ShantanuT01/DACTYL-Pretraining huggingface dataset:
We report on recent progress on the chiral unitary approach, which is shown to have a much larger convergence radius than ordinary chiral perturbation theory, allowing one to reproduce data for meson meson interaction up to 1.2 GeV and meson baryon interaction up to the first baryonic resonances. Applications to physical processes so far unsuited for a standard chiral perturbative approach are presented, concretely the K^- p\to\Lambda(1405)\gamma reaction and the N^\ast (1535)N^\ast(1535)\pi and \eta couplings.
We formulate a mixed-state analog of the NLTS conjecture [FH14] by asking whether there exist topologically-ordered systems for which the thermal Gibbs state for constant temperature is globally-entangled in the sense that it cannot even be approximated by shallow quantum circuits. We then prove this conjecture holds for nearly optimal parameters: when the "inverse temperature" is almost a constant (temperature decays as 1/loglog(n))) and the Hamiltonian is nearly local (log(n)-local). The construction and proof combine quantum codes that arise from high-dimensional manifolds [Has17, LLZ19], the local-decoding approach to quantum codes [LTZ15, FGL18] and quantum locally-testable codes [AE15].
One-shot pose estimation for tasks such as body joint localization, camera pose estimation, and object tracking are generally noisy, and temporal filters have been extensively used for regularization. One of the most widely-used methods is the Kalman filter, which is both extremely simple and general. However, Kalman filters require a motion model and measurement model to be specified a priori, which burdens the modeler and simultaneously demands that we use explicit models that are often only crude approximations of reality. For example, in the pose-estimation tasks mentioned above, it is common to use motion models that assume constant velocity or constant acceleration, and we believe that these simplified representations are severely inhibitive. In this work, we propose to instead learn rich, dynamic representations of the motion and noise models. In particular, we propose learning these models from data using long short term memory, which allows representations that depend on all previous observations and all previous states. We evaluate our method using three of the most popular pose estimation tasks in computer vision, and in all cases we obtain state-of-the-art performance.
Let $-D < -4$ denote a fundamental discriminant which is either odd or divisible by 8, so that the canonical Hecke character of $\Bbb Q(\sqrt{-D})$ exists. Let $d$ be a fundamental discriminant prime to $D$. Let $2k-1$ be an odd natural integer prime to the class number of $\Bbb Q(\sqrt{-D})$. Let $\chi$ be the twist of the $(2k-1)$th power of a canonical Hecke character of $\Bbb Q(\sqrt{-D})$ by the Kronecker's symbol $n\mapsto(\frac{d}{n})$. It is proved that the order of the Hecke $L$-function $L(s,\chi)$ at its central point $s=k$ is determined by its root number when $|d| \leq c(\epsilon)D^{{1/24}-\epsilon}$ or, when $|d| \leq c(\epsilon)D^{\frac1{12} -\epsilon}$ and $k\geq 2$, where $\epsilon > 0$ and $c(\epsilon)$ is a constant depending only on $\epsilon$.
Most carbon nanotube field-effect transistors (CNTFETs) directly attach metal source/drain contacts to an intrinsic nanotube channel. When the gate oxide thickness is reduced, such transistors display strong ambipolar conduction, even when the Schottky barrier for electrons (or for holes) is zero. The resulting leakage current, which increases exponentially with the drain voltage, constrains the potential applications of such devices. In this paper, we use numerical simulations to show that if CNT based metal-oxide-semiconductor (MOS) FETs can be achieved by using heavily doped CNT sections as source and drain, ambipolar conduction will be suppressed, leakage current will be reduced, and the scaling limit imposed by source-drain tunneling will be extended. By eliminating the Schottky barrier between the source and channel, the transistor will be capable of delivering more on-current. The leakage current of such devices will be controlled by the full bandgap of CNTs (instead of half of the bandgap for SB CNTFETs) and band-to-band tunneling. These factors will depend on the diameter of nanotubes and the power supply voltage.
