ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study the problem of the energetic cost of information erasure by looking at it through the lens of the Jarzynski equality. We observe that the Landauer bound, $\langle W \rangle \geq kT \ln 2$, on average dissipated work $\langle W \rangle$ associated to an erasure process, literally emerges from the underlying second law bound as formulated by Kelvin, $\langle W \rangle \geq 0$, as consequence of a spontaneous breaking of the Crooks-Tasaki fluctuation-symmetry, that accompanies logical irreversibility. We illustrate and corroborate this insight with numerical simulations of the process of information erasure performed on a 2D Ising ferromagnet.
We study the dynamical generation of resonances in isospin singlet channels with mixing between two- and four-quark states. To this end we generalise a Bethe-Salpeter approach to four-quark states employed previously \cite{Heupel:2012ua} to accommodate for mixing diagrams. The $q\bar{q}q\bar{q}$ and $q\bar{q}$ components of the Bethe-Salpeter wave function (with light quarks $q\in\{u,d\}$) are determined consistently in a symmetry-preserving truncation of the underlying Dyson-Schwinger equations. As a prominent example we deal with the isospin-singlet $0^{++}$ meson with light quark content. We find that the $\pi\pi$ contribution of the four-quark component is mainly responsible for the low (real part of the) mass of the resulting state. We also study the analytic structure in the complex momentum plane and find a branch cut at the two-pion threshold and a singularity in the second Riemann sheet indicating a considerable decay width. Our findings are in excellent qualitative agreement with the general picture for the $\sigma/f_0(500)$ that emerged in the past two decades from dispersive approaches \cite{Pelaez:2015qba}.
The phase of a single-mode field can be measured in a single-shot measurement by interfering the field with an effectively classical local oscillator of known phase. The standard technique is to have the local oscillator detuned from the system (heterodyne detection) so that it is sometimes in phase and sometimes in quadrature with the system over the course of the measurement. This enables both quadratures of the system to be measured, from which the phase can be estimated. One of us [H.M. Wiseman, Phys. Rev. Lett. 75, 4587 (1995)] has shown recently that it is possible to make a much better estimate of the phase by using an adaptive technique in which a resonant local oscillator has its phase adjusted by a feedback loop during the single-shot measurement. In Ref.~[H.M. Wiseman and R.B. Killip, Phys. Rev. A 56, 944] we presented a semiclassical analysis of a particular adaptive scheme, which yielded asymptotic results for the phase variance of strong fields. In this paper we present an exact quantum mechanical treatment. This is necessary for calculating the phase variance for fields with small photon numbers, and also for considering figures of merit other than the phase variance. Our results show that an adaptive scheme is always superior to heterodyne detection as far as the variance is concerned. However the tails of the probability distribution are surprisingly high for this adaptive measurement, so that it does not always result in a smaller probability of error in phase-based optical communication.
A non perturbative renormalization scheme for Nucleon-Nucleon interaction based on boundary conditions at short distances is presented and applied to the One Pion Exchange Potential. It is free of off-shell ambiguities and ultraviolet divergences, provides finite results at any step of the calculation and allows to remove the short distance cut-off in a suitable way. Low energy constants and their non-perturbative evolution can directly be obtained from experimental threshold parameters in a completely unique and model independent way when the long range explicit pion effects are eliminated. This allows to compute scattering phase shifts which are, by construction consistent with the effective range expansion to a given order in the C.M. momentum $p$. In the singlet $^1S_0$ and triplet $^3S_1- ^3D_1$ channels ultraviolet fixed points and limit cycles are obtained respectively for the threshold parameters. Data are described satisfactorily up to CM momenta of about $p \sim m_\pi$.
