ShantanuT01/DACTYL-Pretraining huggingface dataset:
The implementation of ultrasoft pseudopotentials into time-dependent density-functional perturbation theory is detailed for both the Sternheimer approach and the Liouville-Lanczos (LL) method, and equations are presented in the scalar relativistic approximation for periodic solids with finite momentum transfer q. The LL method is applied to calculations of the electron energy loss (EEL) spectrum of face-centered cubic bulk Au both at vanishing and finite q. Our study reveals the richness of the physics underlying the various contributions to the density fluctuation in gold. In particular, our calculations suggest the existence in gold of two quasi-separate 5d and 6s electron gasses, each one oscillating with its own frequency at resp. 5.1 eV and 10.2 eV. We find that the contribution near 2.2 eV comes from 5d to 6s interband transitions modified by the intraband contribution to the real part of the dielectric function, which we call a mixed excitation.
We consider direct bounds on the coefficients of higher dimensional top quark dipole operators from their contributions to anomalous top couplings that affect some related processes at the LHC. Several observables are studied. In particular, we incorporate for the first time in this type of analysis the recently measured associated $t \bar{t} V$ production, which is currently the only measured direct observable sensitive to the dipole operator involving the hypercharge field. We perform a Bayesian analysis to derive the $1(2)\sigma$ confidence level (CL) intervals on these coefficients.
We introduce the quantum complexity class FQMA. This class describes the complexity of generating a quantum state that serves as a witness for a given QMA problem. In a certain sense, FQMA is the quantum analogue of FNP (function problems associated with NP). The latter describes the complexity of finding a succinct proof for a NP decision problem. Whereas all FNP problems can be reduced to NP, there is no obvious reduction of FQMA to QMA since the solution of FQMA is a quantum state and the solution of QMA the answer yes or no.   We consider quantum state generators that get classical descriptions of 3-local Hamiltonians on n qubits as input and prepare low energy states for these systems as output. We show that such state generators can be used to prepare witnesses for QMA problems. Hence low energy state preparation is FQMA-complete. Our proofs are extensions of the proofs by Kitaev et al. and Kempe and Regev for the QMA-completeness of k-local Hamiltonian problems. We show that FQMA can be solved by preparing thermal equilibrium states with an appropriate temperature decreasing as the reciprocal of a polynomial in n.
We investigate some modifications of the static BTZ black hole solution due to a chosen asymptotically constant dilaton/scalar. New classes of static black hole solutions are obtained. One of the solutions contains the Martinez-Zanelli conformal black hole solution as a special case. Using quasilocal formalism, we calculate their mass for a finite spatial region that contains the black hole. Their temperatures are also computed. Finally, using some of the curvature singularities as examples, we investigate whether a quantum particle behaves singularly or not.
The quantum Hall effect is one of the most important developments in condensed matter physics of the 20th century. The standard explanations of the famous integer quantized Hall plateaus in the transverse resistivity are qualitative, and involve assumptions about disorder, localized states, extended states, edge states, Fermi levels pinned by Landau levels, etc. These standard narratives give plausible reasons for the existence of the plateaus, but provide little in the way of even a qualitative understanding of the shape and width of the Hall plateaus, much less a first principles calculation. The injection model presented in this paper changes that situation. Rather than focusing on the middle of the Hall device, we follow the electrons to their source: one corner of the Hall bar and its steep electric field gradients. We find the entire resistivity curve including the Hall plateaus is calculable as a function of magnetic field, temperature, and current. The new higher current experiments reported here show remarkable half integer features for the first time; these are faithfully reproduced by the injection theory. The Hall plateaus and half integer inflections are shown to result from the local density of states appropriate to the magnetic field and the strong electric field gradient at the injection corner.
