ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper we predict many interesting new properties of vortices in highly anisotropic density wave systems subject to strong transverse electric fields. We mainly concentrate on ground state properties. Besides electric field-induced vortices we consider also thermally activated vortices. A new type of temperature-driven transition between two different phases of density waves in strong fields is predicted and several new properties of those phases are reported.
We report the experimental study of resonant Rayleigh scattering in GaAs-AlGaAs superlattices with ordered and intentionally disordered potential profiles (correlated and uncorrelated) in the growth direction z. We show that the intentional disorder along z modify markedly the energy dispersion of the dephasing rates of the excitons. The application of an external magnetic field in the same direction allows the continuous tuning of the in plane exciton localization and to study the interplay between the in plane and vertical disorder.
Let $p$ be a multilinear polynomial in several non-commuting variables with coefficients in an arbitrary field $K$. Kaplansky conjectured that for any $n$, the image of $p$ evaluated on the set $M_n(K)$ of $n$ by $n$ matrices is either zero, or the set of scalar matrices, or the set $sl_n(K)$ of matrices of trace $0$, or all of $M_n(K)$. This conjecture was proved for $n=2$ when $K$ is closed under quadratic extensions. In this paper the conjecture is verified for $K=\mathbb{R}$ and $n=2$, also for semi-homogeneous polynomials $p$, with a partial solution for an arbitrary field $K$.
Radio jets play an important role in quasar feedback, but direct observations showing how the jets interact with the multi-phase interstellar medium of galaxy disks are few and far between. In this work, we provide new millimeter interferometric observations of PG 1700+518 in order to investigate the effect of its radio jet on the surrounding molecular gas. PG 1700 is a radio-quiet, low-ionization broad absorption line quasar whose host galaxy has a nearby interacting companion. On sub-kiloparsec scales, the ionized gas is driven to high velocities by a compact radio jet that is identified by radio interferometry. We present observations from the NOrthern Extended Millimeter Array (NOEMA) interferometer with a 3.8 arcsec (16 kpc) synthesized beam where we detect the CO (1-0) emission line at $30\sigma$ significance with a total flux of $3.12\pm0.02$ Jy km s$^{-1}$ and a typical velocity dispersion of $125\pm5$ km s$^{-1}$. Despite the outflow in ionized gas, we find no concrete evidence that the CO gas is being affected by the radio jet on size scales of a kiloparsec or more. However, a $\sim\!1$ arcsec drift in the spatial centroid of the CO emission as a function of velocity across the emission line and the compact nature of the jet hint that higher spatial resolution observations may reveal a signal of interaction between the jet and molecular gas.
This paper explores of the role of unitary braiding operators in quantum computing. We show that a single specific solution R (the Bell basis change matrix) of the Yang-Baxter Equation is a universal gate for quantum computing, in the presence of local unitary transformations. We show that this same R generates a new non-trivial invariant of braids, knots, and links. Other solutions of the Yang-Baxter Equation are also shown to be universal for quantum computation. The paper discusses these results in the context of comparing quantum and topological points of view. In particular, we discuss quantum computation of link invariants, the relationship between quantum entanglement and topological entanglement, teleportation, and the structure of braiding in a topological quantum field theory.
Using Monte Carlo simulations on different system sizes we determine with high precision the critical thresholds of two families of directed percolation models on a square lattice. The thresholds decrease exponentially with the degree of connectivity. We conjecture that $p_{c}$ decays exactly as the inverse of the coodination number.
We study two-dimensional ${\cal N}=(2,2)$ gauge theory and its dualized system in terms of complex (linear) superfields and their alternatives. Although this technique itself is not new, we can obtain a new model, the so-called "semi-doubled" GLSM. Similar to doubled sigma model, this involves both the original and dual degrees of freedom simultaneously, whilst the latter only contribute to the system via topological interactions. Applying this to the ${\cal N}=(4,4)$ GLSM for H-monopoles, i.e., smeared NS5-branes, we obtain its T-dualized systems in quite an easy way. As a bonus, we also obtain the semi-doubled GLSM for an exotic $5^3_2$-brane whose background is locally nongeometric. In the low energy limit, we construct the semi-doubled NLSM which also generates the conventional string worldsheet sigma models. In the case of the NLSM for $5^3_2$-brane, however, we find that the Dirac monopole equation does not make sense any more because the physical information is absorbed into the divergent part via the smearing procedure. This is nothing but the signal which indicates that the nongeometric feature emerges in the considering model.
