ShantanuT01/DACTYL-Pretraining huggingface dataset:
Engineering chiral $p$-wave superconductivity in semiconductor structures offers fascinating ways to obtain and study Majorana modes in a condensed matter context. Here, we theoretically investigate chiral $p$-wave superconductivity in quantum dots and quantum rings. Using both analytical as well as numerical methods, we calculate the quasiparticle excitation spectra in these structures and the corresponding excitation amplitudes and charge densities. In the topological regime, we can observe the chiral edge modes localized at the boundaries and possessing finite energy in quantum dots and quantum rings. By applying a magnetic field which is expelled from the quantum ring, but which creates a flux that is an odd integer multiple of $\Phi_0/2=\pi\hbar/e$, Majorana modes, that is, (approximately) degenerate edge modes with zero energy and zero charge density, become possible in the topological regime. Furthermore, we investigate finite-size effects that split these degenerate edge modes as well as the effect of a magnetic field penetrating into the superconducting region that can under certain circumstances still support edge modes with approximately zero energy and charge.
String-scalar duality proposed by Y. Hosotani and membrane-scalar duality by A. Sugamoto are reexamined in the context of Kawaguchi Lagrangian formulation. The characteristic feature of this formulation is the indifferent nature of fields and parameters. Therefore even the exchange of roles between fields and parameters is possible. In this manner, dualities above can be proved easily. Between Kawaguchi metrics of the dually related theories, a simple relation is found. As an example of the exchange between fermionic fields and parameters, a replacement of the role of Grassmann parameters of the 2-dimensional superspace by the 9th component of Neveu-Schwarz-Ramond (NSR) fermions is studied in superstring model. Compactification is also discussed in this model.
In this theoretical study, we report an investigation on the behavior of two neutron separation energy, differential variation of the separation energy and the abnormality in nuclear charge radius along the isotopic and isotonic chains of transition nuclei. We have used relativistic mean field formalism with NL3 and NL3$^*$ forces for this present analysis. The study refers to {\it even-even} nuclei such as Zr, Mo, Ru and Pd with $N$ = 40$-$ 86, where a rich collective phenomena such as proton radioactivity, cluster or nucleus radioactivity, exotic shapes, {\it Island of Inversion} and etc. are observed. These non-monotonic aspects over the isotopic chain are mainly correlated with the structural properties like shell/sub-shell closures, shape transition, clustering and magicity etc. In addition to these, we have shown the internal configuration of these nuclei to get a further insight into the reason for these discrepancies.
Necessary and sufficient conditions for the existence of an entropy structure for certain classes of cross-diffusion systems with diffusion matrix $A(u)$ are derived, based on results from matrix factorization. The entropy structure is important in the analysis for such equations since $A(u)$ is typically neither symmetric nor positive definite. In particular, the normal ellipticity of $A(u)$ for all $u$ and the symmetry of the Onsager matrix implies its positive definiteness and hence an entropy structure. If $A$ is constant or nearly constant in a certain sense, the existence of an entropy structure is equivalent to the normal ellipticity of $A$. Several applications and examples are presented, including the $n$-species population model of Shigesada, Kawasaki, and Teramoto, a volume-filling model, and a fluid mixture model with partial pressure gradients. Furthermore, the normal elipticity of these models is investigated and some extensions are discussed.
In this note, we introduce the notion of $\alpha$-IDT processes which is obtained from a slight and fundamental modification of the IDT property. Several examples of $\alpha$-IDT processes are given and Gaussian processes which are $\alpha$-IDT are characterized. A kind example of this Gaussian $\alpha$-IDT is the standard fractional Brownian motion. Also, we invest some links between the $\alpha$-IDT property, with selfdecomposability, temporal selfdecomposability, stability and self similarity.
