ShantanuT01/DACTYL-Pretraining huggingface dataset:
The fundamental controversy about the electronic structure for 3d-electron states in FeBr2 is discussed. We advocate for the localized electron atomic-like many-electron crystal-field approach that yields the discrete energy spectrum, in the scale of 1 meV, associated with the atomic-like states of the Fe2+ ions in contrary to the (semi-)continuous energy spectrum yielded by band theories. In our approach the six d electrons of the Fe2+ ion form the highly-correlated atomic-like electron system 3d6 described by two Hund's rules quantum numbers S=2 and L=2 with taking into account the spin-orbit coupling. The superiority of our model relies in the fact that it explains consistently properties of FeBr2, the insulating and the magnetic ground state as well as thermodynamics and Raman low-energy spectra, using well-established physical concepts.   Keywords: 3d magnetism, Hund's rules, spin-orbit coupling, crystal field, FeBr2 PACS: No: 75.50.Ee : 71.15.Mb
We explore the effects of considering various infrared (IR) cutoffs, including the particle horizon, Ricci horizon and Granda-Oliveros (GO) cutoffs, on the properties of Tsallis holographic dark energy (THDE) model, proposed inspired by Tsallis generalized entropy formalism \cite{THDE}. Interestingly enough, we find that for the particle horizon as IR cutoff, the obtained THDE model can describe the accelerated universe. This is in contrast to the usual HDE model which cannot lead to an accelerated universe, if one consider the particle horizon as IR cutoff. We also investigate the cosmological consequences of THDE under the assumption of a mutual interaction between the dark sectors of the Universe. It is shown that the evolution history of the Universe can be described by these IR cutoffs and thus the current cosmic acceleration can also been realized. The sound instability of THDE models for each cutoff are also explored, separately.
The BRST cohomology of the N=2 supersymmetric Yang-Mills theory in four dimensions is discussed by making use of the twisted version of the N=2 algebra. By the introduction of a set of suitable constant ghosts associated to the generators of N=2, the quantization of the model can be done by taking into account both gauge invariance and supersymmetry. In particular, we show how the twisted N=2 algebra can be used to obtain in a straightforward way the relevant cohomology classes. Moreover, we shall be able to establish a very useful relationship between the local gauge invariant polynomial $tr\phi^2$ and the complete N=2 Yang-Mills action. This important relation can be considered as the first step towards a fully algebraic proof of the one-loop exactness of the N=2 beta function.
We use the Aharonov-Bohm effect in a four-terminal ring based on a Ga[Al]As heterostructure for the measurement of the relative transmission phase. In each of the two interfering paths we induce a quantum dot. The number of electrons in the two dots can be controlled independently. The transmission phase is measured as electrons are added to or taken away from the individual quantum dots.
(Li,Al)-co-doped magnesium spinel (Li$_x$Mg$_{1-2x}$Al$_{2+x}$O$_4$) is a solid lithium-ion electrolyte with potential use in all-solid-state lithium-ion batteries. Interfaces with spinel electrodes, such as Li$_y$Mn$_2$O$_4$ and Li$_{4+3z}$Ti$_5$O$_{12}$, may be lattice-matched, with potentially low interfacial resistances. Small lattice parameter differences across a lattice-matched interface are unavoidable, causing residual epitaxial strain. This strain potentially modifies lithium diffusion near the interface, contributing to interfacial resistance. Here we report a density functional theory study of strain effects on lithium diffusion pathways for (Li,Al)-co-doped magnesium spinel, for $x_\mathrm{Li} = 0.25$ and $x_\mathrm{Li} = 0.5$. We have calculated diffusion profiles for the un-strained materials, and for isotropic and biaxial tensile strains of up to 6%, corresponding to {100} epitaxial interfaces with Li$_y$Mn$_2$O$_4$ and Li$_{4+3z}$Ti$_5$O$_{12}$. We find that isotropic tensile strain reduces lithium diffusion barriers by as much as 0.32 eV, with typical barriers reduced by ~0.1 eV. This effect is associated with increased volumes of transitional octahedral sites, and broadly follows local electrostatic potentials. For biaxial (epitaxial) strain changes in octahedral site volumes and in lithium diffusion barriers are much smaller than under isotropic strain. Typical barriers are reduced by only ~ 0.05 eV. Individual effects, however, depend on the pathway considered and the relative strain orientation. These results predict that isotropic strain strongly affects ionic conductivities in (Li,Al)-co-doped magnesium spinel electrolytes, and that tensile strain is a potential route to enhanced lithium transport. For a lattice-matched interface with candidate spinel-structured electrodes epitaxial strain has a small, but complex, effect on lithium diffusion barriers.
