ShantanuT01/DACTYL-Pretraining huggingface dataset:
We employ the spin cluster perturbation theory to investigate the dynamical properties of the antiferromagnetic $J_{1}$-$J_{2}$ Heisenberg model on the honeycomb lattice. We obtain the excitation spectra for all possible phases in the phase diagram, including the N\'{e}el phase, plaquette valence-bond-solid phase, dimer valence-bond-solid phase and stripe antiferromagnetic phase. In the N\'{e}el phase, besides the obvious renormalization of the magnon dispersion, we find that the spectrum exhibits a dome-shaped broad continuum around the second Brillouin zone (BZ) and the additional strong continuum close to the corner of the BZ. In the valence-bond-solid phases, the spectra are dominated by a strong broad continuum all the way down to below $J_1$ coexisting with the lowest-energy triplon modes characterizing the plaquette and dimer phases. We ascribe this strong broad continuum and the additional continuum close to the BZ corner in the N\'{e}el phase to the contributions of fractionalized spinon excitations. In the stripe phase, a clear difference from the linear spin wave approximation is that the spectrum is gapped at the $M$ point while that obtained by the latter is gapless due to the strong quantum fluctuations. We point out that the features observed in the N\'{e}el phase are consistent with the recent neutron scattering experiments on YbCl$_{3}$ and YbBr$_{3}$.
We establish an exact asymptotic formula for the square variation of certain partial sum processes. Let $\{X_{i}\}$ be a sequence of independent, identically distributed mean zero random variables with finite variance $\sigma$ and satisfying a moment condition $\mathbb{E}[|X_{i}|^{2+\delta} ] < \infty$ for some $\delta > 0$. If we let $\mathcal{P}_{N}$ denote the set of all possible partitions of the interval $[N]$ into subintervals, then we have that $\max_{\pi \in \mathcal{P}_{N}} \sum_{I \in \pi} | \sum_{i\in I} X_{i}|^2 \sim 2 \sigma^2N \ln \ln(N)$ holds almost surely. This can be viewed as a variational strengthening of the law of the iterated logarithm and refines results of J. Qian on partial sum and empirical processes. When $\delta = 0$, we obtain a weaker `in probability' version of the result.
Gravitomagnetic equations result from applying quaternionic differential operators to the energy-momentum tensor. These equations are similar to the Maxwell's EM equations. Both sets of the equations are isomorphic after changing orientation of either the gravitomagnetic orbital force or the magnetic induction. The gravitomagnetic equations turn out to be parent equations generating the following set of equations: (a) the vorticity equation giving solutions of vortices with nonzero vortex cores and with infinite lifetime; (b) the Hamilton-Jacobi equation loaded by the quantum potential. This equation in pair with the continuity equation leads to getting the \Schrodinger equation describing a state of the superfluid quantum medium (a modern version of the old ether); (c) gravitomagnetic wave equations loaded by forces acting on the outer space. These waves obey to the Planck's law of radiation.
Starting from a realistically sheared magnetic arcade connecting chromospheric, transition region to coronal plasma, we simulate the in-situ formation and sustained growth of a quiescent prominence in the solar corona. Contrary to previous works, our model captures all phases of the prominence formation, including the loss of thermal equilibrium, its successive growth in height and width to macroscopic dimensions, and the gradual bending of the arched loops into dipped loops, as a result of the mass accumulation. Our 2.5-dimensional, fully thermodynamically and magnetohydrodynamically consistent model mimics the magnetic topology of normal-polarity prominences above a photospheric neutral line, and results in a curtain-like prominence above the neutral line through which the ultimately dipped magnetic field lines protrude at a finite angle. The formation results from concentrated heating in the chromosphere, followed by plasma evaporation and later rapid condensation in the corona due to thermal instability, as verified by linear instability criteria. Concentrated heating in the lower atmosphere evaporates plasma from below to accumulate at the top of coronal loops and supply mass to the later prominence constantly. This is the first evaporation-condensation model study where we can demonstrate how the formed prominence stays in a force balanced state, which can be compared to the Kippenhahn-Schluter type magnetohydrostatic model, all in a finite low-beta corona.
