions as sum of simple tensors, so it is not 8-identifiable. This is the highest known example of balanced tensors of dimension 3, which are not k-identifiable, when k is smaller than the generic rank.
We report on searches for neutrino sources at energies above 200 GeV in the Northern sky of the galactic plane, using the data collected by the South Pole neutrino telescopes IceCube and AMANDA. The galactic region considered here includes the Local Arm towards the Cygnus region and our closest approach to the Perseus Arm. The data have been collected between 2007 and 2009 when AMANDA was an integrated part of IceCube, which was still under construction and operated with 22-strings (2007-8) and 40-strings (2008-9) of optical modules deployed in the ice. By combining the larger IceCube detector with the lower energy threshold of the more compact AMANDA detector, we obtain an improved sensitivity at energies below $\sim$10 TeV with respect to previous searches. The analyses presented here are: a scan for point sources within the galactic plane; a search optimized for multiple and extended sources in the Cygnus region, which might be below the sensitivity of the point source scan; and studies of seven pre-selected neutrino source candidates. For one of them, Cygnus X-3, a time-dependent search for neutrinos in coincidence with observed radio and X-ray flares has been performed. No evidence of a signal is found, and upper limits are reported for each of the searches. We investigate neutrino spectra proportional to E$^{-2}$ and E$^{-3}$ to cover the entire range of possible spectra. The soft E$^{-3}$ spectrum results in an energy distribution similar to a source with cut-off below $\sim$50 TeV. For the considered region of the galactic plane, the 90% confidence level muon neutrino flux upper limits are in the range E$^3$dN/dE$\sim 5.4 - 19.5 \times 10^{-11} \rm{TeV^{2} cm^{-2} s^{-1}}$ for point-like neutrino sources in the energy region [180.0 GeV - 20.5 TeV]. These represent the most stringent upper limits for soft-spectra neutrino sources within the Galaxy reported to date.
In our own solar system, the necessity of understanding space weather is readily evident. Fortunately for Earth, our nearest stellar neighbor is relatively quiet, exhibiting activity levels several orders of magnitude lower than young, solar-type stars. In protoplanetary systems, stellar magnetic phenomena observed are analogous to the solar case, but dramatically enhanced on all physical scales: bigger, more energetic, more frequent. While coronal mass ejections (CMEs) could play a significant role in the evolution of protoplanets, they could also affect the evolution of the central star itself. To assess the consequences of prominence eruption/CMEs, we have invoked the solar-stellar connection to estimate, for young, solar-type stars, how frequently stellar CMEs may occur and their attendant mass and angular momentum loss rates. We will demonstrate the necessary conditions under which CMEs could slow stellar rotation.
This paper combines the graph-theoretical ideas behind Moravcsik's theorem with a completely analytic derivation of discrete phase-ambiguities, recently published by Nakayama. The result is a new graphical procedure for the derivation of certain types of complete sets of observables for an amplitude-extraction problem with $N$ helicity-amplitudes. The procedure is applied to pseudoscalar meson photoproduction ($N = 4$ amplitudes) and electroproduction ($N = 6$ amplitudes), yielding complete sets with minimal length of $2N$ observables. For the case of electroproduction, this is the first time an extensive list of minimal complete sets is published. Furthermore, the generalization of the proposed procedure to processes with a larger number of amplitudes, i.e. $N > 6$ amplitudes, is sketched. The generalized procedure is outlined for the next more complicated example of two-meson photoproduction ($N = 8$ amplitudes).