Zigzags and generalized zigzags in thin chamber complexes are investigated, in particular, all zigzags in the Coxeter complexes are described. Using this description, we show that the lengths of all generalized zigzags in the simplex $\alpha_{n}$, the cross-polytope $\beta_{n}$, the $24$-cell, the icosahedron and the $600$-cell are equal to the Coxeter numbers of $A_{n}$, $B_{n}=C_{n}$, $F_{4}$ and $H_{i}$, $i=3,4$, respectively. Also, we discuss the following problem: in which cases two faces in a thin chamber complex can be connected by a zigzag?
We study the supercurrent in quasi-one-dimensional Josephson junctions with a weak link involving magnetism, either via magnetic impurities or via ferromagnetism. In the case of weak links longer than {\color{black}the magnetic pair-breaking} length, the Josephson effect is dominated by mesoscopic fluctuations. We establish the supercurrent-phase dependence $I(\varphi)$ along with statistics of its sample-dependent properties in junctions with transparent contacts between leads and link. High transparency gives rise to the inverse proximity effect, while the direct proximity effect is suppressed by magnetism in the link. We find that all harmonics are present in $I(\varphi)$. Each harmonic has its own sample-dependent amplitude and phase shift with no correlation between different harmonics. Depending on the type of magnetic weak link, the system can realize a $\varphi_0$ or $\varphi$ junction in the fluctuational regime. Full supercurrent statistics is obtained at arbitrary relation between temperature, superconducting gap, and the Thouless energy of the weak link.
We consider the set M_n of all n-truncated power moment sequences of probability measures on [0,1]. We endow this set with the uniform probability. Picking randomly a point in M_n, we show that the upper canonical measure associated with this point satisfies a large deviation principle. Moderate deviation are also studied completing earlier results on asymptotic normality given by \citeauthorChKS93 [Ann. Probab. 21 (1993) 1295-1309]. Surprisingly, our large deviations results allow us to compute explicitly the (n+1)th moment range size of the set of all probability measures having the same n first moments. The main tool to obtain these results is the representation of M_n on canonical moments [see the book of \citeauthorDS97].
Many hot subdwarf stars show composite spectral energy distributions indicative of cool main sequence companions. Binary population synthesis (BPS) models demonstrate such systems can be formed via Roche lobe overflow or common envelope evolution but disagree on whether the resulting orbital periods will be long (years) or short (days). Few studies have been carried out to assess the orbital parameters of these spectroscopic composite binaries; current observations suggest the periods are long. To help address this problem, we selected fifteen moderately-bright (V~13) hot subdwarfs with F-K dwarf companions and monitored their radial velocities (RVs) from January 2005 to July 2008 using the bench-mounted Medium Resolution Spectrograph on the Hobby-Eberly Telescope (HET). Here we describe the details of our observing, reduction, and analysis techniques and present preliminary results for all targets. By combining the HET data with recent observations from the Mercator telescope, we are able to calculate precise orbital solutions for three systems using more than 6 years of observations. We also present an up-to-date period histogram for all known hot subdwarf binaries, which suggests those with F-K main sequence companions tend to have orbital periods on the order of several years. Such long periods challenge the predictions of conventional BPS models, although a larger sample is needed for a thorough assessment of the models' predictive success. Lastly, one of our targets has an eccentric orbit, implying some composite-spectrum systems might have formerly been hierarchical triple systems, in which the inner binary merged to create the hot subdwarf.
