ShantanuT01/DACTYL-Pretraining huggingface dataset:
The temperature dependence of the generation linewidth for an auto-oscillator with a nonlinear frequency shift is calculated. It is shown that the frequency nonlinearity creates a finite correlation time, tau, for the phase fluctuations. In the low-temperature limit in which the spectral linewidth is smaller than 1/tau, the line shape is approximately Lorentzian and the linewidth is linear in temperature. In the opposite high-temperature limit in which the linewidth is larger than 1/tau, the nonlinearity leads to an apparent "inhomogeneous broadening" of the line, which becomes Gaussian in shape and has a square-root dependence on temperature. The results are illustrated for the spin-torque nano-oscillator.
Fix a smooth projetive curve $\mathcal {C}$ of genus $g\geq 2$ and a line bundle $\mathcal{L}$ on $\mathcal{C}$ of degree $d$. Let $M:= \mathcal{SU}_{\mathcal{C}}(r, \mathcal{L})$ be the moduli space of stable vector bundles on $\mathcal{C}$ of rank $r$ and with fixed determinant $\mathcal{L}$. We prove that any rational curve on $M$ is a generalized Hecke curve. Furthermore, we study the lines on $M$, and prove that $M$ is covered by the lines when $(r, d)=r$; for the case $(r,d)<r$, the lines fill up a closed subvariety of $M$, and we determine the number of its irreducible components and the dimension of each irreducible component when $g>(r,d)+1$. Finally, we prove that there are no $(1,0)$-stable (resp., $(0,1)$-stable) bundles for $g=2$, $r=2$ and $d$ is odd as an application.
Spin splitting of energy bands can be induced by relativistic spin-orbit interactions in materials without inversion symmetry. Whereas polar space group symmetries permit Rashba (R-1) spin splitting with helical spin textures in momentum space, which could be reversed upon switching a ferroelectric polarization via applied electric fields, the ordinary Dresselhaus effect (D-1A) is ac-tive only in materials exhibiting nonpolar noncentrosymmetric crystal classes with atoms occupy-ing exclusively non-polar lattice sites. Consequently, the spin-momentum locking induced by D-1A is not electric field-switchable. An alternative type of Dresselhaus symmetry, referred to as D-1B, exhibits crystal class constraints similar to D-1A (all dipoles add up to zero), but unlike D-1A, at least one polar site is occupied. We find that this behavior exists in a class of ferri-chiral crys-tals, which in principle could be reversed upon a change in chirality. Focusing on alkali metal chalcogenides, we identify NaCu5S3 in the nonentiamorphic ferri-chiral structure, which exhibits CuS3 chiral units differing in the magnitude of their Cu displacements. We then synthesize NaCu5S3 (space group P6322) and confirm its ferri-chiral structure with power x-ray diffraction. Our electronic structure calculations demonstrate it exhibits D-1B spin splitting as well as a ferri-chiral phase transition, revealing spin splitting interdependent on chirality. Our electronic struc-ture calculations show that a few percent biaxial tensile strain can reduce (or nearly quench) the switching barrier separating the monodomain ferri-chiral P6322 states. We discuss what type of external stimuli might switch the chirality so as to reverse the (non-helical) Dresselhaus D-1B spin texture, offering an alternative to the traditional reversal of the (helical) Rashba spin texture.
We present results from Hubble Space Telescope UV spectroscopy of the massive X-ray binary system, HD226868 = Cyg X-1. The spectra were obtained at both orbital conjunction phases in two separate runs in 2002 and 2003 when the system was in the X-ray high/soft state. The stellar wind lines suffer large reductions in strength when the black hole is in the foreground due to the X-ray ionization of the wind ions. A comparison of HST and archival IUE spectra shows that similar photoionization effects occur in both the X-ray states. We constructed model UV wind line profiles assuming that X-ray ionization occurs everywhere in the wind except the zone where the supergiant blocks the X-ray flux. The good match between the observed and model profiles indicates that the wind ionization extends to near to the hemisphere of the supergiant facing the X-ray source. The H-alpha emission strength is generally lower in the high/soft state compared to the low/hard state, but the He II 4686 emission is relatively constant between states. The results suggest that mass transfer in Cyg X-1 is dominated by a focused wind flow that peaks along the axis joining the stars and that the stellar wind contribution is shut down by X-ray photoionization effects. The strong stellar wind from the shadowed side of the supergiant will stall when Coriolis deflection brings the gas into the region of X-ray illumination. This stalled gas component may be overtaken by the orbital motion of the black hole and act to inhibit accretion from the focused wind. The variations in the strength of the shadow wind component may then lead to accretion rate changes that ultimately determine the X-ray state.