In this paper we look at the history behind Chowla's problem on the solutions to $L(1,f) = 0$ for periodic $f$. We focus on the results given by Baker, Birch and Wirsing on the topic. We briefly discuss recent results due to Chatterjee, Murty and Pathak which give a full solution when combined with the work of Baker, Birch and Wirsing.
Jahn-Teller (JT) effect both in the absence and presence of the strong Coulomb correlation is studied theoretically focusing on the reduction $\Delta K$ of the kinetic energy gain which is directly related to the spin wave stiffness. Without the Coulomb interaction, the perturbative analysis gives $\Delta K / (g^2/M\Omega^2) \cong 0.05-0.13$ depending on the electron number [$g$: electron-phonon(el-ph) coupling constant, $M$: mass of the oxygen atom,   $\Omega$: frequency of the phonon]. Although there occurs many channels of the JT el-ph interaction in the multiband system, the final results of $\Delta K$ roughly scales with the density of states at the Fermi energy. In the limit of strong electron correlation, the magnitude of the orbital polarization saturate and the relevant degrees of freedom are the direction (phase) of it. An effective action is derived for the phase variable including the effect of the JT interaction. In this limit, JT interaction is {\it{enhanced}} compared with the non-interacting case, and $\Delta K$ is given by the lattice relaxation energy $E_{L}$ for the localized electrons, although the electrons remains itinerant. Discussion on experiments are given based on these theoretical results.
Dark matter drops out of kinetic equilibrium with standard model particles when the momentum-transfer rate equals the expansion rate. In a radiation-dominated universe, this occurs at essentially the same time as dark matter kinetically decouples from the plasma. Dark matter may also fall out of kinetic equilibrium with standard model particles during an early matter-dominated era (EMDE), which occurs when the energy content of the Universe is dominated by either a decaying oscillating scalar field or a semistable massive particle before big bang nucleosynthesis. Until now, it has been assumed that kinetic decoupling during an EMDE happens similarly to the way it does in a radiation-dominated era. We show that this is not the case. By studying the evolution of the dark matter temperature, we establish a quasidecoupled state for dark matter in an EMDE, during which the dark matter temperature cools faster than the plasma temperature but slower than it would cool if the dark matter were fully decoupled. The dark matter does not fully decouple until the EMDE ends and the Universe becomes radiation dominated. We also extend the criteria for quasidecoupling to other nonstandard thermal histories and consider how quasidecoupling affects the free-streaming length of dark matter.
For a generic $f(R)$ which admits a polynomial expansion of at least third order (i.e. $\frac{d^{3}f}{dR^{3}}\neq 0$) we find the near-throat wormhole solution. Necessary conditions for the existence of wormholes in such $f(R)$ theories are derived for both zero and non-zero matter sources. A particular choice of energy-momentum reveals that the wormhole geometry satisfies the weak energy condition (WEC). For a range of parameters even the strong energy condition (SEC) is shown to be satisfied.
Quantum mechanics postulates that any measurement influences the state of the investigated system. Here, by means of angle-, spin-, and time-resolved photoemission experiments and ab initio calculations we demonstrate how non-equal depopulation of the Dirac cone (DC) states with opposite momenta in V-doped and pristine topological insulators (TIs) created by a photoexcitation by linearly polarized synchrotron radiation (SR) is followed by the hole-generated uncompensated spin accumulation and the SR-induced magnetization via the spin-torque effect. We show that the photoexcitation of the DC is asymmetric, that it varies with the photon energy, and that it practically does not change during the relaxation. We find a relation between the photoexcitation asymmetry, the generated spin accumulation and the induced spin polarization of the DC and V 3d states. Experimentally the SR-generated in-plane and out-of-plane magnetization is confirmed by the $k_{\parallel}$-shift of the DC position and by the splitting of the states at the Dirac point even above the Curie temperature. Theoretical predictions and estimations of the measurable physical quantities substantiate the experimental results.