The aim of this paper is to prove an important generalization of the construction of the Incidence Divisor given in [BMg]. Let Z be a complex manifold and (X_{s})_{s\in S}an family of n-cycles (not necessarily compact) in Z parametrized by reduced complex space S. Then, to any n+1- codimensional cycle Y in Z wich satisfies the following condition : the analytic set (S\times |Y|)\cap |X| in S\times Z is S-proper and generically finite on its image |\Sigma_{Y}| wich is nowhere dense in S, is associated a Cartier Divisor \Sigma_{Y} with support |\Sigma_{Y}|. Nice functorial properties of this correspondance are proven and we deduce the intersection number of this divisor with a curve in S.
Supernova 2011kl, associated with the ultra-long gamma-ray burst (ULGRB) 111209A, exhibited a higher-than-normal peak luminosity, placing it in the parameter space between regular supernovae and super-luminous supernovae. Its light curve can only be matched by an abnormally high fraction of $^{56}$Ni that appears inconsistent with the observed spectrum, and as a result it has been suggested that the supernova, and by extension the gamma-ray burst, are powered by the spin-down of a highly magnetised millisecond pulsar, known as a magnetar. We investigate the broadband observations of ULGRB 111209A, and find two independent measures that suggest a high density circumburst environment. However, the light curve of the GRB afterglow shows no evidence of a jet break (the steep decline that would be expected as the jet slows due to the resistance of the external medium) out to three weeks after trigger, implying a wide jet. Combined with the high isotropic energy of the burst, this implies that only a magnetar with a spin period of ~ 1 ms or faster can provide enough energy to power both ULGRB 111209A and Supernova 2011kl.
In coin tossing two remote participants want to share a uniformly distributed random bit. At the least in the quantum version, each participant test whether or not the other has attempted to create a bias on this bit. It is requested that, for b = 0,1, the probability that Alice gets bit b and pass the test is smaller than 1/2 whatever she does, and similarly for Bob. If the bound 1/2 holds perfectly against any of the two participants, the task realised is called an exact coin tossing. If the bound is actually $1/2 + \xi$ where the bias $\xi$ vanishes when a security parameter m defined by the protocol increases, the task realised is a (non exact) coin tossing. It is found here that exact coin tossing is impossible. At the same time, an unconditionally secure quantum protocol that realises a (non exact) coin tossing is proposed. The protocol executes m biased quantum coin tossing procedures at the same time. It executes the first round in each of these m procedures sequentially, then the second rounds are executed, and so on until the end of the n procedures. Each procedure requires 4n particles where $n \in O(\lg m)$. The final bit x is the parity of the m random bits. The information about each of these m bits is announced a little bit at a time which implies that the principle used against bit commitment does not apply. The bias on x is smaller than $1/m$. The result is discussed in the light of the impossibility result for exact coin tossing.
Sequential tunneling model is used to study electron transport in molecular rectifiers based on structures of donor-bridge-acceptor type. The device is made of two metallic electrodes connected by a molecule, which contains acceptor and donor subunits, separated by insulating bridge. Both subunits are modeled as quantum dots with discrete energy levels, isolated from each other by potential barrier and weakly coupled to both electrodes through tunnel junctions. Intervalence donor-acceptor tunneling process is treated as a superexchange mechanism or equivalently through the use of Marcus theory. Analytic formula for the current is found in the case of the Aviram-Ratner ansatz of rectification and current-voltage characteristic is obtained at an arbitrary strength of the potential drop over the tunneling region. It is shown that rectification current depends on the position of the acceptor's LUMO and donor's HOMO levels with respect to the Fermi energy of the electrodes before bias is applied, and their shift due to the bias voltage.
The Birch and Swinnerton-Dyer conjecture predicts that the parity of the algebraic rank of an abelian variety over a global field should be controlled by the expected sign of the functional equation of its $L$-function, known as the global root number. In this paper, we give explicit formulae for the local root numbers as a product of Jacobi symbols. This enables one to compute the global root number, generalising work of Rohrlich who studies the case of elliptic curves. We provide similar formulae for the root numbers after twisting the abelian variety by a self-dual Artin representation. As an application, we find a rational genus two hyperelliptic curve with a simple Jacobian whose root number is invariant under quadratic twist.
