ShantanuT01/DACTYL-Pretraining huggingface dataset:
The ability to design, fabricate and control systems that can convert photons with dissimilar frequencies has technological implications in classical as well as quantum communications. Laser heating and thermal-mechanical motion in conventional micro/nanoscale optomechanical systems hamper the use of these systems in quantum information processing networks. In contrast, we propose an unconventional system comprising of a bulk quartz crystal placed within a Fabry-Perot cavity. The pumping laser is in the far-infrared region. We explore the possibility of efficient mode conversion between two optical modes supported by the system, mediated by the bulk acoustic phonons of the quartz crystal. Unlike the earlier optomechanical systems, the dark mode in our proposed system is not decoupled from the mechanical mode and yet it enables the efficient mode conversion. The novel results found in our study can be used to harness the dark state for quantum state transfer. The proposed system is robust against excessive heating.
The feasibility of shell-model calculations is radically extended by the Quantum Monte Carlo Diagonalization method with various essential improvements. The major improvements are made in the sampling for the generation of shell-model basis vectors, and in the restoration of symmetries such as angular momentum and isospin. Consequently the level structure of low-lying states can be studied with realistic interactions. After testing this method on $^{24}$Mg, we present first results for energy levels and $E2$ properties of $^{64}$Ge, indicating its large and $\gamma$-soft deformation.
We introduce a novel bandlimited manifold framework and an algorithm to recover freebreathing and ungated cardiac MR images from highly undersampled measurements. The image frames in the free breathing and ungated dataset are assumed to be points on a bandlimited manifold. We introduce a novel kernel low-rank algorithm to estimate the manifold structure (Laplacian) from a navigator-based acquisition scheme. The structure of the manifold is then used to recover the images from highly undersampled measurements. A computationally efficient algorithm, which relies on the bandlimited approximation of the Laplacian matrix, is used to recover the images. The proposed scheme is demonstrated on several patients with different breathing patterns and cardiac rates, without requiring the need for manually tuning the reconstruction parameters in each case. The proposed scheme enabled the recovery of free-breathing and ungated data, providing reconstructions that are qualitatively similar to breath-held scans performed on the same patients. This shows the potential of the technique as a clinical protocol for free-breathing cardiac scans.
We report the magnetic features of a new one-dimensional stack of antiferromagnetically coupled equilateral copper(II) triangles. High-field magnetization measurements show that the interaction between the copper triangles is of the same order of magnitude as the intra-triangle exchange although only coupled via hydrogen bonds. The infinite chain turns out to be an interesting example of a frustrated cylindrical three-leg ladder with competing intra- and inter-triangle interactions. We demonstrate that the ground state is a spin singlet which is gaped from the triplet excitation.
We prove the local well-posedness for a nonlinear equation modeling the evolution of the free surface for waves of moderate amplitude in the shallow water regime.
The Boltzmann equation is solved in the relaxation time approximation using a hierarchy of angular moments of the distribution function. Our solution is obtained for an azimuthally symmetric radially expanding boost-invariant conformal system that is undergoing Gubser flow. The solution of moments that we get after truncating the infinite set of equations at various orders is compared to the exact kinetic solution. The dynamics of transition is described by the presence of fixed points which describes the evolution of the system from an early time collisionless free streaming to the hydrodynamic regime at intermediate times and back to free streaming at late times. The attractor solution is found for various orders of moments as an interpolation between these fixed points. The relation of moments to various approximations of relativistic viscous hydrodynamics is investigated.
The tiny graviton matrix theory [hep-th/0406214] is proposed to describe DLCQ of type IIB string theory on the maximally supersymmetric plane-wave or AdS_5xS^5 background. In this paper we provide further evidence in support of the tiny graviton conjecture by focusing on the zero energy, half BPS configurations of this matrix theory and classify all of them. These vacua are generically of the form of various three sphere giant gravitons. We clarify the connection between our solutions and the half BPS configuration in N=4 SYM theory and their gravity duals. Moreover, using our half BPS solutions, we show how the tiny graviton Matrix theory and the mass deformed D=3, N=8 superconformal field theories are related to each other.