We study the convergence of a class of Runge-Kutta type schemes for backward stochastic differential equations (BSDEs) in a Markovian framework. The schemes belonging to the class under consideration benefit from a certain stability property. As a consequence, the overall rate of the convergence of these schemes is controlled by their local truncation error. The schemes are categorized by the number of intermediate stages implemented between consecutive partition time instances. We show that the order of the schemes matches the number $p$ of intermediate stages for $p\le3$. Moreover, we show that the so-called order barrier occurs at $p=3$, that is, that it is not possible to construct schemes of order $p$ with $p$ stages, when $p>3$. The analysis is done under sufficient regularity on the final condition and on the coefficients of the BSDE.
A class of games for finding a leader among a group of candidates is studied in detail. This class covers games based on coin-tossing and rock-paper-scissors as special cases and its complexity exhibits similar stochastic behaviors: either of logarithmic mean and bounded variance or of exponential mean and exponential variance. Many applications are also discussed.
Evolved stars are among the largest and brightest stars and they are ideal targets for the new generation of sensitive, high resolution instrumentation that pro- vides spectrophotometric, interferometric, astrometric, and imaging observables. The interpretation of the complex stellar surface images requires numerical simulations of stellar convection that take into account multi-dimensional time-dependent radiation hydrodynamics with realistic input physics. We show how the evolved star simulations are obtained using the radiative hydrodynamics code CO5BOLD and how the accurate observables are computed with the post-processing radiative transfer code Optim3D. The synergy between observations and theoretical work is supported by a proper and quantitative analysis using these simulations, and by strong constraints from the obser- vational side.
We present broad band photometry and photometric redshifts for 187611 sources located in ~0.5deg^2 in the Lockman Hole area. The catalog includes 389 X-ray detected sources identified with the very deep XMM-Newton observations available for an area of 0.2 deg^2. The source detection was performed on the Rc, z' and B band images and the available photometry is spanning from the far ultraviolet to the mid infrared, reaching in the best case scenario 21 bands. Astrometry corrections and photometric cross-calibrations over the entire dataset allowed the computation of accurate photometric redshifts. Special treatment is undertaken for the X-ray sources, the majority of which is active galactic nuclei. Comparing the photometric redshifts to the available spectroscopic redshifts we achieve for normal galaxies an accuracy of \sigma_{\Delta z/(1+z)}=0.036, with 12.7% outliers, while for the X-ray detected sources the accuracy is \sigma_{\Delta z/(1+z)}=0.069, with 18.3% outliers, where the outliers are defined as sources with |z_{phot}-z_{spec}|>0.15 (1+z_{spec})}. These results are a significant improvement over the previously available photometric redshifts for normal galaxies in the Lockman Hole, while it is the first time that photometric redshifts are computed and made public for AGN for this field.
Quantum dots attached to BCS superconducting leads exhibit a $0-\pi$ impurity quantum phase transition, which can be experimentally controlled either by the gate voltage or by the superconducting phase difference. For the pertinent superconducting single-impurity Anderson model, we newly present two simple analytical formulae describing the position of the phase boundary in parameter space for the weakly correlated and Kondo regime, respectively. Furthermore, we show that the two-level approximation provides an excellent description of the low temperature physics of superconducting quantum dots near the phase transition. We discuss reliability and mutual agreement of available finite temperature numerical methods (Numerical Renormalization Group and Quantum Monte Carlo) and suggest a novel approach for efficient determination of the quantum phase boundary from measured finite temperature data. Our results enable fast and efficient, yet reliable characterization and design of such nanoscopic tunable Josephson junction devices.
Thermal fluctuations in non-equilibrium steady states generically lead to power law decay of correlations for conserved quantities. Embedded bodies which constrain fluctuations in turn experience fluctuation induced forces. We compute these forces for the simple case of parallel slabs in a driven diffusive system. The force falls off with slab separation $d$ as $k_B T/d$ (at temperature $T$, and in all spatial dimensions), but can be attractive or repulsive. Unlike the equilibrium Casimir force, the force amplitude is non-universal and explicitly depends on dynamics. The techniques introduced can be generalized to study pressure and fluctuation induced forces in a broad class of non-equilibrium systems.