Many researchers have performed cosmological-model-independent tests for the distance duality (DD) relation. Theoretical work has been conducted based on the results of these tests. However, we find that almost all of these tests were perhaps not cosmological-model-independent after all, because the distance moduli taken from a given type Ia supernovae (SNe Ia) compilation are dependent on a given cosmological model and Hubble constant. In this Letter, we overcome these defects and by creating a new cosmological-model-independent test for the DD relation. We use the original data from the Union2 SNe Ia compilation and the angular diameter distances from two galaxy cluster samples compiled by De Filippis et al. and Bonamente et al. to test the DD relation. Our results suggest that the DD relation is compatible with observations, and the spherical model is slightly better than the elliptical model at describing the intrinsic shape of galaxy clusters if the DD relation is valid. However, these results are different from those of previous work.
We study the production of charginos e^+ e^- -> chi^+_i chi^-_j, (i,j=1,2) with polarized beams and the subsequent decays chi^+_i -> chi^0_k ell^+ nu and chi^-_j -> chi^0_l ell^- nu, (k,l=1,...,4), including the complete spin correlations between production and decay. Analytical formulae are presented for the joint spin-density matrix of the charginos, for the chargino decay matrix and for the differential cross section of the combined processes of production and decays. We present numerical results for pair production of the lighter chargino with unpolarized beams and the leptonic decay of chi^+_1 into the lightest neutralino chi^0_1. The lepton angular distribution and the forward-backward asymmetry are studied in four representative scenarios for sqrt{s}=192 GeV and sqrt{s}=200 GeV.
For purposes of designing targeted cataclysmic variable (CV) detection surveys and interpreting results of other projects with many CV detections such as the ChaMPlane Survey, we have created a model of the CV distribution in the Galaxy. It is modeled as a warped, flared exponential disk with a gaussian vertical distribution. Extinction is based on a detailed Galactic dust and gas model. A luminosity function for CVs is also incorporated, based on a smoothed version of published data. We calculate predicted field detection rates as a function of the limiting magnitude expected for the detecting system (i.e. WIYN/Hydra or NOAO 4m/Mosaic). Monte-Carlo techniques are used to assess statistical fluctuations in these rates. We have created maps of the expected CV distribution for the full non-bulge Galactic plane (20<l<340, |b|<15) for use in both the ChaMPlane Survey and future CV surveys. Assuming a CV distribution with a scale height of 160 pc, the ChaMPlane observational result of 5 CVs in 13 northern fields is best fit by a CV local space density of 0.9^{+1.5}_{-0.5}*10^-5 pc^-3, with the range representing the 95% confidence interval.
In an array of coupled cavities where the cavities are doped with an atomic V-system, and the two excited levels couple to cavity photons of different polarizations, we show how to construct various spin models employed in characterizing phenomena in condensed matter physics, such as the spin-1/2 Ising, XX, Heisenberg, and XXZ models. The ability to construct networks of arbitrary geometry also allows for the simulation of topological effects. By tuning the number of excitations present, the dimension of the spin to be simulated can be controlled, and mixtures of different spin types produced. The facility of single-site addressing, the use of only the natural hopping photon dynamics without external fields, and the recent experimental advances towards strong coupling, makes the prospect of using these arrays as efficient quantum simulators promising.
We study long time behavior of integrated trawl processes introduced by Barndorff-Nielsen. The trawl processes form a class of stationary infinitely divisible processes, described by an infinitely divisible random measure (L\'evy base) and a family of shifts of a fixed set (trawl). We assume that the L\'evy base is symmetric and homogeneous and that the trawl set is determined by the trawl function that decays slowly. Depending on the geometry of the trawl set and on the L\'evy measure corresponding to the L\'evy base we obtain various types of limits in law of the normalized integrated trawl processes for large times. The limit processes are always stable and self-similar with stationary increments. In some cases they have independent increments - they are stable L\'evy processes where the index of stability depends on the parameters of the model. We show that stable limits with stability index smaller than 2 may appear even in cases when the underlying L\'evy base has all its moments finite. In other cases, the limit process has dependent increments and it may be considered as a new extension of fractional Brownian motion to the class of stable processes.