The seller's risk-indifference price evaluation is studied. We propose a dynamic risk-indifference pricing criteria derived from a fully-dynamic family of risk measures on the $L_p$-spaces for $p\in [1,\infty]$. The concept of fully-dynamic risk measures extends the one of dynamic risk measures by adding the actual possibility of changing the risk perspectives over time. The family is then characterised by a double time index. Our framework fits well the study of both short and long term investments. In this dynamic framework we analyse whether the risk-indifference pricing criterion actually provides a proper convex price system, for which time-consistency is guaranteed. It turns out that the analysis is quite delicate and necessitates an adequate setting. This entails the use of capacities and an extension of the whole price system to the Banach spaces derived by the capacity seminorms.   Furthermore, we consider the relationship of the fully-dynamic risk-indifference price with no-good-deal bounds. Recall that no-good-deal pricing guarantees that not only arbitrage opportunities are excluded, but also all deals that are "too good to be true". We shall provide necessary and sufficient conditions on the fully-dynamic risk measures so that the corresponding risk-indifference prices satisfy the no-good-deal bounds. The use of no-good-deal bounds also provides a method to select the risk measures and then construct a proper fully-dynamic risk-indifference price system in the $L_2$-spaces.
In this work, inspired by the study of semidefinite programming for block-diagonalizing matrix *-algebras, we propose an algorithm that can find the algebraic structure of decoherence-free subspaces (DFS's) for a given noisy quantum channel. We prove that this algorithm will work for all cases with probability one, and it is more efficient than the algorithm proposed by Holbrook, Kribs, and Laflamme [Quant. Inf. Proc. 80, 381 (2003)]. In fact, our results reveal that this previous algorithm only works for special cases. As an application, we discuss how this method can be applied to increase the efficiency of an optimization procedure for finding an approximate DFS.
Spin transport electronics - spintronics - focuses on utilizing electron spin as a state variable for quantum and classical information processing and storage. Some insulating materials, such as diamond, offer defect centers whose associated spins are well-isolated from their environment giving them long coherence times; however, spin interactions are important for transport, entanglement, and read-out. Here, we report direct measurement of pure spin transport - free of any charge motion - within a nanoscale quasi 1D 'spin wire', and find a spin diffusion length ~ 700 nm. We exploit the statistical fluctuations of a small number of spins ($\sqrt{N}$ < 100 net spins) which are in thermal equilibrium and have no imposed polarization gradient. The spin transport proceeds by means of magnetic dipole interactions that induce flip-flop transitions, a mechanism that can enable highly efficient, even reversible, pure spin currents. To further study the dynamics within the spin wire, we implement a magnetic resonance protocol that improves spatial resolution and provides nanoscale spectroscopic information which confirms the observed spin transport. This spectroscopic tool opens a potential route for spatially encoding spin information in long-lived nuclear spin states. Our measurements probe intrinsic spin dynamics at the nanometre scale, providing detailed insight needed for practical devices which seek to control spin.
We complete and extend the analysis of arXiv:1903.10504 in several directions: we put the 4d theory, arising from the IIA consistent truncation of the universal sector of Calabi-Yau compactification, in a form manifestly consistent with 4d $\mathcal{N}=2$ supergravity. We go beyond the universal sector and construct the 4d effective action of IIA compactified on Calabi-Yau's with $h^{1,1}=1$, $h^{2,1}\geq1$, in the presence of background flux and fermionic condensates. For ALE gravitational instantons, we show that the putative quartic gravitino condensate is non-negative, as required for the existence of (formal) de Sitter solutions of the 4d theory. We discuss some of the issues in promoting these formal solutions to full-fledged string theory de Sitter solutions. We also extend the Nearly-K\"ahler consistent truncation of arXiv:1810.06344 to the complete bosonic sector of one vector multiplet and one hypermultiplet.
