ShantanuT01/DACTYL-Pretraining huggingface dataset:
We construct a recurrent diffusion process with values in the space of probability measures over an arbitrary closed Riemannian manifold of dimension $d\ge 2$. The process is associated with the Dirichlet form defined by integration of the Wasserstein gradient w.r.t. the Dirichlet-Ferguson measure, and is the counterpart on multi-dimensional base spaces to the Modified Massive Arratia Flow over the unit interval described in V. Konarovskyi, M.-K. von Renesse, Comm. Pure Appl. Math., 72, 0764-0800 (2019). Together with two different constructions of the process, we discuss its ergodicity, invariant sets, finite-dimensional approximations, and Varadhan short-time asymptotics.
This paper uses the machinery of almost periodic functions to prove that even without uniform convergence the connection between a pair of almost periodic functions and the constants of the associated Fourier series exists for both the convolution and cross-correlation.   The general results for two almost periodic functions are narrowed and applied to Ramanujan sums and finally applied to support the specific relation of the Wiener-Khinchin formula for arithemic functions with a Ramanujan-Fourier Series.
We report on surface effects on the electronic properties of interfaces in epitaxial LaAlO$_3$/SrTiO$_3$ heterostructures. Our results are based on first-principles electronic structure calculations for well-relaxed multilayer configurations, terminated by an ultrathin LaAlO$_3$ surface layer. On varying the thickness of this layer, we find that the interface conduction states are subject to almost rigid band shifts due to a modified Fermi energy. Confirming experimental data, the electronic properties of heterointerfaces therefore can be tuned systematically by alterating the surface-interface distance. We expect that this mechanism is very general and applies to most oxide heterostructures.
We present medium-resolution spectroscopy of a sample of stars in the second Galactic quadrant selected from the literature because their colours suggest that they are moderately-reddened early-type stars at very large distances.   From the derived spectral types and observed colours, we calculate distances to all these objects. For a sizable fraction of our sample, we find distances well in excess of what is expected for Perseus Arm objects, even allowing for rather generous errors. In the interval l=150degr-180degr, there is a large number of objects with distances in excess of 4 kpc, which are likely tracing the Outer or Cygnus Arm. In particular, we find that the association Cam OB3 is placed on this Arm. Based on our results, the extent and definition of the associations Cas OB4 and Aur OB2 need to be reevaluated.
We investigate the Mott transition in weakly-coupled one-dimensional (1d) fermionic chains. Using a generalization of Dynamic Mean Field Theory, we show that the Mott gap is suppressed at some critical hopping $t_{\perp}^{c2}$. The transition from the 1d insulator to a 2d metal proceeds through an intermediate phase where the Fermi surface is broken into electron and hole pockets. The quasiparticle spectral weight is strongly anisotropic along the Fermi surface, both in the intermediate and metallic phases. We argue that such pockets would look like `arcs' in photoemission experiments.
Key to realising quantum computers is minimising the resources required to build logic gates into useful processing circuits. While the salient features of a quantum computer have been shown in proof-of-principle experiments, difficulties in scaling quantum systems have made more complex operations intractable. This is exemplified in the classical Fredkin (controlled-SWAP) gate for which, despite theoretical proposals, no quantum analogue has been realised. By adding control to the SWAP unitary, we use photonic qubit logic to demonstrate the first quantum Fredkin gate, which promises many applications in quantum information and measurement. We implement example algorithms and generate the highest-fidelity three-photon GHZ states to-date. The technique we use allows one to add a control operation to a black-box unitary, something impossible in the standard circuit model. Our experiment represents the first use of this technique to control a two-qubit operation and paves the way for larger controlled circuits to be realised efficiently.
We consider a stochastic variant of the Abelian Sandpile Model (ASM) on a finite graph, introduced by Chan, Marckert and Selig. Even though it is a more general model, some nice properties still hold. We show that on a certain probability space, even if we lose the group structure due to topplings not being deterministic, some operators still commute. As a corollary, we show that the stationary distribution still does not depend on how sand grains are added onto the graph in our model, answering a conjecture of Selig.
The 3 alpha orthogonality condition model using the Pauli-forbidden bound states of the Buck, Friedlich and Wheatly alpha alpha potential can yield a compact 3 alpha ground state with a large binding energy, in which a small admixture of the redundant components can never be eliminated.
