ShantanuT01/DACTYL-Pretraining huggingface dataset:
We propose a model of run-and-tumble particles (RTPs) on a line with a fertile site at the origin. After going through the fertile site, a run-and-tumble particle gives rise to new particles until it flips direction. The process of creation of new particles is modelled by a fertility function (of the distance to the fertile site), multiplied by a fertility rate. If the initial conditions correspond to a single RTP with even probability density, the system is parity-invariant. The equations of motion can be solved in the Laplace domain, in terms of the density of right-movers at the origin. At large time, this density is shown to grow exponentially, at a rate that depends only on the fertility function and fertility rate. Moreover, the total density of RTPs (divided by the density of right-movers at the origin), reaches a stationary state that does not depend on the initial conditions, and presents a local minimum at the fertile site.
We calculate the zeroes of angular observables $P_4^{'}$ and $P_5^{'}$ of 4 - body angular distribution of $B\rightarrow K^{*} (\rightarrow K \pi) l^+ l^-$ where LHCb, in its analysis of form factor independent angular observables, has found deviations from standard model predictions in one of the $q^2$ bins. In the large recoil region, we obtain relations between the zeroes of $P_4^{'}$, $P_5^{'}$ and the zero of forward-backward asymmetry of lepton pair. These relations, in the considered region, are independent of hadronic uncertainties and depend only on Wilson coefficients. We also construct a new observable, $\mathcal{O}_T^{L,R}$, whose zero in the standard model coincides with the zero of forward-backward asymmetry but in presence of new physics contributions will show different behavior. Moreover, the profile of the new observable, even within the standard model, is very different from the forward backward asymmetry. We point out that precise measurements of these zeroes in near future would provide crucial test of the standard model and would be useful in distinguishing between different possible new physics contributions to Wilson coefficients.
Magnetic systems are an exciting realm of study that is being explored on smaller and smaller scales. One extremely interesting magnetic state that has gained momentum in recent years is the skyrmionic state. It is characterized by a vortex where the edge magnetic moments point opposite to the core. Although skyrmions have many possible realizations, in practice, creating them in a lab is a difficult task to accomplish. In this work, new methods for skyrmion generation and customization are suggested. Skyrmionic behavior was numerically observed in minimally customized simulations of spheres, hemisphere, ellipsoids, and hemi-ellipsoids, for typ- ical Cobalt parameters, in a range from approximately 40 nm to 120 nm in diameter simply by applying a field.
There is considerable interest in understanding the demographics of galaxies within the local universe (defined, for our purposes, as the volume within a radius of 200 Mpc or z<0.05). In this pilot paper, using supernovae (SNe) as signposts to galaxies, we investigate the redshift completeness of catalogs of nearby galaxies. In particular, type Ia SNe are bright and are good tracers of the bulk of the galaxy population, since they arise in both old and young stellar populations. Our input sample consists of SNe with redshift < 0.05, discovered by the flux-limited ASAS-SN survey. We define the redshift completeness fraction (RCF) as the number of SN host galaxies with known redshift prior to SN discovery, determined, in this case, via the NASA Extragalactic Database (NED), divided by the total number of newly discovered SNe. Using SNe Ia, we find RCF = 78 (+6, -7, 90% confidence interval) for z < 0.03. We examine the distribution of host galaxies with and without cataloged redshifts as a function of absolute magnitude and redshift, and, unsurprisingly, find that higher-z and fainter hosts are less likely to have a known redshift prior to the detection of the SN. However, surprisingly, some L* galaxies are also missing. We conclude with thoughts on the future improvement of RCF measurements that will be made possible from large SN samples resulting from ongoing and especially upcoming time-domain surveys.
