ShantanuT01/DACTYL-Pretraining huggingface dataset:
The onset of the pseudogap in high-$T_c$ superconducting cuprates (HTSC) is marked by the $T^*$ line in the doping-temperature phase diagram, which ends at a point $p^*$ at zero temperature within the superconducting dome. Although various theoretical and experimental studies indicate a competition between the pseudogap and superconductivity, there is no general consensus on the effects of the pseudogap within the superconducting phase. We use cluster dynamical mean field theory on a three-band Hubbard model for the HTSC to study the superconducting phase at $T=0$, obtained when doping the charge-transfer insulator, for several values of $U$. We observe a first-order transition within the superconducting phase, which separates the underdoped and overdoped solutions. The transition to the underdoped solution is marked by a discontinuous increase in the spectral gap, and on further underdoping the spectral gap increases while the superconducting order parameter decreases. We conclude that this is due to the onset of the pseudogap in the underdoped region, which contributes to the increasing spectral gap; this is further consistent with the appearance of a pole in the normal component of the self-energy, in the antinodal region, in the underdoped solution. This is accompanied by a change in the source of the condensation energy from potential energy, in the overdoped region, to kinetic energy in the underdoped region. Further, we also observe that the $d$-wave node vanishes smoothly within the superconducting phase at low values of hole doping, within the underdoped region. We see this as a manifestation of Mott physics operating at very low doping. Various aspects of the results and their implications are discussed.
We prove the global-in-time existence of weak solutions to the Navier-Stokes equations of compressible isentropic flow in three space dimensions with adiabatic exponent $\gamma\ge1$. Initial data and solutions are small in $L^2$ around a non-constant steady state with densities being positive and essentially bounded. No smallness assumption is imposed on the external forces when $\gamma=1$. A great deal of information about partial regularity and large-time behavior is obtained.
Recent advances in synthesis and electrical characterization of nanofibers and nanotubes made out of various conjugated polymers attract attention of the research community to studies of transport properties of these materials. In this work we present a theoretical analysis of electron transport in polymer nanofibers assuming them to be in conducting state. We treat a conducting polymer as a network of metallic-like grains embedded in poorly conducting environment, which consists of randomly distributed polymeric chains. We analyze the contribution from intergrain electron resonance tunneling via intermediate states localized on the polymeric chains between the grains. Correspondingly, we apply the quantum theory of conduction in mesoscopic systems to analyze this transport mechanism. We show that the contribution of resonance electron tunneling to the intergrain electron transport may be predominating, as follows from experiments on the electrical characterization of single polyaniline nanofibers. We study the effect of temperature on the transport characteristics. We represent the thermal environment as a phonon bath coupled to the intermediate state, which provides electron tunneling between the metallic-like grains. Using the Buttiker model within the scattering matrix formalism combined with the nonequilibrium Green's functions technique, we show that temperature dependencies of both current and conductance associated with the intergrain electron tunneling, differ from those typical for other conduction mechanisms in conducting polymers. Also, we demonstrate that under certain conditions the phonon bath may cause suppression of the original intermediate state accompanied by emergence of new states for electron tunneling. The temperature dependencies of the magnitudes of the peaks in the transmission corresponding to these new states are analyzed.
We present three different matrix bases that can be used to decompose density matrices of $d$--dimensional quantum systems, so-called qudits: the \emph{generalized Gell-Mann matrix basis}, the \emph{polarization operator basis}, and the \emph{Weyl operator basis}. Such a decomposition can be identified with a vector --the Bloch vector, i.e. a generalization of the well known qubit case-- and is a convenient expression for comparison with measurable quantities and for explicit calculations avoiding the handling of large matrices. We present a new method to decompose density matrices via so--called standard matrices, consider the important case of an isotropic two--qudit state and decompose it according to each basis. In case of qutrits we show a representation of an entanglement witness in terms of expectation values of spin 1 measurements, which is appropriate for an experimental realization.
Observations of gravitational lenses in strong gravitational fields give us a clue to understanding dark compact objects. In this paper, we extend a method to obtain a deflection angle in a strong deflection limit provided by Bozza [Phys. Rev. D 66, 103001 (2002)] to apply to ultrastatic spacetimes. We also discuss on the order of an error term in the deflection angle. Using the improved method, we consider gravitational lensing by an Ellis wormhole, which is an ultrastatic wormhole of the Morris-Thorne class.
We present Very Low Mass stellar models as computed including non-grey model atmospheres for selected assumptions about the star metallicities. The role of atmospheres is discussed and the models are compared with models based on the Eddington approximation and with similar models appeared in the recent literature. Theoretical predictions concerning both the HR diagram location and the mass-luminosity relation are presented and discussed in terms of expectations in selected photometric bands. Comparison with available observational data concerning both galactic globular clusters and dwarfs in the solar neighborhood reveals a satisfactory agreement together with the existence of some residual mismatches.