Observations reveal that mature spiral galaxies consist of stars, gases and plasma approximately distributed in a thin disk of circular shape, usually with a central bulge. The rotation velocities quickly increase from the galactic center and then achieve a constant velocity from the core to the periphery. The basic dynamic behavior of a mature spiral galaxy, such as the Milky Way, is well described by simple models balancing Newtonian gravitational forces against the centrifugal forces associated with a rotating thin axisymmetric disk. In this research, we investigate the effects of adding central bulges to thin disk gravitational models. Even with the addition of substantial central bulges, all the critical essential features of our thin disk gravitational models are preserved. (1) Balancing Newtonian gravitational and centrifugal forces at every point within the disk yields computed radial mass distributions that describe the measured rotation velocity profiles of mature spiral galaxies successfully. (2) There is no need for gravity deviations or ``massive peripheral spherical halos of mysterious Dark Matter''. (3) The calculated total galactic masses are in good agreement with star count data. (4) The addition of central bulges increases the calculated total galactic masses, possibly more consistent with the presence of galactic gases, dust, grains, lumps, planets and plasma in addition to stars. (5) Compared with the light distribution, our mass distributions within the disk are larger out toward the galactic periphery which is cooler with lower opactiy/emissivity (and thus darker). This is apparent from edge-on views of galaxies which display a dark disk-line against a much brighter galactic halo.
An anomaly is said to occur when a symmetry that is valid classically becomes broken as a result of quantization. Although most manifestations of this phenomenon are in the context of quantum field theory, there are at least two cases in quantum mechanics--the two dimensional delta function interaction and the 1/r^2 potential. The former has been treated in this journal; in this article we discuss the physics of the latter together with experimental consequences.
The manipulation of the self-organized critical systems by repeatedly deliberate local relaxations (fillips) affect considerably the dynamics of avalanches and change their evolution. During a fillip, the energy diffuses to the neighboring regions, causing a smoothening of the height filed over the system. The fillips are controlled by a parameter $\zeta$ which is related to the number of local smoothening events in an avalanche. The system shows a new (mass and time) scales, leading to some oscillatory behaviors. A bifurcation occurs at some $\zeta$ value, above which some oscillations occur in the mean energy, and also in the autocorrelation functions. These oscillations are associated with \textit{spanning avalanches} which are due to the accumulation of energy in the smoothed system. The analysis of the rare event waiting time (REWT) confirms also the appearance of this new time scale. A mean field analysis is presented to explain some results.
We perform large-space shell-model calculations for the low-lying energy spectra of a few light nuclei, $^4\mbox{He}$, $^5\mbox{He}$, $^6\mbox{Li}$ and $^7\mbox{Li}$, in a no-core model space with a realistic effective two-body interaction (Brueckner G-matrix). Our G-matrices are calculated for the Reid-soft-core potential in a harmonic oscillator basis. Single-particle ``-U'' insertions are replaced by two-particle ``-U'' insertions and are included in the G matrix calculations, which sum them to all orders. With the starting energy of the G-matrix chosen to give approximately the experimental binding energy, we obtain nuclear energy spectra which are in reasonable agreement with experiment. We also investigate the dependence of our results on the size of the model space and on the harmonic oscillator basis parameter ($\hbar\Omega$).
A short overview is presented of current issues concerning the production and evolution of Li, Be and B in the Milky Way. In particular, the observed "primary-like" evolution of Be is re-assessed in the light of a novel idea: it is argued that Galactic Cosmic Rays are accelerated from the wind material of rotating massive stars, hit by the forward shock of the subsequent supernova explosions. The pre-galactic levels of both Li isotopes remain controversial at present, making it difficult to predict their Galactic evolution. A quantitative estimate is provided of the contributions of various candidate sources to the solar abundance of Li.
We present the results of a search for new members of the Taurus star-forming region using data from the Spitzer Space Telescope and the XMM-Newton Observatory. We have obtained optical and near-infrared spectra of 44 sources that exhibit red Spitzer colors that are indicative of stars with circumstellar disks and 51 candidate young stars that were identified by Scelsi and coworkers using XMM-Newton. We also performed spectroscopy on four possible companions to members of Taurus that were reported by Kraus and Hillenbrand. Through these spectra, we have demonstrated the youth and membership of 41 sources, 10 of which were independently confirmed as young stars by Scelsi and coworkers. Five of the new Taurus members are likely to be brown dwarfs based on their late spectral types (>M6). One of the brown dwarfs has a spectral type of L0, making it the first known L-type member of Taurus and the least massive known member of the region (M=4-7 M_Jup). Another brown dwarf exhibits a flat infrared spectral energy distribution, which indicates that it could be in the protostellar class I stage (star+disk+envelope). Upon inspection of archival images from various observatories, we find that one of the new young stars has a large edge-on disk (r=2.5=350 AU). The scattered light from this disk has undergone significant variability on a time scale of days in optical images from the Canada-France-Hawaii Telescope. Using the updated census of Taurus, we have measured the initial mass function for the fields observed by XMM-Newton. The resulting mass function is similar to previous ones that we have reported for Taurus, showing a surplus of stars at spectral types of K7-M1 (0.6-0.8 M_sun) relative to other nearby star-forming regions like IC 348, Chamaeleon I, and the Orion Nebula Cluster.
