ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study the ground state phase diagram of the Anderson-Hubbard model with correlated hopping at half filling in one-dimension. The Hamiltonian has a local Coulomb repulsion $U$ and a disorder potential with local energies randomly distributed in the interval $(-W,+W)$ with equal probability, acting on the singly occupied sites. The hopping process which modifies the number of doubly occupied sites is forbidden. The hopping between nearest-neighbor singly occupied and empty sites or between singly occupied and doubly occupied sites have the same amplitude $t$. We identify three different phases as functions of the disorder amplitude $W$ and Coulomb interaction strength $U>0$. When $U<4t$ the system shows a metallic phase (i) only when no disorder is present $W=0$ or an Anderson-localized phase (ii) when disorder is introduced $W\neq 0$. When $U>4t$ the Anderson-localized phase survives as long as disorder effects dominates on the interaction effects, otherwise a Mott insulator phase (iii) arises. The phases (i) and (ii) are characterized by a finite density of doublons and a vanishing charge gap between the ground state and the excited states. The phase (iii) is characterized by vanishing density of doublons and a finite gap for the charge excitations.
We will generalize the combinatorial algorithms for computing $\pi(x)$ to compute sums ${F(x) = \sum_{p \leq x} p^k}$ for $k \in \mathbb{Z}_{\geq 0}$. The detailed exposition of algorithms is included along with implementation details.
The vulnerability of automated fingerprint recognition systems to presentation attacks (PA), i.e., spoof or altered fingers, has been a growing concern, warranting the development of accurate and efficient presentation attack detection (PAD) methods. However, one major limitation of the existing PAD solutions is their poor generalization to new PA materials and fingerprint sensors, not used in training. In this study, we propose a robust PAD solution with improved cross-material and cross-sensor generalization. Specifically, we build on top of any CNN-based architecture trained for fingerprint spoof detection combined with cross-material spoof generalization using a style transfer network wrapper. We also incorporate adversarial representation learning (ARL) in deep neural networks (DNN) to learn sensor and material invariant representations for PAD. Experimental results on LivDet 2015 and 2017 public domain datasets exhibit the effectiveness of the proposed approach.
We prove a set of tight entanglement inequalities for arbitrary $N$-qubit pure states. By focusing on all bi-partite marginal entanglements between each single qubit and its remaining partners, we show that the inequalities provide an upper bound for each marginal entanglement, while the known monogamy relation establishes the lower bound. The restrictions and sharing properties associated with the inequalities are further analyzed with a geometric polytope approach, and examples of three-qubit GHZ-class and W-class entangled states are presented to illustrate the results.
We studied the stellar population and star clusters around six regions in the Large Magellanic Cloud (LMC) in order to understand the correlation between star formation and cluster formation episodes. We used the stellar data base of OGLE II LMC survey and the star cluster catalogues. The analysis of the colour-magnitude diagrams (CMDs) were used to estimate the ages of the stellar population. It is found that most of the regions have undergone three major star formation episodes. The star formation which began about 4 Gyr ago, continued upto 1 Gyr, or continued further. The other two events have taken place around 300 Myr, and 100 Myr. A few star clusters were formed during the first of the three star formation events in 5 regions. On all the six regions, a good correlation is seen between the star and cluster formation events which occurred at 300 Myr and 100 Myr. The cluster formation events and the fraction of star clusters formed were found to be very similar for two regions located to the south-east of the Bar, suggesting similar cluster formation triggers at almost similar instances. The two recent star formation events seem to correlate with the interaction of LMC with Small Magellanic Cloud (SMC) and Galaxy. Hence it is quite likely that the young populous star clusters in the LMC are formed as a result of the star formation events started due to galaxy-galaxy interactions and the further propagation of such star formation.
We analyze the space-times admitting two shear-free geodesic null congruences. The integrability conditions are presented in a plain tensorial way as equations on the volume element $U$ of the time-like 2--plane that these directions define. From these we easily deduce significant consequences. We obtain explicit expressions for the Ricci and Weyl tensors in terms of $U$ and its first and second order covariant derivatives. We study the different compatible Petrov-Bel types and give the necessary and sufficient conditions that characterize every type in terms of $U$. The type D case is analyzed in detail and we show that every type D space-time admitting a 2+2 conformal Killing tensor also admits a conformal Killing-Yano tensor.
Generalizing Amari's work titled "Information geometry on hierarchy of probability distributions", we define the degrees of irreducible multiparty correlations in a multiparty quantum state based on quantum relative entropy. We prove that these definitions are equivalent to those derived from the maximal von Neaumann entropy principle. Based on these definitions, we find a counterintuitive result on irreducible multiparty correlations: although the degree of the total correlation in a three-party quantum state does not increase under local operations, the irreducible three-party correlation can be created by local operations from a three-party state with only irreducible two-party correlations. In other words, even if a three-party state is initially completely determined by measuring two-party Hermitian operators, the determination of the state after local operations have to resort to the measurements of three-party Hermitian operators.