We have studied theoretically the effect of a tuneable lateral confinement on two-dimensional hole systems realised in III-V semiconductor heterostructures. Based on the 4x4 Luttinger description of the valence band, we have calculated quasi-onedimensional (quasi-1D) hole subband energies and anisotropic Lande g-factors. Confinement-induced band mixing results in the possibility to manipulate electronic and spin properties of quasi-1D hole states over a much wider range than is typically possible for confined conduction-band electrons. Our results are relevant for recent experiments where source-drain-bias spectroscopy was used to measure Zeeman splitting of holes in p-type quantum point contacts.
Imaginary time is often used in quantum tunnelling calculations. This article advocates a conceptually sounder alternative: complex lapse. In the ``3+1'' action for the Einstein gravitational field minimally coupled to a Klein-Gordon field, allowing the lapse function to be complex yields a complex action which generates both the usual Lorentzian theory and its Riemannian analogue, and in particular allows a change of signature between the two. The action and variational equations are manifestly well defined in the Hamiltonian representation, with the momentum fields consequently being complex. The complex action interpolates between the Lorentzian and Riemannian actions as they appear formally in the respective path integrals. Thus the complex-lapse theory provides a unified basis for a path-integral quantum theory of gravity involving both Lorentzian and Riemannian aspects. A major motivation is the quantum-tunnelling scenario for the origin of the universe. Taken as an explanation for the observed quantum tunnelling of particles, the complex-lapse theory determines that the argument of the lapse for the universe now is extremely small but negative.
Spatially-resolved neutron powder diffraction with gauge volume 2x2x20 mm3 has been applied to probe the lithium concentration in the graphite anode of different Li-ion cells of 18650-type in situ in charged state. Structural studies performed in combination with electrochemical measurements and X-ray computed tomography under real cell operating conditions unambiguously revealed non-homogeneity of lithium distribution in the graphite anode. Deviations from a homogeneous behaviour have been found in both radial and axial directions of 18650-type cells and were discussed in the frame of cell geometry and electrical connection of electrodes, which might play a crucial role in the homogeneity of the lithium distribution in the active materials within each electrode.
Let p be a prime = 3 (mod 4). A number of elegant number-theoretical properties of the sums T(p) = \sqrt{p}sum_{n=1}^{(p-1)/2} tan(n^2\pi/p) and C(p) = \sqrt{p}sum_{n=1}^{(p-1)/2} cot(n^2\pi/p) are proved. For example, T(p) equals p times the excess of the odd quadratic residues over the even ones in the set {1,2,...,p-1}; this number is positive if p = 3 (mod 8) and negative if p = 7 (mod 8). In this revised version the connection of these sums with the class-number h(-p) is also discussed. For example, a very simple formula expressing h(-p) by means of the aforementioned excess is proved. The bibliography has been considerably enriched. This article is of an expository nature.
We present a theoretical and experimental analysis of the elliptical-like orbits of a marble rolling on a warped spandex fabric. We arrive at an expression describing the angular separation between successive apocenters, or equivalently successive pericenters, in both the small and large slope regimes. We find that a minimal angular separation of approximately 197 degrees is predicted for orbits with small radial distances when the surface is void of a central mass. We then show that for small radii and large central masses, when the orbiting marble is deep within the well, the angular separation between successive apocenters transitions to values greater than 360 degrees. We lastly compare these expressions to those describing elliptical-like orbits about a static, spherically symmetric massive object in the presence of a constant vacuum energy, as described by general relativity.
This paper revisits a homogenization problem studied by L. Tartar related to a tridimensional Stokes equation perturbed by a drift (connected to the Coriolis force). Here, a scalar equation and a two-dimensional Stokes equation with a $L^2$-bounded oscillating drift are considered. Under higher integrability conditions the Tartar approach based on the oscillations test functions method applies and leads to a limit equation with an extra zero-order term. When the drift is only assumed to be equi-integrable in $L^2$, the same limit behaviour is obtained. However, the lack of integrability makes difficult the direct use of the Tartar method. A new method in the context of homogenization theory is proposed. It is based on a parametrix of the Laplace operator which permits to write the solution of the equation as a solution of a fixed point problem, and to use truncated functions even in the vector-valued case. On the other hand, two counter-examples which induce different homogenized zero-order terms actually show the optimality of the equi-integrability assumption.
