ShantanuT01/DACTYL-Pretraining huggingface dataset:
We show that measuring pairs of qubits in the Bell basis can be used to obtain a simple quantum algorithm for efficiently identifying an unknown stabilizer state of n qubits. The algorithm uses O(n) copies of the input state and fails with exponentially small probability.
We prove Liouville type theorems for $p$-harmonic functions on exterior domains of the $d$-dimensional Euclidean space, where $1<p<\infty$ and $d\geq 2$. We show that every positive $p$-harmonic function satisfying zero Dirichlet, Neumann or Robin boundary conditions and having zero limit as $|x|$ tends to infinity is identically zero. In the case of zero Neumann boundary conditions, we establish that any semi-bounded $p$-harmonic function is constant if $1<p<d$. If $p\ge d$, then it is either constant or it behaves asymptotically like the fundamental solution of the homogeneous $p$-Laplace equation.
In this article we study derived (auto)equivalences of generalized Kummer varieties $\mathrm{Kum}^n(A)$. We provide an answer to a question raised by Namikawa by showing that the generalized Kummer varieties $\mathrm{Kum}^n(A)$ and $\mathrm{Kum}^n(A^\vee)$ are derived equivalent as long as $n$ is even and the abelian surface $A$ admits a polarization whose exponent is coprime to $n+1$. Furthermore we obtain exact sequences involving groups of autoequivalences in the style of Orlov's short exact sequence for autoequivalences of abelian varieties.
We discuss diffusion of particles in a spatially inhomogeneous medium. From the microscopic viewpoint we consider independent particles randomly evolving on a lattice. We show that the reversibility condition has a discrete geometric interpretation in terms of weights associated to un--oriented edges and vertices. We consider the hydrodynamic diffusive scaling that gives, as a macroscopic evolution equation, the Fokker--Planck equation corresponding to the evolution of the probability distribution of a reversible spatially inhomogeneous diffusion process. The geometric macroscopic counterpart of reversibility is encoded into a tensor metrics and a positive function. The Fick's law with inhomogeneous diffusion matrix is obtained in the case when the spatial inhomogeneity is associated exclusively with the edge weights. We discuss also some related properties of the systems like a non-homogeneous Einstein relation and the possibility of uphill diffusion.
Using the superembedding formalism we construct supermembrane actions with higher derivative terms which can be viewed as possible higher order terms in effective actions. In particular, we provide the first example of an action for an extended supersymmetric object with fully $\kappa$-symmetric extrinsic curvature terms.
Let X be a quasi-compact and quasi-separated (not necessarily semiseparated) scheme. The category QcoX of all quasi-coherent sheaves of OX-modules has several diferent pure derived categories. Recently, categorical pure derived categories of X have been studied in more details. In this work, we focus on the geometrical purity and find replacements for geometrical pure derived categories of X.
Let $G$ be a finite group, $S\subseteq G\setminus\{1\}$ be a set such that if $a\in S$, then $a^{-1}\in S$, where $1$ denotes the identity element of $G$. The undirected Cayley graph $Cay(G,S)$ of $G$ over the set $S$ is the graph whose vertex set is $G$ and two vertices $a$ and $b$ are adjacent whenever $ab^{-1}\in S$. The adjacency spectrum of a graph is the multiset of all eigenvalues of the adjacency matrix of the graph. A graph is called integral whenever all adjacency spectrum elements are integers. Following Klotz and Sander, we call a group $G$ Cayley integral whenever all undirected Cayley graphs over $G$ are integral. Finite abelian Cayley integral groups are classified by Klotz and Sander as finite abelian groups of exponent dividing $4$ or $6$. Klotz and Sander have proposed the determination of all non-abelian Cayley integral groups. In this paper we complete the classification of finite Cayley integral groups by proving that finite non-abelian Cayley integral groups are the symmetric group $S_{3}$ of degree $3$, $C_{3} \rtimes C_{4}$ and $Q_{8}\times C_{2}^{n}$ for some integer $n\geq 0$, where $Q_8$ is the quaternion group of order $8$.