Surface reconstruction from point clouds is vital for 3D computer vision. State-of-the-art methods leverage large datasets to first learn local context priors that are represented as neural network-based signed distance functions (SDFs) with some parameters encoding the local contexts. To reconstruct a surface at a specific query location at inference time, these methods then match the local reconstruction target by searching for the best match in the local prior space (by optimizing the parameters encoding the local context) at the given query location. However, this requires the local context prior to generalize to a wide variety of unseen target regions, which is hard to achieve. To resolve this issue, we introduce Predictive Context Priors by learning Predictive Queries for each specific point cloud at inference time. Specifically, we first train a local context prior using a large point cloud dataset similar to previous techniques. For surface reconstruction at inference time, however, we specialize the local context prior into our Predictive Context Prior by learning Predictive Queries, which predict adjusted spatial query locations as displacements of the original locations. This leads to a global SDF that fits the specific point cloud the best. Intuitively, the query prediction enables us to flexibly search the learned local context prior over the entire prior space, rather than being restricted to the fixed query locations, and this improves the generalizability. Our method does not require ground truth signed distances, normals, or any additional procedure of signed distance fusion across overlapping regions. Our experimental results in surface reconstruction for single shapes or complex scenes show significant improvements over the state-of-the-art under widely used benchmarks.
We propose new confinement structures similar to heterostructures and superlattices. The new heteostructures can be obtained by applying strain to a single material in a periodic or aperiodic way. The conversion of an indirect gap into an optical active direct or quasi-direct gap problem has also been investigated together with the role of zone folding in this phenomenon.
The Erd\"os-Moser conjecture states that the Diophantine equation $S_k(m) = m^k$, where $S_k(m)=1^k+2^k+...+(m-1)^k$, has no solution for positive integers $k$ and $m$ with $k \geq 2$. We show that stronger conjectures about consecutive values of the function $S_k$, that seem to be more naturally, imply the Erd\"os-Moser conjecture.
Several results are obtained concerning the function $\Delta_k(x)$, which represents the error term in the general Dirichlet divisor problem. These include the estimates for the integral of this function, as well as for the corresponding mean square integral. The mean square integral of $\Delta_2(x)$ is investigated in detail.
We apply the Effective Field Theory approach to General Relativity, introduced by Goldberger and Rothstein, to study point-like and string-like sources in the context of scalar-tensor theories of gravity. Within this framework we compute the classical energy-momentum tensor renormalization to first Post-Newtonian order or, in the case of extra scalar fields, up to first order in the (non-derivative) trilinear interaction terms: this allows to write down the corrections to the standard (Newtonian) gravitational potential and to the extra-scalar potential. In the case of one-dimensional extended sources we give an alternative derivation of the renormalization of the string tension enabling a re-analysis of the discrepancy between the results obtained by Dabholkar and Harvey in one paper and by Buonanno and Damour in another, already discussed in the latter.
Using a specialized technique sensitive to the presence of expanding ionized gas we have detected a set of three concentric expanding shells in an HII region in the nearby spiral galaxy M33. After mapping the kinematics in H{\alpha} with Fabry-Perot spectroscopy we used slit spectra to measure the intensities of the [SII] doublet at {\lambda}{\lambda} 671.9, 673.1 nm and the [NII] doublet at {\lambda}{\lambda} 645.8, 658.3 nm to corroborate the kinematics and apply diagnostic tests using line ratios. These showed that the expanding shells are shock dominated as would be the case if they had originated with supernova explosions. Estimating their kinetic energies we find fairly low values, indicating a fairly advanced stage of evolution. We obtain density, mass and parent star mass estimates, which, along with the kinetic energies, are inconsistent with the simplest models of shock-interstellar medium interaction. We propose that the presence and properties of an inhomogeneous medium offer a scenario which can account for these observations, and discuss the implications. Comparing our results with data from the literature supports the combined presence of an HII region and supernova remnant material at the observed position.