Motivated by recent studies of colloidal particles in optical tweezer arrays, we study a two-dimensional model of a colloidal suspension in a periodic potential. The particles tend to stay near potential minima, approximating a lattice gas. The interparticle interaction, a sum of Yukawa terms, features short-range repulsion and attraction at somewhat larger separations, such that two particles cannot occupy the same potential well, but occupation of adjacent cells is energetically favored. Monte Carlo simulation reveals that the equilibrium system exhibits condensation, as in the Ising model/lattice gas with conserved magnetization; the transition appears to be continuous at a half occupancy. We study the effect of biased hopping probabilities favoring motion along one lattice direction, as might be generated by a steady flow relative to the potential array. This system is found to exhibit features of the driven lattice gas: the interface is oriented along the drive, and appears to be smooth. A weak drive facilitates ordering of the particles into high- and low-density regions, while stronger bias tends to destroy order, and leads to very large energy fluctuations. Our results suggest possible realizations of equilibrium and driven lattice gases in a colloidal suspension subject to an optical tweezer array.
The choice of poses for camera calibration with planar patterns is only rarely considered - yet the calibration precision heavily depends on it. This work presents a pose selection method that finds a compact and robust set of calibration poses and is suitable for interactive calibration. Consequently, singular poses that would lead to an unreliable solution are avoided explicitly, while poses reducing the uncertainty of the calibration are favoured. For this, we use uncertainty propagation.   Our method takes advantage of a self-identifying calibration pattern to track the camera pose in real-time. This allows to iteratively guide the user to the target poses, until the desired quality level is reached. Therefore, only a sparse set of key-frames is needed for calibration.   The method is evaluated on separate training and testing sets, as well as on synthetic data. Our approach performs better than comparable solutions while requiring 30% less calibration frames.
Heisenberg's uncertainty principle was originally posed for the limit of the accuracy of simultaneous measurement of non-commuting observables as stating that canonically conjugate observables can be measured simultaneously only with the constraint that the product of their mean errors should be no less than a limit set by Planck's constant. However, Heisenberg with the subsequent completion by Kennard has long been credited only with a constraint for state preparation represented by the product of the standard deviations. Here, we show that Heisenberg actually proved the constraint for the accuracy of simultaneous measurement but assuming an obsolete postulate for quantum mechanics. This assumption, known as the repeatability hypothesis, formulated explicitly by von Neumann and Schr\"{o}dinger, was broadly accepted until the 1970s, but abandoned in the 1980s, when completely general quantum measurement theory was established. We also survey the author's recent proposal for a universally valid reformulation of Heisenberg's uncertainty principle under the most general assumption on quantum measurement.
Cosmic explosions dissipate energy into their surroundings on a very wide range of time-scales: producing shock waves and associated particle acceleration. The historical culprits for the acceleration of the bulk of Galactic cosmic rays are supernova remnants: explosions on ~10000 year time-scales. Increasingly however, time-variable emission points to rapid and efficient particle acceleration in a range of different astrophysical systems. Gamma-ray bursts have the shortest time-scales, with inferred bulk Lorentz factors of ~1000 and photons emitted beyond 100 GeV, but active galaxies, pulsar wind nebulae and colliding stellar winds are all now associated with time-variable emission at ~TeV energies. Cosmic photons and neutrinos at these energies offer a powerful probe of the underlying physical mechanisms of cosmic explosions, and a tool for exploring fundamental physics with these systems. Here we discuss the motivations for high-energy observations of transients, the current experimental situation, and the prospects for the next decade, with particular reference to the major next-generation high-energy observatory CTA.
We predict that an anisotropic charge Kondo effect appears in a triple quantum dot, when the system has two-fold degenerate ground states of (1,1,0) and (0,0,1) charge configurations. Using bosonization and refermionization methods, we find that at low temperature, the system has the two different phases of massive charge fluctuations between the two charge configurations and vanishing fluctuations, which are equivalent with the Kondo-screened and ferromagnetic phases of the anisotropic Kondo model, respectively. The phase transition is identifiable by electron conductance measurement, offering the possibility of experimentally exploring the anisotropic Kondo model. Our charge Kondo effect has similar origin to that in a negative-U Anderson impurity.
