ShantanuT01/DACTYL-Pretraining huggingface dataset:
We consider electron-electron interaction effects in quantum point contacts on the first quantization plateau, taking into account all scattering processes. We compute the low-temperature linear and nonlinear conductance, shot noise, and thermopower, by perturbation theory and a self-consistent nonperturbative method. On the conductance plateau, the low-temperature corrections are solely due to momentum-nonconserving processes that change the relative number of left- and right-moving electrons. This leads to a suppression of the conductance for increasing temperature or voltage. The size of the suppression is estimated for a realistic saddle-point potential, and is largest in the beginning of the conductance plateau. For large magnetic field, interaction effects are strongly suppressed by the Pauli principle, and hence the first spin-split conductance plateau has a much weaker interaction correction. For the nonperturbative calculations, we use a self-consistent nonequilibrium Green's function approach, which suggests that the conductance saturates at elevated temperatures. These results are consistent with many experimental observations related to the so-called 0.7 anomaly.
The energy dependence of forward pion double charge exchange reactions on light nuclei is studied for both the Ground State transition and the Double-Isobaric-Analog-State transitions. A common characteristic of these double reactions is a resonance-like peak around 50 MeV pion lab energy. This peak arises naturally in a two-step process in the conventional pion-nucleon system with proper handling of nuclear structure and pion distortion. A comparison among the results of different nuclear structure models demonstrates the effects of configuration mixing. The angular distribution is used to fix the single particle wave function.
We determine the current exchange amplitudes for free totally symmetric tensor fields $\vf_{\mu_1 ... \mu_s}$ of mass $M$ in a $d$-dimensional $dS$ space, extending the results previously obtained for $s=2$ by other authors. Our construction is based on an unconstrained formulation where both the higher-spin gauge fields and the corresponding gauge parameters $\Lambda_{\mu_1 >... \mu_{s-1}}$ are not subject to Fronsdal's trace constraints, but compensator fields $\alpha_{\mu_1 ... \mu_{s-3}}$ are introduced for $s > 2$. The free massive $dS$ equations can be fully determined by a radial dimensional reduction from a $(d+1)$-dimensional Minkowski space time, and lead for all spins to relatively handy closed-form expressions for the exchange amplitudes, where the external currents are conserved, both in $d$ and in $(d+1)$ dimensions, but are otherwise arbitrary. As for $s=2$, these amplitudes are rational functions of $(ML)^2$, where $L$ is the $dS$ radius. In general they are related to the hypergeometric functions $_3F_2(a,b,c;d,e;z)$, and their poles identify a subset of the "partially-massless" discrete states, selected by the condition that the gauge transformations of the corresponding fields contain some non-derivative terms. Corresponding results for $AdS$ spaces can be obtained from these by a formal analytic continuation, while the massless limit is smooth, with no van Dam-Veltman-Zakharov discontinuity.
In this paper we obtain a parametric solution of the hitherto unsolved diophantine equation $(x_1^5+x_2^5)(x_3^5+x_4^5)=(y_1^5+y_2^5)(y_3^5+y_4^5)$. Further, we show, using elliptic curves, that there exist infinitely many parametric solutions of the aforementioned diophantine equation, and they can be effectively computed.
For a $(3+1)$-dimensional generalization of the Schwinger model, we compute the interaction energy between two test charges. The result shows that the static potential profile contains a linear term leading to the confinement of probe charges, exactly as in the original model in two dimensions. We further show that the same 4-dimensional model also appears as one version of the $ B \wedge F$ models in $(3+1)$ dimensions under dualization of Stueckelberg-like massive gauge theories. Interestingly, this particular model is characterized by the mixing between a $U(1)$ potential and an Abelian $3$-form field of the type that appears in the topological sector of QCD.