The Hubbard model and extended Hubbard model on the honeycomb lattice can be seen as prototype models of single layer graphene placed in a high dielectric constant environment that screens the Coulomb interaction. Taking advantage of the absence of a sign problem at half-filling, we study this problem with clusters up to 96 sites with the Determinant Quantum Monte Carlo Method as an impurity solver for the the Dynamical Cluster Approximation at finite temperatures. After determining the stability of the semi-metallic phase to interaction-induced spin-density wave (SDW), charge-density wave (CDW) and Mott insulating phases, we study the single particle dynamics of the Dirac fermions. We show that when spontaneous symmetry breaking is avoided, the semi-metallic phase is a stable Fermi liquid in the presence of repulsive interactions and that Kondo screening dominates the low temperature regime, even though there is a $\rho(\omega) = |\omega|$ type local density of states. We also investigate the impact of the correlation effects on the renormalization of the Fermi velocity $v_F$. We find that $v_F$ is not renormalized when only on-site repulsion $U$ is present, but that near-neighbor repulsion $V$ does renormalize $v_F$. This may explain the variations between different measurements of $v_F$ in graphene.
In this paper, we study the rotational wormhole and scalar perturbation under the spacetime. We found the Schr\"odinger like equation and consider the asymptotic solutions for the special cases.
We examine model independent constraints on the high redshift and prerecombination expansion history from cosmic microwave background observations, using a combination of principal component analysis and other techniques. This can be translated to model independent limits on early dark energy and the number of relativistic species $N_{\rm eff}$. Models such as scaling (Doran-Robbers), dark radiation ($\Delta N_{\rm eff}$), and barotropic aether fall into distinct regions of eigenspace and can be easily distinguished from each other. Incoming CMB data will map the expansion history from $z=0$--$10^5$, achieving subpercent precision around recombination, and enable determination of the amount of early dark energy and valuable guidance to its nature.
We derive spin operator matrix elements between general eigenstates of the superintegrable Z_N-symmetric chiral Potts quantum chain of finite length. Our starting point is the extended Onsager algebra recently proposed by R.Baxter. For each pair of spaces (Onsager sectors) of the irreducible representations of the Onsager algebra, we calculate the spin matrix elements between the eigenstates of the Hamiltonian of the quantum chain in factorized form, up to an overall scalar factor. This factor is known for the ground state Onsager sectors. For the matrix elements between the ground states of these sectors we perform the thermodynamic limit and obtain the formula for the order parameters. For the Ising quantum chain in a transverse field (N=2 case) the factorized form for the matrix elements coincides with the corresponding expressions obtained recently by the Separation of Variables Method.
We apply the supersymmetry approach to one-dimensional quantum systems with spatially-dependent mass, by including their ordering ambiguities dependence. In this way we extend the results recently reported in the literature. Furthermore, we point out a connection between these systems and others with constant masses. This is done through convenient transformations in the coordinates and wavefunctions.
We present results of a theoretical study of para-hydrogen and ortho-deuterium clusters at low temperature (0.5 K < T < 3.5 K), based on Path Integral Monte Carlo simulations. Clusters of size up to N=21 para-hydrogen molecules are nearly entirely superfluid at T < 1 K. For 21 < N < 30, the superfluid response displays strong variations with N, reflecting structural changes that occur on adding or removing even a single molecule. Some clusters in this size range display quantum melting, going from solid- to liquid-like as T tends to 0. Melting is caused by quantum exchanges of molecules. The largest para-hydrogen cluster for which a significant superfluid response is observed comprises 27 molecules. Evidence of a finite superfluid response is presented for ortho-deuterium clusters of size up to 14 molecules. Magic numbers are observed, at which both types of clusters feature pronounced stability.