We show that finite systems whose Hamiltonians obey a generalized homogeneity relation rigorously follow the nonextensive thermostatistics of Tsallis. In the thermodynamical limit, however, our results indicate that the Boltzmann-Gibbs statistics is always recovered, regardless of the type of potential among interacting particles. This approach provides, moreover, a one-to-one correspondence between the generalized entropy and the Hamiltonian structure of a wide class of systems, revealing a possible origin for the intrinsic nonlinear features present in the Tsallis formalism that lead naturally to power-law behavior. Finally, we confirm these exact results through extensive numerical simulations of the Fermi-Pasta-Ulam chain of anharmonic oscillators.
We perform a Gutzwiller projected wavefunction study for the spin-1/2 Heisenberg model on the Kagome lattice to compare energies of several spin-liquid states. The result indicates that a U(1)-Dirac spin-liquid state has the lowest energy. Furthermore, even without variational parameters, the energy turns out to be very close to that found by exact diagonalization. We show that such a U(1)-Dirac state represents a quantum phase whose low energy physics is governed by four flavors of two-component Dirac fermions coupled to a U(1) gauge field. These results are discussed in the context of recent experiments on ZnCu$_3$(OH)$_6$Cl$_2$.
We propose a new method for semantic instance segmentation, by first computing how likely two pixels are to belong to the same object, and then by grouping similar pixels together. Our similarity metric is based on a deep, fully convolutional embedding model. Our grouping method is based on selecting all points that are sufficiently similar to a set of "seed points", chosen from a deep, fully convolutional scoring model. We show competitive results on the Pascal VOC instance segmentation benchmark.
Weak gravitational lensing provides a unique method to map directly the distribution of dark matter in the universe and to measure cosmological parameters. This cosmic-shear technique is based on the measurement of the weak distortions that lensing induces in the shape of background galaxies as photons travel through large-scale structures. This technique is now widely used to measure the mass distribution of galaxy clusters and has recently been detected in random regions of the sky. In this review, we present the theory and observational status of cosmic shear. We describe the principles of weak lensing and the predictions for the shear statistics in favored cosmological models. Next, we review the current measurements of cosmic shear and show how they constrain cosmological parameters. We then describe the prospects offered by upcoming and future cosmic-shear surveys as well as the technical challenges that have to be met for the promises of cosmic shear to be fully realized.
A random multiplicative process with additive noise is described by a Langevin equation. We show that the fluctuation-dissipation relation is satisfied in the Langevin model, if the noise strength is not so strong.
We propose the use of feedback mechanism to control the level of quantum noise in a radiation field emerging from a pendular Fabry-Perot cavity. It is based on the possibility to perform quantum nondemolition measurements by means of optomechanical coupling.
Hierarchical theories of structure formation predict that clusters of galaxies should be embedded in a web like structure, with filaments emanating from them to large distances. The amount of mass contained within such filaments near a cluster can be comparable to the collapsed mass of the cluster itself. Diffuse infalling material also contains a large amount of mass. Both these components can contribute to the cluster weak lensing signal. This ``projection bias'' is maximized if a filament lies close to the line-of-sight to a cluster. Using large--scale numerical simulations of structure formation in a cosmological constant dominated cold dark matter model, we show that the projected mass typically exceeds the actual mass by several tens of percent. This effect is significant for attempts to estimate cluster masses through weak lensing observations, and will affect weak lensing surveys aimed at constructing the cluster mass function.
A new kind of dark matter structures, ultracompact minihalos (UCMHs) was proposed recently. They would be formed during the radiation dominated epoch if the large density perturbations are existent. Moreover, if the dark matter is made up of weakly interacting massive particles, the UCMHs can have effect on cosmological evolution because of the high density and dark matter annihilation within them. In this paper, one new parameter is introduced to consider the contributions of UCMHs due to the dark matter annihilation to the evolution of cosmology, and we use the current and future CMB observations to obtain the constraint on the new parameter and then the abundance of UCMHs. The final results are applicable for a wider range of dark matter parameters
The heavy fermion ferromagnet CeRh$_6$Ge$_4$ is the first example of a clean stoichiometric system where the ferromagnetic transition can be continuously suppressed by hydrostatic pressure to a quantum critical point. In order to reveal the outcome when the magnetic lattice of CeRh$_6$Ge$_4$ is diluted with non-magnetic atoms, this study reports comprehensive measurements of the physical properties of both single crystal and polycrystalline samples of La$_x$Ce$_{1-x}$Rh$_6$Ge$_4$. With increasing $x$, the Curie temperature decreases, and no transition is observed for $x$ $>$ 0.25, while the system evolves from exhibiting coherent Kondo lattice behaviors at low $x$, to the Kondo impurity scenario at large $x$. Moreover, non-Fermi liquid behavior (NFL) is observed over a wide doping range, which agrees well with the disordered Kondo model for 0.52 $\leq$ $x$ $\leq$ 0.66, while strange metal behavior is revealed in the vicinity of $x_c$ = 0.26.