The two-dimensional frustrated next nearest neighbor Heisenberg model on the square lattice is a prime example for a spin system where quantum fluctuations can either destroy or stabilize magnetic order. The phase boundaries and staggered moment dependence on the frustration ratio J_2/J_1 of the exchange constants are fairly well understood both from approximate analytical and numerical methods. In this work we use exact diagonalization for finite clusters for an extensive investigation of the more general J_1a,b-J_2 model which includes a spatial exchange anisotropy between next-neighbor spins. We introduce a systematic way of tiling the square lattice and, for this low symmetry model, define a controlled procedure for the finite size scaling that is compatible with the possible magnetic phases. We obtain ground state energies, structure factors and ordered moments and compare with the results of spin wave calculations. We conclude that J_1a,b exchange anisotropy strongly stabilizes the columnar antiferromagnetic phase for all frustration parameters, in particular in the region of the spin nematic phase of the isotropic model.
It is a well established result that, in classical dynamical systems with sufficient time-scale separation, the fast chaotic degrees of freedom are well modeled by (Gaussian) white noise. In this paper, we present the stochastic dynamical description for intermediate time-scale motions with insufficient time-scale separation from the slow dynamical system. First, we analyze how the fast deterministic dynamics can be viewed as stochastic dynamics under experimental observation by intrinsic errors of measurement. Then, we present how the stochastic dynamical description should be modified if intermediate time-scale motions exist: the time correlation of the noise \xi is modified to <\xi(t)\xi(t')> = C(x,p)\delta(t-t'), where C(x,p) is a smooth function of the slow coordinate (x,p), and generally the cumulants of \xi except its average vary as a smooth function of the slow coordinates (x,p). The analysis given in this work actually shows that, regardless of the sufficiency of time-scale separation, any complex (chaotic and ergodic) dynamical system can be well described using Markov process, if we perfectly construct the deterministic part of (extended) stochastic dynamics.
Local realism in recent experiments is excluded on condition of freedom or randomness of choice combined with no signaling between observers by implementations of simple quantum models. Both no-signaling and the underlying quantum model can be directly checked by analysis of experimental data. For particular tests performed on the data, it is shown that two of these experiments give the probability of the data under no-signaling (or choice independence in one of them) hypothesis at the level of 5%, accounting for the look-elsewhere-effect, moderately suggesting that no-signaling is violated with 95% confidence. On the other hand the data from the two other experiments violate the assumption of the simple quantum model. Further experiments are necessary to clarify these issues and freedom and randomness of choice.
We conducted sub-millimeter observations with the Atacama Large Millimeter/sub-millimeter Array (ALMA) of star-forming galaxies at $z\sim3.3$, whose gas-phase metallicities have been previously measured. We investigate the dust and gas contents of the galaxies at $z\sim3.3$ and study how galaxies are interacting with their circumgalactic/intergalactic medium at this epoch by probing their gas mass fractions and gas-phase metallicities. Single-band dust continuum emission tracing dust mass and the relation between the gas-phase metallicity and gas-to-dust mass ratio are used to estimate the gas masses. The estimated gas mass fractions and depletion timescales are $f_{\rm gas}=$ 0.20-0.75 and $t_{\rm dep}=$ 0.09-1.55 Gyr, respectively. Although the galaxies appear to tightly distribute around the star-forming main sequence at $z\sim3.3$, both quantities show a wider spread at a fixed stellar mass than expected from the scaling relation, suggesting a large diversity of fundamental gas properties among star-forming galaxies apparently on the main sequence. Comparing gas mass fraction and gas-phase metallicity between the star-forming galaxies at $z\sim3.3$ and at lower redshifts, star-forming galaxies at $z\sim3.3$ appear to be more metal-poor than local galaxies with similar gas mass fractions. Using the gas regulator model to interpret this offset, we find that it can be explained by a higher mass-loading factor, suggesting that the mass-loading factor in outflows increases at earlier cosmic times.
Let $G$ be a fixed graph. Two paths of length $n-1$ on $n$ vertices (Hamiltonian paths) are $G$-different if there is a subgraph isomorphic to $G$ in their union. In this paper we prove that the maximal number of pairwise triangle-different Hamiltonian paths is equal to the number of balanced bipartitions of the ground set, answering a question of K\"orner, Messuti and Simonyi.