Theoretical models of the spin-orbital liquid (SOL) FeSc$_2$S$_4$ have predicted it to be in close proximity to a quantum critical point separating a spin-orbital liquid phase from a long-range ordered magnetic phase. Here, we examine the magnetic excitations of FeSc$_2$S$_4$ through time-domain terahertz spectroscopy under an applied magnetic field. At low temperatures an excitation emerges that we attribute to a singlet-triplet excitation from the SOL ground state. A three-fold splitting of this excitation is observed as a function of applied magnetic field. As singlet-triplet excitations are forbidden in inversion symmetric pure spin systems, our results demonstrate the non-trivial character of the entangled spin-orbital singlet ground state. Using experimentally obtained parameters we compare to existing theoretical models to determine FeSc$_2$S$_4$'s proximity to the quantum critical point. In the context of these models, we estimate that the characteristic length of the singlet correlations to be $\xi/ (\textbf{a}/2) \approx 8.2$ (where $\textbf{a}/2$ is the nearest neighbor lattice constant) which establishes FeSc$_2$S$_4$ as a SOL with long-range entanglement.
In a sandpile model addition of a hole is defined as the removal of a grain from the sandpile. We show that hole avalanches can be defined very similar to particle avalanches. A combined particle-hole sandpile model is then defined where particle avalanches are created with probability $p$ and hole avalanches are created with the probability $1-p$. It is observed that the system is critical with respect to either particle or hole avalanches for all values of $p$ except at the symmetric point of $p_c=1/2$. However at $p_c$ the fluctuating mass density is having non-trivial correlations characterized by $1/f$ type of power spectrum.
Particle methods are widely used because they can provide accurate descriptions of evolving measures. Recently it has become clear that by stepping outside the Monte Carlo paradigm these methods can be of higher order with effective and transparent error bounds. A weakness of particle methods (particularly in the higher order case) is the tendency for the number of particles to explode if the process is iterated and accuracy preserved. In this paper we identify a new approach that allows dynamic recombination in such methods and retains the high order accuracy by simplifying the support of the intermediate measures used in the iteration. We describe an algorithm that can be used to simplify the support of a discrete measure and give an application to the cubature on Wiener space method developed by Lyons and Victoir [Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 460 (2004) 169-198].
The inherent nodal structures of the wavefunctions of 6-nucleon systems have been investigated. The existence of a group of six low-lying states dominated by L=0 has been deduced. The spatial symmetries of these six states are found to be mainly {4,2} and {2,2,2}.
The method of asymptotic normalization coefficients is a standard approach for studies of two-body non-resonant radiative capture processes in nuclear astrophysics. This method suggests a fully analytical description of the radiative capture cross section in the low-energy region of the astrophysical interest. We demonstrate how this method can be generalized to the case of three-body $2p$ radiative captures. It was found that an essential feature of this process is the highly correlated nature of the capture. This reflects the complexity of three-body Coulomb continuum problem. Radiative capture $^{15}$O+$p$+$p \rightarrow ^{\,17}$Ne+$\gamma$ is considered as an illustration.
We experimentally demonstrate gold microdisc structures that produce confined Tamm plasmons (CTPs), interface modes between a metal layer and a distributed Bragg reflector, resonant around 1.3 {\mu}m. Quantum dots grown within the structures show an order of magnitude increase in the photoluminescence emitted at room temperature. Varying the disc diameter, we show spectral tuning of the resonance and measure the dispersion relation as evidence of mode confinement. The simplicity of fabrication and tuneability of these structures make CTPs an ideal platform for making scalable telecom devices based on quantum dots.
We show that a sliding motion between the two layers of a \moire superlattice induces an electric current and realizes a two-dimensional version of the topological Thouless pump when the Fermi energy lies in one of the minigaps. Interestingly, a chiral charge pump, namely, a transverse current induced by the sliding motion, is possible in twisted homobilayers. This result is confirmed by a concrete calculation of the adiabatic current in twisted bilayer graphene. Our work reveals an interesting link between mechanical motion and electricity unique to \moire superlattices, and may find applications in nanogenerators and nanomotors.