By means of variable moment kernel polynomial method, we analyze the localization properties of $\beta$-graphyne sheet subjected to the Anderson disorder. To detect the localization transition we focus on the scaling behavior of the normalized typical density of states. We find that there takes place a metal-insulator transition and the critical disorder strength is of the order of the bandwidth, which is contrary to the one-parameter scaling theory stating that for infinite two dimensional systems, all the electronic states are localized for an arbitrary strength of the Anderson disorder. As its particular localization properties, it is reasonable to predict there will exist dc conductivity for $\beta$-graphyne at zero temperature.
The average current and the shot noise at correlated sequential tunneling via two localized sites are studied. At zero temperature the Fano factor averaged over the positions and energies of sites is shown to be 0.707. The noise dependence on temperature and frequency is analyzed numerically.
We present here one of the first high resolution spectroscopic observations of coronal rain, performed with the CRISP instrument at the Swedish Solar Telescope. This work constitutes the first attempt to assess the importance of coronal rain in the understanding of the coronal magnetic field in active regions. A large statistical set is obtained in which dynamics (total velocities and accelerations), shapes (lengths and widths), trajectories (angles of fall) and thermodynamic properties (temperatures) of the condensations are derived. Specifically, we find that coronal rain is composed of small and dense chromospheric cores with average widths and lengths of 310 km and 710 km respectively, average temperatures below 7000 K, displaying a broad distribution of falling speeds with an average of 70 km/s and accelerations largely below the effective gravity along loops. Through estimates of the ion-neutral coupling in the blobs we show that coronal rain acts as a tracer of the coronal magnetic field, thus supporting the multi-strand loop scenario, and acts as a probe of the local thermodynamic conditions in loops. We further find that the cooling in neighboring strands occurs simultaneously in general suggesting a similar thermodynamic evolution among strands, which can be explained by a common footpoint heating process. Constraints for coronal heating models of loops are thus provided. Estimates of the fraction of coronal volume with coronal rain give values between 7% and 30%. Estimates of the occurrence time of the phenomenon in loops set times between 5 and 20 hours, implying that coronal rain may be a common phenomenon, in agreement with the frequent observations of cool downflows in EUV lines. The coronal mass drain rate in the form of coronal rain is estimated to be on the order of 5x10^9 g/s, a significant quantity compared to the estimate of mass flux into the corona from spicules.
We present weak lensing and X-ray analysis of 12 low mass clusters from the CFHTLenS and XMM-CFHTLS surveys. We combine these systems with high-mass systems from CCCP and low-mass systems from COSMOS to obtain a sample of 70 systems, spanning over two orders of magnitude in mass. We measure core-excised Lx-Tx, M-Lx and M-Tx scaling relations and include corrections for observational biases. By providing fully bias corrected relations, we give the current limitations for Lx and Tx as cluster mass proxies. We demonstrate that Tx benefits from a significantly lower intrinsic scatter at fixed mass than Lx. By studying the residuals of the bias corrected relations, we show for the first time using weak lensing masses that galaxy groups seem more luminous and warmer for their mass than clusters. This implies a steepening of the M-Lx and M-Tx relations at low masses. We verify the inferred steepening using a different high mass sample from the literature and show that variance between samples is the dominant effect leading to discrepant scaling relations. We divide our sample into subsamples of merging and relaxed systems, and find that mergers may have enhanced scatter in lensing measurements, most likely due to stronger triaxiality and more substructure. For the Lx-Tx relation, which is unaffected by lensing measurements, we find the opposite trend in scatter. We also explore the effects of X-ray cross-calibration and find that Chandra calibration leads to flatter Lx-Tx and M-Tx relations than XMM-Newton.
We introduce a method to construct special holomorphic tensors on orthogonal modular varieties from scalar-valued modular forms, and give applications to the Lang conjecture on the birational type of subvarieties of orthogonal modular varieties.