Let $\Omega \Subset \mathbb R^n$, $f \in C^1(\mathbb R^{N\times n})$ and $g\in C^1(\mathbb R^N)$, where $N,n \in \mathbb N$. We study the minimisation problem of finding $u \in W^{1,\infty}_0(\Omega;\mathbb R^N)$ that satisfies \[ \big\| f(\mathrm D u) \big\|_{L^\infty(\Omega)} \! = \inf \Big\{\big\| f(\mathrm D v) \big\|_{L^\infty(\Omega)} \! : \ v \! \in W^{1,\infty}_0(\Omega;\mathbb R^N), \, \| g(v) \|_{L^\infty(\Omega)}\! =1\Big\}, \] under natural assumptions on $f,g$. This includes the $\infty$-eigenvalue problem as a special case. Herein we prove existence of a minimiser $u_\infty$ with extra properties, derived as the limit of minimisers of approximating constrained $L^p$ problems as $p\to \infty$. A central contribution and novelty of this work is that $u_\infty$ is shown to solve a divergence PDE with measure coefficients, whose leading term is a divergence counterpart equation of the non-divergence $\infty$-Laplacian. Our results are new even in the scalar case of the $\infty$-eigenvalue problem.
It is well known that a large fraction of galaxies have cuspy luminosity profiles in their central regions, at least within the observational resolution. In such cases, the often used, simplified, local approximation for the dynamical friction braking classical term fails when the massive satellite moves through the inner parts of the galaxy, although the scattering integral still converges for phase space distribution singularities that are not too sharp. Here we present preliminary results of our work aiming at finding better and more reliable results from the integration of motion of massive objects (globular clusters) in galaxies where the density diverges to the center in a power law form, with exponent greater than -2.
The Be/X-ray transients V0332+53 and 4U 0115+63 exhibited giant, type-II outbursts in 2015. Here we present Swift/XRT follow-up observations at the end of those outbursts. Surprisingly, the sources did not decay back to their known quiescent levels but stalled at a (slowly decaying) meta-stable state with luminosities ~10 times that observed in quiescence. The spectra in these states are considerably softer than the outburst spectra and appear to soften in time when the luminosity decreases. The physical mechanism behind these meta-stable states is unclear and they could be due to low-level accretion (either directly onto the neutron stars or onto their magnetospheres) or due to cooling of the accretion-heated neutron star crusts. Based on the spectra, the slowly decreasing luminosities, and the spectral softening, we favour the crust cooling hypothesis but we cannot exclude the accretion scenarios. On top of this meta-stable state, weak accretion events were observed that occurred at periastron passage and may thus be related to regular type-I outbursts.
Thermodynamics is continuously spreading in the engineering practice, which is especially true for non-equilibrium models in continuum problems. Although there are concepts and approaches beyond the classical knowledge, which are known for decades, their mathematical properties and consequences of the generalizations are less-known and are still of high interest in current researches. Therefore, we found it essential to collect the most important and still open mathematical questions related to different continuum thermodynamic approaches. First, we start with the example of Classical Irreversible Thermodynamics (CIT) in order to provide the basis for the more general and complex frameworks, such as the Non-Equilibrium Thermodynamics with Internal Variables (NET-IV) and Rational Extended Thermodynamics (RET). Here, we aim to present that each approach has its specific problems, such as how the initial and boundary conditions can be formulated, how the coefficients in the partial differential equations are connected to each other, and how it affects the appearance of nonlinearities. We present these properties and comparing the approach of NET-IV and RET to each other from these points of view.
We study using large deviation theory the fluctuations of time-integrated functionals or observables of the unbiased random walk evolving on Erd\"os-R\'enyi random graphs, and construct a modified, biased random walk that explains how these fluctuations arise in the long-time limit. Two observables are considered: the sum of the degrees visited by the random walk and the sum of their logarithm, related to the trajectory entropy. The modified random walk is used for both quantities to explain how sudden changes in degree fluctuations, akin to dynamical phase transitions, are related to localization transitions. For the second quantity, we also establish links between the large deviations of the trajectory entropy and the maximum entropy random walk.