A SrRuO$_3$ (SRO) thin film and its heterostructure have brought much attention because of the recently demonstrated fascinating properties, such as topological Hall effect and skyrmions. Critical to the understanding of those SRO properties is the study of the spin configuration. Here, we conduct resonant soft x-ray scattering (RSXS) at oxygen K-edge to investigate the spin configuration of a 4 unit-cell SRO film that was grown epitaxially on a single crystal SrTiO$_3$. The RSXS signal under a magnetic field (~0.4 Tesla) clearly shows a magnetic dichroism pattern around the specular reflection. Model calculations on the RSXS signal demonstrate that the magnetic dichroism pattern originates from a N\'eel-type chiral spin structure in this SRO thin film. We believe that the observed spin structure of the SRO system is a critical piece of information for understanding its intriguing magnetic and transport properties.
Given a visual history, multiple future outcomes for a video scene are equally probable, in other words, the distribution of future outcomes has multiple modes. Multimodality is notoriously hard to handle by standard regressors or classifiers: the former regress to the mean and the latter discretize a continuous high dimensional output space. In this work, we present stochastic neural network architectures that handle such multimodality through stochasticity: future trajectories of objects, body joints or frames are represented as deep, non-linear transformations of random (as opposed to deterministic) variables. Such random variables are sampled from simple Gaussian distributions whose means and variances are parametrized by the output of convolutional encoders over the visual history. We introduce novel convolutional architectures for predicting future body joint trajectories that outperform fully connected alternatives \cite{DBLP:journals/corr/WalkerDGH16}. We introduce stochastic spatial transformers through optical flow warping for predicting future frames, which outperform their deterministic equivalents \cite{DBLP:journals/corr/PatrauceanHC15}. Training stochastic networks involves an intractable marginalization over stochastic variables. We compare various training schemes that handle such marginalization through a) straightforward sampling from the prior, b) conditional variational autoencoders \cite{NIPS2015_5775,DBLP:journals/corr/WalkerDGH16}, and, c) a proposed K-best-sample loss that penalizes the best prediction under a fixed "prediction budget". We show experimental results on object trajectory prediction, human body joint trajectory prediction and video prediction under varying future uncertainty, validating quantitatively and qualitatively our architectural choices and training schemes.
In this paper, we shall treat the Schr\"odinger forms with non-local perturbations. We first extend the definitions of subcriticality, criticality and supercriticality for the Schr\"odinger forms by Takeda in [IJM, 2015] to the non-local cases in the context of quasi-regular Dirichlet forms. Then we prove an analytic characterization of these definitions via the bottom of the spectrum set.
Quantum Monte Carlo algorithms based on a world-line representation such as the worm algorithm and the directed loop algorithm are among the most powerful numerical techniques for the simulation of non-frustrated spin models and of bosonic models. Both algorithms work in the grand-canonical ensemble and have a non-zero winding number. However, they retain a lot of intrinsic degrees of freedom which can be used to optimize the algorithm. We let us guide by the rigorous statements on the globally optimal form of Markov chain Monte Carlo simulations in order to devise a locally optimal formulation of the worm algorithm while incorporating ideas from the directed loop algorithm. We provide numerical examples for the soft-core Bose-Hubbard model and various spin-S models.
We present a full calculation of the supersymmetric NLO corrections to Higgs boson production via vector-boson fusion. The supersymmetric QCD corrections turn out to be significantly smaller than the electroweak ones. These higher-order corrections are an important ingredient to a precision analysis of the Higgs sector at the LHC.
Based on Zhang and Li's molecular dynamics calculations, the heat conductivity ($\kappa$) of metallic single-wall Carbon nanotubes (SNTs) was incorrectly concluded as mainly influenced by the radius. Apart from that, their isotope effect interpretation on $\kappa(T)$ for the metallic SNTs using solely the phonon scattering mechanism is also highlighted to be incorrect.
In this paper, we introduce a "coherence equality" that is satisfied by any classical communication -- i.e., conveyed by a localized carrier traveling along well defined directions. In contrast, this equality is violated when the carrier is prepared in a quantum superposition of communication directions. This is phrased in terms of the success probability of a certain communication task, which results to be always constant and equal to 1/2 in the classical case. On the other hand, we develop two simple quantum schemes that deviate systematically from the classical value, thus violating the coherence equality. Such a violation can also be exploited as an operational way to witness spatial quantum superpositions without requiring the use of an interferometer, but only by means of spatially separated local measurements.