In this paper, the twist-3 two parton corrections in charmless $B\to PP$ decays are shown to be factorizable under the QCD factorization approach. The factorizability of the twist-3 two parton corrections is constructed on the following findings. Under the energetic meson limit, the pseudoscalar distribution amplitude for a light pseudoscalar meson is allowed to be non-constant by the equations of motion for the quark. The non-constant pseudoscalar distribution amplitude is then used to regularize the end-point divergences in the hard spectator corrections at twist-3 order. By retaining the momentum fraction variable of the spectator quark of the $B$ meson in the propagators, the end-point divergence in the weak annihilation corrections at twist-3 order is resolved. The factorization of the $O(\alpha_s)$ corrections under the two parton approximation is shown valid up-to $O(1/m_b)$ . The hard scattering kernels of order $O(\alpha_s)$ and $O(\Lambda_{QCD}/m_b)$ are explicitly given and found to be infrared finite. The results are applied for making predictions for the branching ratios of $B\to \pi K $ decays.
Let us consider the pure quartic fields of the form $\K=\Q(\sqrt[4]{p})$ where $0<p\equiv 7\pmod{16}$ is a prime integer. We prove that the $2$-class group of $\K$ has order $2$. As a consequence of this, if the class number of $\K$ is $2$, then the Hilbert class field of $\K$ is $\H_\K=\K(\sqrt{2})$. Finally, we find a criterion to decide if an ideal of the ring of integers or $\K$ is principal or non-principal.
Recent investigations of the double red clump in the color-magnitude diagram of the Milky Way bulge cast serious doubts on the structure and formation origin of the outer bulge. Unlike previous interpretation based on an X-shaped bulge, stellar evolution models and CN-band observations have suggested that this feature is another manifestation of the multiple stellar population phenomenon observed in globular clusters (GCs). This new scenario requires a significant fraction of the outer bulge stars with chemical patterns uniquely observed in GCs. Here we show from homogeneous high-quality spectroscopic data that the red giant branch stars in the outer bulge (> 5.5 degrees from the Galactic center) are clearly divided into two groups according to Na abundance in the [Na/Fe] - [Fe/H] plane. The Na-rich stars are also enhanced in Al, while the differences in O and Mg are not observed between the two Na groups. The population ratio and the Na and Al differences between the two groups are also comparable with those observed in metal-rich GCs. The only plausible explanation for these chemical patterns and characteristics appears to be that the outer bulge was mostly assembled from disrupted proto-GCs in the early history of the Milky Way.
We report on the use of the polarized $^3$He gas filter and neutron resonant enhancement techniques for the measurement of spin-polarized diffuse neutron scattering due to ferromagnetic domains. A CoO/Co exchange biased bilayer was grown on a Ti/Cu/$Al_2O_3$ neutron resonator template. The system is cooled in an applied magnetic field of $H_a=2000$ Oe through the N\'{e}el temperature of the antiferromagnet to 10 K where the applied magnetic field is swept as to measure the magnetic hysteresis loop. After the second magnetization reversal at the coercive field $H_{c2}=+ 230$ Oe, the system is supposed to approach the original magnetic configuration. In order to prove that this is not the case for our exchange biased bilayer, we have measured four off-specular maps I++, I+-, I-+, I-- at $H_a \approx + 370$ Oe, where the Co magnetic spins were mostly reversed. They show a striking behavior in the total reflection region: while the nonspin-flip scattering exhibits no diffuse reflectivity, the spin-flip scattering shows strong diffuse scattering at incident angles which satisfy the resonance conditions. Moreover the spin-flip off-specular part of the reflectivity is asymmetric. The I-+ intensity occurs at higher exit angles than the specularly reflected neutrons, and the I+- intensity is shifted to lower angles. Their intensities are noticeably different and there is a splitting of the resonance positions for the up and down neutron spins ($\alpha_{n} ^{+} \ne \alpha_{n} ^{-}$) . Additionally, a strong influence of the stray fields from magnetic domains to the resonance splitting is observed.