We present the first radiative transfer (RT) model of a non-edge-on disk galaxy in which the large-scale geometry of stars and dust is self-consistently derived through fitting of multiwavelength imaging observations from the UV to the submm. To this end we used the axi-symmetric RT model of Popescu et al. and a new methodology for deriving geometrical parameters, and applied this to decode the{spectral energy distribution (SED) of M33. We successfully account for both the spatial and spectral energy distribution, with residuals typically within $7\%$ in the profiles of surface brightness and within $8\%$ in the spatially-integrated SED. We predict well the energy balance between absorption and re-emission by dust, with no need to invoke modified grain properties, and we find no submm emission that is in excess of our model predictions. We calculate that $80\pm8\%$ of the dust heating is powered by the young stellar populations. We identify several morphological components in M33, a nuclear, an inner, a main and an outer disc, showing a monotonic trend in decreasing star-formation surface-density ($\Sigma_{\rm SFR}$) from the nuclear to the outer disc. In relation to surface density of stellar mass, the $\Sigma_{\rm SFR}$ of these components define a steeper relation than the "main sequence" of star-forming galaxies, which we call a "structurally resolved main sequence". Either environmental or stellar feedback mechanisms could explain the slope of the newly defined sequence. We find the star-formation rate to be ${\rm SFR}=0.28^{+0.02}_{-0.01}{\rm M}_{\odot}{\rm yr}^{-1}$.
We investigate an electronic Mach-Zehnder interferometer with high visibility in the quantum Hall regime. The superposition of the electrostatic potentials from a quantum point contact (QPC) and the residual disorder potential from doping impurities frequently results in the formation of inadvertent quantum dots (QD) in one arm of the interferometer. This gives rise to resonances in the QPC transmission characteristics. While crossing the QD resonance in energy, the interferometer gains a phase shift of $\pi$ in the interference pattern.
Realising controlled quantum dynamics via the magnetic interactions between colour centers in diamond remains a challenge despite recent demonstrations for nanometer separated pairs. Here we propose to use the intrinsic acoustical phonons in diamond as a data bus for accomplishing this task. We show that for nanodiamonds the electron-phonon coupling can take significant values that together with mode frequencies in the THz range, can serve as a resource for conditional gate operations. Based on these results we analyze how to use this phonon-induced interaction for constructing quantum gates among the electron-spin triplet ground states, introducing the phonon dependence via Raman transitions. Combined with decoupling pulses this offers the possibility for creating entangled states within nanodiamonds on the scale of several tens of nanometers, a promising prerequisite for quantum sensing applications.
The intracluster light (ICL) is a faint diffuse stellar component in clusters made of stars not bound to individual galaxies. We have carried out a large scale study of this component in the nearby Virgo cluster. The diffuse light is traced using planetary nebulae (PNe). The PNe are detected in the on-band image due to their strong emission in the [OIII] 5007 line, but disappear in the off-band image. The contribution of Ly-alpha emitters at z=3.14 are corrected statistically using blank field surveys. We have surveyed a total area of 3.3 square degrees in the Virgo cluster with eleven fields located at different radial distances. Those fields located at smaller radii than 80 arcmin from the cluster center contain most of the detected diffuse light. In this central region of the cluster, the ICL has a surface brightness in the range 28.8 - 30 mag per sqarsec in the B band, it is not uniformly distributed, and represents about 7% of the total galaxy light in this area. At distances larger than 80 arcmin the ICL is confined to single fields and individual sub-structures, e.g. in the Virgo sub-clump B, the M60/M59 group. For several fields at 2 and 3 degrees from the Virgo cluster center we set only upper limits. These results indicate that the ICL is not homogeneously distributed in the Virgo core, and it is concentrated in the high density regions of the Virgo cluster, e.g. the cluster core and other sub-structures. Outside these regions, the ICL is confined within areas of 100 kpc in size, where tidal effects may be at work. These observational results link the formation of the ICL with the formation history of the most luminous cluster galaxies.
We consider different aspects of the virtual Compton amplitude in QCD on two examples: small-x physics accessible in the Regge regime and twist-3 approximation in the description of DVCS through the general parton distributions. Using this model, we give an estimate for the cross section of deeply virtual Compton scattering for the kinematics of CEBAF at Jefferson Lab.