We show that suprathermal particles, termed pick-up ions (PUIs), might reduce the postshock temperature of the fast wind and jets in some planetary nebulae (PNs) and in symbiotic systems. The goal is to explain the finding that the temperature of the hot bubble formed by the post-shock gas in some PNs and symbiotic nebulae is lower, sometimes by more than an order of magnitude, than the value expected from simple hydrodynamical calculations. Although various explanations have been proposed, there is as yet no prefered solution for this low tempeature problem. PUIs have been invoked to explain the low temperature behind the termination shock of the solar wind. While in the case of the solar wind the neutral atoms that turn into PUIs penetrate the pre-shock solar wind region from the interstellar medium (ISM), in PNs the PUI source is more likely slowly moving clumps embedded in the fast wind or jets. These clumps are formed by instabilities or from backflowing cold gas. Our estimates indicate that in young PNs these PUIs will thermalize before leaving the system. Only in older PNs whose sizes exceed ~5000 AU and for which the fast-wind mass loss rate is below ~10^{-7} Mo/yr do we expect the PUIs to be an efficient carrier of energy out of the postshock region (the hot bubble).
In this paper we examine to what extent the radio continuum can be used as an extinction free probe of star formation in dwarf galaxies. To that aim we observe $40$ nearby dwarf galaxies with the Very Large Array at 6 cm ($4$-$8$ GHz) in C-configuration. We obtained images with $3$-$8^{\prime\prime}$ resolution and noise levels of $3$-$15{\rm \,\mu Jy\,beam^{-1}}$. We detected emission associated with $22$ of the $40$ dwarf galaxies, $8$ of which are new detections. The general picture is that of an interstellar medium largely devoid of radio continuum emission, interspersed by isolated pockets of emission associated with star formation. We find an average thermal fraction of $\sim 50$-$70$% and an average magnetic field strength of $\sim 5$-$8\,{\rm \mu G}$, only slightly lower than that found in larger, spiral galaxies. At 100 pc scales, we find surprisingly high values for the average magnetic field strength of up to 50$\,{\rm \mu G}$. We find that dwarf galaxies follow the theoretical predictions of the radio continuum-star formation rate relation within regions of significant radio continuum emission but that the non-thermal radio continuum is suppressed relative to the star formation rate when considering the entire optical disk. We examine the far-infrared-star formation rate relation for our sample and find that the far-infrared is suppressed compared to the expected star formation rate. We discuss explanations for these observed relations and the impact of our findings on the radio continuum-far-infrared relation. We conclude that radio continuum emission at centimetre wavelengths has the promise of being a largely extinction-free star formation rate indicator. We find that star formation rates of gas rich, low mass galaxies can be estimated with an uncertainty of $\pm 0.2$ dex between the values of $2 \times 10^{-4}$ and $0.1 {\rm M_\odot\,yr^{-1}}$.
This work considers an Ising model on the Apollonian network, where the exchange constant $J_{i,j}\sim1/(k_ik_j)^\mu$ between two neighboring spins $(i,j)$ is a function of the degree $k$ of both spins. Using the exact geometrical construction rule for the network, the thermodynamical and magnetic properties are evaluated by iterating a system of discrete maps that allows for very precise results in the thermodynamic limit. The results can be compared to the predictions of a general framework for spins models on scale-free networks, where the node distribution $P(k)\sim k^{-\gamma}$, with node dependent interacting constants. We observe that, by increasing $\mu$, the critical behavior of the model changes, from a phase transition at $T=\infty$ for a uniform system $(\mu=0)$, to a T=0 phase transition when $\mu=1$: in the thermodynamic limit, the system shows no exactly critical behavior at a finite temperature. The magnetization and magnetic susceptibility are found to present non-critical scaling properties.
