ShantanuT01/DACTYL-Pretraining huggingface dataset:
One dimensional $(1d)$ interacting systems with local Hamiltonians can be studied with various well-developed analytical methods. Recently novel $1d$ physics was found numerically in systems with either spatially nonlocal interactions, or at the $1d$ boundary of $2d$ quantum critical points, and the critical fluctuation in the bulk also yields effective nonlocal interactions at the boundary. This work studies the edge states at the $1d$ boundary of $2d$ strongly interacting symmetry protected topological (SPT) states, when the bulk is driven to a disorder-order phase transition. We will take the $2d$ Affleck-Kennedy-Lieb-Tasaki (AKLT) state as an example, which is a SPT state protected by the SO(3) spin symmetry and spatial translation. We found that the original $(1+1)d$ boundary conformal field theory of the AKLT state is unstable due to coupling to the boundary avatar of the bulk quantum critical fluctuations. When the bulk is fixed at the quantum critical point, within the accuracy of our expansion method, we find that by tuning one parameter at the boundary, there is a generic direct transition between the long range antiferromagnetic N\'{e}el order and the valence bond solid (VBS) order. This transition is very similar to the N\'{e}el-VBS transition recently found in numerical simulation of a spin-1/2 chain with nonlocal spatial interactions. Connections between our analytical studies and recent numerical results concerning the edge states of the $2d$ AKLT-like state at a bulk quantum phase transition will also be discussed.
We complete the proof of the fact that all principal permutation classes generated by a pattern longer than two have a nonrational generating function.
We show that a realisation of spectral flow as a coordinate transformation for asymptotically four-dimensional solutions can be extended to the non-supersymmetric case. We apply this transformation to smooth geometries describing microstates of the D1-D5-KK monopole system in type IIB supergravity compactified on a six-torus, and obtain solutions with an additional momentum charge. We study the supersymmetric and near-core limits of this construction.
We study the 2-dimensional uniform prudent self-avoiding walk, which assigns equal probability to all nearest-neighbor self-avoiding paths of a fixed length that respect the prudent condition, namely, the path cannot take any step in the direction of a previously visited site. The uniform prudent walk has been investigated with combinatorial techniques in [Bousquet-M\'elou, 2010], while another variant, the kinetic prudent walk has been analyzed in detail in [Beffara, Friedli and Velenik, 2010]. In this paper, we prove that the $2$-dimensional uniform prudent walk is ballistic and follows one of the $4$ diagonals with equal probability. We also establish a functional central limit theorem for the fluctuations of the path around the diagonal.
We investigate the kilohertz quasi-periodic oscillations of low-mass X-ray binaries within the Hartle-Thorne spacetime. On the basis the relativistic precession model we extract the total mass $M$, angular momentum $J$, and quadrupole moment $Q$ of a compact object in a low-mass X-ray binary by analyzing the data of the Z -source GX 5-1. In view of the recent neutron star model we compute the radius, angular velocity and other parameters of this source by imposing the observational and theoretical constraints on the mass-radius relation.
Some software solutions used to obtain the facial transformations can help investigating the artistic metamorphosis of the ancient portraits of the same person. An analysis with a freely available software of portraitures of Julius Caesar is proposed, showing his several "morphs". The software helps enhancing the mood the artist added to a portrait.
We study S=1/2 dimers which are weakly coupled by three-dimensional antiferromagnetic interactions J'. It is commonly known that doping with non-magnetic impurities immediately induces a long-range Neel order. We show that application of an external magnetic field H may drive the system back to a disordered phase. We discuss the zero temperature phase diagram in the (H,J') plane and we propose suggestions for experiments.
The coupling of the breathing and rotational modes of the skyrmion-skyrmion system leads to a nucleon-nucleon spin-orbit interaction of short range, as well as to spin-orbit potentials for the transitions $NN \to N(1440)N$, $NN \to NN(1440)$ and $NN \to N(1440)N(1440)$. The longest range behaviour of these spin-orbit potentials is calculated in closed form.