In this paper, we study $\mathbb{A}^1$-equivalence classes of zero cycles on open complex algebraic surfaces. We prove the logarithmic version of Mumford's theorem on zero cycles and prove that log Bloch's conjecture holds for quasiprojective surfaces with log Kodaira dimension $-\infty$.
In this paper we consider the following question. What is the maximum number of pairwise disjoint $k$-spreads which exist in PG(n,q)? We prove that if k+1 divides n+1 and n>k then there exist at least two disjoint k-spreads in PG(n,q) and there exist at least $2^{k+1}-1$ pairwise disjoint $k$-spreads in PG(n,2). We also extend the known results on parallelism in a projective geometry from which the points of a given subspace were removed.
The diffraction of fast atoms at grazing incidence on crystal surfaces (GIFAD) was first interpreted only in terms of elastic diffraction from a perfectly periodic rigid surface with atoms fixed at equilibrium position. Recently, a new approach have been proposed, referred here as the quantum binary collision model (QBCM). The QBCM takes into account both the elastic and inelastic momentum transfer via the Lamb-Dicke probability. It suggests that the shape of the inelastic diffraction profiles are log-normal distributions with a variance proportional to the nuclear energy loss deposited on the surface. For keV Neon atoms impinging the LiF surface, the predictions of the QBCM in its analytic version are compared with numerical trajectory simulations. Some of the assumptions such as the planar continuous form, the possibility to neglect the role of lithium atoms and the influence of temperature are investigated. A specific energy loss dependence $\Delta E\propto\theta^7$ is identified in the quasi-elastic regime merging progressively to the classical onset $\Delta E\propto\theta^3$. The ratio of these two predictions highlight the role of quantum effects in the energy loss.
We present serial-parallel conversion for a heralded single photon source (heralded SPS). We theoretically show that with the heralding signal, the serial-parallel converter can route a stream of n photons to n different spatial modes more efficiently than is the case without using a heralding signal. We also experimentally demonstrate serial-parallel conversion for two photons generated from a heralded SPS. We achieve a conversion efficiency of 0.533 \pm 0.003, which exceeds the maximum achievable efficiency of 0.5 for serial-parallel conversion using unheralded photons, and is double the efficiency (0.25) for that using beamsplitters. When the losses in the optical converter are corrected for, the efficiency of the current setup can be increased up to 0.996 \pm 0.006.
TikZ-Feynman is a LaTeX package allowing Feynman diagrams to be easily generated within LaTeX with minimal user instructions and without the need of external programs. It builds upon the TikZ package and leverages the graph placement algorithms from TikZ in order to automate the placement of many vertices. TikZ-Feynman still allows fine-tuned placement of vertices so that even complex diagrams can still be generated with ease.
We develop the 1/N expansion for stable string bit models, focusing on a model with bit creation operators carrying only transverse spinor indices a=1,...,s. At leading order (1/N=0), this model produces a (discretized) lightcone string with a "transverse space' of $s$ Grassmann worldsheet fields. Higher orders in the 1/N expansion are shown to be determined by the overlap of a single large closed chain (discretized string) with two smaller closed chains. In the models studied here, the overlap is not accompanied with operator insertions at the break/join point. Then the requirement that the discretized overlap have a smooth continuum limit leads to the critical Grassmann "dimension" of s=24. This "protostring", a Grassmann analog of the bosonic string, is unusual, because it has no large transverse dimensions. It is a string moving in one space dimension and there are neither tachyons nor massless particles. The protostring, derived from our pure spinor string bit model, has 24 Grassmann dimensions, 16 of which could be bosonized to form 8 compactified bosonic dimensions, leaving 8 Grassmann dimensions--the worldsheet content of the superstring. If the transverse space of the protostring could be "decompactified", string bit models might provide an appealing and solid foundation for superstring theory.
We find that a wide variety of families of partition statistics stabilize in a fashion similar to $p_k(n)$, the number of partitions of n with k parts, which satisfies $p_k(n) = p_{k+1}(n + 1), k \geq n/2$. We bound the regions of stabilization, discuss variants on the phenomenon, and give the limiting sequence in many cases as the coefficients of a single-variable generating function. Examples include many statistics that have an Euler product form, partitions with prescribed subsums, and plane overpartitions.