Less explored than their metric (Riemannian) counterparts, metric-affine (or Palatini) theories bring an unexpected phenomenology for gravitational physics beyond General Relativity. Lessons of crystalline structures, where the presence of defects in their microstructure requires the use of non-Riemannian geometry for the proper description of their properties in the macroscopic continuum level, are discussed. In this analogy, concepts such as wormholes and geons play a fundamental role. Applications of the metric-affine formalism developed by the authors in the last three years are reviewed.
Spin dynamics of a polarized spin system is studied when the latter is coupled with a resonant electric circuit and is under the action of an external pumping supporting a stationary nonequilibrium magnetization. A complete classification of possible regimes of spin motion is given. In addition to seven regimes considered earlier, two other transient regimes are found and thoroughly described: One is an oscillatory regime, when spins always move coherently but the degree of coherence fluctuates with time. Another is a pulsing regime, when spins reveal coherent motion during short pulses separated from each other by intervals of incoherent motion. These regimes are, in principle, transient, although may be extremely long lasting; their duration may be several orders longer than the transverse relaxation time and twice longer than the longitudinal relaxation time. Both transient regimes end with a coherent quasistationary regime.
Despite extensive research on the skutterudites for the last decade, their electric crystalline field ground state is still a matter of controversy. We show that Electron Spin Resonance (ESR) measurements can determine the full set of crystal field parameters (CFPs) for the Th cubic symmetry (Im3) of the Ce$_{1-x}$R$_{x}$Fe$_{4}$P$_{12}$ (R = Dy, Er, Yb, $x\lesssim 0.003$) skutterudite compounds. From the analysis of the ESR data the three CFPs, B4c, B6c and B6t were determined for each of these rare-earths at the Ce$^{3+}$ site. The field and temperature dependence of the measured magnetization for the doped crystals are in excellent agreement with the one predicted by the CFPs Bnm derived from ESR.
We present a theoretical study of the quantum critical behavior in heat transport via a two-state system with sub-ohmic reservoirs. We calculate the temperature dependence of the thermal conductance near the quantum phase transition via the continuous-time quantum Monte Carlo method and discuss its critical exponents. We also propose a superconducting circuit to realize the sub-ohmic spin-boson model that can be used to observe quantum critical phenomena.
The ladder-rainbow truncation of the set of Dyson-Schwinger equations is used to study a variety of electroweak and strong processes involving light mesons. The parameters in the effective interaction are constrained by the chiral condensate and f_\pi; the current quark masses are fitted to m_\pi and m_K. The obtained electromagnetic form factors are in good agreement with the data. Also the weak K_{l3} decay and the radiative and strong decays of the vector mesons agree reasonably well with the data. Finally, we indicate how processes such as \pi-\pi scattering can be described within this framework as well.
We show that the requirement of the relativistic invariance for any self-interacting, abelian p-form theory uniquely determines the form of the corresponding quantization condition.
Mixed-spin Ising model on a decorated Bethe lattice is rigorously solved by combining the decoration-iteration transformation with the method of exact recursion relations. Exact results for critical lines, compensation temperatures, total and sublattice magnetizations are obtained from a precise mapping relationship with the corresponding spin-1/2 Ising model on a simple (undecorated) Bethe lattice. The effect of next-nearest-neighbour interaction and single-ion anisotropy on magnetic properties of the ferrimagnetic model is investigated in particular. It is shown that the total magnetization may exhibit multicompensation phenomenon and the critical temperature vs. the single-ion anisotropy dependence basically changes with the coordination number of the underlying Bethe lattice. The possibility of observing reentrant phase transitions is related to a high enough coordination number of the underlying Bethe lattice.
We propose a scheme that utilizes the collective enhancement of a photonic mode inside an atomic ensemble together with a proper Zeeman manifold in order to achieve a heralded polarization entangled Bell state. The entanglement is between two photons that are separated in time and can be used as a post selected deterministic source for applications such as quantum repeaters where a subsequent entanglement swapping measurement is employed. We present a detailed analysis of the practical limitation of the scheme.