These notes represent an extended version of a talk I gave for the participants of the IMO 2009 and other interested people. We introduce diophantine equations and show evidence that it can be hard to solve them. Then we demonstrate how one can solve a specific equation related to numbers occurring several times in Pascal's Triangle with state-of-the-art methods.
In this work, we introduce a purely combinatorial way to obtain realizable orientations of a gammoid from a total order on the arc set of the digraph representing it, without first obtaining a matrix representing the gammoid over the reals.
The quantum formalism can be completed by assuming that a density operator can also represent a pure state. An 'extended Bloch representation' (EBR) then results, in which not only states, but also the measurement-interactions can be represented. The Born rule is obtained as an expression of the subjective lack of knowledge about the measurement-interaction that is each time actualized. Entanglement can also be consistently described in the EBR, as it remains compatible with the principle according to which a composite entity exists only if its components also exist, and therefore are in pure states.
Strominger and collaborators recently proposed that soft theorems for gauge and gravity amplitudes can be interpreted as Ward identities of a 2d CFT at null infinity. In this paper, we will consider a specific realization of this CFT known as ambitwistor string theory, which describes 4d Yang-Mills and gravity with any amount of supersymmetry. Using 4d ambitwistor string theory, we derive soft theorems in the form of an infinite series in the soft momentum which are valid to subleading order in gauge theory and sub-subleading order in gravity. Furthermore, we describe how the algebra of soft limits can be encoded in the braiding of soft vertex operators on the worldsheet and point out a simple relation between soft gluon and soft graviton vertex operators which suggests an interesting connection to color-kinematics duality. Finally, by considering ambitwistor string theory on a genus one worldsheet, we compute the 1-loop correction to the subleading soft graviton theorem due to infrared divergences.
Controlling coherent interaction at avoided crossings is at the heart of quantum information processing. The regime between sudden switches and adiabatic transitions is characterized by quantum superpositions that enable interference experiments. Here, we implement periodic passages at intermediate speed in a GaAs-based two-electron charge qubit and observe Landau-Zener-St\"uckelberg-Majorana (LZSM) quantum interference of the resulting superposition state. We demonstrate that LZSM interferometry is a viable and very general tool to not only study qubit properties but beyond to decipher decoherence caused by complex environmental influences. Our scheme is based on straightforward steady state experiments. The coherence time of our two-electron charge qubit is limited by electron-phonon interaction. It is much longer than previously reported for similar structures.
The history of quantum Hall standards stretches several decades and mostly begins with the use of GaAs given that 2D electron systems exhibit interesting quantum phenomena. At the end 2000s, research in 2D materials like graphene became prevalent. The QHE was observed and quickly became accessible to metrologists. QHR devices were becoming graphene-based, with fabrications performed by chemical vapor deposition (CVD), epitaxial growth, and the exfoliation of graphite. Given the many methods of available graphene synthesis, efforts to find an optimal synthesis method for metrological purposes were underway. Exfoliated graphene was widely known to exhibit the highest mobilities due to its pristine crystallinity. It was a primary initial candidate as far as metrological testing was concerned.
We present the first accurate characterization of high-degree modes, derived using the best MDI full-disk full-resolution data set available. A ninety day long time series of full-disk two arc-second per pixel resolution dopplergrams was acquired in 2001. These dopplergrams were spatially decomposed using our best estimate of the image scale and the known components of MDI's image distortion. A multi-taper power spectrum estimator was used to generate power spectra up to l = 1000, with a large number of tapers to reduce the realization noise, while the blending at high degrees negates the need for high spectral resolution. These power spectra were fitted for all degrees and all azimuthal orders, between l = 100 and l = 1000. This fitting generated in excess of 6x10^6 individual estimates of ridge frequencies, line-widths, amplitudes and asymmetries (singlets: l,n,m), corresponding to some 6,000 multiplets (l,n). Fitting at high degrees generates ridge characteristics, characteristics that do not correspond to the underlying mode characteristics. We used a sophisticated forward modeling to recover the best possible estimate of the underlying mode characteristics (mode frequencies, as well as line-widths, amplitudes and asymmetries). We describe in detail this modeling and its validation. The modeling has been extensively reviewed and refined, by including an iterative process to improve its input parameters to better match the observations. Also, the contribution of the leakage matrix on the accuracy of the procedure has been carefully assessed. We present the derived set of corrected mode characteristics, discuss their uncertainties and the precision of the ridge to mode correction schemes. In our conclusions, we address how to further improve these estimates, and the implications for other data sets, like GONG+ and HMI.