The narrow-line Seyfert 1 galaxy 1H0707-495 has previously been identified as showing time lags between flux variations in the soft- (0.3-1 keV) and medium-energy (1-4 keV) X-ray bands that oscillate between positive and negative values as a function of the frequency of the mode of variation. Here we measure and analyse the lags also between a harder X-ray band (4-7.5 keV) and the soft and medium bands, using existing XMM-Newton data, and demonstrate that the entire spectrum of lags, considering both the full energy range, 0.3-7.5 keV, and the full frequency range, 10^-5 < nu < 10^-2 Hz, are inconsistent with previous claims of arising as reverberation associated with the inner accretion disk. Instead we demonstrate that a simple reverberation model, in which scattering or reflection is present in all X-ray bands, explains the full set of lags without requiring any ad hoc explanation for the time lag sign changes. The range of time delays required to explain the observed lags extends up to about 1800 s in the hard band. The results are consistent with reverberation caused by scattering of X-rays passing through an absorbing medium whose opacity decreases with increasing energy and that partially-covers the source. A high covering factor of absorbing and scattering circumnuclear material is inferred.
Let $k$ be any field, $G$ be a finite group acing on the rational function field $k(x_g:g\in G)$ by $h\cdot x_g=x_{hg}$ for any $h,g\in G$. Define $k(G)=k(x_g:g\in G)^G$. Noether's problem asks whether $k(G)$ is rational (= purely transcendental) over $k$. It is known that, if $\bm{C}(G)$ is rational over $\bm{C}$, then $B_0(G)=0$ where $B_0(G)$ is the unramified Brauer group of $\bm{C}(G)$ over $\bm{C}$. Bogomolov showed that, if $G$ is a $p$-group of order $p^5$, then $B_0(G)=0$. This result was disproved by Moravec for $p=3,5,7$ by computer calculations. We will prove the following theorem. Theorem. Let $p$ be any odd prime number, $G$ be a group of order $p^5$. Then $B_0(G)\ne 0$ if and only if $G$ belongs to the isoclinism family $\Phi_{10}$ in R. James's classification of groups of order $p^5$.
We have performed a muon spin rotation study on polycrystalline samples of electron-doped layered manganites, La$_{2-2x}$Sr$_{1+2x}$Mn$_2$O$_7$ (0.4< x<1), in order to investigate the local magnetic structure and spin dynamics. Our results provide evidence for phase separation into A-type antiferromagnetic and charge-ordered phases for x=0.52 and spin freezing at low temperatures (T<100K) for 0.52<x<0.75. A new phase diagram which includes this spin freezing region is proposed.
In interconnection networks, matching preclusion is a measure of robustness when there is a link failure. Let $G$ be a graph of even order. The matching preclusion number $mp(G)$ is defined as the minimum number of edges whose deletion results in a subgraph without perfect matchings. Many interconnection networks are super matched, that is, their optimal matching preclusion sets are precisely those induced by a single vertex. In this paper, we obtain general results of vertex-transitive graphs including many known networks. A $k$-regular connected vertex-transitive graph has matching preclusion number $k$ and is super matched except for six classes of graphs. From this many previous results can be directly obtained and matching preclusion for some other networks, such as folded $k$-cubes, Hamming graphs and halved $k$-cubes, are derived.
We present an in-depth weak lensing analysis of the cluster MS1008 based on deep multicolor imaging obtained during the Science Verification of FORS1 at the VLT. The image quality (half arcsec seeing) and depth of the VLT images allow the shear signal to be mapped with high signal-to-noise and to be traced out to 1.2 h_50^-1 Mpc, near the edge of the 6'.8x6'.8 field of view. Using BVRI color information, as well as 81 redshifts in the field from the CNOC survey, background galaxies can be effectively separated from cluster and foreground objects. PSF distorsions are found to be moderate across the FORS images and thus easily removed. Due to the small statistical errors in the mass reconstruction, this dataset provides a testing ground where several systematic effects (e.g. mass-sheet degeneracy, redshift distribution of the background sources, cluster galaxy contamination) can be quantified. Several methods are used to remove the mass-sheet degeneracy which is found to dominate the systematic error budget. We measure a lower limit to the mass of 2.6 10^14 h_50^-1 M_sun within 1 h_50^-1 Mpc and a ``total'' mass of 5.3 10^14 h_50^-1 M_sun by fitting a softened isothermal sphere. The availability of the CNOC redshift data and X-ray observations on this cluster allow a comparison of different determinations of the mass radial profile. We find the lensing and X-ray measurements in excellent agreement, while the mass derived from the virial analysis is marginally (1-2 sigma) in agreement at radii where both methods are reliable.