Different from many other attributes, facial expression can change in a continuous way, and therefore, a slight semantic change of input should also lead to the output fluctuation limited in a small scale. This consistency is important. However, current Facial Expression Recognition (FER) datasets may have the extreme imbalance problem, as well as the lack of data and the excessive amounts of noise, hindering this consistency and leading to a performance decreasing when testing. In this paper, we not only consider the prediction accuracy on sample points, but also take the neighborhood smoothness of them into consideration, focusing on the stability of the output with respect to slight semantic perturbations of the input. A novel method is proposed to formulate semantic perturbation and select unreliable samples during training, reducing the bad effect of them. Experiments show the effectiveness of the proposed method and state-of-the-art results are reported, getting closer to an upper limit than the state-of-the-art methods by a factor of 30\% in AffectNet, the largest in-the-wild FER database by now.
We study the many-body physics in thin film topological band insulator, where the inter-edge Coulomb interaction can lead to an exciton condensation transition. We investigate the universality class of the exciton condensation quantum critical point. With different chemical potentials and interactions, the exciton condensation can belong to z = 2 mean field, or 3d XY, or Yukawa-Higgs universality classes. The interplay between exciton condensate and the time-reversal symmetry breaking is also discussed. Predictions of our work can be tested experimentally by tuning the chemical potentials on both surfaces of the thin film through gate voltage. We also show that all the analysis of the exciton condensate can be directly applied to a spin-triplet superconductor phase with attractive inter-edge interaction.
Motivated by recent proposal by Potter et al. [Phys. Rev. X 6, 031026 (2016)] concerning possible thermoelectric signatures of Dirac composite fermions, we perform a systematic experimental study of thermoelectric transport of an ultrahigh-mobility GaAs/AlxGa1-xAs two dimensional electron system at filling factor v = 1/2. We demonstrate that the thermopower Sxx and Nernst Sxy are symmetric and anti-symmetric with respect to B = 0 T, respectively. The measured properties of thermopower Sxx at v = 1/2 are consistent with previous experimental results. The Nernst signals Sxy of v = 1/2, which have not been reported previously, are non-zero and show a power law relation with temperature in the phonon-drag dominant region. In the electron-diffusion dominant region, the Nernst signals Sxy of v = 1/2 are found to be significantly smaller than the linear temperature dependent values predicted by Potter et al., and decreasing with temperature faster than linear dependence.
We show that the introduction of frustration into the spin-1/2 two-dimensional (2D) antiferromagnetic Heisenberg model on a square lattice via a next-nearest neighbor exchange interaction can lead to a Peierls-like transition, from a tetragonal to an orthorhombic phase, when the spins are coupled to adiabatic phonons. The two different orthorhombic ground states define an Ising order parameter, which is expected to lead to a finite temperature transition. Implications for ${\rm Li_2VOSiO_4}$, the first realization of that model, will be discussed.
The quasar 3C 454.3 is a blazar known for its rapid and violent outbursts seen across the electromagnetic spectrum. Using gamma-ray, X-ray, multi-band optical, and very long baseline interferometric data we investigate the nature of two such events that occurred in 2013 and 2014 accompanied by strong variations in optical polarization, including a 230 degree electric vector position angle (EVPA) rotation. Our results suggest that a single disturbance was responsible for both flaring events. We interpret the disturbance as a shock propagating down the jet. Under this interpretation the 2013-flare originated most likely due to changes in the viewing angle caused by perhaps a bent or helical trajectory of the shock upstream of the radio core. The 2014-flare and optical polarization behavior are the result of the shock exiting the 43 GHz radio core, suggesting that shock crossings are one of the possible mechanisms for EVPA rotations.
We establish a congruence formula between $p$-adic logarithms of Heegner points for two elliptic curves with the same mod $p$ Galois representation. As a first application, we use the congruence formula when $p=2$ to explicitly construct many quadratic twists of analytic rank zero (resp. one) for a wide class of elliptic curves $E$. We show that the number of twists of $E$ up to twisting discriminant $X$ of analytic rank zero (resp. one) is $\gg X/\log^{5/6}X$, improving the current best general bound towards Goldfeld's conjecture due to Ono--Skinner (resp. Perelli--Pomykala). We also prove the 2-part of the Birch and Swinnerton-Dyer conjecture for many rank zero and rank one twists of $E$, which was only recently established for specific CM elliptic curves $E$.