Randomly evolving systems composed by elements which interact among each other have always been of great interest in several scientific fields. This work deals with the synchronization phenomenon, that could be roughly defined as the tendency of different components to adopt a common behavior. We continue the study of a model of interacting stochastic processes with reinforcement, that recently has been introduced in Crimaldi et al. (2016, arXiv:1602.06217). Generally speaking, by reinforcement we mean any mechanism for which the probability that a given event occurs has an increasing dependence on the number of times that events of the same type occurred in the past. The particularity of systems of such stochastic processes is that synchronization is induced along time by the reinforcement mechanism itself and does not require a large-scale limit. We focus on the relationship between the topology of the network of the interactions and the long-time synchronization phenomenon. After proving the almost sure synchronization, we provide some CLTs in the sense of stable convergence that establish the convergence rates and the asymptotic distributions for both convergence to the common limit and synchronization. The obtained results lead to the construction of asymptotic confidence intervals for the limit random variable and of statistical tests to make inference on the topology of the network given the observation of the reinforced stochastic processes positioned at the vertices.
It is argued that by the end of the 1920s a quantum-mechanical model could have been in place, that not only produces the atomic and molecular energy levels of the many-body Pauli equation with Coulomb interactions and external classical electro- and magneto-static fields without putting these interactions in by hand, but that also accurately describes the interaction of charged particles with electromagnetic radiation, in particular the transitions between atomic or molecular energy levels associated with emission or absorption of radiation. This model suggests a re-interpretation of Maxwell's electromagnetic field equations on spacetime as quantum-mechanical expected values of wave equations on time X configuration space for photons and electrons. The creation / annihilation formalism for photons emerges without invoking second-quantizing the classical Maxwell equations, and without involving the concept of creation / annihilation, thus suggesting an alternative physical interpretation of this formalism. Furthermore, the model suggests that Lorentz covariance of macroscopic physics models emerges through a law of large numbers from a fundamental microscopic model that is not itself Lorentz covariant.
The specific band structure of graphene, with its unique valley structure and Dirac neutrality point separating hole states from electron states has led to the observation of new electronic transport phenomena such as anomalously quantized Hall effects, absence of weak localization and the existence of a minimum conductivity. In addition to dissipative transport also supercurrent transport has already been observed. It has also been suggested that graphene might be a promising material for spintronics and related applications, such as the realization of spin qubits, due to the low intrinsic spin orbit interaction, as well as the low hyperfine interaction of the electron spins with the carbon nuclei. As a first step in the direction of graphene spintronics and spin qubits we report the observation of spin transport, as well as Larmor spin precession over micrometer long distances using single graphene layer based field effect transistors. The non-local spin valve geometry was used, employing four terminal contact geometries with ferromagnetic cobalt electrodes, which make contact to the graphene sheet through a thin oxide layer. We observe clear bipolar (changing from positive to negative sign) spin signals which reflect the magnetization direction of all 4 electrodes, indicating that spin coherence extends underneath all 4 contacts. No significant changes in the spin signals occur between 4.2K, 77K and room temperature. From Hanle type spin precession measurements we extract a spin relaxation length between 1.5 and 2 micron at room temperature, only weakly dependent on charge density, which is varied from n~0 at the Dirac neutrality point to n = 3.6 10^16/m^2. The spin polarization of the ferromagnetic contacts is calculated from the measurements to be around 10%.
Determining the evolution of the ejecta morphology of novae provides valuable information on the shaping mechanisms in operation at early stages of the nova outburst. Understanding such mechanisms has implications for studies of shaping for example in proto-Planetary Nebulae. Here we perform morpho-kinematical studies of V2491 Cyg using spectral data to determine the likely structure of the ejecta and its relationship to the central system and shaping mechanisms. We use Shape to model different morphologies and retrieve their spectra. These synthetic spectra are compared with observed spectra to determine the most likely morphology giving rise to them, including system inclination and expansion velocity of the nova ejecta. We find the best fit remnant morphology to be that of polar blobs and an equatorial ring with an implied inclination of 80$^{+3}_{-12}$ degrees and an maximum expansion velocity of the polar blobs of 3100$^{+200}_{-100}$ km/s and for the equatorial ring 2700$^{+200}_{-100}$ km/s. This inclination would suggest that we should observe eclipses which will enable us to determine more precisely important parameters of the central binary. We also note that the amplitude of the outburst is more akin to the found in recurrent nova systems.