Let $A(n,m)$ be a graph chosen uniformly at random from the class of all vertex-labelled outerplanar graphs with $n$ vertices and $m$ edges. We consider $A(n,m)$ in the sparse regime when $m=n/2+s$ for $s=o(n)$. We show that with high probability the giant component in $A(n,m)$ emerges at $m=n/2+O\left(n^{2/3}\right)$ and determine the typical order of the 2-core. In addition, we prove that if $s=\omega\left(n^{2/3}\right)$, with high probability every edge in $A(n,m)$ belongs to at most one cycle.
We characterize galaxy correlations in the Sloan Digital Sky Survey by measuring several moments of galaxy counts in spheres. We firstly find that the average counts grows as a power-law function of the distance with an exponent D= 2.1+- 0.05 for r in [0.5,20] Mpc/h and D = 2.8+-0.05 for r in [30,150] Mpc/h. In order to estimate the systematic errors in these measurements we consider the counts variance finding that it shows systematic finite size effects which depend on the samples sizes. We clarify, by making specific tests, that these are due to galaxy long-range correlations extending up to the largest scales of the sample. The analysis of mock galaxy catalogs, generated from cosmological N-body simulations of the standard LCDM model, shows that for r<20 Mpc/h the counts exponent is D~2.0, weakly dependent on galaxy luminosity, while D=3 at larger scales. In addition, contrary to the case of the observed galaxy samples, no systematic finite size effects in the counts variance are found at large scales, a result that agrees with the absence of large scale, r~100 Mpc/h, correlations in the mock catalogs. We thus conclude that the observed galaxy distribution is characterized by correlations, fluctuations and hence structures, which are larger, both in amplitude and in spatial extension, than those predicted by the standard model LCDM of galaxy formation.
In this work we show how sublabel-accurate multilabeling approaches can be derived by approximating a classical label-continuous convex relaxation of nonconvex free-discontinuity problems. This insight allows to extend these sublabel-accurate approaches from total variation to general convex and nonconvex regularizations. Furthermore, it leads to a systematic approach to the discretization of continuous convex relaxations. We study the relationship to existing discretizations and to discrete-continuous MRFs. Finally, we apply the proposed approach to obtain a sublabel-accurate and convex solution to the vectorial Mumford-Shah functional and show in several experiments that it leads to more precise solutions using fewer labels.
We present a new method for the analysis of peculiar velocity surveys which removes contributions to velocities from small scale, nonlinear velocity modes while retaining information about large scale motions. Our method utilizes Karhunen--Lo\`eve methods of data compression to construct a set of moments out of the velocities which are minimally sensitive to small scale power. The set of moments are then used in a likelihood analysis. We develop criteria for the selection of moments, as well as a statistic to quantify the overall sensitivity of a set of moments to small scale power. Although we discuss our method in the context of peculiar velocity surveys, it may also prove useful in other situations where data filtering is required.
The Skorokhod reflection of a continuous semimartingale is unfolded, in a possibly skewed manner, into another continuous semimartingale on an enlarged probability space according to the excursion-theoretic methodology of Prokaj (2009). This is done in terms of a skew version of the Tanaka equation, whose properties are studied in some detail. The result is used to construct a system of two diffusive particles with rank-based characteristics and skew-elastic collisions. Unfoldings of conventional reflections are also discussed, as are examples involving skew Brownian Motions and skew Bessel processes.
The M\"uller-Israel-Stewart second order theory of relativistic imperfect fluids based on Grad's moment method is used to study the expansion of hot matter produced in ultra-relativistic heavy ion collisions. The temperature evolution is investigated in the framework of the Bjorken boost-invariant scaling limit. The results of these second-order theories are compared to those of first-order theories due to Eckart and to Landau and Lifshitz and those of zeroth order (perfect fluid) due to Euler.