We analyse the parity-odd ("type P") surface anomalies of the energy-momentum tensor correlators in conformal field theories, with an emphasis on d=4 and d=3 dimensional spacetimes. Using cohomology analysis we construct the expression for the most general P-type surface trace anomaly on a singular 2-dimensional surface in 4-dimensional bulk spacetimes. As an important example, we specialise to the case when the singular surface is a conical defect and show that the bulk P-type Pontryagin trace anomaly induces such a surface trace anomaly. We show that this conical type P surface trace anomaly is given purely by the outer curvature tensor. In addition, we analyse parity-odd surface contact terms in energy-momentum tensor correlators in the flat spacetime induced by the conical defect by studying two special cases in which the contact terms are induced by, (1) type P trace anomaly in d=4 and, (2) gravitational Chern-Simons Lagrangian term in d=3 spacetime dimensions. In both cases we show that the surface contact terms appear in correlators of the lower rank than the corresponding bulk surface terms.
Let $\pi$ be a permutation of $[n]=\{1,\dots,n\}$ and denote by $\ell(\pi)$ the length of a longest increasing subsequence of $\pi$. Let $\ell_{n,k}$ be the number of permutations $\pi$ of $[n]$ with $\ell(\pi)=k$. Chen conjectured that the sequence $\ell_{n,1},\ell_{n,2},\dots,\ell_{n,n}$ is log concave for every fixed positive integer $n$. We conjecture that the same is true if one is restricted to considering involutions and we show that these two conjectures are closely related. We also prove various analogues of these conjectures concerning permutations whose output tableaux under the Robinson-Schensted algorithm have certain shapes. In addition, we present a proof of Deift that part of the limiting distribution is log concave. Various other conjectures are discussed.
In quantum information processing, one of the most useful interaction between qubits is the Ising type interaction. We propose a scheme to implement the exact Ising interaction through magnetic dipole-dipole interaction. Although magnetic dipolar interaction is Heisenberg type in general, this interaction can bring about the exact mathematical form of the Ising interaction if qubit levels are chosen among the highest magnetic quantum number states. Real physical systems to which our scheme can be applied include rotational states of molecules, hyperfine states of atoms, or electronic states of nitrogen-vacancy centers in diamond. We analyze the feasibility of our scheme for these systems. For example, when the hyperfine levels of rubidium 87 atoms are chosen as qubits and the distance of the two atoms is 0.1 micrometer, controlled-Z gate time will be 8.5 ms. We suggest diverse search and study to achieve optimal implementation of this scheme.
Atmospheric parameters (Teff, log g and log(He/H)) are derived for 42 hot horizontal branch (HB) stars in the globular cluster NGC 6752. For 19 stars MgII and FeII lines are detected indicating an iron enrichment by a factor 50 on average with respect to the cluster abundance whereas the magnesium abundances are consistent with the cluster metallicity. This finding adds to the growing evidence that radiative levitation plays a significant role in determining the physical parameters of blue HB stars. Indeed, we find that iron enrichment can explain part, but not all, of the problem of anomalously low gravities along the blue HB. Thus the physical parameters of horizontal branch stars hotter than about 11,500K in NGC 6752, as derived in this paper, are best explained by a combination of helium mixing and radiative levitation effects.
Using Monte Carlo simulations and finite-size scaling, we study three-state Potts antiferromagnet on layered square lattice with two and four layers $L_z=2$ and $4$. As temperature decreases, the system develops quasi-long-range order via a Berezinskii-Kosterlitz-Thouless transition at finite temperature $T_{c1}$. For $L_z=4$, as temperature is further lowered, a long-range order breaking the $Z_6$ symmetry develops at a second transition at $T_{c2} < T_{c1}$. The transition at $T_{c2}$ is also Berezinskii-Kosterlitz-Thouless-like, but has magnetic critical exponent $\eta=1/9$ instead of the conventional value $\eta = 1/4$. The emergent $U(1)$ symmetry is clearly demonstrated in the quasi-long-range ordered region $T_{c2} \leq T \leq T_{c1}$.
