ShantanuT01/DACTYL-Pretraining huggingface dataset:
We calculate the photonic band gap of triply periodic bicontinuous cubic structures and of tubular structures constructed from the skeletal graphs of triply periodic minimal surfaces. The effect of the symmetry and topology of the periodic dielectric structures on the existence and the characteristics of the gaps is discussed. We find that the C(I2-Y**) structure with Ia3d symmetry, a symmetry which is often seen in experimentally realized bicontinuous structures, has a photonic band gap with interesting characteristics. For a dielectric contrast of 11.9 the largest gap is approximately 20% for a volume fraction of the high dielectric material of 25%. The midgap frequency is a factor of 1.5 higher than the one for the (tubular) D and G structures.
The degree/diameter problem for mixed graphs asks for the largest possible order of a mixed graph with given diameter and degree parameters. Similarly the \emph{degree/geodecity} problem concerns the smallest order of a $k$-geodetic mixed graph with given minimum undirected and directed degrees; this is a generalisation of the classical degree/girth problem. In this paper we present new bounds on the order of mixed graphs with given diameter or geodetic girth and exhibit new examples of directed and mixed geodetic cages. In particular, we show that any $k$-geodetic mixed graph with excess one must have geodetic girth two and be totally regular, thereby proving an earlier conjecture of the authors.
We propose a parametrization of anomalous Higgs-boson couplings that is both systematic and practical. It is based on the electroweak chiral Lagrangian, including a light Higgs boson, as the effective field theory (EFT) at the electroweak scale $v$. This is the appropriate framework for the case of sizeable deviations in the Higgs couplings of order $10\%$ from the Standard Model, considered to be parametrically larger than new-physics effects in the sector of electroweak gauge interactions. The role of power counting in identifying the relevant parameters is emphasized. The three relevant scales, $v$, the scale of new Higgs dynamics $f$, and the cut-off $\Lambda=4\pi f$, admit expansions in $\xi=v^2/f^2$ and $f^2/\Lambda^2$. The former corresponds to an organization of operators by their canonical dimension, the latter by their loop order or chiral dimension. In full generality the EFT is thus organized as a double expansion. However, as long as $\xi\gg 1/16\pi^2$ the EFT systematics is closer to the chiral counting. The leading effects in the consistent approximation provided by the EFT, relevant for the presently most important processes of Higgs production and decay, are given by a few (typically six) couplings. These parameters allow us to describe the properties of the Higgs boson in a general and systematic way, and with a precision adequate for the measurements to be performed at the LHC. The framework can be systematically extended to include loop corrections and higher-order terms in the EFT.
In this article, we prove the existence of at least three positive solutions for the following nonlocal singular problem \begin{equation*} (P_\la)\left\{ \begin{split} (-\De)^su &= \la\frac{f(u)}{u^q}, \; \; u>0 \;\; \text{in}\;\; \Om,\\ u &= 0\;\; \text{in}\;\; \mb R^n \setminus \Om \end{split} \right. \end{equation*} where $(-\De)^s$ denotes the fractional Laplace operator for $s\in (0,1)$, $n>2s$, $q \in (0,1)$, $\la>0$ and $\Om$ is smooth bounded domain in $\mb R^n$. Here $f :[0,\infty) \to [0,\infty)$ is a continuous nondecreasing map satisfying $\lim\limits_{u\to \infty}\frac{f(u)}{u^{q+1}}=0$. We show that under certain additional assumptions on $f$, $(P_\la)$ possesses at least three distinct solutions for a certain range of $\la$. We use the method of sub-supersolutions and a critical point theorem by Amann \cite{amann} to prove our results. Moreover, we prove a new existence result for a suitable infinite semipositone nonlocal problem which played a crucial role to obtain our main result and is of independent interest. \medskip
We formulate and prove a version of the arithmetic Siegel-Weil formula for (zero dimensional) Shimura varieties attached to tori, equipped with some additional data. More precisely, we define a family of ``special" divisors in terms of Green functions at archimedean and non-archimedean places, and prove that their degrees coincide with the Fourier coefficients of the central derivative of an Eisenstein series. The proof relies on the usual Siegel-Weil formula to provide a direct link between both sides of the identity, and in some sense, offers a more conceptual point of view on prior results in the literature.
