ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study BPS string-like solutions in the 3+1 dimensional gauged CP(1) non-linear sigma model. The same analysis can be applied to study instantons in 2 euclidean dimensions. We use the moduli matrix approach to construct analytically the moduli space and and solve numerically the BPS equations. We identify two topologically inequivalent type of magnetic vortices, which we call S and N vortices. Moreover we discuss their relation to "lump-string" solutions present in the un-gauged case. In particular, we describe how a lump is split into a couple of component S-N vortices after gauging. We extend this analysis to the case of the extended Abelian Higgs model with two flavors, which is known to admit semi-local vortices. When we gauge the relative phase between fields, semi-local vortices are also split into component vortices. We discuss interesting applications of this simple set-up. First, gauging of non-linear sigma models reveals a "partonic" nature of instantons in 1+1 dimensions, an idea long studied also in connection with four dimensional instantons. Second, weak gauging provides for an interesting regularization of the metric of semi-local vortices which preserves supersymmetry and does not lift the moduli space of the string.
We examine an effectively repulsive Bose-Einstein condensate of atoms, that rotates in a quadratic-plus-quartic trapping potential. We investigate the phase diagram of the system as a function of the angular frequency of rotation and of the coupling constant, demonstrating that there are phase transitions between multiply- and singly-quantized vortex states. The derived phase diagram is shown to be universal and exact in the limits of small anharmonicity and weak coupling constant.
With the exception of gravitation, the known fundamental interactions of Nature are mediated by gauge fields. A comparison of the candidate groups for a gauge theory possibly describing gravitation favours the Poincar\'e group as the obvious choice. This theory gives Einstein's equations in a particular case, and Newton's law in the static non-relativistic limit, being seemingly sound at the classical level. But it comes out that it is not quantizable. The usual procedure of adding counterterms to make it a consistent and renormalizable theory leads to two possible theories, one for each of the two de Sitter groups, SO(4,1) and SO(3,2). The consequences of changing from the Poincar\'e to the de Sitter group, as well as the positive aspects, perspectives and drawbacks of the resulting theory are discussed.
In the last decade, for studying 3$N$ bound states and $Nd$ scattering the Tucson-Melbourne (TM) and Urbana 3$N$ force derived from the chiral EFT have been applied. We plan to use the TM 3$N$ force for studying the $Nd$ scattering on the basis of the Faddeev equations in configuration space. In the given paper, we present our final formulas for components of the TM 3$N$ potential obtained in the coordinate space.
We present an EXAFS study of the Mn atomic environment in Mn-doped GaAs nanowires. Mn doping has been obtained either via the diffusion of the Mn used as seed for the nanowire growth or by providing Mn during the growth of Au-induced wires. As a general finding, we observe that Mn forms chemical bonds with As but is not incorporated in a substitutional site. In Mn-induced GaAs wires, Mn is mostly found bonded to As in a rather disordered environment and with a stretched bond length, reminiscent of that exhibited by MnAs phases. In Au-seeded nanowires, along with stretched Mn-As coordination we have found the presence of Mn in a Mn-Au intermetallic compound.
Designing and realizing various magnetization textures in magnetic nanostructures are essential for developing novel magnetic nanodevices in modern information industry. Among all these textures, planar transverse domain walls (pTDWs) are the simplest and the most basic, which make them popular in device physics. In this work, we report the engineering of pTDWs with arbitrary tilting attitude in biaxial magnetic nanostrips by transverse magnetic field profiles with uniform orientation but tunable strength distribution. Both statics and axial-field-driven dynamics of these pTDWs are analytically investigated. It turns out that for statics these pTDWs are robust again disturbances which are not too abrupt, while for dynamics it can be tailored to acquire higher velocity than Walker's ansatz predicts. These results should provide inspirations for designing magnetic nanodevices with novel one-dimensional magnetization textures, such as 360$^\circ$ walls, or even two-dimensional ones, for example vortices, skyrmions, etc.
Multi-band quasi-particle calculations based on perturbation theory and dynamical mean field methods show that the creation of a photoemission hole state in Sr$_2$RuO$_4$ is associated with a highly anisotropic self-energy. Since the narrow Ru-derived $d_{xz,yz}$ bands are more strongly distorted by Coulomb correlations than the wide $d_{xy}$ band, charge is partially transferred from $d_{xz,yz}$ to $d_{xy}$, thereby shifting the $d_{xy}$ van Hove singularity close to the Fermi level.