We study the Maker-Breaker tournament game played on the edge set of a given graph $G$. Two players, Maker and Breaker claim unclaimed edges of $G$ in turns, and Maker wins if by the end of the game she claims all the edges of a pre-defined goal tournament. Given a tournament $T_k$ on $k$ vertices, we determine the threshold bias for the $(1:b)$ $T_k$-tournament game on $K_n$. We also look at the $(1:1)$ $T_k$-tournament game played on the edge set of a random graph ${\mathcal{G}_{n,p}}$ and determine the threshold probability for Maker's win. We compare these games with the clique game and discuss whether a random graph intuition is satisfied.
The Sun provides the energy necessary to sustain our existence. While the Sun provides for us, it is also capable of taking away. The weather and climatic scales of solar evolution and the Sun-Earth connection are not well understood. There has been tremendous progress in the century since the discovery of solar magnetism - magnetism that ultimately drives the electromagnetic, particulate and eruptive forcing of our planetary system. There is contemporary evidence of a decrease in solar magnetism, perhaps even indicators of a significant downward trend, over recent decades. Are we entering a minimum in solar activity that is deeper and longer than a typical solar minimum, a "grand minimum"? How could we tell if we are? What is a grand minimum and how does the Sun recover? These are very pertinent questions for modern civilization. In this paper we present a hypothetical demonstration of entry and exit from grand minimum conditions based on a recent analysis of solar features over the past 20 years and their possible connection to the origins of the 11(-ish) year solar activity cycle.
The phase transition in the mean-field XY model is shown analytically to be related to a topological change in its configuration space. Such a topology change is completely described by means of Morse theory allowing a computation of the Euler characteristic--of suitable submanifolds of configuration space--which shows a sharp discontinuity at the phase transition point, also at finite N. The present analytic result provides, with previous work, a new key to a possible connection of topological changes in configuration space as the origin of phase transitions in a variety of systems.
The temperature dependence of a vortex-based nano-oscillator induced by spin transfer torque (STVO) in magnetic tunnel junctions (MTJ) is considered. We obtain emitted signals with large output power and good signal coherence. Due to the reduced non-linearities compared to the uniform magnetization case, we first observe a linear decrease of linewidth with decreasing temperature. However, this expected behavior no longer applies at lower temperature and a bottom limit of the linewidth is measured.
We report a detailed dc magnetization, ac susceptibility and magnetocaloric properties of a binary intermetallic compound Tb5Pd2. Our dc magnetization and heat capacity results reveal absence of long range ordering in this compound. Two distinct frequency dependent peaks (Tf1~60 K and Tf2~21 K) had been observed in the ac-susceptibility. Analysis of these frequency dependent peaks by Mydosh parameter, power and Vogel-Fulcher law reveals that around Tf1 the compound is at the boundary of spin glass (SG) like-cluster glass (CG) like state and it undergoes a cluster glass-like freezing below Tf2. Zero field cooled memory effect and non-linear dc susceptibility also confirmed the presence of two glassy transitions in this compound. The transformation from SG/CG boundary to CG phase was also confirmed by the magnetic relaxation measurement and Arrott plots study. Remarkably, a significant magnetic entropy change was also observed in the temperature range of 60-120 K. Additionally a large relative cooling power also observed in this compound. The observed value is comparable to those of promising refrigerant material in this temperature range and is quite notable as in this compound magnetic hysteresis was absent in this temperature range. It was noted that in this compound short-range interactions persist up to a higher temperature above Tf1 and this is responsible for the observation of significant MCE over a wide temperature range. Our studies suggest that this compound is an example of a glassy magnetic compound which shows large magnetocaloric effect.