The spin Hall effect (SHE) is an important spintronics phenomenon, which allows transforming a charge current into a spin current and vice versa without the use of magnetic materials or magnetic fields. To gain new insight into the physics of the SHE and to identify materials with a substantial spin Hall conductivities (SHC), we performed high-precision, high-throughput ab initio electronic structure calculations of the intrinsic SHC for over 20,000 non-magnetic crystals. The calculations reveal a strong and unexpected relation of the magnitude of the SHC with the crystalline symmetry, which we show exists because large SHC is typically associated with mirror symmetry protected nodal lines in the band structure. From the new developed database, we identify new promising materials. This includes eleven materials with a SHC comparable or even larger than that the up to now record Pt as well as materials with different types of spin currents, which could allow for new types of spin-obitronics devices.
The production of two weak bosons at the Large Hadron Collider will be one of the most important sources of SM backgrounds for final states with multiple leptons. In this paper we consider several quantities that can help normalize the production of weak boson pairs. Ratios of inclusive cross-sections for production of two weak bosons and Drell-Yan are investigated and the corresponding theoretical errors are evaluated. The possibility of predicting the jet veto survival probability of VV production from Drell-Yan data is also considered. Overall, the theoretical errors on all quantities remain less than 5-20%. The dependence of these quantities on the center of mass energy of the proton-proton collision is also studied.
After a short introduction to the generalized uncertainty principle (GUP), we discuss heuristic derivations of the Casimir effect, first from the usual Heisenberg uncertainty principle (HUP), and then from GUP. Results are compared with those obtained from more standard calculations in Quantum Field Theory (QFT).
We consider stimulated Raman adiabatic passage (STIRAP) processes in tripod systems and show how to generate purely geometric phase changes of the quantum states involved. The geometric phases are controlled by three laser fields where pulse shapes, relative field strength and phases can be controlled. We present a robust set of universal gates for quantum computing based on these geometric phases: a one-qubit phase gate, a Hadamard gate and a two-qubit phase gate.
These are the lecture notes based on earlier papers with some additional new results. New and simple proofs are given for local freeness theorem and the semipositivity theorem. A decomposition theorem for higher direct images of dualizing sheaves of Koll\'ar is extended to the sheaves of differential forms of arbitrary degrees in the case of a well prepared birational model. We will also prove the log versions of some of the results, i.e., the case where we allow horizontal boundary components.
This paper studies the invertibility property of continuous time moving average processes driven by a L\'evy process. We provide of sufficient conditions for the recovery of the driving noise. Our assumptions are specified via the kernel involved and the characteristic triplet of the background driving L\'evy process.
In this paper we show weak convergence of the empirical eigenvalue distribution and of the weighted spectral measure of the Jacobi ensemble, when one or both parameters grow faster than the dimension $n$. In these cases the limit measure is given by the Marchenko-Pastur law and the semicircle law, respectively. For the weighted spectral measure we also prove large deviation principles under this scaling, where the rate functions are those of the other classical ensembles.