For any natural number n, the Hurwitz graph $\mathcal{H}(S_n )$ has vertices corresponding to reduced words of the cycle $(1 . . . n)$ in terms of transpositions in $S_n$, and has edges corresponding to local shifts. This graph is known to be connected, and some of its graph theoretic properties, such as its radius and upper bounds on its diameter, are known. We explore further the structure of the Hurwitz Graph, in particular its center and its connection to the geometric tree graph $G_n$. Finally, the extended Hurwitz Graph is defined and its properties such as the radius, characterization of some central elements and bounds on the diameter are obtained. Part of fulfillment of the requirements for the Master's Degree.
We introduce a pixel space method to detect dipole modulation or hemispherical power asymmetry in the cosmic microwave background (CMB) polarization. The method relies on the use of squared total polarized flux whose ensemble average picks up a dipole due to the dipole modulation in the CMB polarization. The method is useful since it can be applied easily to partial sky. We define several statistics to characterize the amplitude of the detected signal. By simulations we show that the method can be used to reliably extract the signal at 2.7$\sigma$ level or higher in future CORE-like missions, assuming that the signal is present in the CMB polarization at the level detected by the Planck mission in the CMB temperature. An application of the method to the 2018 Planck data does not detect a significant effect, when taking into account the presence of correlated detector noise and residual systematics in data. Using the FFP10 we find the presence of a very strong bias which might be masking any real effect.
We study the parity of 2-Selmer ranks in the family of quadratic twists of an arbitrary elliptic curve E over an arbitrary number field K. We prove that the fraction of twists (of a given elliptic curve over a fixed number field) having even 2-Selmer rank exists as a stable limit over the family of twists, and we compute this fraction as an explicit product of local factors. We give an example of an elliptic curve E such that as K varies, these fractions are dense in [0, 1]. More generally, our results also apply to p-Selmer ranks of twists of 2-dimensional self-dual F_p-representations of the absolute Galois group of K by characters of order p.
Given a real symmetric $n\times n$ matrix, the sepr-sequence $t_1\cdots t_n$ records information about the existence of principal minors of each order that are positive, negative, or zero. This paper extends the notion of the sepr-sequence to matrices whose entries are of prescribed signs, that is, to sign patterns. A sufficient condition is given for a sign pattern to have a unique sepr-sequence, and it is conjectured to be necessary. The sepr-sequences of sign semi-stable patterns are shown to be well-structured; in some special circumstances, the sepr-sequence is enough to guarantee the sign pattern being sign semi-stable. In alignment with previous work on symmetric matrices, the sepr-sequences for sign patterns realized by symmetric nonnegative matrices of orders two and three are characterized.
An embedding superspace, whose Bosonic part is the flat 2 + 1 dimensional embedding space for AdS2, is introduced. Superfields and several supersymmetric models are examined in the embedded AdS2 superspace.
The $2M$-boson representations of KP hierarchy are constructed in terms of $M$ mutually independent two-boson KP representations for arbitrary number $M$. Our construction establishes the multi-boson representations of KP hierarchy as consistent Poisson reductions of standard KP hierarchy within the $R$-matrix scheme. As a byproduct we obtain a complete description of any finitely-many-field formulation of KP hierarchy in terms of Darboux coordinates with respect to the first Hamiltonian structure. This results in a series of representations of $\Win1\,$ algebra made out of arbitrary even number of boson fields.
\textit{A star edge coloring} of a graph is a proper edge coloring without bichromatic paths and cycles of length four. In this paper we establish tight upper bounds for trees and subcubic outerplanar graphs, and derive an upper bound for outerplanar graphs.