Millimeter wavelength polarimetry of accreting black hole systems can provide a tomographic probe of the accretion flow on a wide range of linear scales. We searched for linear polarization in two low luminosity active galactic nuclei (LLAGN), M81 and M84, using the Combined Array for Millimeter Astronomy (CARMA) and the Submillimeter Array (SMA). We find upper limits of $\sim 1 - 2\%$ averaging over the full bandwidth and with a rotation measure (RM) synthesis technique. These low polarization fractions, along with similar low values for LLAGN M87 and 3C84, suggest that LLAGN have qualitatively different polarization properties than radio-loud sources and Sgr A*. If the sources are intrinsically polarized and then depolarized by Faraday rotation then we place lower limits on the RM of a few times $10^7\, {\rm rad\, m^{-2}}$ for the full bandwidth case and $\sim 10^9\, {\rm rad\, m^{-2}}$ for the RM synthesis analysis. These limits are inconsistent with or marginally consistent with expected accretion flow properties. Alternatively, the sources may be depolarized by cold electrons within a few Schwarzschild radii from the black hole, as suggested by numerical models.
We extend SL(2)-orbit theorems for degeneration of mixed Hodge structures to a situation in which we do not assume the polarizability of graded quotients. We also obtain analogous results on Deligne systems.
We consider a model in which the quantum fluctuation can be controlled and show that the system responds to a spatially periodic external field at zero temperature. This signifies the occurrence of spatial stochastic resonance where the fluctuations are purely quantum in nature. Various features of the phenomenon are discussed.
A new powerful method to calculate Feynman diagrams is proposed. It consists in setting up a Taylor series expansion in the external momenta squared (in general multivariable). The Taylor coefficients are obtained from the original diagram by differentiation and putting the external momenta equal to zero, which means a great simplification. It is demonstrated that it is possible to obtain by analytic continuation of the original series high precision numerical values of the Feynman integrals in the whole cut plane. For this purpose conformal mapping and subsequent resummation by means of Pad\'{e} approximants or Levin transformation are applied.
We explored the anomalously low moment in MnSi found by experiment (~0.4 $\mu_{\text{B}}$/Mn) vs the moment predicted by density functional theory (~1.0 $\mu_{\text{B}}$/Mn). With the addition of a Hubbard-U correction, we found several solutions with lower moments. These lower moment solutions show an unusual magnetic order and a magnetic quadrupole moment. The behavior of the moment under pressure does not follow the experimental trend.
The influence of background states with increasing level of complexity on the strength distribution of the isoscalar and isovector giant quadrupole resonance in $^{40}$Ca is studied. It is found that the background characteristics, typical for chaotic systems, strongly affects the fluctuation properties of the strength distribution. In particular, the small components of the wave function obey a scaling law analogous to self-organized systems at the critical state. This appears to be consistent with the Porter-Thomas distribution of the transition strength.
The universal hypermultiplet arises as a subsector of every Calabi-Yau compactification of M-theory or Type II string theory. Classically its moduli space is the quaternionic space $SU(2,1)/U(2)$. We show that this moduli space receives a one-loop correction proportional to the Euler character of the Calabi-Yau, which can locally be absorbed by a certain constant shift of the fields. The correction vanishes in the limit that the Planck mass is taken to infinity, and hence is essentially gravitational in nature.
Motivated by recent experiments on the triangular lattice Mott-Hubbard system kappa-(BEDT-TTF)2Cu2(CN)3, we develop a general formalism to investigate quantum spin liquid insulators adjacent to the Mott transition in Hubbard models. This formalism, dubbed the SU(2) slave-rotor formulation, is an extension of the SU(2) gauge theory of the Heisenberg model to the case of the Hubbard model. Furthermore, we propose the honeycomb lattice Hubbard model (at half-filling) as a candidate for a spin liquid ground state near the Mott transition; this is an appealing possibility, as this model can be studied via quantum Monte Carlo simulation without a sign problem. The pseudospin symmetry of Hubbard models on bipartite lattices turns out to play a crucial role in our analysis, and we develop our formalism primarily for the case of a bipartite lattice. We also sketch its development for a general Hubbard model. We develop a mean-field theory and apply it to the honeycomb lattice. On the insulating side of the Mott transition, we find an SU(2) algebraic spin liquid (ASL), described by gapless S = 1/2 Dirac fermions (spinons) coupled to a fluctuating SU(2) gauge field. We construct a low-energy effective theory describing the ASL phase, the conducting semimetal phase and the Mott transition between them. This physics can be detected in numerical simulations via the simultaneous presence of substantial antiferromagnetic and valence-bond solid correlations. Our analysis suggests that both a third-neighbor electron hopping, and/or pseudospin-breaking terms such as a nearest-neighbor density interaction, may help to stabilize a spin liquid phase.