Spectral statistics of weakly-disordered triangular graphene flakes with zigzag edges are revisited. Earlier, we have found numerically that such systems may shown spectral fluctuations of GUE, signalling the time-reversal symmetry breaking at zero magnetic field, accompanied by approximate twofold valley degeneracy of each energy level [Phys. Rev. B 85, 245424 (2012)]. Atomic-scale disorder induce the scattering of charge carriers between the valleys and restores the spectral fluctuations of GOE. A simplified description of such a nonstandard GUE-GOE transition, employing the mixed ensemble of 4x4 real symmetric matrices was also proposed. Here we complement our previous study by analyzing numerically the spectral fluctuations of large matrices belonging the same mixed ensemble. Resulting scaling laws relate the ensemble parameter to physical size and the number of atomic-scale defects in graphene flake. A phase diagram, indicating the regions in which the signatures of GUE may by observable in the size-doping parameter plane, is presented.
Entanglement and symmetrization lead to non-separable states that can modify physical properties. Using the example of atomic absorption we compare both types of effects when they are relevant at once. The presence of multi-particle superpositions largely alters the absorption rates of identical atoms, even inhibiting the dependence on overlapping for fermions. We also identify a set of non-standard excluded states related to multi-fermion superposition that naturally emerge in this context. We propose an arrangement based on the dissociation of molecules to test these ideas.
Semi-quantum key distribution protocols are allowed to set up a secure secret key between two users. Compared with their full quantum counterparts, one of the two users is restricted to perform some "classical" or "semi-quantum" operations, which makes them easily realizable by using less quantum resource. However, the semi-quantum key distribution protocols mainly rely on a two-way quantum channel. The eavesdropper has two opportunities to intercept the quantum states transmitted in the quantum communication stage. It may allow the eavesdropper to get more information and make the security analysis more complicated. In the past ten years, many semi-quantum key distribution protocols have been proposed and proved to be robust. But there are few works concerned about their unconditional security. It is doubted that how secure the semi-quantum ones are and how much noise can they tolerate to establish a secure secret key. In this paper, we prove the unconditional security of a single-state semi-quantum key distribution protocol proposed by $Zou$ et al. in [Phys. Rev. A. 79]. We present a complete proof from information theory aspect by deriving a lower bound of the protocol's key rate in the asymptotic scenario. Using this bound, we figure out an error threshold value such that all error rates are less than this threshold value, the secure secret key can be established between the legitimate users definitely. Otherwise, the users should abort the protocol. we make an illustration of the protocol under the circumstance of the reverse quantum channel is a depolarizing one with parameter $q$. Additionally, we compare the error threshold value with some full quantum protocols and several existing semi-quantum ones whose unconditional security proofs have been provided recently.
Symbiotic X-ray binaries (SyXBs) comprise a rare class of low-mass X-ray binaries. We study the Galactic SyXBs, which we consider as detached binaries composed of low-mass giants and wind-fed neutron star companions, by simulation of the interaction of a magnetized neutron star (NS) with its environment and utilizing a population synthesis code. We focus mainly on the parameters that influence observational appearance of the SyXB: the donor wind velocity (vw) and the angular momentum distribution in the shell of matter settling onto NS. We estimate the birthrate of SyXB as $\sim 4.1\times 10^{-5}$ yr$^{-1}$ to $ \sim 6.6\times 10^{-6}$ yr$^{-1}$ and their number in the Galaxy as $\sim$(100 -- 1000). Assumed stellar wind velocity from cool giants is the input parameter that influences the model SyXBs population most.   Among known SyXBs or candidate systems, 4U 1954+31 and IGR J16358-4724 in which NS have very long spin periods may host quasi-spherically accreting NSs. GX 1+4 has a peculiar long-term spin behaviour and it may also be a quasi-spherical wind-accreting source. We cannot identify whether there are wind-fed accretion disks in 4U 1700+24, Sct X-1, IRXS J180431.1-273932 and 2XMM J174016.0-290337.