The possibility that nuclear matter at a density relevant to the interior of massive neutron stars may be a quarkynoic matter has attracted considerable recent interest. In this work, we construct a field theoretical model to describe the quarkyonic matter, that would allow quantitative and systematic calculations of its various properties. This is implemented by synthesizing the Walecka model together with the quark-meson model, where both quark and nucleon degrees of freedom are present based on the quarkyonic scenario. With this model we compute at mean-field level the thermodynamic properties of the symmetric nuclear matter and calibrate model parameters through well-known nuclear physics measurements. We find this model gives a very good description of the symmetric nuclear matter from moderate to high baryon density and demonstrates a continuous transition from nucleon-dominance to quark-dominance for the system.
The problem of an apparent inconsistency between the fission rates derived on the basis of Bohr-Wheeler's transition-state method and Kramers' dynamical model of nuclear fission, first pointed out by Strutinsky in 1973, is revisited. The study is based on studying the features of individual trajectories on the fission path.
We construct a viable cosmological model based on velocity diffusion of matter particles. In order to ensure the conservation of the total energy-momentum tensor in the presence of diffusion, we include a cosmological scalar field $\phi$ which we identify with the dark energy component of the Universe. The model is characterized by only one new degree of freedom, the diffusion parameter $\sigma$. The standard $\Lambda$CDM model can be recovered by setting $\sigma=0$. If diffusion takes place ($\sigma >0$) the dynamics of the matter and of the dark energy fields are coupled. We argue that the existence of a diffusion mechanism in the Universe can serve as a theoretical motivation for interacting models. We constrain the background dynamics of the diffusion model with Supernovae, H(z) and BAO data. We also perform a perturbative analysis of this model in order to understand structure formation in the Universe. We calculate the impact of diffusion both on the CMB spectrum, with particular attention to the integrated Sachs-Wolfe signal, and on the matter power spectrum $P(k)$. The latter analysis places strong constraints on the magnitude of the diffusion mechanism but does not rule out the model.
The Schr\"{o}dinger equation and ladder operators for the harmonic oscillator are shown to simplify through the use of an isometric conformal transformation. These results are discussed in relation to the Bargmann representation. It is further demonstrated that harmonic interactions can be introduced into quantum mechanics as an imaginary component of time equivalent to adding the oscillator potential into the hamiltonian for the confined particle.
In this study, a tight-binding model on square octagon lattice with nearest-neighbour and next-nearest-neighbour hoppings is considered. The system is topologically trivial although it exhibits quadratic band-touching points in its band-structure. It is shown that the system drives towards topologically non-trivial phases as soon as it is exposed to monochromatic circularly polarized light. Multiple topological phases are found to emerge with the variation of amplitude of light. An effective time-independent Hamiltonian of the system is obtained following the Floquet-Bloch formulation. Quasi-energy band-structures along with definite values of Chern numbers for respective bands are obtained. Characterization of topological phases are made in terms of band structure and Chern numbers. In addition, Hall conductance and topologically protected chiral edge states are obtained to explain the topological properties. Density of states is obtained in every case. The system undergoes a series of topological phase transitions among various topological phases upon variations of both amplitude of light and hopping strengths. It exhibits Chern insulating and Chern semimetallic phases depending on the values of lattice filling.
By applying the classic telescoping summation formula and its variants to identities involving inverse hyperbolic tangent functions having inverse powers of the golden ratio as arguments and employing subtle properties of the Fibonacci and Lucas numbers, we derive interesting general infinite product identities involving these numbers.
Three-dimensional Topologically Massive Gravity at its critical point has been conjectured to be holographically dual to a Logarithmic CFT. However, many details of this correspondence are still lacking. In this work, we study the 1-loop partition function of Critical Cosmological Topologically Massive Gravity, previously derived by Gaberdiel, Grumiller and Vassilevich, and show that it can be usefully rewritten as a Bell polynomial expansion. We also show that there is a relationship between this Bell polynomial expansion and the Plethystic Exponential. Our reformulation allows us to match the TMG partition function to states on the CFT side, including the multi-particle states of t (the logarithmic partner of the CFT stress tensor) which had previously been elusive. We also discuss the appearance of a ladder action between the different multi-particle sectors in the partition function, which induces an interesting sl(2) structure on the n-particle components of the partition function.
We update our work ``Two Higgs Doublet Model predictions for B->X_s gamma in NLO QCD'', hep-ph/9802391 by taking into account the recently calculated electromagnetic corrections. We present a new exclusion contour plot (tan(\beta),m_H), where these corrections are included.