A twisted ring is a ring endowed with a family of endomorphisms satisfying certain relations. One may then consider the notions of twisted module and twisted differential module. We study them and show that, under some general hypothesis, the categories of twisted modules and integrable twisted differential modules are equivalent. As particular cases, one recovers classical results from the theory of finite difference equations or q-difference equations.
The double Gamow-Teller strength distributions in the lightest double beta-decay candidate $^{48}$Ca and its isotope $^{46}$Ca were calculated using the nuclear shell model by applying the single Gamow-Teller operator two times sequentially on the ground state of parent nucleus. The nuclear matrix element of the double Gamow-Teller transition from the ground state to the ground state that goes into the double beta decay calculation was shown as a small fraction of the total transition.
We present optical broad- and narrow-band imaging of a sample of a dozen barred galaxies. These images are analyzed in conjunction with our previously published near-infrared imaging of their central regions and with literature values for, e.g., bar strengths and the total star formation activity of the galaxies. We present B, I and H alpha images, and radial profiles derived from these, to infer geometric and dynamical parameters of the structural components of the galaxies, such as bar lengths, bar ellipticities, and location of star formation and dust. We find that the more centrally concentrated the H alpha emission in a galaxy is, i.e., the higher the fraction of star formation originating in the circumnuclear region, the higher the overall star formation rate, as measured from far-infrared flux ratios. Stronger bars host smaller nuclear rings, but the strength of the bar does not correlate with either the intrinsic ellipticity of the ring or the offset between the position angles of the bar and the ring. We interpret these results in comparison with modelling of gas inflow in the circumnuclear region, and show that they were theoretically expected. We confirm observationally, and for the first time, the anti-correlation predicted from theory and modelling between the degree of curvature of the bar dust lanes and the strength of the bar, where stronger bars have straighter dust lanes.
A new set of exact scattering matrices in 1+1 dimensions is proposed by solving the bootstrap equations. Extending earlier constructions of colour valued scattering matrices this new set has its colour structure associated to non simply-laced Lie algebras. This in particular leads to a coupling of different affine Toda models whose fusing structure has to be matched in a suitable manner. The definition of the new S-matrices is motivated by the semi-classical particle spectrum of the non simply-laced Homogeneous Sine-Gordon (HSG) models, which are integrable perturbations of WZNW cosets. In particular, the S-matrices of the simply-laced HSG models are recovered as a special case.
We discuss a generalization of Kummer construction which, on the base of an integral representation of a finite group and local resolution of its quotient, produces a higher dimensional variety with trivial canonical class. As an application we compute cohomology of some generalized Kummer varieties.
We construct families of optimal Hardy-weights for a subcritical linear second-order elliptic operator $(P,B)$ with degenerate mixed boundary conditions. By an optimal Hardy-weight for a subcritical operator we mean a nonzero nonnegative weight function $W$ such that $(P-W,B)$ is critical and null-critical with respect to $W$. Our results rely on a recently developed criticality theory for positive solutions of the corresponding mixed boundary value problem.
We present the observational evidence of the 2-halo term in the stacked shear profile of a sample of about 1200 optically selected galaxy clusters based on imaging data and the public shear catalog from the CFHTLenS. We find that the halo bias, a measure of the correlated distribution of matter around galaxy clusters, has amplitude and correlation with galaxy cluster mass in very good agreement with the predictions based on the LCDM standard cosmological model. The mass-concentration relation is flat but higher than theoretical predictions. We also confirm the close scaling relation between the optical richness of galaxy clusters and their mass.
We study the computational complexity of the problem SFT (Sum-free Formula partial Trace): given a tensor formula F over a subsemiring of the complex field (C,+,.) plus a positive integer k, under the restrictions that all inputs are column vectors of L2-norm 1 and norm-preserving square matrices, and that the output matrix is a column vector, decide whether the k-partial trace of $F\dagg{F}$ is superior to 1/2. The k-partial trace of a matrix is the sum of its lowermost k diagonal elements. We also consider the promise version of this problem, where the 1/2 threshold is an isolated cutpoint. We show how to encode a quantum or reversible gate array into a tensor formula which satisfies the above conditions, and vice-versa; we use this to show that the promise version of SFT is complete for the class BPP for formulas over the semiring (Q^+,+,.) of the positive rational numbers, for BQP in the case of formulas defined over the field (Q,+,.), and for P in the case of formulas defined over the Boolean semiring, all under logspace-uniform reducibility. This suggests that the difference between probabilistic and quantum polynomial-time computers may ultimately lie in the possibility, in the latter case, of having destructive interference between computations occuring in parallel.