We analyze the ground-state energy, magnetization, magnetic susceptibility, and Kondo screening cloud of the symmetric single-impurity Anderson model (SIAM) that is characterized by the band width $W$, the impurity interaction strength $U$, and the local hybridization $V$. We compare Gutzwiller variational and magnetic Hartree-Fock results in the thermodynamic limit with numerically exact data from the Density-Matrix Renormalization Group (DMRG) method on large rings. To improve the DMRG performance, we use a canonical transformation to map the SIAM onto a chain with half the system size and open boundary conditions. We compare to Bethe-Ansatz results for the ground-state energy, magnetization, and spin susceptibility that become exact in the wide-band limit. Our detailed comparison shows that the field-theoretical description is applicable to the SIAM on a ring for a broad parameter range. Hartree-Fock theory gives an excellent ground-state energy and local moment for intermediate and strong interactions. However, it lacks spin fluctuations and thus cannot screen the impurity spin. The Gutzwiller variational energy bound becomes very poor for large interactions because it does not describe properly the charge fluctuations. Nevertheless, the Gutzwiller approach provides a qualitatively correct description of the zero-field susceptibility and the Kondo screening cloud. The DMRG provides excellent data for the ground-state energy and the magnetization for finite external fields. At strong interactions, finite-size effects make it extremely difficult to recover the exponentially large zero-field susceptibility and the mesoscopically large Kondo screening cloud.
Non-Gaussian statistics of late-time cosmological fields contain information beyond that captured in the power spectrum. Here we focus on one such example: the one-point probability distribution function (PDF) of the thermal Sunyaev-Zel'dovich (tSZ) signal in maps of the cosmic microwave background (CMB). It has been argued that the one-point PDF is a near-optimal statistic for cosmological constraints from the tSZ signal, as most of the constraining power in tSZ $N$-point functions is contained in their amplitudes (rather than their shapes), which probe differently-weighted integrals over the halo mass function. In this paper, we develop a new analytic halo model for the tSZ PDF, discarding simplifying assumptions made in earlier versions of this approach. In particular, we account for effects due to overlaps of the tSZ profiles of different halos, as well as effects due to the clustering of halos. We verify the accuracy of our analytic model via comparison to numerical simulations. We demonstrate that this more accurate model is necessary for the analysis of the tSZ PDF in upcoming CMB experiments. The novel formalism developed here may be useful in modeling the one-point PDF of other cosmological observables, such as the weak lensing convergence field.
In a granular gas of rough particles the axis of rotation is shown to be correlated with the translational velocity of the particles. The average relative orientation of angular and linear velocities depends on the parameters which characterise the dissipative nature of the collision. We derive a simple theory for these correlations and validate it with numerical simulations for a wide range of coefficients of normal and tangential restitution. The limit of smooth spheres is shown to be singular: even an arbitrarily small roughness of the particles gives rise to orientational correlations.
Constant composition codes have been proposed as suitable coding schemes to solve the narrow band and impulse noise problems associated with powerline communication. In particular, a certain class of constant composition codes called frequency permutation arrays have been suggested as ideal, in some sense, for these purposes. In this paper we characterise a family of neighbour transitive codes in Hamming graphs in which frequency permutation arrays play a central rode. We also classify all the permutation codes generated by groups in this family.
We study relativistic nuclear matter in the $\sigma - \omega$ model including the ring-sum correlation energy. The model parameters are adjusted self-consistently to give the canonical saturation density and binding energy per nucleon with the ring energy included. Two models are considered, mean-field-theory where we neglect vacuum effects, and the relativistic Hartree approximation where such effects are included but in an approximate way. In both cases we find self-consistent solutions and present equations of state. In the mean-field case the ring energy completely dominates the attractive part of the energy density and the elegant saturation mechanism of the standard approach is lost, namely relativistic quenching of the scalar attraction. In the relativistic Hartree approach the vacuum effects are included in an approximate manner using vertex form factors with a cutoff of 1 - 2 GeV, the range expected from QCD. Due to the cutoff, the ring energy for this case is significantlysmaller, and we obtain self-consistent solutions which preserve the basic saturation mechanism of the standard relativistic approach.
Given a proper edge-coloring of a loopless multigraph, the palette of a vertex is defined as the set of colors of the edges which are incident with it. The palette index of a multigraph is defined as the minimum number of distinct palettes occurring among the vertices, taken over all proper edge-colorings of the multigraph itself. In this framework, the palette multigraph of an edge-colored multigraph is defined in this paper and some of its properties are investigated. We show that these properties can be applied in a natural way in order to produce the first known family of multigraphs whose palette index is expressed in terms of the maximum degree by a quadratic polynomial. We also attempt an analysis of our result in connection with some related questions.
In our recent paper, we classified plane symmetric kinematic self-similar perfect fluid and dust solutions of the second, zeroth and infinite kinds. However, we have missed some solutions during the process. In this short communication, we add up those missing solutions. We have found a total of seven solutions, out of which five turn out to be independent and cannot be found in the earlier paper
We synthesized bismuth - cobalt oxide doped by erbium with general formula Bi3-xErxCoO3-y. Compound has structure of delta-form bismuth oxide. Magnetic properties of the compound were measured by Faraday's method using quartz scales in the temperature range of 80-500 K. The magnetic susceptibility and effective magnetic moment were calculated.