The solution for the radial distribution of pressure, density, temperature and flow velocity fields in a blast wave propagating through a medium at rest, following an intense explosion, starting from hydrodynamic equations, is one of the classic problems in gas dynamics. However, there is very little direct verification of the theory and its assumptions from simulations of microscopic models. In this paper, we compare the results and assumptions of the hydrodynamic theory with results from large scale event driven molecular dynamics simulations of a hard sphere gas in three dimensions. We find that the predictions for the radial distribution of the thermodynamic quantities do not match well with the numerical data. We improve the theory by replacing the ideal gas law with a more realistic virial equation of state for the hard sphere gas. While this improves the theoretical predictions, we show that they still fail to describe the data well. To understand the reasons for this discrepancy, the different assumptions of the hydrodynamic theory are tested within the simulations. A key assumption of the theory is the existence of a local equation of state. We validate this assumption by showing that the local pressure, temperature and density obey the equation of state for a hard sphere gas. However, the probability distribution of the velocity fluctuations has non-gaussian tails, especially away from the shock front, showing that the assumption of local equilibrium is violated. This, along with neglect of heat conduction, could be the possible reasons for the mismatch between theory and simulations.
We study global in time existence versus blow-up in finite time of solutions to the Cauchy problem for the porous medium equation with a variable density $\rho(x)$ and a power-like reaction term posed in the one dimensional interval $(-R,R)$, $R>0$. Here the weight function is singular at the boundary of the domain $(-R,R)$, indeed it is such that $\rho(x)\sim (R-|x|)^{-q}$ as $|x|\to R$, with $q\ge0$. We show a different behavior of solutions depending on the three cases when $q>2$, $q=2$ and $q<2$.
In this paper we study the influence of the Hardy potential in the fractional heat equation. In particular, we consider the problem $$(P_\theta)\quad \left\{ \begin{array}{rcl} u_t+(-\Delta)^{s} u&=&\l\dfrac{\,u}{|x|^{2s}}+\theta u^p+ c f\mbox{ in } \Omega\times (0,T),\\ u(x,t)&>&0\inn \Omega\times (0,T),\\ u(x,t)&=&0\inn (\ren\setminus\Omega)\times[ 0,T),\\ u(x,0)&=&u_0(x) \mbox{ if }x\in\O, \end{array} \right. $$ where $N> 2s$, $0<s<1$, $(-\Delta)^s$ is the fractional Laplacian of order $2s$, $p>1$, $c,\l>0$, $u_0\ge 0$, $f\ge 0$ are in a suitable class of functions and $\theta=\{0,1\}$. Notice that $(P_0)$ is a linear problem, while $(P_1)$ is a semilinear problem.   The main features in the article are: \begin{enumerate} \item Optimal results about \emph{existence} and \emph{instantaneous and complete blow up} in the linear problem $(P_0)$, where the best constant $\Lambda_{N,s}$ in the fractional Hardy inequality provides the threshold between existence and nonexistence. Similar results in the local heat equation were obtained by Baras and Goldstein in \cite{BaGo}. However, in the fractional setting the arguments are much more involved and they require the proof of a weak Harnack inequality for a weighted operator that appear in a natural way. Once this Harnack inequality is obtained, the optimal results follow as a simpler consequence than in the classical case. \item The existence of a critical power $p_+(s,\lambda)$ in the semilinear problem $(P_1)$ such that: \begin{enumerate} \item If $p> p_+(s,\lambda)$, the problem has no weak positive supersolutions and a phenomenon of \emph{complete and instantaneous blow up} happens. \item If $p< p_+(s,\lambda)$, there exists a positive solution for a suitable class of nonnegative data. \end{enumerate} \end{enumerate}
The dual concepts of coverings and packings are well studied in graph theory. Coverings of graphs with balls of radius one and packings of vertices with pairwise distances at least two are the well-known concepts of domination and independence, respectively. In 2001, Erwin introduced \emph{broadcast domination} in graphs, a covering problem using balls of various radii, where the cost of a ball is its radius. The minimum cost of a dominating broadcast in a graph $G$ is denoted by $\gamma_b(G)$. The dual (in the sense of linear programming) of broadcast domination is \emph{multipacking}: a multipacking is a set $P \subseteq V(G)$ such that for any vertex $v$ and any positive integer $r$, the ball of radius $r$ around $v$ contains at most $r$ vertices of $P$. The maximum size of a multipacking in a graph $G$ is denoted by $mp(G)$. Naturally, $mp(G) \leq \gamma_b(G)$. Hartnell and Mynhardt proved that $\gamma_b(G) \leq 3 mp(G) - 2$ (whenever $mp(G)\geq 2$). In this paper, we show that $\gamma_b(G) \leq 2mp(G) + 3$. Moreover, we conjecture that this can be improved to $\gamma_b(G) \leq 2mp(G)$ (which would be sharp).