Thanks to the recent very high-precision photometry of red giants from satellites such as Kepler, precise mass and radius values as well as accurate information of evolutionary stages are already established by asteroseismic approach for a large number of G-K giants. Based on the high-dispersion spectra of selected such 55 red giants in the Kepler field with precisely known seismic parameters (among which parallaxes are available for 9 stars), we checked the accuracy of the determination method of stellar parameters previously applied to many red giants by Takeda et al. (2008, PASJ, 60, 781), since it may be possible to discriminate their complex evolutionary status by using the surface gravity vs. mass diagram. We confirmed that our spectroscopic gravity and the seismic gravity satisfactorily agree with each other (to within ~0.1 dex) without any systematic difference. However, the mass values of He-burning red clump giants derived from stellar evolutionary tracks (~2-3 Msun) were found to be markedly larger by ~50% compared to the seismic values (~1-2 Msun) though such discrepancy is not seen for normal giants in the H-burning phase, which reflects the difficulty of mass determination from intricately overlapping tracks on the luminosity vs. effective temperature diagram. This consequence implies that the mass results of many red giants in the clump region determined by Takeda et al. (2008) are likely to be significantly overestimated. We also compare our spectroscopically established parameters with recent literature values, and further discuss the prospect of distinguishing the evolutionary status of red giants based on the conventional (i.e., non-seismic) approach.
We discuss some aspects of the Cosmological Gene Project started at the Special Astrophysical Observatory (Russia) in 1999. The goal of the project is to measure the anisotropy and polarization of the Cosmic Microwave Background (CMB) and investigation of atmospheric fluctuations and foreground on arcmin-scales using the radio-telescope RATAN-600. We develop the cluster analysis of one-dimensional random fields for the application to the RATAN-600 scans. We analyze the specific properties of peak clusterisation in the RATAN-600 scans which to separate the primordial CMB signal from noise.
We calculate the electronic structure of germanium-tin (Ge$_{1-x}$Sn$_{x}$) binary alloys for $0 \leq x \leq 1$ using density functional theory (DFT). Relaxed alloys with semiconducting or semimetallic behaviour as a function of Sn composition $x$ are identified, and the impact of epitaxial strain is included by constraining supercell lattice constants perpendicular to the [001] growth direction to the lattice constants of Ge, zinc telluride (ZnTe), or cadmium telluride (CdTe) substrates. It is found that application of 1% tensile strain reduces the Sn composition required to bring the (positive) direct band gap to zero by approximately 5% compared to a relaxed Ge$_{1-x}$Sn$_{x}$ alloy having the same gap at $\Gamma$. On the other hand, compressive strain has comparatively less impact on the alloy band gap at $\Gamma$. Using DFT calculated alloy lattice and elastic constants, the critical thickness for Ge$_{1-x}$Sn$_{x}$ thin films as a function of $x$ and substrate lattice constant is estimated, and validated against supercell DFT calculations. The analysis correctly predicts the Sn composition range at which it becomes energetically favourable for Ge$_{1-x}$Sn$_{x}$/Ge to become amorphous. The influence of stoichiometry and strain is examined in relation to reducing the magnitude of the inverted (``negative'') $\Gamma_{7}^{-}$-$\Gamma_{8}^{+}$ band gap, which is characteristic of semimetallic alloy electronic structure. Based on our findings, strategies for engineering the semimetal-to-semiconductor transition via strain and quantum confinement in Ge$_{1-x}$Sn$_{x}$ nanostructures are proposed.
We present a new Monte Carlo method which couples Path Integral for finite temperature protons with Quantum Monte Carlo for ground state electrons, and we apply it to metallic hydrogen for pressures beyond molecular dissociation. This method fills the gap between high temperature electron-proton Path Integral and ground state Diffusion Monte Carlo methods. Our data exhibit more structure and higher melting temperatures of the proton crystal than Car-Parrinello Molecular Dynamics results using LDA. We further discuss the quantum motion of the protons and the zero temperature limit.