We study the self-consistency of the first order formulation of quantum gravity, which may be attained by introducing, apart from the graviton field, another auxiliary quantum field. By comparing the forms of the generating functional $Z$ before and after integrating out the additional field, we derive a set of structural identities which must be satisfied by the Green's functions at all orders. These are distinct from the usual Ward identities, being necessary for the self-consistency of the first order formalism. They relate the Green's functions involving the additional quantum field to those containing a certain composite graviton field, which corresponds to its classical value. Thereby, the structural identities lead to a simple interpretation of the auxiliary field.
We study the emission properties of confined polariton states in shallow zero-dimensional traps under non-resonant excitation. We evidence several relaxation regimes. For slightly negative photon-exciton detuning, we observe a nonlinear increase of the emission intensity, characteristic of carrier-carrier scattering assisted relaxation under strong-coupling regime. This demonstrates the efficient relaxation towards a confined state of the system. For slightly positive detuning, we observe the transition from strong to weak coupling regime and then to single-mode lasing.
This paper investigates the central limit theorem for linear spectral statistics of high dimensional sample covariance matrices of the form $\mathbf{B}_n=n^{-1}\sum_{j=1}^{n}\mathbf{Q}\mathbf{x}_j\mathbf{x}_j^{*}\mathbf{Q}^{*}$ where $\mathbf{Q}$ is a nonrandom matrix of dimension $p\times k$, and $\{\mathbf{x}_j\}$ is a sequence of independent $k$-dimensional random vector with independent entries, under the assumption that $p/n\to y>0$. A key novelty here is that the dimension $k\ge p$ can be arbitrary, possibly infinity. This new model of sample covariance matrices $\mathbf{B}_n$ covers most of the known models as its special cases. For example, standard sample covariance matrices are obtained with $k=p$ and $\mathbf{Q}=\mathbf{T}_n^{1/2}$ for some positive definite Hermitian matrix $\mathbf{T}_n$. Also with $k=\infty$ our model covers the case of repeated linear processes considered in recent high-dimensional time series literature. The CLT found in this paper substantially generalizes the seminal CLT in Bai and Silverstein (2004). Applications of this new CLT are proposed for testing the structure of a high-dimensional covariance matrix. The derived tests are then used to analyse a large fMRI data set regarding its temporary correlation structure.
The scenario of spontaneous positron emission, caused by the supercritical Coulomb source with charge $Z$ and size $R$, is explored in essentially non-perturbative approach with emphasis on the vacuum energy $\mathcal{E}_{VP}$\footnote{Throughout the paper the abbreviation "VP"\, stands for "vacuum polarization"\,.}, considered as a function of $R$ with fixed $Z>Z_{cr,1}\simeq 170$. It is shown that in the supercritical region the behavior of $\mathcal{E}_{VP}(R)$ turns out to be quite different in dependence on the value of the Coulomb charge $Z$. In particular, spontaneous emission becomes a visible effect starting only from $Z \sim 300$. With further growth of $Z$ its intensity increases very rapidly, which opens up the possibility for unambiguous detection. For such $Z$ the appearing picture of spontaneous emission turns out to be well-established and quite transparent in terms of the resonance decay combined with vacuum shells formation. The intimate, but crucial role of $\mathcal{E}_{VP}(R)$ in the total energy balance in the system is outlined. The additional problems of spontaneous emission, caused by the lepton number conservation, are also discussed.