Let a(n,k) be the kth coefficient of the nth cyclotomic polynomial. The first two authors showed in part I that if m is a prime power and n and k range over the non-negative integers, then a(mn,k) assumes every integer value. Here this result is extended to the case where m is arbitrary.   The proof use some properties of reciprocal cyclotomic polynomials (see arXiv:0709.1570).
We have investigated shot noise in graphene field effect devices in the temperature range of 4.2--30 K at low frequency ($f$ = 600--850 MHz). We find that for our graphene samples with large width over length ratio $W/L$, the Fano factor $\mathfrak{F}$ reaches a maximum $\mathfrak{F} \sim$ 1/3 at the Dirac point and that it decreases strongly with increasing charge density. For smaller $W/L$, the Fano factor at Dirac point is significantly lower. Our results are in good agreement with the theory describing that transport at the Dirac point in clean graphene arises from evanescent electronic states.
We explore the quantum-classical crossover of two coupled, identical, superconducting quantum interference device (SQUID) rings. We note that the motivation for this work is based on a study of a similar system comprising two coupled Duffing oscillators. In that work we showed that the entanglement characteristics of chaotic and periodic (entrained) solutions differed significantly and that in the classical limit entanglement was preserved only in the chaotic-like solutions. However, Duffing oscillators are a highly idealised toy model. Motivated by a wish to explore more experimentally realisable systems we now extend our work to an analysis of two coupled SQUID rings. We observe some differences in behaviour between the system that is based on SQUID rings rather than on Duffing oscillators. However, we show that the two systems share a common feature. That is, even when the SQUID ring's trajectories appear to follow (semi) classical orbits entanglement persists.
The production/absorption rate of particles in compressed and heated asymmetric matter is studied using a Relativistic Mean Field (RMF) transport model with an isospin dependent collision term. Just from energy conservation in the elementary production/absorption processes we expect to see a strong dependence of the yields on the basic Lorentz structure of the isovector effective interaction, due to isospin effects on the scalar and vector self-energies of the hadrons. This will be particularly evident for the ratio of the rates of particles produced with different charges: results are shown for \pi(+)/\pi(-), K(+)/K(0) yields. In order to simplify the analysis we perform RMF cascade simulations in a box with periodic boundary conditions. In this way we can better pin down all such fine relativistic effects in particle production, that could likely show up even in realistic heavy ion collisions. In particular, K(+,0) production is expected to be directly related to the high density behaviour of the symmetry energy, since kaons are produced very early during the high density stage of the collision and their mean free path is rather large. We show that the K(+)/K(0) ratio reflects important isospin contributions on the production rates just because of the large sensitivity around the threshold. The results are very promising for the possibility of a direct link between particle production data in exotic Heavy Ion Collisions and the isospin dependent part of the Equation of State at high baryon densities.
The origin of the variation of photoluminescence (PL) spectra of monolayer tungsten disulfide (WS2) is investigated systematically. Dependence of the PL spectrum on the excitation power show that the relatively sharp component corresponds to excitons whereas the broader component at slightly lower energy corresponds to negatively charged trions. PL imaging and second harmonic generation measurements show that the trion signals are suppressed more than the exciton signals near the edges, thereby relatively enhancing the excitonic feature in the PL spectrum and that such relative enhancement of the exciton signals is more pronounced near approximately armchair edges. This effect is interpreted in terms of depletion of free electrons near the edges caused by structural defects and adsorption of electron acceptors such as oxygen atoms.
We provide a geometric characterization of the minimal and maximal minimizer of the prescribed curvature functional $P(E)-\kappa |E|$ among subsets of a Jordan domain $\Omega$ with no necks of radius $\kappa^{-1}$, for values of $\kappa$ greater than or equal to the Cheeger constant of $\Omega$. As an application, we describe all minimizers of the isoperimetric profile for volumes greater than the volume of the minimal Cheeger set, relative to a Jordan domain $\Omega$ which has no necks of radius $r$, for all $r$. Finally, we show that for such sets and volumes the isoperimetric profile is convex.