Our goal in this paper is to apply a normal forms method to estimate the Sobolev norms of the solutions of the water waves equation. We construct a paradifferential change of unknown, without derivatives losses, which eliminates the part of the quadratic terms that bring non zero contributions in a Sobolev energy inequality. Our approach is purely Eulerian: we work on the Craig-Sulem-Zakharov formulation of the water waves equation. In addition to these Sobolev estimates, we also prove $L^2$-estimates for the $\partial_x^\alpha Z^\beta$-derivatives of the solutions of the water waves equation, where $Z$ is the Klainerman vector field $t\partial_t +2x\partial_x$. These estimates are used in another paper where we prove a global existence result for the water waves equation with smooth, small, and decaying at infinity Cauchy data, and we obtain an asymptotic description in physical coordinates of the solution, which shows that modified scattering holds. The proof of this global in time existence result relies on the simultaneous bootstrap of some H\"older and Sobolev a priori estimates for the action of iterated Klainerman vector fields on the solutions of the water waves equation. The present paper contains the proof of the Sobolev part of that bootstrap.
We verify the Hardy-Littlewood conjecture on primes in quadratic progressions on average. The results in the present paper significantly improve those of a previous paper of the authors(arXiv:math.NT/0605563).
We present very deep WFPC2 images and FOS spectroscopy from the Hubble Space Telescope (HST) together with numerous supporting ground-based observations of the field of the quasar 3C 336 ($z_{em}=0.927$). The observations are designed to investigate the nature of galaxies producing metal line absorption systems in the spectrum of the QSO. Along a single line of sight, we find at least 6 metal line absorption systems (of which 3 are newly discovered) ranging in redshift from 0.317 to 0.892. Through an extensive program of optical and IR imaging, QSO spectroscopy, and faint galaxy spectroscopy, we have identified 5 of the 6 metal line absorption systems with luminous (L_K > 0.1 L*_K) galaxies. These have morphologies ranging from very late-type spiral to S0, and exhibit a wide range of inclination and position angles with respect to the QSO sightline. The only unidentified absorber, despite our intensive search, is a damped Lyman $\alpha$ system at $z_{abs}=0.656$. Analysis of the absorption spectrum suggests that the metal abundances ([Fe/H]$=-1.2$) in this system are similar to those in damped systems at $z \sim 2$, and to the two other damped systems for which abundances have been determined at $z <1$. We have found no examples of intrinsically faint galaxies ($L < 0.1 L^{\ast}$) at small impact parameters that might have been missed as absorber candidates in our previous ground-based imaging and spectroscopic programs on MgII absorbing galaxies. There are no bright galaxies (L > 0.1 L_K) within 50h^{-1} kpc which do not produce detectable metal lines (of Mg II 2796, 2803 and/or C IV 1548, 1550) in the QSO spectrum. All of these results generally support the inferences which we have previously reached from a larger survey for absorption-selected galaxies at $z\simlt 1$.
Ammoniation in metal borohydrides (MBs) with the form $\mathcal{M}$(BH$_4$)$_x$ has been shown to lower their decomposition temperatures with $\mathcal{M}$ of low electronegativity ($\chi_p \lesssim 1.6$), but raise it for high-$\chi_p$ MBs ($\chi_p \gtrsim 1.6$). Although this behavior is just as desired, an understanding of the mechanisms that cause it is still lacking. Using \emph{ab initio} methods, we elucidate those mechanisms and find that ammoniation always causes thermodynamic destabilization, explaining the observed lower decomposition temperatures for low-$\chi_p$ MBs. For high-$\chi_p$ MBs, we find that ammoniation blocks B$_2$H$_6$ formation---the preferred decomposition mechanism in these MBs---and thus kinetically stabilizes those phases. The shift in decomposition pathway that causes the distinct change from destabilization to stabilization around $\chi_p=1.6$ thus coincides with the onset of B$_2$H$_6$ formation in MBs. Furthermore, with our analysis we are also able to explain why these materials release either H$_2$ or NH$_3$ gas upon decomposition. We find that NH$_3$ is much more strongly coordinated with higher-$\chi_p$ metals and direct H$_2$ formation/release becomes more favorable in these materials. Our findings are of importance for unraveling the hydrogen release mechanisms in an important new and promising class of hydrogen storage materials, allowing for a guided tuning of their chemistry to further improve their properties.