We present a concept of a new gamma ray detector in order to observe undetected TeV gamma ray background. We measure a track of an electron-positron pair made by a pair creation in a magnet. By using Si as a tracker in a magnetic field 3 T, an energy range is up to 10 TeV.
We consider the minimization of the NLS energy on a metric tree, either rooted or unrooted, subject to a mass constraint. With respect to the same problem on other types of metric graphs, several new features appear, such as the existence of minimizers with positive energy, and the emergence of unexpected threshold phenomena. We also study the problem with a radial symmetry constraint that is in principle different from the free problem due to the failure of the P\'olya-Szeg\H{o} inequality for radial rearrangements. A key role is played by a new Poincar\'e inequality with remainder.
We report the detection of an X-ray flare on the Bp star sigma Ori E with the ROSAT high resolution imager (HRI). The flare is shown to have likely occurred on the early-type star, rather than on an hypothesized late-type companion. We derive flare parameters such as total energy release, coarse estimates of size and density, and also present arguments for a magnetic origin of the flare. We place our observations in the context of a magnetic character of Bp-type stars and speculate on a common physical basis and connection between Bp and Be stars.
The embedding of a Taub-NUT space in the directions transverse to the world volume of branes describes branes at (spherical) orbifold singularities. Similarly, the embedding of a pp-wave in the brane world volume yields an AdS orbifold. In case of the D1-D5--brane system, the AdS3 orbifolds yields a BTZ black hole; as we will show, the same holds for D3-branes corresponding to AdS5. In addition we will show that the AdS orbifolds and the spherical orbifolds are U-dual to each other. However in contrast to spherical orbifolds the AdS orbifolds lead to a running coupling, which is in the IR inverse to the coupling of the spherical orbifold. A discussion of the general pp-wave solution in AdS space is added.
Zero forcing is a deterministic iterative graph colouring process in which vertices are coloured either blue or white, and in every round, any blue vertices that have a single white neighbour force these white vertices to become blue. Here we study probabilistic zero forcing, where blue vertices have a non-zero probability of forcing each white neighbour to become blue. We explore the propagation time for probabilistic zero forcing on hypercubes and grids.
This paper investigates a new family of special functions referred to as hypergeometric zeta functions. Derived from the integral representation of the classical Riemann zeta function, hypergeometric zeta functions exhibit many properties analogous to their classical counterpart, including the intimate connection to Bernoulli numbers. These new properties are treated in detail and are used to demonstrate a functional inequality satisfied by second-order hypergeometric zeta functions.
A Besicovitch set in AG(n,q) is a set of points containing a line in every direction. The Kakeya problem is to determine the minimal size of such a set. We solve the Kakeya problem in the plane, and substantially improve the known bounds for n greater than 4.
We present the science database produced by the Formation and Evolution of Planetary Systems (FEPS) Spitzer Legacy program. Data reduction and validation procedures for the IRAC, MIPS, and IRS instruments are described in detail. We also derive stellar properties for the FEPS sample from available broad-band photometry and spectral types, and present an algorithm to normalize Kurucz synthetic spectra to optical and near-infrared photometry. The final FEPS data products include IRAC and MIPS photometry for each star in the FEPS sample and calibrated IRS spectra.
Context. Be stars are physically complex systems that continue to challenge theory to understand their rapid rotation, complex variability and decretion disks. $\gamma$ Cassiopeiae ($\gamma$ Cas) is one such star but is even more curious because of its unexplained hard thermal X-ray emission. Aims. We aim to examine the optical variability of $\gamma$ Cas and thereby to shed more light on its puzzling behaviour. Methods. Three hundred twenty-one archival H$\alpha$ spectra from 2006 to 2017 are analysed to search for frequencies corresponding to the 203.5 day orbit of the companion. Space photometry from the SMEI satellite from 2003 to 2011 and the BRITE-Constellation of nano-satellites between 2015 and 2019 is investigated in the period range from a couple of hours to a few days. Results. The orbital period of the companion of 203.5 days is confirmed with independent measurements from the structure of the H$\alpha$ line emission. A strong blue/red asymmetry in the amplitude distribution across the H$\alpha$ emission line could hint at a spiral structure in the decretion disk. With the space photometry, the known frequency of 0.82 d$^{-1}$ is confirmed in data from the early 2000s. A higher frequency of 2.48 d$^{-1}$ is present in the data from 2015 to 2019 and possibly also in the early 2000s. A third frequency at 1.25 d$^{-1}$ is proposed to exist in both SMEI and BRITE data. The only explanation covering all three rapid variations seems to be nonradial pulsation. The two higher frequencies are incompatible with rotation.