The theoretical possibility to use an electron microscope as a spin polarizer is studied. It turns out that a Bessel beam passing a standard magnetic objective lens is intrinsically spin polarized. In the limit of infinitely small detectors on axis, the spin polarisation tends to 100 % . Increasing the detector size, the polarisation decreases rapidly, dropping below 10^-4 for standard settings of medium voltage microscopes. For extremely low voltages, the figure of merit increases by two orders of magnitude, approaching that of existing Mott detectors. Our findings may lead to new desings of spin filters, an attractive option in view of its inherent combination with the electron microscope, especially at low voltage.
Using detailed balance and scaling properties of integrals that appear in the Coulomb gas reformulation of quantum impurity problems, we establish exact relations between the nonequilibrium transfer rates of the boundary sine-Gordon and the anisotropic Kondo model at zero temperature. Combining these results with findings from the thermodynamic Bethe ansatz, we derive exact closed form expressions for the transfer rate in the biased spin-boson model in the scaling limit. They illustrate how the crossover from weak to strong tunneling takes place. Using a conjectured correspondence between the transfer and the decoherence rate, we also determine the exact lower bound for damping of the coherent oscillation as a function of bias and dissipation strength in this paradigmic model for NMR and superposition of macroscopically distinct states (qubits).
We show that exact sampling of the first passage event can be done for a Levy process with unbounded variation, if the process can be embedded in a subordinated standard Brownian motion. By sampling a series of first exit events of the Brownian motion and first passage events of the subordinator, the first passage event of interest can be obtained. The sampling of the first exit time and pre-exit location of the Brownian motion may be of independent interest.
The theoretical limit of the minimal magnetization switching field and the optimal field pulse design for uniaxial Stoner particles are investigated. Two results are obtained. One is the existence of a theoretical limit of the smallest magnetic field out of all possible designs. It is shown that the limit is proportional to the damping constant in the weak damping regime and approaches the Stoner-Wohlfarth (SW) limit at large damping. For a realistic damping constant, this limit is more than ten times smaller than that of so-called precessional magnetization reversal under a non-collinear static field. The other is on the optimal field pulse design: If the magnitude of a magnetic field does not change, but its direction can vary during a reversal process, there is an optimal design that gives the shortest switching time. The switching time depends on the field magnitude, damping constant, and magnetic anisotropy. However, the optimal pulse shape depends only on the damping constant.
We study the Central Limit Theorem (CLT) in the so-called hybrid Lebesgue-continuous spaces and tail behavior of normed sums of centered random independent variables (vectors) with values in these spaces.
Starting from the results of Charles Fefferman and Janos Koll\`ar in Continuous Solutions of Linear Equations [1], we adopt a new approach based on Fefferman's techniques of Glaeser refinement to show a more general result than the one proved by Koll\`ar by using techniques from algebraic geometry. Considering a system of linear equations with semialgebraic (not only polynomial as in [1]) coefficients on R^n, we get a necessary and sufficient condition for the existence of a continuous and semialgebraic solution on R^n. This is different from what Fefferman and Luli obtained in Semialgebraic Sections Over the Plane [3] since they stated their result for solutions of regularity C^m on the plane R^2. More in depth, we prove that a continuous and semialgebraic solution on Rn exists if and only if there is a continuous solution i.e., if the Glaeser-stable bundle associated to the system has no empty fiber.