In this study the magnetic order of the spin-1/2 XXZ chain system Cs$_2$CoCl$_4$ in a temperature range from 50 mK to 0.5 K and in applied magnetic fields up to 3.5 T is investigated by high-resolution measurements of the thermal expansion and the specific heat. Applying magnetic fields along a or c suppresses $T_\textrm{N}$ completely at about 2.1 T. In addition, we find an adjacent intermediate phase before the magnetization saturates close to 2.5 T. For magnetic fields applied along b, a surprisingly rich phase diagram arises. Two additional transitions are observed at critical fields $\mu_0 H_{SF1}\simeq 0.25$ T and $\mu_0 H_{SF2}\simeq 0.7$ T, which we propose to arise from a two-stage spin-flop transition.
Ensembles of indirect or interlayer excitons (IXs) are intriguing systems to explore classical and quantum phases of interacting bosonic ensembles. IXs are composite bosons that feature enlarged lifetimes due to the reduced overlap of the electron-hole wave functions. We demonstrate electric Field control of indirect excitons in MoS2/WS2 hetero-bilayers embedded in a field effect structure with few-layer hexagonal boron nitrite as insulator and few-layer graphene as gate-electrodes. The different strength of the excitonic dipoles and a distinct temperature dependence identify the indirect excitons to stem from optical interband transitions with electrons and holes located in different valleys of the hetero-bilayer featuring highly hybridized electronic states. For the energetically lowest emission lines, we observe a field-dependent level anticrossing at low temperatures. We discuss this behavior in terms of coupling of electronic states from the two semiconducting monolayers resulting in spatially delocalized excitons of the hetero-bilayer behaving like an artificial van der Waals solid. Our results demonstrate the design of novel nano-quantum materials prepared from artificial van der Waals solids with the possibility to in-situ control their physical properties via external stimuli such as electric fields.
Franco, Galloni, Penante, and Wen have proposed a boundary measurement map for a graph on any closed orientable surface with boundary. We consider this boundary measurement map which takes as input an edge weighted directed graph embedded on a surface and produces on element of a Grassmannian. Computing the boundary measurement requires a choice of fundamental domain. Here the boundary measurement map is shown to be independent of the choice of fundamental domain Also, a formula for the Pl\"ucker coordinates of the element of Grassmannian in the image of the boundary measurement map is given. The formula expresses the Pl\"ucker coordinates as a rational function which can be combinatorially described in terms of paths and cycles in the directed graph.
An anisotropic (Bianchi type I) cosmology is considered in the four-dimensional NS-NS sector of low-energy effective string theory coupled to a dilaton and an axion-like $H$-field within a de Sitter-Einstein frame background. The time evolution of this Universe is discussed in both the Einstein and string frames.
We prove that the Ring Learning With Errors (RLWE) and the Polynomial Learning With Errors (PLWE) problems over the cyclotomic field $\mathbb{Q}(\zeta_n)$ are not equivalent. Precisely, we show that reducing one problem to the other increases the noise by a factor that is more than polynomial in $n$. We do so by providing a lower bound, holding for infinitely many positive integers $n$, for the condition number of the Vandermonde matrix of the $n$th cyclotomic polynomial.
Although indications are that a single chiral quantum anomalous Hall(QAH) edge mode might have been experimentally detected. There have been very many recent experiments which conjecture that a single chiral QAH edge mode always materializes along with a pair of quasi-helical quantum spin Hall (QSH) edge modes. The reason for this seems to lie in the origin of QAH edge modes. These evolve from QSH edge modes via suppression of one of the spin edge modes by application of a ferromagnet or magnetic impurity. In this work we deal with a substantial 'What If ?' question- in case the QSH edge modes, from which these QAH edge modes evolve, are not topologically protected then the QAH edge modes wont be topologically protected too and thus unfit for use in any applications. Further, as a corollary one can also ask if the topological protection of QSH edge modes does not carry over during the evolution process to QAH edge modes then again our 'What if?' scenario becomes apparent. The "how" of the resolution of this 'What if?' conundrum is the main objective of our work. We show in similar set-ups affected by disorder and inelastic scattering, transport via trivial QAH edge mode leads to quantization of Hall resistance and not that via topological QAH edge modes. This perhaps begs a substantial reinterpretation of those experiments which purported to find signatures of chiral(topological) QAH edge modes albeit in conjunction with quasi helical QSH edge modes.