We present an one-time-pad key communication protocol that allows secure direct communication with entanglement. Alice can send message to Bob in a deterministic manner by using local measurements and public communication. The theoretical efficiency of this protocol is double compared with BB84 protocol. We show this protocol is unconditional secure under arbitrary quantum attack. And we discuss that this protocol can be perfectly implemented with current technologies.
This paper explores properties and applications of an ordered subset of the quadratic integer ring $\mathbb{Z}\left[\frac{1+\sqrt{5}}{2}\right]$. The numbers are shown to exhibit a parity triplet, as opposed to the familiar even/odd doublet of the regular integers. Operations on these numbers are defined and used to generate a succinct recurrence relation for the well-studied Fibonacci diatomic sequence, providing the means for generating analogues to the famed Calkin-Wilf and Stern-Brocot trees. Two related fractal geometries are presented and explored, one of which exhibits several identities between the Fibonacci numbers and golden ratio, providing a unique geometric expression of the Fibonacci words and serving as a powerful tool for quantifying the cardinality of ordinal sets. The properties of the presented set of numbers illuminate the symmetries behind ordinals in general, as well as provide perspective on the natural numbers and raise questions about the dynamics of transfinite values. In particular, the first transfinite ordinal $\omega$ is shown to be logically consistent with a value whose cardinality is dual: both zero and one. Considerations of these points and opportunities for further study are discussed.
We consider a particle in a one-dimensional box of length $L$ with a Maxwell bath at one end and a reflecting wall at the other end. Using a renewal approach, as well as directly solving the master equation, we show that the system exhibits a slow power law relaxation with a logarithmic correction towards the final equilibrium state. We extend the renewal approach to a class of confining potentials of the form $U(x) \propto x^\alpha$, $x>0$, where we find that the relaxation is $\sim t^{-(\alpha+2)/(\alpha-2)}$ for $\alpha >2$, with a logarithmic correction when $(\alpha+2)/(\alpha-2)$ is an integer. For $\alpha <2$ the relaxation is exponential. Interestingly for $\alpha=2$ (harmonic potential) the localised bath can not equilibrate the particle.
In this paper we establish an improved bound for the number of incidences between a set $P$ of $m$ points and a set $H$ of $n$ planes in $\mathbb R^3$, provided that the points lie on a two-dimensional nonlinear irreducible algebraic variety $V$ of constant degree. Specifically, the bound is $$ O\left( m^{2/3}n^{2/3} + m^{6/11}n^{9/11}\log^\beta(m^3/n) + m + n + \sum_\ell |P_\ell|\cdot |H_\ell| \right) , $$ where the constant of proportionality and the constant exponent $\beta$ depend on the degree of $V$, and where the sum ranges over all lines $\ell$ that are fully contained in $V$ and contain at least one point of $P$, so that, for each such $\ell$, $P_\ell = P\cap\ell$ and $H_\ell$ is the set of the planes of H that contain $\ell$. In addition, $\sum_\ell |P_\ell| = O(m)$ and $\sum_\ell |H_\ell| = O(n)$.   This improves, for this special case, the earlier more general bound of Apfelbaum and Sharir (see also Brass and Knauer as well as Elekes and T\'oth).   This is a generalization of the incidence bound for points and circles in the plane (cf. Aronov et al., Aronov and Sharir, Marcus and Tardos), and is based on a recent result of Sharir and Zahl on the number of cuts that turn a collection of algebraic curves into pseudo-segments.   The case where $V$ is a quadric is simpler to analyze, does not require the result of Sharir and Zahl, and yields the same bound as above, with $\beta=2/11$.   We present an interesting application of our results to a problem, studied by Rudnev, on obtaining a lower bound on the number of distinct cross-ratios determined by $n$ real points, where our bound leads to a slight improvement in Rudnev's bound.