The purpose of this article is to generalize some results of Vatsal on studying the special values of Rankin-Selberg L-functions in an anticyclotomic $\mathbb{Z}_{p}$-extension. Let $g$ be a cuspidal Hilbert modular form of parallel weight (2,...,2) and level $\mathcal{N}$ over a totally real field F, and let K/F be a totally imaginary quadratic extension of relative discriminant $\mathcal{D}$. We study the $l$-adic valuation of the special values $L(g,\chi,\frac{1}{2})$ as \chi varies over the ring class characters of K of $\mathcal{P}$-power conductor, for some fixed prime ideal $\mathcal{P}$. We prove our results under the only assumption that the prime to $\mathcal{P}$ part of $\mathcal{N}$ is relatively prime to $\mathcal{D}$.
We develop an explicit algebriac de Rham theory for relative completion of $\mathrm{SL}_2(\mathbb{Z})$. This allows the construction of iterated integrals involving modular forms of the second kind, generalizing iterated integrals of holomorphic modular forms that were previously studied by Brown and Manin. These newly constructed iterated integrals provide all 'multiple modular values' defined by Brown.
We address nonperturbative power corrections to inclusive decay widths of heavy flavor hadrons in the context of the 't Hooft model (two-dimensional QCD at N_c->oo), with the emphasis on the spectator-dependent effects sensitive to the flavor of the spectator. The summation of exclusive widths is performed analytically using the `t Hooft equation. We show that the 1/m_Q expansion of both the Weak Annihilation and Pauli Interference widths coincides with the OPE predictions, to the computed orders. Violation of local duality in the inclusive widths is quantified, and the new example is identified where the OPE prediction and the actual effect are completely saturated by a single final state. The qualitative aspects of quark hadronization emerging from the analysis in the 't Hooft model are discussed. Certain aspects of summation of spectator-independent hadronic weak decay widths are given in more detail, which were not spelled out previously. We also give some useful details of the 1/m_Q expansion in the 't~Hooft model.
We propose a description of open universes in the Chern-Simons formulation of (2+1)-dimensional gravity where spatial infinity is implemented as a puncture. At this puncture, additional variables are introduced which lie in the cotangent bundle of the Poincar\'e group, and coupled minimally to the Chern-Simons gauge field. We apply this description of spatial infinity to open universes of general genus and with an arbitrary number of massive spinning particles. Using results of [9] we give a finite dimensional description of the phase space and determine its symplectic structure. In the special case of a genus zero universe with spinless particles, we compare our result to the symplectic structure computed by Matschull in the metric formulation of (2+1)-dimensional gravity. We comment on the quantisation of the phase space and derive a quantisation condition for the total mass and spin of an open universe.
Li3VO4/C composites have been synthesized by a sol-gel method and post-annealing at 650 {\deg}C for 1 h in N2 flow using either tartaric acid, malic acid, or glucose as both chelating agents and carbon source. The presence of these organic additives crucially affects morphology and crystallite size of the final product. It is found that the electrochemical properties of Li3VO4/C as anode material for Li-ion batteries (LIBs) are influenced by the morphology, texture and carbon content of the material. When using carboxylic acids as carbon source composites with mesoporous structure and a high surface area are obtained that display an enhanced electrochemical activity. Initially, reversible capacity of about 400 mAh g-1 is obtained. In contrast, Li3VO4/C synthesized with glucose outperforms in terms of cycling stability. It exhibits a discharge capacity of 299 mAh g-1 after 100 cycles corresponding to an excellent capacity retention of 96 %. The favorable effect of carbon composites on the electrochemical performance of Li3VO4 is shown.