Let $K$ be an imaginary quadratic field, with associated quadratic character $\alpha$. We construct an analytic $p$-adic $L$-function interpolating the twisted adjoint $L$-values $L(1, \mathrm{ad}(f) \otimes \alpha)$ as $f$ varies in a Hida family; these special values are non-critical in the sense of Deligne. Our approach is based on Greenberg--Stevens' idea of $\Lambda$-adic modular symbols, which considers cohomology with values in a space of $p$-adic measures.
We review the status of light sterile neutrino searches, motivated by the original Short BaseLine (SBL) anomalies. Here, we discuss how sterile neutrino properties can be constrained by different types of neutrino oscillation experiments (considering appearance or disappearance probes in different oscillation channels) and non-oscillation measurements. These latter include experiments aiming at obtaining a value for the absolute scale of neutrino masses ($\beta$ decay probes) and the indirect constraints that we could obtain from cosmological observations.
Here we utilize operator--valued Lq-Lp Fourier multiplier theorems to establish lower bound estimates for large class of elliptic integro-differential equations in Rd. Moreover, we investigate separability properties of parabolic convolution operator equations that arise in heat conduction problems in materials with fading memory. Finally, we give some remarks on optimal regularity of elliptic differential equations and Cauchy problem for parabolic equations.
For NGC3516 we find that the X-ray warm absorption and the broad UV associated absorption features can be produced by the same absorbing material. We argue that the evolution of the XUV absorber from pre-1992 to 1995 is consistent with expectation for an expanding, outflowing material.
We present theoretical calculations for the differential distribution of stellar orbital eccentricity in a galaxy halo, assuming that the stars constitute a spherical, collisionless system in dynamical equilibrium with a dark matter halo. In order to define the eccentricity e of a halo star for given energy E and angular momentum L, we adopt two types of gravitational potential, such as an isochrone potential and a Navarro-Frenk-White potential, that could form two ends covering in-between any realistic potential of dark matter halo. Based on a distribution function of the form f(E,L) that allows constant anisotropy in velocity dispersions characterized by a parameter \beta, we find that the eccentricity distribution is a monotonically increasing function of e for the case of highly radially anisotropic velocity dispersions (\beta > 0.6), while showing a hump-like shape for the cases from radial through tangential velocity anisotropy (\beta < 0.6). We also find that when the velocity anisotropy agrees with that observed for the Milky Way halo stars (\beta = 0.5-0.7), a nearly linear eccentricity distribution of N(e) \alpha e results at e < 0.7, largely independent of the potential adopted. Our theoretical eccentricity distribution would be a vital tool of examining how far out in the halo the dynamical equilibrium has been achieved, through comparison with kinematics of halo stars sampled at greater distances. Given that large surveys of the SEGUE and Gaia projects would be in progress, we discuss how our results would serve as a new guide in exploring the formation and evolution of the Milky Way halo.
I show how the Lindblad Plus equation will follow from the Feynman-Vernon theory. The Plus refers to the inclusion of non-Markov processes in the Lindblad equation resulting in an integro-differential general master equation. The equivalence of this general master equation and not the Lindblad equation alone to the Feynman-Vernon theory should be expected because the sum over histories approach of the FV theory clearly includes non-Markov processes, which Lindblad equation ignores. This should close the seeming gap between these two approaches to quantum open systems.
Image-based vibration mode identification gained increased attentions in civil and construction communities. A recent video-based motion magnification method was developed to measure and visualize small structure motions. This new approach presents a potential for low-cost vibration measurement and mode shape identification. Pilot studies using this approach on simple rigid body structures was reported. Its validity on complex outdoor structures have not been investigated. The objective is to investigate the capacity of video-based motion magnification approach in measuring the modal frequency and visualizing the mode shapes of complex steel bridges. A novel method that increases the performance of the current motion magnification for efficient structure modal analysis is introduced. This method was tested in both indoor and outdoor environments for validation. The results of the investigation show that motion magnification can be an efficient tool for modal analysis on complex bridge structures. With the developed method, mode frequencies of multiple structures are simultaneously measured and mode shapes of each structure are automatically visualized.