We show that memristive systems can be used very efficiently to generate passively both double and higher frequency harmonics. A technique for maximizing the power conversion efficiency into any given harmonic is developed and applied to a single memristive system and memristive bridge circuits. We find much higher rates of power conversion compared to the standard diode bridge, with the memristive bridge more efficient for second and higher harmonics generation compared to the single memristive system. The memristive bridge circuit optimized for second harmonic generation behaves as a two-quarter-wave rectifier.
A great open problem is: can one learn the topology of the non-smooth path spaces with an L2 Hodge-deRham theory This one hopes to establish through a suitable complex of differential forms. Since the space is a Banach manifolds, and the Hodge theory is based on Hilbert spaces, it is trick to find such a complex. The relatively simpler Bismut tangent spaces and their tensor products, whose dual spaces are natural candidates for the complex, cannot be used, because these spaces are not necessarily closed under the Lie bracket operation if there is the effect of curvature. In this article we seek out a class of nice vector fields whose brackets behaves are calculable and behave nicely the damped tensor vector fields, using an It\^o mp, which is also used by the authors in `Special It\^o maps and an L2 Hodge theory for one forms on path spaces. Stochastic processes, physics and geometry: new interplays, I (Leipzig, 1999), 145-162, CMS Conf. Proc., 28, Amer. Math. Soc., Providence, RI, 2000').
We present high-resolution ALMA Band 6 and 7 observations of the tidally disrupted protoplanetary disks of the RW Aurigae binary. Our observations reveal the presence of additional tidal streams to the previously observed tidal arm around RW Aur A. The observed configuration of tidal streams surrounding RW Aur A and B is incompatible with a single star--disk tidal encounter, suggesting that the RW Aurigae system has undergone multiple fly-by interactions. We also resolve the circumstellar disks around RW Aur A and B, with CO radii of 58 au and 38 au consistent with tidal truncation, and 2.5 times smaller dust emission radii. The disks appear misaligned by 12$^{\circ}$ or 57$^{\circ}$. Using new photometric observations from the American Association of Variable Star Observers (AAVSO) and All Sky Automated Survey for SuperNovae (ASAS-SN) archives, we have also identified an additional dimming event of the primary that began in late 2017 and is currently ongoing. With over a century of photometric observations, we are beginning to explore the same spatial scales as ALMA.
We study the characterisation of efficient and non-efficient families of Grover's algorithms according to the majorization principle. We develop a geometrical interpretation based on the parameters that appears on these algorithms. Using this interpretation we observe a step-by-step majorization in all efficient Grover's algorithms, whereas the non-efficient Grover's algorithms fail to abide by this majorization principle. These Majorization results are first obtained from numerical calculations. Motivated by these numerical results, we also obtained an analytical demonstration. Finally, the geometrical interpretation found for these parameters is used to obtain additional results of Grover's algorithms that improves our understanding of how they work.
A linked cluster expansion for the distorted one-body mixed density matrix is obtained within the Glauber multiple scattering theory with correlated wave functions. The nuclear transparency for 16O is calculated using realistic central and non-central correlations. The convergence of the expansion is investigated in the case of 4He for which the transparency and the distorted momentum distributions are calculated to all order in the correlations using a variational wave function obtained from realistic NN interactions. The important role played by non central correlations is illustrated.
We provide sharp Large Deviation estimates for the probability of exit from a domain for the bridge of a $d$-dimensional general diffusion process $X$, as the conditioning time tends to $0$. This kind of results is motivated by applications to numerical simulation. In particular we investigate the influence of the drift $b$ of $X$. It turns out that the sharp asymptotics for the exit time probability are independent of the drift, provided $b$ enjoyes a simple condition that is always satisfied in dimension $1$. On the other hand, we show that the drift can be influential if this assumption is not satisfied. }
We study the set D of positive integers d for which the equation $\phi(a)-\phi(b)=d$ has infinitely many solution pairs (a,b), where $\phi$ is Euler's totient function. We show that the minumum of D is at most 154, exhibit a specific A so that every multiple of A is in D, and show that any progression a mod d with 4|a and 4|d, contains infinitely many elements of D. We also show that the Generalized Elliott-Halberstam Conjecture, as defined in [6], implies that D equals the set of all positive, even integers.