We study several aspects of nonvanishing Fourier coefficients of elliptic modular forms $\bmod \ell$, partially answering a question of Bella\"iche-Soundararajan concerning the asymptotic formula for the count of the number of Fourier coefficients upto $x$ which do not vanish $\bmod \ell$. We also propose a precise conjecture as a possible answer to this question. Further, we prove several results related to the nonvanishing of arithmetically interesting (e.g., primitive or fundamental) Fourier coefficients $\bmod \ell $ of a Siegel modular form with integral algebraic Fourier coefficients provided $\ell$ is large enough. We also make some efforts to make this "largeness" of $\ell$ effective.
Finite thermostats are studied in the context of nonequilibrium statistical mechanics. Entropy production rate has been identified with the mechanical quantity expressed by the phase space contraction rate and the currents have been linked to its derivatives with respect to the parameters measuring the forcing intensities. In some instances Green-Kubo formulae, hence Onsager reciprocity, have been related to the fluctuation theorem. However, mainly when dissipation takes place at the boundary (as in gases or liquids in contact with thermostats), phase space contraction may be independent on some of the forcing parameters or, even in absence of forcing, phase space contraction may not vanish: then the relation with the fluctuation theorem does not seem to apply. On the other hand phase space contraction can be altered by changing the metric on phase space: here this ambiguity is discussed and employed to show that the relation between the fluctuation theorem and Green-Kubo formulae can be extended and is, by far, more general.
We investigate theoretically and experimentally the static magnetic properties of single crystals of the molecular-based Single-Chain Magnet (SCM) of formula [Dy(hfac)$_{3}$NIT(C$_{6}$H$_{4}$OPh)]$_{\infty}$ comprising alternating Dy$^{3+}$ and organic radicals. A peculiar inversion between maxima and minima in the angular dependence of the magnetic molar susceptibility $\chi_{M}$ occurs on increasing temperature. Using information regarding the monomeric building block as well as an {\it ab initio} estimation of the magnetic anisotropy of the Dy$^{3+}$ ion, this anisotropy-inversion phenomenon can be assigned to weak one-dimensional ferromagnetism along the chain axis. This indicates that antiferromagnetic next-nearest-neighbor interactions between Dy$^{3+}$ ions dominate, despite the large Dy-Dy separation, over the nearest-neighbor interactions between the radicals and the Dy$^{3+}$ ions. Measurements of the field dependence of the magnetization, both along and perpendicularly to the chain, and of the angular dependence of $\chi_{M}$ in a strong magnetic field confirm such an interpretation. Transfer matrix simulations of the experimental measurements are performed using a classical one-dimensional spin model with antiferromagnetic Heisenberg exchange interaction and non-collinear uniaxial single-ion anisotropies favoring a canted antiferromagnetic spin arrangement, with a net magnetic moment along the chain axis. The fine agreement obtained with experimental data provides estimates of the Hamiltonian parameters, essential for further study of the dynamics of rare-earths based molecular chains.
A recursion technique of obtaining the asymptotical expansions for the bound-state energy eigenvalues of the radial Schr\"odinger equation with a position-dependent mass is presented. As an example of the application we calculate the energy eigenvalues for the Coulomb potential in the presence of position-dependent mass and we derive the inequalities regulating the shifts of the energy levels from their constant-mass positions.