The human activity recognition in the IoT environment plays the central role in the ambient assisted living, where the human activities can be represented as a concatenated event stream generated from various smart objects. From the concatenated event stream, each activity should be distinguished separately for the human activity recognition to provide services that users may need. In this regard, accurately segmenting the entire stream at the precise boundary of each activity is indispensable high priority task to realize the activity recognition. Multiple human activities in an IoT environment generate varying event stream patterns, and the unpredictability of these patterns makes them include redundant or missing events. In dealing with this complex segmentation problem, we figured out that the dynamic and confusing patterns cause major problems due to: inclusive event stream, redundant events, and shared events. To address these problems, we exploited the contextual relationships associated with the activity status about either ongoing or terminated/started. To discover the intrinsic relationships between the events in a stream, we utilized the LSTM model by rendering it for the activity segmentation. Then, the inferred boundaries were revised by our validation algorithm for a bit shifted boundaries. Our experiments show the surprising result of high accuracy above 95%, on our own testbed with various smart objects. This is superior to the prior works that even do not assume the environment with multi-user activities, where their accuracies are slightly above 80% in their test environment. It proves that our work is feasible enough to be applied in the IoT environment.
For any field $\mathbb{F}$ and polynomials $f_{2},f_{3}\in\mathbb{F}[x,y]$, let $\Gamma_{\mathbb{F}}(f_{2},f_{3})$ denote the bipartite graph with vertex partition $P\cup L$, where $P$ and $L$ are two copies of $\mathbb{F}^{3}$, and $(p_{1},p_{2},p_{3})\in P$ is adjacent to $[l_{1},l_{2},l_{3}]\in L$ if and only if $p_{2}+l_{2}=f_{2}(p_{1},l_{1})$ and $p_{3}+l_{3}=f_{3}(p_{1},l_{1})$. The graph $\Gamma_{3}(\mathbb{F})=\Gamma_{\mathbb{F}}(xy,xy^{2})$ is known to be of girth eight. When $\mathbb{F}=\mathbb{F}_q$ is a finite field of odd size $q$ or $\mathbb{F}=\mathbb{F}_{\infty}$ is an algebraically closed field of characteristic zero, the graph $\Gamma_{3}(\mathbb{F})$ is conjectured to be the unique one with girth at least eight among those $\Gamma_{\mathbb{F}}(f_{2},f_{3})$ up to isomorphism. This conjecture has been confirmed for the case that both $f_{2},f_{3}$ are monomials over $\mathbb{F}_q$, and for the case that at least one of $f_{2},f_{3}$ is a monomial over $\mathbb{F}_{\infty}$. If one of $f_{2},f_{3}\in\mathbb{F}_q[x,y]$ is a monomial, it has also been proved the existence of a positive integer $M$ such that $G=\Gamma_{\mathbb{F}_{q^{M}}}(f_2,f_3)$ is isomorphic to $\Gamma_{3}(\mathbb{F}_{q^{M}})$ provided $G$ has girth at least eight. In this paper, these results are shown to be valid when the restriction on the polynomials $f_2,f_3$ is relaxed further to that one of them is the product of two univariate polynomials. Furthermore, all of such polynomials $f_2,f_3$ are characterized completely.
By the example of the Hubbard model we analytically and numerically examine the formating and coexisting of localized electron--electron pairs (doublons) and localized electron--hole pairs (Frenkel--type excitons) . Here we demonstrate that at a variation of the on-site Coulomb repulsion U there occurs a quantum transition from the doublon to the exciton regime that is conditioned by the low-energy effective hybridization of the valence and conductivity subbands. We calculate momentum distribution functions and electronic spectrum functions for different U, which reveal topologically nontrivial behaviour at the Fermi level.
By finding orthogonal representation for a family of simple connected called $\delta$-graphs it is possible to show that $\delta$-graphs satisfy delta conjecture. An extension of the argument to graphs of the form $\overline{P_{\Delta(G)+2}\sqcup G}$ where $P_{\Delta(G)+2}$ is a path and $G$ is a simple connected graph it is possible to find an orthogonal representation of $\overline{P_{\Delta(G)+2}\sqcup G}$ in $\mathbb{R}^{\Delta(G)+1}$. As a consequence we prove delta conjecture.
We present a method for enhancing the cross-correlation of gravitational wave signals eventually present in data streams containing otherwise uncorrelated noise. Such method makes use of the wavelet decomposition to cast the cross-correlation time series in time-frequency space. Then an entropy criterion is applied to identify the best time frequency resolution, i.e. the resolution allowing to concentrate the signal in the smallest number of wavelet coefficients. By keeping only the coefficients above a certain threshold, it is possible to reconstruct a cross-correlation time series where the effect of common signal is stronger. We tested our method against signals injected over two data streams of uncorrelated white noise.
A lattice path matroid is a transversal matroid corresponding to a pair of lattice paths on the plane. A matroid base polytope is the polytope whose vertices are the incidence vectors of the bases of the given matroid. In this paper, we study facial structures of matroid base polytopes corresponding to lattice path matroids.