We investigate the clustering and dark halo properties for the narrow-line active galactic nuclei (AGN) in the SDSS, particularly examining the joint dependence on galaxy mass and color. AGN in galaxies with blue colors or massive red galaxies with M*>~10^{10.5}Msun are found to show almost identical clustering amplitudes at all scales to control galaxies of the same mass, color and structural parameters. This suggests AGN activity in blue galaxies or massive red galaxies is regulated by internal processes, with no correlation with environment. The antibias of AGN at scales between ~100kpc and a few Mpc, as found in Li et al. (2006) for the AGN as a whole, is observed only for the AGN hosted by galaxies with red colors and relatively low masses <10^{10.5}Msun. A simple halo model in which AGN are preferentially found at dark halo centers can reproduce the observational results, but requiring a mass-dependent central fraction which is a factor of ~4 higher than the fraction estimated from the SDSS group catalogue. The same group catalogue reveals that the host groups of AGN in red satellites tend to have lower halo masses than control galaxies, while the host groups of AGN in red centrals tend to form earlier, as indicated by a larger stellar mass gap between the two most massive galaxies in the groups. Our result implies that the mass assembly history of dark halos may play an additional role in the AGN activity in low-mass red galaxies.
The main result of this paper is to extend from $\Q$ to each of the nine imaginary quadratic fields of class number one a result of Serre (1987) and Mestre-Oesterl\'e (1989), namely that if $E$ is an elliptic curve of prime conductor then either $E$ or a $2$-, $3$- or $5$-isogenous curve has prime discriminant. For four of the nine fields, the theorem holds with no change, while for the remaining five fields the discriminant of a curve with prime conductor is either prime or the square of a prime. The proof is conditional in two ways: first that the curves are modular, so are associated to suitable Bianchi newforms; and second that a certain level-lowering conjecture holds for Bianchi newforms. We also classify all elliptic curves of prime power conductor and non-trivial torsion over each of the nine fields: in the case of $2$-torsion, we find that such curves either have CM or with a small finite number of exceptions arise from a family analogous to the Setzer-Neumann family over $\Q$.
Magnetic multilayers of (Ir/Co/Pt)$_6$ with interfacial Dzyaloshinskii-Moriya interaction (IDMI) were deposited by magnetron sputtering with Co thickness $d=1.8$ nm. Exploiting magneto-optical Kerr effect in longitudinal mode microscopy, magnetic force microscopy, and vibrating sample magnetometry, the magnetic field-driven evolution of domain structures and magnetization hysteresis loops have been studied. The existence of weak stripe domains structure was deduced -- tens micrometers size domains with in-plane "core" magnetization modulated by hundred of nanometers domains with out-of-plane magnetization. Micromagnetic simulations interpreted such magnetization distribution. Quantitative evaluation of IDMI was carried out using Brillouin light scattering (BLS) spectroscopy as the difference between Stokes and anti-Stokes peak frequencies $\Delta f$. Due to the additive nature of IDMI, the asymmetric combination of Ir and Pt covers led to large values of effective IDMI energy density $D_\mathrm{eff}$. It was found that Stokes and anti-Stokes frequencies as well as $\Delta f$, measured as a function of in-plane applied magnetic field, show hysteresis. These results are explained under the consideration of the influence of IDMI on the dynamics of the in-plane magnetized "core" with weak stripe domains.
When the behaviour of the singularities, which are used to represent masses, charges or currents in exact solutions to the field equations of the Hermitian theory of relativity, is restricted by a no-jump rule, conditions are obtained, which determine the relative positions of masses, charges and currents. Due to these conditions the Hermitian theory of relativity appears to provide a unified description of gravitational, colour and electromagnetic forces.
The problem of recovering a diffusion coefficient $a$ in a second-order elliptic partial differential equation from a corresponding solution $u$ for a given right-hand side $f$ is considered, with particular focus on the case where $f$ is allowed to take both positive and negative values. Identifiability of $a$ from $u$ is shown under mild smoothness requirements on $a$, $f$, and on the spatial domain $D$, assuming that either the gradient of $u$ is nonzero almost everywhere, or that $f$ as a distribution does not vanish on any open subset of $D$. Further results of this type under essentially minimal regularity conditions are obtained for the case of $D$ being an interval, including detailed information on the continuity properties of the mapping from $u$ to $a$.
The causality principle imposes the constraints on the cosmological parameters in the relativistic theory of gravitation. As a result, X-matter causes the quite definite cosmological scenario with the alternate acceleration and deceleration and the final recollapse