We study the electrodisintegration of deuteron at quasi-elastic kinematics and high transferred momentum as a probe for the short distance structure in nuclei. In this reaction, an electron hits a nucleus of deuterium, which breaks up into a proton-neutron pair. We focus our attention on events where fast nucleons emerge, corresponding to nuclear configurations where the bound nucleons have a high relative momentum (exceeding 700 MeV/c). The present research is relevant to physical systems where high-density nuclear matter is present. This condition covers a wide range of physics, from neutron stars to nuclei stability and the repulsive nuclear core.   The present work differs from previous studies in two crucial features. One is the definition of the deuteron wave function, which include terms of a relativistic origin that can be ordered based on their relative contribution to the deuteron's internal momentum distribution. These terms, related to the off-shell properties of the nucleon-nucleon bound-state, do not occur in non-relativistic quantum mechanics. However, they become increasingly important in describing configurations with a high nucleon-nucleon relative momentum. The second difference is that we account for the off-shell nature of the bound nucleon that enters on the definition of the (half-off-shell) electromagnetic current. We avoid many of the difficulties inherent to the relativistic nature of the processes involved by adopting a theoretical framework known as Light Front dynamics. Simultaneous simplifications in the definition of the relativistic wave function for the proton-neutron bound state and the treatment of the (half-off-shell) electromagnetic current for the bound nucleon are among the essential advantages resulting from the use of the Light Front dynamics.
It is shown that the Weyl semimetal TaAs can have a significant polar vector contribution to its optical activity. This is quantified by ab initio calculations of the resonant x-ray diffraction at the Ta L1 edge. For the Bragg vector (400), this polar vector contribution to the circular intensity differential between left and right polarized x-rays is predicted to be comparable to that arising from linear dichroism. Implications this result has in regards to optical effects predicted for topological Weyl semimetals are discussed.
In photoluminescence spectra of symmetric [111] grown GaAs/AlGaAs quantum dots in longitudinal magnetic fields applied along the growth axis we observe in addition to the expected bright states also nominally dark transitions for both charged and neutral excitons. We uncover a strongly non-monotonous, sign changing field dependence of the bright neutral exciton splitting resulting from the interplay between exchange and Zeeman effects. Our theory shows quantitatively that these surprising experimental results are due to magnetic-field-induced \pm 3/2 heavy-hole mixing, an inherent property of systems with C_3v point-group symmetry.
One of the obstacles in the search for exoplanets via transits is the large number of candidates that must be followed up, few of which ultimately prove to be exoplanets. Any method that could make this process more efficient by somehow identifying the best candidates and eliminating the worst would therefore be very useful. Seager and Mallen-Ornelas (2003) demonstrated that it was possible to discern between blends and exoplanets using only the photometric characteristics of the transits. However, these techniques are critically dependent on the shape of the transit, characterization of which requires very high precision photometry of a sort that is atypical for candidates identified from transit searches. We present a method relying only on transit duration, depth, and period, which require much less precise photometry to determine accurately. The numerical tool we derive, the exoplanet diagnostic \eta, is intended to identify the subset of candidates from a transit search that is most likely to contain exoplanets, and thus most worthy of subsequent follow-up studies. The effectiveness of the diagnostic is demonstrated with its success in separating modeled exoplanetary transits and interlopers, and by applying it to actual OGLE transit candidates.
The discovery of a binary neutron star merger (NSM) through both its gravitational wave and electromagnetic emission has revealed these events to be key sites of r-process nucleosynthesis. Here, we evaluate the prospects of finding the remnants of Galactic NSMs by detecting the gamma-ray decay lines from their radioactive r-process ejecta. We find that $^{126}$Sn, which has several lines in the energy range 415-695 keV and resides close to the second r-process peak, is the most promising isotope, because of its half-life $t_{1/2}=2.30(14)\times 10^{5}$ yr being comparable to the ages of recent NSMs. Using a Monte Carlo procedure, we predict that multiple remnants are detectable as individual sources by next-generation gamma-ray telescopes which achieve sub-MeV line sensitivities of $\sim 10^{-8}$-$10^{-6}$ $\gamma$ cm$^{-2}$ s$^{-1}$. However, given the unknown locations of the remnants, the most promising search strategy is a systematic survey of the Galactic plane and bulge extending to high Galactic latitudes. Individual known supernova remnants which may be mis-classified NSM remnants could also be targeted, especially those located outside the Galactic plane. Detection of a moderate sample of Galactic NSM remnants would provide important clues to unresolved issues such as the production of actinides in NSMs, properties of merging NS binaries, and even help distinguish them from rare supernovae as current Galactic r-process sources. We also investigate the diffuse flux from longer-lived nuclei (e.g. $^{182}$Hf) that could in principle trace the Galactic spatial distribution of NSMs over longer timescales, but find that the detection of the diffuse flux appears challenging even with next-generation telescopes.