In this paper it is shown that the steady-state weights of the asymmetric simple exclusion process (ASEP) with open boundaries and parallel update can be written as a product of a scalar pair-factorized and a matrix-product state. This type of state is also obtained for an ASEP on a ring in which particles can move one or two sites. The dynamics leads to the formation of an excess hole that plays the role of a defect. We expect the process to play a similar role for parallel dynamics as the well-known ASEP with a single defect-particle (that is obtained in the continuous-time limit) especially for the study of shocks. The process exhibits a first-order phase transition between two phases with different defect velocities. These are calculated exactly from the process-generating function.
We show central limit theorems (CLT) for the Stieltjes transforms or more general analytic functions of symmetric matrices with independent heavy tailed entries, including entries in the domain of attraction of $\alpha$-stable laws and entries with moments exploding with the dimension, as in the adjacency matrices of Erd\"os-R\'enyi graphs. For the second model, we also prove a central limit theorem of the moments of its empirical eigenvalues distribution. The limit laws are Gaussian, but unlike to the case of standard Wigner matrices, the normalization is the one of the classical CLT for independent random variables.
We consider leptogenesis induced by soft supersymmetry breaking terms ("soft leptogenesis"), in the context of the inverse seesaw mechanism. In this model there are lepton number (L) conserving and L-violating soft supersymmetry-breaking B-terms involving the singlet sneutrinos which, together with the -- generically small-- L-violating parameter responsible of the neutrino mass, give a small mass splitting between the four singlet sneutrino states of a single generation. In combination with the trilinear soft supersymmetry breaking terms they also provide new CP violating phases needed to generate a lepton asymmetry in the singlet sneutrino decays. We obtain that in this scenario the lepton asymmetry is proportional to the L-conserving soft supersymmetry-breaking B-term, and it is not suppressed by the L-violating parameters. Consequently we find that, as in the standard see-saw case, this mechanism can lead to sucessful leptogenesis only for relatively small value of the relevant soft bilinear coupling. The right-handed neutrino masses can be sufficiently low to elude the gravitino problem. Also the corresponding Yukawa couplings involving the lightest of the right-handed neutrinos are constrained to be \sum |Y_{1k}|^2\lesssim 10^{-7} which generically implies that the neutrino mass spectrum has to be strongly hierarchical.
In electromagnetism a current along a wire tightly wound on a torus makes a solenoid whose magnetic field is confined within the torus. In Einstein's gravity we give a corresponding solution in which a current of matter moves up on the inside of a toroidal shell and down on the outside, rolling around the torus by the short way. The metric is static outside the torus but stationary inside with the gravomagnetic field confined inside the torus, running around it by the long way. This exact solution of Einstein's equations is found by fitting Bonnor's solution for the metric of a light beam, which gives the required toroidal gravomagnetic field inside the torus, to the general Weyl static external metric in toroidal coordinates, which we develop. We deduce the matter tensor on the torus and find when it obeys the energy conditions. We also give the equipotential shells that generate the simple Bach-Weyl metric externally and find which shells obey the energy conditions.
In the transition metal dichalcogenide IrTe$_2$, low-temperature charge-ordered phase transitions involving Ir dimers lead to the occurrence of stripe phases of different periodicities, and nearly degenerate energies. Bulk-sensitive measurements have shown that, upon cooling, IrTe$_2$ undergoes two such first-order transitions to $(5\times1\times5)$ and $(8\times1\times8)$ reconstructed phases at $T_{c_1}\sim 280$~K and $T_{c_2}\sim 180$~K, respectively. Here, using surface sensitive probes of the electronic structure of IrTe$_2$, we reveal the first-order phase transition at $T_{c_3}=165$~K to the $(6\times1)$ stripes phase, previously proposed to be the surface ground state. This is achieved by combining x-ray photoemission spectroscopy and angle-resolved photoemission spectroscopy, which give access to the evolution of stripe domains and a particular surface state, the energy of which is dependent on the Ir dimer length. By performing measurements over a full thermal cycle, we also report the complete hysteresis of all these phases.
Pixel-wise operations between polarimetric images are important for processing polarization information. For the lack of such operations, the polarization information cannot be fully utilized in convolutional neural network(CNN). In this paper, a novel end-to-end CNN framework for polarization vision tasks is proposed, which enables the networks to take full advantage of polarimetric images. The framework consists of two sub-networks: a polarization-parameter-constructing network (PPCN) and a task network. PPCN implements pixel-wise operations between images in the CNN form with 1x1 convolution kernels. It takes raw polarimetric images as input, and outputs polarization-parametric images to task network so as to complete a vison task. By training together, the PPCN can learn to provide the most suitable polarization-parametric images for the task network and the dataset. Taking faster R-CNN as task network, the experimental results show that compared with existing methods, the proposed framework achieves much higher mean-average-precision (mAP) in object detection task
This talk summarized the proof of hard-scattering factorization for hard exclusive electroproduction processes: deeply virtual Compton scattering and exclusive meson production.