Thermal properties of low-density neutron matter are investigated by determinantal quantum Monte Carlo lattice calculations on 3+1 dimensional cubic lattices. Nuclear effective field theory (EFT) is applied using the pionless single- and two-parameter neutron-neutron interactions, determined from the $^1S_0$ scattering length and effective range. The determination of the interactions and the calculations of neutron matter are carried out consistently by applying EFT power counting rules. The thermodynamic limit is taken by the method of finite-size scaling, and the continuum limit is examined in the vanishing lattice filling limit. The $^1S_0$ pairing gap at $T \approx 0$ is computed directly from the off-diagonal long-range order of the spin pair-pair correlation function, and is found to be approximately 30% smaller than BCS calculations with the conventional nucleon-nucleon potentials. The critical temperature $T_c$ of the normal-to-superfluid phase transition and the pairing temperature scale $T^\ast$ are determined, and the temperature-density phase diagram is constructed. The physics of low-density neutron matter is clearly identified as being a BCS-Bose-Einstein condensation crossover.
A mechanism explaining a strong enhancement of nonleptonic weak decays was suggested in 1975, later to be dubbed the penguin. This mechanism extends Wilson's ideas about the operator product expansion at short distances and reveals an intricate interplay of subtle features of the theory such as heavy quark masses in Glashow-Iliopoulos-Maini cancellation, light quarks shaping the chiral properties of QCD, etc. The penguins have subsequently evolved to play a role in a variety of fields in present-day particle phenomenology. I will describe the history of this idea and review its subsequent development. The recent measurement of direct CP violation in K decays gives a new confirmation of the penguin mechanism.
We have implemented the LPM effect into a microscopic transport model with partonic degrees of freedom by following the algorithm of Zapp & Wiedemann. The Landau-Pomeranchuk-Migdal (LPM) effect is a quantum interference process that modifies the emission of radiation in the presence of a dense medium. In QCD this results in a quadratic length dependence for radiative energy loss. This is an important effect for the modification of jets by their passage through the QGP.   We verify the leading parton energy loss in the model against the leading order Baier-Dokshitzer-Mueller-Peigne-Schiff-Zakharov (BDMPS-Z) result.   We apply our model to the recent observations of the modification of di-jets at the LHC.
In this paper, we construct the common eigenstates of "translation" operators $\{U_{s}\}$ and establish the generalized $Kq$ representation on integral noncommutative torus $T^{2N}$. We then study the finite rotation group $G$ in noncommutative space as a mapping in the $Kq$ representation and prove a Blocking Theorem. We finally obtain the complete set of projection operators on the integral noncommutative orbifold $T^{2N}/G$ in terms of the generalized $Kq$ representation. Since projectors are soliton solutions on noncommutative space in the limit $\alpha ^{\prime}B_{ij}\to \infty (\Theta_{ij}/\alpha ^{\prime}\to 0)$, we thus obtain all soliton solutions on that orbifold $T^{2N}/G$.
We investigate the asymptotic structure of a random perfect graph $P_n$ sampled uniformly from the perfect graphs on vertex set $\{1,\ldots,n\}$. Our approach is based on the result of Pr\"omel and Steger that almost all perfect graphs are generalised split graphs, together with a method to generate such graphs almost uniformly.   We show that the distribution of the maximum of the stability number $\alpha(P_n)$ and clique number $\omega(P_n)$ is close to a concentrated distribution $L(n)$ which plays an important role in our generation method. We also prove that the probability that $P_n$ contains any given graph $H$ as an induced subgraph is asymptotically $0$ or $\frac12$ or $1$. Further we show that almost all perfect graphs are $2$-clique-colourable, improving a result of Bacs\'o et al from 2004; they are almost all Hamiltonian; they almost all have connectivity $\kappa(P_n)$ equal to their minimum degree; they are almost all in class one (edge-colourable using $\Delta$ colours, where $\Delta$ is the maximum degree); and a sequence of independently and uniformly sampled perfect graphs of increasing size converges almost surely to the graphon $W_P(x, y) = \frac12(\mathbb{1}[x \le 1/2] + \mathbb{1}[y \le 1/2])$.
Mechanism for the single transverse spin asymmeties in the pion production, p^\uparrow + p'\to \pi(\ell_T) + X, and the \Lambda hyperon polarization, p + p' \to \Lambda^\uparrow (\ell_T)+ X, is investigated in the framework of QCD factorization theorem. We identify all the soft-gluon pole contributions coming from the twist-3 distribution and/or fragmentation functions and show that they give rise to large asymmetries at large x_F.