The search for thermodynamic admissibility moreover reveals a fundamental difference between liquids and gases in relativistic fluid dynamics, as the reversible convection mechanism is much simpler for liquids than for gases. In relativistic fluid mechanics, positive entropy production is known to be insufficient for guaranteeing stability. Much more restrictive criteria for thermodynamic admissibility have become available in nonequilibrium thermodynamics. We here perform a linear stability analysis for a model of relativistic hydrodynamics that is based on the GENERIC (general equation for the nonequilibrium reversible-irreversible coupling) framework of nonequilibrium thermodynamics. Assuming a simple form of the entropy function, we find stability for the entire range of physically meaningful model parameters. For relativistic fluid dynamics, full thermodynamic admissibility indeed leads to stability.
We present a generic mechanism that explains why many Kondo materials show magnetic ordering along directions that are not favoured by the crystal-field anisotropy. Using a renormalization-group (RG) analysis of single impurity Kondo models with single-ion anisotropy, we demonstrate that strong fluctuations above the Kondo temperature drive a moment re-orientation over a wide range of parameters, e.g. for different spin values $S$ and number of Kondo channels $N$. In tetragonal systems this can happen for both easy-plane or easy axis anisotropy. The characteristic crossing of magnetic susceptibilities is not an artefact of the weak-coupling RG treatment but can be reproduced in brute-force perturbation theory. Employing numerical renormalization group (NRG), we show that for an under-screened moment ($S=1$, $N=1$) with easy-plane anisotropy, a crossing of magnetic susceptibilities can also occur in the strong-coupling regime (below the Kondo temperature). This suggests that collective magnetic ordering of such under-screened moments would develop along the magnetic hard axis.
Suppose $s$ and $t$ are coprime positive integers, and let $\sigma$ be an $s$-core partition and $\tau$ a $t$-core partition. In this paper we consider the set $\mathcal P_{\sigma,\tau}(n)$ of partitions of $n$ with $s$-core $\sigma$ and $t$-core $\tau$. We find the smallest $n$ for which this set is non-empty, and show that for this value of $n$ the partitions in $\mathcal P_{\sigma,\tau}(n)$ (which we call $(\sigma,\tau)$-minimal partitions) are in bijection with a certain class of $(0,1)$-matrices with $s$ rows and $t$ columns.   We then use these results in considering conjugate partitions: we determine exactly when the set $\mathcal P_{\sigma,\tau}(n)$ consists of a conjugate pair of partitions, and when $\mathcal P_{\sigma,\tau}(n)$ contains a unique self-conjugate partition.
With the help of AMPT default model, we study the influence of initial size (centrality of collisions) on higher cumulant ratios of net-proton distributions. If the centrality is presented by impact parameter, there is a strong centrality dependent, in particular, in those peripheral collisions. This dependence is slightly reduced if the centrality is presented by number of participant, or charged multiplicity. However, the dynamical ratios are almost centrality independent. So the centrality dependence of dynamical ratios at RHIC beam energy scan are presented.
We study periodic arrays of non-Abelian vortices in an $SU(N) \times U(1)$ gauge theory with $N_f$ flavors of fundamental matter multiplets. We carefully discuss the corresponding twisted boundary conditions on the torus and propose an ansatz to solve the first order Bogomolnyi equations which we find by looking to a bound of the energy. We solve the equations numerically and construct explicit vortex solutions.