We study the high-energy emission of the Galactic black hole candidate GX 339-4 using INTEGRAL/SPI and simultaneous RXTE/PCA data. By the end of January 2007, when it reached its peak luminosity in hard X-rays, the source was in a bright hard state. The SPI data from this period show a good signal to noise ratio, allowing a detailed study of the spectral energy distribution up to several hundred keV. As a main result, we report on the detection of a variable hard spectral feature (>150 keV) which represents a significant excess with respect to the cutoff power law shape of the spectrum. The SPI data suggest that the intensity of this feature is positively correlated with the 25 - 50 keV luminosity of the source and the associated variability time scale is shorter than 7 hours. The simultaneous PCA data, however, show no significant change in the spectral shape, indicating that the source is not undergoing a canonical state transition. We analyzed the broad band spectra in the lights of several physical models, assuming different heating mechanisms and properties of the Comptonizing plasma. For the first time, we performed quantitative model fitting with the new versatile Comptonization code BELM, accounting self-consistently for the presence of a magnetic field. We show that a magnetized medium subject to pure non-thermal electron acceleration provides a framework for a physically consistent interpretation of the observed 4 - 500 keV emission. Moreover, we find that the spectral variability might be triggered by the variations of only one physical parameter, namely the magnetic field strength. Therefore, it appears that the magnetic field is likely to be a key parameter in the production of the Comptonized hard X-ray emission.
We present a short overview of radio surveys for AGN, including the `complete' flux limited surveys and `filtered' surveys. We also describe our ultra-steep spectrum search for the highest redshift radio galaxies, and our follow-up VLA and ATCA observations of the most distant (z=5.19) and the most luminous z<2 radio galaxy known.
Systematic studies of the two high-temperature monolayer oxygen structures that exist on the (110) tungsten surface were performed using low-energy electron microscopy and diffraction measurements. Our work questions the commonly accepted interpretation from the literature that striped oxygen superstructures arise from alternating site-exchanged (S-E) domains. We postulate that the superstructures originate from a misfit between tungsten and oxygen lattices while the striped appearance corresponds to a moir\'e pattern. Moreover, we show that the two structures, indicated as 113- and 337-phases due to the characteristic directions of the respective moir\'e patterns, differ considerably in their symmetry properties. This suggests that oxygen atoms in the two overlayers occupy different adsorption sites on average. In particular, the 113-phase features rotational domains that retain mirror symmetries with respect to the [001] and [1-10] directions, whereas the 337-phase is characterized by the appearance of additional domains due to the breaking of these symmetries. We propose structural models for both phases that consistently explain their unusual properties and suggest a universal mechanism for the thermal evolution of oxygen monolayer adsorbed on W(110).
The spin-boson model has nontrivial quantum phase transitions in the sub-Ohmic regime. For the bath spectra exponent $0 \leqslant s<1/2$, the bosonic numerical renormalization group (BNRG) study of the exponents $\beta$ and $\delta$ are hampered by the boson state truncation which leads to artificial interacting exponents instead of the correct Gaussian ones. In this paper, guided by a mean-field calculation, we study the order parameter function $m(\tau=\alpha-\alpha_c, \epsilon, \Delta)$ using BNRG. Scaling analysis with respect to the boson state truncation $N_{b}$, the logarithmic discretization parameter $\Lambda$, and the tunneling strength $\Delta$ are carried out. Truncation-induced multiple-power behaviors are observed close to the critical point, with artificial values of $\beta$ and $\delta$. They cross over to classical behaviors with exponents $\beta=1/2$ and $\delta=3$ on the intermediate scales of $\tau$ and $\epsilon$, respectively. We also find $\tau/\Delta^{1-s}$ and $\epsilon/\Delta$ scalings in the function $m(\tau, \epsilon, \Delta)$. The role of boson state truncation as a scaling variable in the BNRG result for $0 \leqslant s<1/2$ is identified and its interplay with the logarithmic discretization revealed. Relevance to the validity of quantum-to-classical mapping in other impurity models is discussed.
We study the hadron-quark phase transition in the interior of neutron stars. The relativistic mean field (RMF) theory is adopted to describe the hadronic matter phase, while the Nambu-Jona-Lasinio (NJL) model is used for the quark matter phase. The influence of the hadronic equation of state on the phase transition and neutron star properties are investigated. We find that a neutron star possesses a large population of hyperons, but it is not dense enough to possess a pure quark core. Whether the mixed phase of hadronic and quark matter exist in the core of neutron stars depends on the RMF parameters used.