In this paper, we report stochastic resonance (SR) in a single electron turnstile. It has been known that SR emerges by the cooperation of a weak periodic signal and noise in a bistable system. A periodic signal produces switching between two stable states by lowering the potential barrier. Even if the amplitude of the signal is not large enough to make the potential barrier disappear, the switching can occur with the help of noise. As a result, an output signal-to-noise ratio (SNR), which shows how much the switching is synchronized with the signal, can be enhanced by increasing the noise. We have formulated the SR in a single electron turnstile into the adiabatic two-state theory of McNamara-Wiesenfeld and confirmed its manifestation by numerical simulation. These results could be applied to detection of the periodic motion of very small electric charge under noisy environment.
We obtain a solution for the hydrodynamic outflow of the polytropic gas from the gravitating center, in presence of the uniform Dark Energy (DE). The antigravity of DE is enlightening the outflow and make the outflow possible at smaller initial temperature, at the same density. The main property of the wind in presence of DE is its unlimited acceleration after passing the critical point. In application of this solution to the winds from galaxy clusters we suggest that collision of the strongly accelerated wind with another galaxy cluster, or with another galactic cluster wind could lead to the formation of a highest energy cosmic rays.
The point process of vertices of an iteration infinitely divisible or more specifically of an iteration stable random tessellation in the Euclidean plane is considered. We explicitly determine its covariance measure and its pair-correlation function as well as the cross-covariance measure and the cross-pair-correlation function of the vertex point process and the random length measure in general non-stationary regime, and we specialize it to the stationary and isotropic setting. Exact formulas are given for vertex count variances in compact and convex sampling windows and asymptotic relations are derived. Our results are then compared with those for a Poisson line tessellation having the same length density parameter. Moreover, a functional central limit theorem for the joint process of suitably rescaled total edge count and edge length is established with the process $(\xi,t\xi)$, $t>0,$ arising in the limit, where $\xi$ is a centered Gaussian variable with explicitly known variance.
Given an algebraic surface $X$, the Hilbert scheme $X^{[n]}$ of $n$-points on $X$ admits a contraction morphism to the $n$-fold symmetric product $X^{(n)}$ with the extremal ray generated by a class $\beta_n$ of a rational curve. We determine the two point extremal GW-invariants of $X^{[n]}$ with respect to the class $d\beta_n$ for a simply-connected projective surface $X$ and the quantum first Chern class operator of the tautological bundle on $X^{[n]}$. The methods used are vertex algebraic description of $H^*(X^{[n]})$, the localization technique applied to $X=\mathbb P^2$, and a generalization of the reduction theorem of Kiem-J. Li to the case of meromorphic 2-forms.
We discuss the conclusions on the symmetry of hidden order (HO) in URu2Si2 that may be drawn from recent torque experiments in rotating magnetic field by Okazaki et al. [1]. They are very sensitive to changes in the magnetic susceptibility induced by HO. We show that the observed twofold angular torque oscillations give evidence that hidden order has degenerate E- type (yz,zx) symmetry where both components are realised. The oscillations have the wrong characteristics or are absent for the 1D nontrivial representations like quadrupolar B1 (x^2-y^2) and B2 (xy) type HO or hexadecapolar A2(xy(x^2-y^2)) type HO. Therefore they may be excluded as candidates for hidden order. We also predict the field-angular variation of possible field-induced Bragg peaks based on underlying E-type order parameter and discuss the expected elastic constant anomalies.
We report a first-principles density functional theory study on the role of grain boundary and dislocation loop in H blistering in W. At low temperature, the {\Sugma}3(111) tilt grain boundary, when combined with a vacancy of vanishing formation energy, can trap up to nine H atoms per (1x1) unit in (111) plane. This amount of H weakens the cohesion across the boundary to an extent that a cleavage along the GB is already exothermic. At high temperature, this effect can be still significant. For an infinitely large dislocation loop in (100) plane, four H can be trapped per (1x1) unit even above room temperature, incurring a decohesion strong enough to break the crystal. Our numerical results demonstrate unambiguously the grain boundaries and dislocation loops can serve as precursors of H blistering. In addition, no H2 molecules can be formed in either environment before fracture of W bonds starts, well explaining the H blistering in the absence of voids during non-damaging irradiation.