Motivated by the recent experimental evidence of commensurate surface charge density waves (CDW) in Pb/Ge(111) and Sn/Ge(111) sqrt{3}-adlayer structures, as well as by the insulating states found on K/Si(111):B and SiC(0001), we have investigated the role of electron-electron interactions, and also of electron-phonon coupling, on the narrow surface state band originating from the outer dangling bond orbitals of the surface. We model the sqrt{3} dangling bond lattice by an extended two-dimensional Hubbard model at half-filling on a triangular lattice. We include an on-site Hubbard repulsion U and a nearest-neighbor Coulomb interaction V, plus a long-ranged Coulomb tail. The electron-phonon interaction is treated in the deformation potential approximation. We have explored the phase diagram of this model including the possibility of commensurate 3x3 phases, using mainly the Hartree-Fock approximation. For U larger than the bandwidth we find a non-collinear antiferromagnetic SDW insulator, possibly corresponding to the situation on the SiC and K/Si surfaces. For U comparable or smaller, a rich phase diagram arises, with several phases involving combinations of charge and spin-density-waves (SDW), with or without a net magnetization. We find that insulating, or partly metallic 3x3 CDW phases can be stabilized by two different physical mechanisms. One is the inter-site repulsion V, that together with electron-phonon coupling can lower the energy of a charge modulation. The other is a novel magnetically-induced Fermi surface nesting, stabilizing a net cell magnetization of 1/3, plus a collinear SDW, plus an associated weak CDW. Comparison with available experimental evidence, and also with first-principle calculations is made.
Operator method and cumulant expansion are used for nonperturbative calculation of the partition function and the free energy in quantum statistics. It is shown for Boltzmann diatomic molecular gas with some model intermolecular potentials that the zeroth order approximation of the proposed method interpolates the thermodynamic values with rather good accuracy in the entire range of both the Hamiltonian parameters and temperature. The systematic procedure for calculation of the corrections to the zeroth order approximation is also considered.
We propose an architecture of quantum-error-correction-based quantum repeaters that combines techniques used in discrete- and continuous-variable quantum information. Specifically, we propose to encode the transmitted qubits in a concatenated code consisting of two levels. On the first level we use a continuous-variable GKP code encoding the qubit in a single bosonic mode. On the second level we use a small discrete-variable code. Such an architecture has two important features. Firstly, errors on each of the two levels are corrected in repeaters of two different types. This enables for achieving performance needed in practical scenarios with a reduced cost with respect to an architecture for which all repeaters are the same. Secondly, the use of continuous-variable GKP code on the lower level generates additional analog information which enhances the error-correcting capabilities of the second-level code such that long-distance communication becomes possible with encodings consisting of only four or seven optical modes.
We classify minimal pairs (X, G) for smooth rational projective surface X and finite group G of automorphisms on X. We also determine the fixed locus X^G and the quotient surface Y = X/G as well as the fundamental group of the smooth part of Y. The realization of each pair is included. Mori's extremal ray theory and recent results of Alexeev and also Ambro on the existence of good anti-canonical divisors are used.
The triggering process for coronal mass ejections (CME) in the solar atmosphere is not fully understood. We use observations from different spacecraft at several wavelengths to detect an instability process for a prominence/filament with a subsequent eruption of CME. Time series of spectral lines at 304, 171, 193, and 211 {\AA} have been obtained with the SDO spacecraft, and at 304, 171, 195, and 284 {\AA} with the STEREO spacecraft. A prominence/filament system was observed during November 8-23, 2011, at different angles by SDO, STEREO_A, and STEREO_B. The observations show that a giant tornado began to develop near the base of the prominence at 20:00 UT on November 20, which later caused the appearance of droplets of coronal rain (at 16:00 UT, November 21) which fell downward from the main mass of the prominence. The coronal rain continued until 20:20 UT, November 22, and caused instability of the prominence, after which a CME took place at 22:30 UT on November 22. We assume that the loss of mass owing to coronal rain may lead to instability of prominences and their subsequent eruption. Observations of coronal rain falling from the main part of the mass of prominences could be used for predicting space weather.