The possibility that the strength of gravitational interactions might slowly increase with distance, is explored by formulating a set of effective field equations, which incorporate the gravitational, vacuum-polarization induced, running of Newton's constant $G$. The resulting long distance (or large time) behaviour depends on only one adjustable parameter $\xi$, and the implications for the Robertson-Walker universe are calculated, predicting an accelerated power-law expansion at later times $t \sim \xi \sim 1/H$.
Like the Coxeter graph became reattached into the Klein graph in [2], the Levi graphs of the $9_3$ and $10_3$ self-dual configurations, known as the Pappus and Desargues ($k$-transitive) graphs $\mathcal P$ and $\mathcal D$ (where $k=3$), also admit reattachments of the distance-$(k-1)$ graphs of half of their oriented shortest cycles via orientation assignments on their common $(k-1)$-arcs, concurrent for ${\mathcal P}$ and opposite for $\mathcal D$, now into 2 disjoint copies of their corresponding Menger graphs. Here, $\mathcal P$ is the unique cubic distance-transitive (or CDT) graph with the concurrent-reattachment behavior while $\mathcal D$ is one of 7 CDT graphs with the opposite-reattachment behavior, that include the Coxeter graph. Thus, $\mathcal P$ and $\mathcal D$ confront each other in these respects, obtained via $\mathcal C$-ultrahomogeneous graph techniques [3,4] that allow to characterize the obtained reattachment Menger graphs in the same terms.
Let $X$ be a very general hypersurface of degree $d$ in $\mathbb{P}^n$. We investigate positivity properties of the spaces $R_e(X)$ of degree $e$ rational curves in $X$. We show that for small $e$, $R_e(X)$ has no rational curves meeting the locus of smooth embedded curves. We show that for $n \leq d$, there are no rational curves in the locus $Y \subset X$ swept out by lines. And we exhibit differential forms on a smooth compactification of $R_e(X)$ for every $e$ and $n-2 \geq d \geq \frac{n+1}{2}$.
By combining the Malliavin calculus with Fourier techniques, we develop a high-order asymptotic expansion theory for a sequence of vector-valued random variables. Our asymptotic expansion formulas give the development of the characteristic functional and of the local density of the random vectors up to an arbitrary order. We analyzed in details an example related to the wave equation with space-time white noise which also provides interesting facts on the correlation structure of the solution to this equation.
Various kinds of fingerprinting codes and their related combinatorial structures are extensively studied for protecting copyrighted materials. This paper concentrates on one specialised fingerprinting code named wide-sense frameproof codes in order to prevent innocent users from being framed. Let $Q$ be a finite alphabet of size $q$. Given a $t$-subset $X=\{x ^1,\ldots, x ^t\}\subseteq Q^n$, a position $i$ is called undetectable for $X$ if the values of the words of $X$ match in their $i$th position: $x_i^1=\cdots=x_i^t$. The wide-sense descendant set of $X$ is defined by $\wdesc(X)=\{y\in Q^n:y_i=x_i^1,i\in {U}(X)\},$ where ${U}(X)$ is the set of undetectable positions for $X$. A code ${\cal C}\subseteq Q^n$ is called a wide-sense $t$-frameproof code if $\wdesc(X) \cap{\cal C} = X$ for all $X \subseteq {\cal C}$ with $|X| \le t$. The paper improves the upper bounds on the sizes of wide-sense $2$-frameproof codes by applying techniques on non $2$-covering Sperner families and intersecting families in extremal set theory.
We present the discovery and refinement by neutron powder diffraction of a new magnetic phase in the Na1-xCaxMn7O12 quadruple perovskite phase diagram, which is the incommensurate analogue of the well-known pseudo-CE phase of the simple perovskite manganites. We demonstrate that incommensurate magnetic order arises in quadruple perovskites due to the exchange interactions between A and B sites. Furthermore, by constructing a simple mean field Heisenberg exchange model that generically describes both simple and quadruple perovskite systems, we show that this new magnetic phase unifies a picture of the interplay between charge, magnetic and orbital ordering across a wide range of compounds.