Each platonic solid defines a single-qubit positive operator valued measure (POVM) by interpreting its vertices as points on the Bloch sphere. We construct simple circuits for implementing this kind of measurements and other simple types of symmetric POVMs on one qubit. Each implementation consists of a discrete Fourier transform and some elementary quantum operations followed by an orthogonal measurement in the computational basis.
Poly(Methyl Methacrylate) (PMMA) and CaCu3Ti4O12 (CCTO) composites were fabricated via melt mixing followed by hot pressing technique. These were characterized using X-ray diffraction (XRD), thermo gravimetric (TGA), Thermo Mechanical (TMA), Differential scanning calorimetry (DSC), Fourier transform infrared (FTIR), and Impedance analyser for their structural, thermal and dielectric properties. Composites were found to have better thermal stability than that of pure PMMA. However, there was no significant difference in the glass transition (Tg) temperature between the polymer and the composite. The appearance of additional vibrational frequencies in the range 400-600 cm-1 in FTIR spectra indicated a possible interaction between PMMA and CCTO. The composite, with 38 Vol % of CCTO (in PMMA), exhibited remarkably low dielectric loss at high frequencies and the low frequency relaxation is attributed to the space charge polarization/MWS effect. The origin of AC conductivity particularly in the high frequency region was attributed to the electronic polarization.
In this paper we classify complex K3 surfaces with non-symplectic automorphism of order 8 that leaves invariant a smooth elliptic curve. We show that the rank of the Picard group is either 10, 14 or 18 and the fixed locus is the disjoint union of elliptic curves, rational curves and points, whose number does not exceed 1, 2, respectively 14. We give examples corresponding to several types of fixed locus in the classification.
The generalized quantal distribution functions are investigated concerning systems of non-interacting bosons and fermions. The formulae for the number of particles and energy are presented and applications to the Chandrasekhar limit of white dwarfs stars and to the Bose-Einstein condensation are commented.
A number of recent results in Euclidean Harmonic Analysis have exploited several adjacent systems of dyadic cubes, instead of just one fixed system. In this paper, we extend such constructions to general spaces of homogeneous type, making these tools available for Analysis on metric spaces. The results include a new (non-random) construction of boundedly many adjacent dyadic systems with useful covering properties, and a streamlined version of the random construction recently devised by H. Martikainen and the first author. We illustrate the usefulness of these constructions with applications to weighted inequalities and the BMO space; further applications will appear in forthcoming work.
Considering plane gravitational waves propagating through flat spacetime, it is shown that curvatures experienced both in the starting point and during their arrival at the earth can cause a considerable shift in the frequencies as measured by earth and space-based detectors. Particularly for the case of resonant bar detectors this shift can cause noise-filters to smother the signal.
K 3-35 is a planetary nebula (PN) where H2O maser emission has been detected, suggesting that it departed from the proto-PNe phase only some decades ago. Interferometric VLA observations of the OH 18 cm transitions in K~3-35 are presented.OH maser emission is detected in all four ground state lines (1612, 1665, 1667, and 1720 MHz). All the masers appear blueshifted with respect to the systemic velocity of the nebula and they have different spatial and kinematic distributions.The OH 1665 and 1720 MHz masers appear spatially coincident with the core of the nebula, while the OH 1612 and 1667 MHz ones exhibit a more extended distribution. We suggest that the 1665 and 1720 masers arise from a region close to the central star, possibly in a torus, while the 1612 and 1667 lines originate mainly from the extended northern lobe of the outflow. It is worth noting that the location and velocity of the OH 1720 MHz maser emission are very similar to those of the H2O masers (coinciding within 0.1" and ~2 km/s, respectively). We suggest that the pumping mechanism in the H2O masers could be produced by the same shock that is exciting the OH 1720 MHz transition. A high degree of circular polarization (>50%) was found to be present in some features of the 1612, 1665, and 1720 MHz emission.For the 1665 MHz transition at ~ +18 km/s the emission with left and right circular polarizations (LCP and RCP) coincide spatially within a region of ~0.03" in diameter.Assuming that these RCP and LCP 1665 features come from a Zeeman pair, we estimate a magnetic field of ~0.9 mG within 150 AU from the 1.3 cm continuum peak. This value is in agreement with a solar-type magnetic field associated with evolved stars.