We consider a semilinear elliptic equation with a nonsmooth, locally \hbox{Lipschitz} potential function (hemivariational inequality). Our hypotheses permit double resonance at infinity and at zero (double-double resonance situation). Our approach is based on the nonsmooth critical point theory for locally Lipschitz functionals and uses an abstract multiplicity result under local linking and an extension of the Castro--Lazer--Thews reduction method to a nonsmooth setting, which we develop here using tools from nonsmooth analysis.
I derived a geometrical model of the penumbral magnetic field topology from an uncombed inversion setup that aimed at reproducing the NCP of simultaneous spectra in near-IR (1.56 mu) and VIS (630 nm) spectral lines. I inverted the spectra of five photospheric lines with a model that mimicked vertically interlaced magnetic fields with two components, labeled background field and flow channels. The flow channels were modeled as a perturbation of the background field with a Gaussian shape using the SIRGAUS code. The location and extension of the Gaussian perturbation in the optical depth scale was then converted to a geometrical height scale. I investigated the relative amount of magnetic flux in the flow channels and the background field atmosphere. The uncombed model is able to reproduce the NCP well on the limb side of the spot and worse on the center side; the VIS lines are better reproduced than the near-IR lines. The Evershed flow happens along nearly horizontal field lines close to the solar surface. The magnetic flux that is related to the flow channels makes up about 20-50% of the total magnetic flux in the penumbra. The gradients obtainable by a Gaussian perturbation are too small for a perfect reproduction of the NCP in the IR lines with their small formation height range. Two peculiarities of the observed NCP, a sign change of the NCP of the VIS lines on the center side and a ring structure around the umbra in the Ti line at 630.37nm and the FeI line at 1565.2nm deserve closer attention. The large fraction of magnetic flux related to the flow channel component could allow to replenish the penumbral radiative losses in the flux tube picture.
For $0\le \alpha\le 1$, Nikiforov proposed to study the spectral properties of the family of matrices $A_{\alpha}(G)=\alpha D(G)+(1-\alpha)A(G)$ of a graph $G$, where $D(G)$ is the degree diagonal matrix and $A(G)$ is the adjacency matrix. The $\alpha$-spectral radius of $G$ is the largest eigenvalue of $A_{\alpha}(G)$. We give upper bounds for $\alpha$-spectral radius for unicyclic graphs $G$ with maximum degree $\Delta\ge 2$, connected irregular graphs with given maximum degree and and some other graph parameters, and graphs with given domination number, respectively. We determine the unique tree with second maximum $\alpha$-spectral radius among trees, and the unique tree with maximum $\alpha$-spectral radius among trees with given diameter. For a graph with two pendant paths at a vertex or at two adjacent vertex, we prove results concerning the behavior of the $\alpha$-spectral radius under relocation of a pendant edge in a pendant path. We also determine the unique graphs such that the difference between the maximum degree and the $\alpha$-spectral radius is maximum among trees, unicyclic graphs and non-bipartite graphs, respectively.
We consider recurrent diffusive random walks on a strip. We present constructive conditions on Green functions of finite sub-domains which imply a Central Limit Theorem with polynomial error bound, a Local Limit Theorem, and mixing of environment viewed by the particle process. Our conditions can be verified for a wide class of environments including independent environments, quasiperiodic environments, and environments which are asymptotically constant at infinity. The conditions presented deal with a fixed environment, in particular, no stationarity conditions are imposed.
In the era of precision cosmology and ever-improving cosmological simulations, a better understanding of different galaxy components such as bulges and discs will give us new insight into galactic formation and evolution. Based on the fact that the stellar populations of the constituent components of galaxies differ by their dynamical properties, we develop two simple models for galaxy decomposition using the IllustrisTNG cosmological hydrodynamical simulation. The first model uses a single dynamical parameter and can distinguish 4 components: thin disc, thick disc, counter-rotating disc and bulge. The second model uses one more dynamical parameter, was defined in a probabilistic manner, and distinguishes two components: bulge and disc. The number fraction of disc-dominated galaxies at a given stellar mass obtained by our models agrees well with observations for masses exceeding $ \log_{10}(M_*/M_\odot)=10$. S\'ersic indices and half-mass radii for the bulge components agree well with those for real galaxies. The mode of the distribution of S\'ersic indices for the disc components is at the expected value of $n=1$. However, disc half-mass radii are smaller than those for real galaxies, in accordance with previous findings that the IllustrisTNG simulation produces undersized discs.