This article presents and discusses a method for measuring the proper motions of the Galactic dwarf spheroidal galaxies using images taken with the Hubble Space Telescope. The method involves fitting an effective point spread function to the image of a star or quasi-stellar object to determine its centroid with an accuracy of about 0.005 pixel (0.25 milliarcseconds) -- an accuracy sufficient to measure the proper motion of a dwarf spheroidal galaxy using images separated by just a few years. The data consist of images, dithered to reduce the effects of undersampling, taken at multiple epochs with the Space Telescope Imaging Spectrograph or the Wide Field Planetary Camera. The science fields are in the directions of the Carina, Fornax, Sculptor, and Ursa Minor dwarf spheroidal galaxies and each has at least one quasi-stellar object whose identity has been established by other studies. The rate of change with time of the centroids of the stars of the dwarf spheroidal with respect to the centroid of the quasi-stellar object is the proper motion.   Four independent preliminary measurements of the proper motion of Fornax for three fields agree within their uncertainties. The weighted average of these measurements is mu_alpha = 49 +- 13 milliarcseconds/century and mu_delta = -59 +- 13 milliarcseconds/century. The Galactocentric velocity derived from the proper motion implies that Fornax is near perigalacticon, may not be bound to the Milky Way, and is not a member of any of the proposed streams of galaxies and globular clusters in the Galactic halo. If Fornax is bound, the Milky Way must have a mass of at least (1.6 +- 0.8) x 10^{12} solar masses.
Sub-arcsecond lensing statistics depend sensitively on the inner mass profiles of low-mass objects and the faint-end slopes of the Schechter luminosity function and the Press-Schechter mass function. By requiring the luminosity and mass functions to give consistent predictions for the distribution of image separation below 1'', we show that dark matter halos with masses below 10^12 M_sun cannot have a single type of profile, be it the singular isothermal sphere (SIS) or the shallower ``universal'' dark matter profile. Instead, consistent results are achieved if we allow a fraction of the halos at a given mass to be luminous with the SIS profile, and the rest be dark with an inner logarithmic slope shallower than -1.5 to compensate for the steeper faint-end slope of the mass function compared with the luminosity function. We quantify how rapidly the SIS fraction must decrease with decreasing halo mass, thereby providing a statistical measure for the effectiveness of feedback processes on the baryon content in low-mass halos.
Ten years ago, Beresnevich-Dickinson-Velani initiated a project that develops the general Hausdorff measure theory of dual approximation on non-degenerate manifolds. In particular, they established the divergence part of the theory based on their general ubiquity framework. However, the convergence counterpart of the project remains wide open and represents a major challenging question in the subject. Until recently, it was not even known for any single non-degenerate manifold. In this paper, we settle this problem for all curves in $\mathbb{R}^2$, which represents the first complete theory of its kind for a general class of manifolds.
We use basic algebraic topology and Ellingsrud-Stromme results on the Betti numbers of punctual Hilbert schemes of surfaces to compute a generating function for the Euler characteristic numbers of the Douady spaces of "n-points" associated with a complex surface. The projective case was first proved by L. G\"ottsche.
One of the most often implied benefits of high-dimensional (HD) quantum systems is to lead to stronger forms of correlations, featuring increased robustness to noise. Here, we experimentally demonstrate the $n$-setting linear HD quantum steering criterion. We verify the large violation of the steering inequalities without full-state tomography. The lower bound of the violation is $2.24\pm0.01$ in 11 dimensions, exceeding the bound ($V<2$) of 2-setting criteria. Hence, a higher strength of steering has been revealed. Moreover, we demonstrate the method for enhancing the noise robustness without increasing dimension, alternatively, by increasing measurement settings. Using the entanglement in 11 dimensions, we experimentally retrieve steering nonlocality with $63.4\pm1.4\%$ isotropic noise fraction, surpassing the $50\%$ limitation of 2-setting criteria. Our work offers the potential for practical one-sided device-independent quantum information processing that tolerates the noisy environment, lossy detection, and transcends the present transmission distance limitation.