We present an upgraded calculation of the effects of resonance-continuum interference for the Higgs boson decaying to two photons at the Large Hadron Collider, at next-to-leading order in the strong coupling $\alpha_S$, $O(\alpha_S^3)$, and including transverse-momentum ($q_T$) resummation at next-to-leading logarithmic accuracy. We study the importance of the interference contribution in different transverse-momentum regions, with a particular focus on the low $q_T$ region $q_T^2 << Q^2$ (with $Q^2$ being the invariant diphoton mass) where resummation becomes essential for a reliable calculation.
We have studied precursors of the global failure in some self-organised critical models of sand-pile (in BTW and Manna models) and in the random fiber bundle model (RFB). In both BTW and Manna model, as one adds a small but fixed number of sand grains (heights) to any central site of the stable pile, the local dynamics starts and continues for an average relaxation time (\tau) and an average number of topplings (\Delta) spread over a radial distance (\xi). We find that these quantities all depend on the average height (h_{av}) of the pile and they all diverge as (h_{av}) approaches the critical height (h_{c}) from below: (\Delta) (\sim (h_{c}-h_{av}))(^{-\delta}), (\tau \sim (h_{c}-h_{av})^{-\gamma}) and (\xi) (\sim) ((h_{c}-h_{av})^{-\nu}). Numerically we find (\delta \simeq 2.0), (\gamma \simeq 1.2) and (\nu \simeq 1.0) for both BTW and Manna model in two dimensions. In the strained RFB model we find that the breakdown susceptibility (\chi) (giving the differential increment of the number of broken fibers due to increase in external load) and the relaxation time (\tau), both diverge as the applied load or stress (\sigma) approaches the network failure threshold (\sigma_{c}) from below: (\chi) (\sim) ((\sigma_{c}) (-)(\sigma)^{-1/2}) and (\tau) (\sim) ((\sigma_{c}) (-)(\sigma)^{-1/2}). These self-organised dynamical models of failure therefore show some definite precursors with robust power laws long before the failure point. Such well-characterised precursors should help predicting the global failure point of the systems in advance.
Eclipses in the 14.4-day period double-lined binary SS Lac were observed photographically and visually early in the 20th century, but stopped some 50 or 60 years ago. This has been explained by the presence of a distant third star in the system, which has now been detected spectroscopically with a period of 679 days. The plane of the orbit of the binary is changing relative to the line of sight in response to perturbations from this third object. A recent analysis by Milone et al. (M00) of all photometric material available for the system, including a re-measurement of original Harvard plates, has confirmed earlier reports of changes in the depth of the eclipses as a function of time, which are due to the third star. In this paper we discuss our detailed analysis of the eclipse amplitude measurements, and extract from them information on the change in the inclination angle of the binary over the last century. Our use of a much improved ephemeris for the system by Torres & Stefanik was found to be crucial, and prompted us to re-determine all the amplitudes from the historical data at our disposal, including the Harvard material used by M00. Systematically lower measurements on the branches of the minima were properly accounted for, and we made use of both a linear approximation to the time variation of the inclination angle and a more realistic model based on the theory of three-body interactions ("regression of the nodes" effect). The nodal cycle is found to be about 600 yr, within which TWO eclipse "seasons" occur, each lasting about 100 yr. The non-eclipsing status of the system is expected to continue until the beginning of the 23rd century.
The content of the present thesis is based on the papers [arXiv:1510.07886 [hep-th]][arXiv:1505.02287 [hep-th]][arXiv:1401.6303 [hep-th]][arXiv:1309.1402 [hep-th]][arXiv:1305.4155 [hep-th]][arXiv:1212.1003 [hep-th]][arXiv:1210.4734 [hep-th]] and is devoted to the study of aspects of the Gribov problem in Euclidean Yang-Mills theories coupled to matter fields. Here, we present some, mathematical and physical, evidences that point to the existence of a possible interplay between the gauge sector and the matter sector, in regimes of sufficiently ow energy (known as the infrared regime). In other words, we claim that an effect in the vector boson sector of Nature due to strong interactions (the Standard Model), at low energies, may be reflected in the matter sector, in the same regime. Specifically, we propose that the Gribov horizon function of the gauge sector may be felt by the matter field, and that it would be described by an effective non-local mass term attached to the matter field. Such a term seems to be dynamically generated and accounts for non-perturbative aspects of the matter field.
We compute the Drude weight and the critical exponents as functions of the density in non-integrable generalizations of XXZ or Hubbard chains, in the critical zero temperature regime where Luttinger liquid description breaks down and Bethe ansatz cannot be used. Even in the regions where irrelevant terms dominate, no difference between integrable and non integrable models appear in exponents and conductivity. Our results are based on a fully rigorous two-regime multiscale analysis and a recently introduced partially solvable model.