Magnetic flux redistribution lies at the heart of the problem of star formation in dense cores of molecular clouds that are magnetized to a realistic level. If all of the magnetic flux of a typical core were to be dragged into the central star, the stellar field strength would be orders of magnitude higher than the observed values. This well-known "magnetic flux problem" can in principle be resolved through non-ideal MHD effects. Two dimensional (axisymmetric) calculations have shown that ambipolar diffusion, in particular, can transport magnetic flux outward relative to matter, allowing material to enter the central object without dragging the field lines along. We show through simulations that such axisymmetric protostellar accretion flows are unstable in three dimensions to magnetic interchange instability in the azimuthal direction. The instability is driven by the magnetic flux redistributed from the matter that enters the central object. It typically starts to develop during the transition from the prestellar phase of star formation to the protostellar mass accretion phase. In the latter phase, the magnetic flux is transported outward mainly through advection, by strongly magnetized low-density regions that expand against the collapsing inflow. The tussle between the gravity-driven infall and magnetically driven expansion leads to a filamentary inner accretion flow, more disordered than previously pictured. The efficient outward transport of magnetic flux by advection lowers the field strength at small radii, making the magnetic braking less efficient and the formation of rotationally supported disks easier in principle. However, we find no evidence for such disks in any of our rotating collapse simulations. We conclude that the inner protostellar accretion flow is shaped to a large extent by this magnetic interchange instability. How disks form in such an environment is unclear.
Relativistic jets of radio loud active galactic nuclei (AGN) produce highly directed, intense beams of radiation. A fraction of this beamed radiation scatters on the thermal plasma generally surrounding an AGN. The morphology of the scattered emission can thus provide constraints on the physical properties of the jet. We present a model to study the feasibility of constraining the parameters of a jet, especially its inclination angle and bulk Lorentz factor in this way. We apply our model to the well studied jet of M87 and the surrounding diffuse gas and find that the observational limits of the surface brightness measured in the region of the putative counterjet provide the tightest constraints on the jet parameters consistent with constraints derived by other methods. We briefly discuss the applicability of our model to other sources exhibiting relativistic motions
Facial micro-expressions (MEs) are involuntary facial motions revealing peoples real feelings and play an important role in the early intervention of mental illness, the national security, and many human-computer interaction systems. However, existing micro-expression datasets are limited and usually pose some challenges for training good classifiers. To model the subtle facial muscle motions, we propose a robust micro-expression recognition (MER) framework, namely muscle motion-guided network (MMNet). Specifically, a continuous attention (CA) block is introduced to focus on modeling local subtle muscle motion patterns with little identity information, which is different from most previous methods that directly extract features from complete video frames with much identity information. Besides, we design a position calibration (PC) module based on the vision transformer. By adding the position embeddings of the face generated by PC module at the end of the two branches, the PC module can help to add position information to facial muscle motion pattern features for the MER. Extensive experiments on three public micro-expression datasets demonstrate that our approach outperforms state-of-the-art methods by a large margin.
We identify a diffeomorphism Lie algebra in the self-dual sector of Yang-Mills theory, and show that it determines the kinematic numerators of tree-level MHV amplitudes in the full theory. These amplitudes can be computed off-shell from Feynman diagrams with only cubic vertices, which are dressed with the structure constants of both the Yang-Mills colour algebra and the diffeomorphism algebra. Therefore, the latter algebra is the dual of the colour algebra, in the sense suggested by the work of Bern, Carrasco and Johansson. We further study perturbative gravity, both in the self-dual and in the MHV sectors, finding that the kinematic numerators of the theory are the BCJ squares of the Yang-Mills numerators.
We develop a gauge theory of the critical behavior of the topological excitations-driven Berezinskii-Kosterlitz-Thouless (BKT) phase transition in the XY model with weak quenched disorder. We find that while in two-dimensions the liquid of topological defects exhibits the BKT critical behavior, the three-dimensional system shows more singular Vogel-Fulcher-Tamman criticality heralding its freezing into a spin glass. Our findings provide insights into the topological origin of spin glass formation.
A series of (Ga,In)As/GaAs/Ga(As,Sb) multi-quantum well heterostructures is analyzed using temperature- and power-dependent photoluminescence (PL) spectroscopy. Pronounced PL variations with sample temperature are observed and analyzed using microscopic many-body theory and band structure calculations based on the k$\cdot$p method. This theory-experiment comparison reveals an unusual, temperature dependent variation of the band alignment between the (Ga,In)As and Ga(As,Sb) quantum wells.