We pursue our work on the dynamical stability of dark solitons for the one-dimensional Gross-Pitaevskii equation. In this paper, we prove their asymptotic stability under small perturbations in the energy space. In particular, our results do not require smallness in some weighted spaces or a priori spectral assumptions. Our strategy is reminiscent of the one used by Martel and Merle in various works regarding generalized Korteweg-de Vries equations. The important feature of our contribution is related to the fact that while Korteweg-de Vries equations possess unidirectional dispersion, Schr\"odinger equations do not.
We present a study of the phononic thermal conductivity of isotopically disordered carbon nanotubes. In particular, the behavior of the thermal conductivity as a function of the system length is investigated, using Green's function techniques to compute the transmission across the system. The method is implemented using linear scaling algorithms, which allows us to reach systems of lengths up to $L=2.5\mu$m (with up to 400,000 atoms). As for 1D systems, it is observed that the conductivity diverges with the system size $L$. We also observe a dramatic decrease of the thermal conductance for systems of experimental sizes (roughly 80% at room temperature for $L = 2.5$ $\mu$m), when a large fraction of isotopic disorder is introduced. The results obtained with Green's function techniques are compared to results obtained with a Boltzmann description of thermal transport. There is a good agreement between both approaches for systems of experimental sizes, even in presence of Anderson localization. This is particularly interesting since the computation of the transmission using Boltzmann's equation is much less computationally expensive, so that larger systems may be studied with this method.
We construct the compatible system of $l$-adic representations associated to a regular algebraic cuspidal automorphic representation of $GL_n$ over a CM (or totally real) field and check local-global compatibility for the $l$-adic representation away from $l$ and finite number of rational primes above which the CM field or the automorphic representation ramify. The main innovation is that we impose no self-duality hypothesis on the automorphic representation.
At sufficiently large proton energies, Glauber multiple-scattering theory offers good opportunities for describing the final state interactions in electro-induced proton emission off nuclear targets. A fully unfactorized relativistic formulation of Glauber multiple-scattering theory is presented. The effect of truncating the Glauber multiple-scattering series is discussed. Relativistic effects in the description of the final-state interactions are found not to exceed the few percent level. Also the frequently adopted approximation of replacing the wave functions for the individual scattering nucleons by some average density, is observed to have a minor impact on the results. Predictions for the separated $^4$He$(e,e'p)$ response functions are given in quasi-elastic kinematics and a domain corresponding with $1 \leq Q^2 \leq 2$ (GeV)$^2$.
We introduce {\em quadri-tilings} and show that they are in bijection with dimer models on a {\em family} of graphs $\{R^*\}$ arising from rhombus tilings. Using two height functions, we interpret a sub-family of all quadri-tilings, called {\em triangular quadri-tilings}, as an interface model in dimension 2+2. Assigning "critical" weights to edges of $R^*$, we prove an explicit expression, only depending on the local geometry of the graph $R^*$, for the minimal free energy per fundamental domain Gibbs measure; this solves a conjecture of \cite{Kenyon1}. We also show that when edges of $R^*$ are asymptotically far apart, the probability of their occurrence only depends on this set of edges. Finally, we give an expression for a Gibbs measure on the set of {\em all} triangular quadri-tilings whose marginals are the above Gibbs measures, and conjecture it to be that of minimal free energy per fundamental domain.
We report the dynamics of soft phonon modes and their role towards the various structural transformations in Aurivillius materials by employing terahertz frequency-domain spectroscopy, atomic pair distribution function analysis, and first-principles calculations. We have chosen Bi4Ti3O12 as a model system and identified soft phonon modes associated with the paraelectric tetragonal to the ferroelectric monoclinic transition. Three soft phonon modes have been discovered which exhibit a strong temperature dependence. We have determined that the anharmonicity in Bi-O bonds plays a significant role in phonon softening and that Bi cations play an important role in the emergence of ferroelectricity.