In it's usual presentation, classical mechanics appears to give time a very special role. But it is well known that mechanics can be formulated so as to treat the time variable on the same footing as the other variables in the extended configuration space. Such covariant formulations are natural for relativistic gravitational systems, where general covariance conflicts with the notion of a preferred physical-time variable. The standard presentation of quantum mechanics, in turns, gives again time a very special role, raising well known difficulties for quantum gravity. Is there a covariant form of (canonical) quantum mechanics? We observe that the preferred role of time in quantum theory is the consequence of an idealization: that measurements are instantaneous. Canonical quantum theory can be given a covariant form by dropping this idealization. States prepared by non-instantaneous measurements are described by "spacetime smeared states". The theory can be formulated in terms of these states, without making any reference to a special time variable. The quantum dynamics is expressed in terms of the propagator, an object covariantly defined on the extended configuration space.
An analysis of IGR J16207-5129 is presented based on observations taken with Suzaku. The data set represents ~80 ks of effective exposure time in a broad energy range between 0.5 and 60 keV, including unprecedented spectral sensitivity above 15 keV. The average source spectrum is well described by an absorbed power law in which we measured a large intrinsic absorption of nH = 16.2(-1.1/+0.9)x10^22 /cm2. This confirms that IGR J16207-5129 belongs to the class of absorbed HMXBs. We were able to constrain the cutoff energy at 19(-4/+8) keV which argues in favor of a neutron star as the primary. Our observation includes an epoch in which the source count rate is compatible with no flux suggesting a possible eclipse. We discuss the nature of this source in light of these and of other recent results.
In this paper we give a simple proof of the existence of global-in-time smooth solutions for the convective Brinkman-Forchheimer equations (also called in the literature the tamed Navier-Stokes equations) $$ \partial_tu -\mu\Delta u + (u \cdot \nabla)u + \nabla p + \alpha u + \beta|u|^{r - 1}u = 0 $$ on a $3$D periodic domain, for values of the absorption exponent $r$ larger than $3$. Furthermore, we prove that global, regular solutions exist also for the critical value of exponent $r = 3$, provided that the coefficients satisfy the relation $4\mu\beta \geq 1$. Additionally, we show that in the critical case every weak solution verifies the energy equality and hence is continuous into the phase space $L^2$. As an application of this result we prove the existence of a strong global attractor, using the theory of evolutionary systems developed by Cheskidov.
EuTiO3, a band insulator, and LaTiO3, a Mott insulator, are both antiferromagnetic with transition temperatures ~ 5.5 K and ~ 160 K, respectively. Here, we report the synthesis of Eu1-xLaxTiO3 thin films with x = 0 to 1 by oxide molecular beam epitaxy. The films in the full range have high crystalline quality and show no phase segregation, allowing us carry out transport measurements to study their electrical and magnetic properties. From x = 0.03 to 0.95, Eu1-xLaxTiO3 films show conduction by electrons as charge carriers, with differences in carrier densities and mobilities, contrary to the insulating nature of pure EuTiO3 and LaTiO3. Following a rich phase diagram, the magnetic ground states of the films vary with increasing La-doping level, changing Eu1-xLaxTiO3 from an antiferromagnetic insulator to an antiferromagnetic metal, a ferromagnetic metal, a paramagnetic metal, and back to an antiferromagnetic insulator. These emergent properties reflect the evolutions of the band structure, mainly at the Ti t2g bands near the Fermi level, when Eu2+ are gradually replaced by La3+. This work sheds light on this method for designing the electrical and magnetic properties in strongly-correlated oxides and completes the phase diagram of the titanate Eu1-xLaxTiO3.