We study ground-state properties and the low-lying excitations of Heisenberg spin ladders composed of two ferrimagnetic chains with alternating site spins $(S_1>S_2)$ by using the bosonic Dyson-Maleev formalism and Lanczos numerical techniques. The emphasis is on properties of the ferrimagnetic phase which is stable for antiferromagnetic interchain couplings $J_{\perp}\geq 0$. There are two basic implications of the underlying lattice structure: (i) the spin-wave excitations form folded acoustic and optical branches in the extended Brillouin zone and (ii) the ground state parameters (such as the on-site magnetizations and spin-stiffness constant) show a crossover behavior in the weak-coupling region $0<J_{\perp}<1$. The above peculiarities of the ladder ferrimagnetic state are studied up to second order in the quasiparticle interaction and by a numerical diagonalization of ladders containing up to N=12 rungs. The presented results for the ground-state parameters and the excitation spectrum can be used in studies on the low-temperature thermodynamics of ferrimagnetic ladders.
The relative acceleration between two nearby particles moving along accelerated trajectories is studied, which generalizes the geodesic deviation equation. The polarization content of the gravitational wave in Horndeski theory is investigated by examining the relative acceleration between two self-gravitating particles. It is found out that the longitudinal polarization exists no matter whether the scalar field is massive or not. It would be still very difficult to detect the enhanced longitudinal polarization with the interferometer, as the violation of the strong equivalence principle of mirrors used by interferometers is extremely small. However, the pulsar timing array is promised to relatively easily detect the effect of the violation as neutron stars have large self-energy. The advantage of using this method to test the violation of the strong equivalence principle is that neutron stars are not required to be present in the binary systems.
The quantum entanglement is an important feature of many protocols in the field of quantum computing. In this paper we evaluate a level of entanglement in short qutrit chains. This evaluation is carried out with use of the CCNR criterion and the concurrence measure. We also present some explicit formulae describing the values of CCNR criterion and concurrence for exemplary short spin chains. Utilizing the obtained results, we indicate that analyzing the level of entanglement allows to detect the noise or deviation in the transfer process, in comparison to the perfect transfer where only operation realizing transfer is present.
In this paper we deal with Drinfeld modular forms, defined and taking values in complete fields of positive characteristic. Our aim is to study a sequence of families of Drinfeld modular forms depending on a parameter t that produces, for certain values of t, several kinds of Eisenstein series considered by Gekeler. We obtain formulas involving these functions. To obtain our results, we introduce and discuss tau-linear recurrent sequences and deformations of vectorial modular forms in this setting.
Most nuclear physics ranges from insensitive to relatively insensitive to many-nucleon forces. The dominant ingredient in calculations of nuclear properties is the nucleon-nucleon potential. Three-nucleon forces nevertheless play an important role in nuclear physics because of the great precision of modern calculational methods for systems of relatively few nucleons. We explore the reasons why many-body forces are weak in nuclei by using a classification scheme for such forces that is based on dimensional power counting, which is used to organize chiral perturbation theory. An assessment will be made of how close we are to a ``standard'' three-nucleon force. Recent advances in determining the significance of three-nucleon forces will also be discussed.
For a black hole of Schwarzschild radius $a$, we argue that the back-reaction of the vacuum energy-momentum tensor is in general important at the apparent horizon when the time scale of a process is larger than order $a$. In particular, in a double-shell model, we show that the ignorance of the back-reaction leads to a divergence in the outgoing vacuum energy flux. The main result of this paper is that, once the back-reaction is included, the vacuum energy density for observers on top of the trapping horizon in vacuum is given by ${\cal E} \simeq -1/2\ell_p^2 a^2$, which is of the same order of magnitude as the classical matter but opposite in sign. Remarkably, this formula is independent of both the details about the collapsing matter and the vacuum energy-momentum tensor.