We study the phenomenology of the neutral Higgs sector of a non-SUSY non-minimal Standard Model. Models with more than one Higgs doublet are possible, and may contain neutral Higgs scalars with branching ratios significantly different to those of the Minimal Standard Model Higgs boson. We show how these differences may be exploited at LEP2 in order to distinguish the non-minimal Standard Model from the minimal version.
The origin of Galactic cosmic rays (with energies up to 10^15 eV) remains unclear, though it is widely believed that they originate in the shock waves of expanding supernova remnants. Currently the best way to investigate their acceleration and propagation is by observing the gamma-rays produced when cosmic rays interact with interstellar gas. Here we report observations of an extended region of very high energy (VHE, >100 GeV) gamma-ray emission correlated spatially with a complex of giant molecular clouds in the central 200 pc of the Milky Way. The hardness of the gamma-ray spectrum and the conditions in those molecular clouds indicate that the cosmic rays giving rise to the gamma-rays are likely to be protons and nuclei rather than electrons. The energy associated with the cosmic rays could have come from a single supernova explosion around 10,000 years ago.
Stanley's formula for the number of reduced expressions of a permutation regarded as a Coxeter group element raises the question of how to enumerate the reduced expressions of an arbitrary Coxeter group element. We provide a framework for answering this question by constructing combinatorial objects that represent the inversion set and the reduced expressions for an arbitrary Coxeter group element. The framework also provides a formula for the length of an element formed by deleting a generator from a Coxeter group element. Fan and Hagiwara, et al$.$ showed that for certain Coxeter groups, the short-braid avoiding elements characterize those elements that give reduced expressions when any generator is deleted from a reduced expression. We provide a characterization that holds in all Coxeter groups. Lastly, we give applications to the freely braided elements introduced by Green and Losonczy, generalizing some of their results that hold in simply-laced Coxeter groups to the arbitrary Coxeter group setting.
We describe the construction of a conserved reaction-diffusion system that exhibits self-organized critical (avalanche-like) behavior under the action of a slow addition of particles. The model provides an illustration of the general mechanism to generate self-organized criticality in conserving systems. Extensive simulations in d=2 and 3 reveal critical exponents compatible with the universality class of the stochastic Manna sandpile model.
Operating quantum sensors and quantum computers would make data in the form of quantum states available for purely quantum processing, opening new avenues for studying physical processes and certifying quantum technologies. In this Perspective, we review a line of works dealing with measurements that reveal structural properties of quantum datasets given in the form of product states. These algorithms are universal, meaning that their performances do not depend on the reference frame in which the dataset is provided. Requiring the universality property implies a characterization of optimal measurements via group representation theory.
We study the linear fractional transformations in the Hecke group $G(\Phi)$ where $\Phi$ is either root of $x^2 - x -1$ (the larger root being the "golden ratio" $\phi = 2 \cos \frac {\pi}5$.) Let $g \in G(\Phi)$ and let $z$ be a generic element of the upper half-plane. Exploiting the fact that $\Phi^2 = \Phi -1$, we find that $g(z)$ is a quotient of linear polynomials in $z$ such that the coefficients of $z^1$ and $z^0$ in the numerator and denominator of $g(z)$ appear themselves to be linear polynomials in $\Phi$ with coefficients that are certain multiples of Fibonacci numbers. We make somewhat less detailed observations along similar lines about the functions in $G(2 \cos \frac {\pi}k)$ for $k \geq 5$.