We describe an algebraic approach to the time-dependent noncommutative geometry of a six-dimensional Cahen-Wallach pp-wave string background supported by a constant Neveu-Schwarz flux, and develop a general formalism to construct and analyse quantum field theories defined thereon. Various star-products are derived in closed explicit form and the Hopf algebra of twisted isometries of the plane wave is constructed. Scalar field theories are defined using explicit forms of derivative operators, traces and noncommutative frame fields for the geometry, and various physical features are described. Noncommutative worldvolume field theories of D-branes in the pp-wave background are also constructed.
The FUV continuum spectrum of many accreting pre-main sequence stars, Classical T Tauri Stars (CTTSs), does not continue smoothly from the well-studied Balmer continuum emission in the NUV, suggesting that additional processes contribute to the short-wavelength emission in these objects. The most notable spectral feature in the FUV continuum of some CTTSs is a broad emission approximately centered at 1600~\AA, which has been referred to as the "1600 A Bump". The origin of this feature remains unclear. We have assembled archival FUV spectra of 37 disk-hosting systems observed by the {\it Hubble Space Telescope}. Clear 1600 A Bump emission is observed above the smooth, underlying 1100-1800 A continuum spectrum in 19/37 Classical T Tauri disks in the HST sample, with the detection rate in transition disks (8/8) being much higher than in primordial or non-transition sources (11/29). We describe a spectral deconvolution analysis to separate the Bump (spanning 1490~--~1690 A) from the underlying FUV continuum, finding an average Bump luminosity, $L$(Bump7 x 10^{29} erg s^{-1}. We find that the 1600 A Bump is characterized by a peak wavelength of 1598.6 +/- 3.3 A.   Contrary to previous studies, we find that this feature is inconsistent with models of H2 excited by electron-impact. We show that this Bump emits roughly 10-80% of the total fluorescent H2 luminosity for stars with well-defined Bump features. Energetically, this suggests that the carrier of the 1600 A Bump emission is powered by Ly-a photons. We argue that the most likely mechanism is Ly-a-driven dissociation of H2O in the inner disk, r < 2 AU. We demonstrate that non-thermally populated H2O fragments can qualitatively account for the observed emission (discrete and continuum), and find that the average Ly-a-driven H2O dissociation rate is 1.7x 10^{42} water molecules s^{-1}.
This work is motivated by a paper of Davenport and Schmidt, which treats the question of when Dirichlet's theorems on the rational approximation of one or of two irrationals can be improved and if so, by how much. We consider a generalization of this question in the simplest case of a single irrational but in the context of the geometry of numbers in $\mathbb R^2$, with the sup-norm replaced by a more general one. Results include sharp bounds for how much improvement is possible under various conditions. The proofs use semi-regular continued fractions that are characterized by a certain best approximation property determined by the norm.
The present article aims to provide a brief account of the theories of Drinfeld modules and Anderson's $t$-modules and $t$-motives. As such the article is not meant to be comprehensive, but we have endeavored to summarize aspects of the theory that are of current interest and to include a number of examples.
We investigate the ground state and finite-temperature properties of the spin-1/2 Heisenberg antiferromagnet on an infinite octa-kagome lattice by utilizing state-of-the-art tensor network-based numerical methods. It is shown that the ground state has a vanishing local magnetization and possesses a $1/2$-magnetization plateau with up-down-up-up spin configuration. A quantum phase transition at the critical coupling ratio $J_{d}/J_{t}=0.6$ is found. When $0<J_{d}/J_{t}<0.6$, the system is in a valence bond state, where an obvious zero-magnetization plateau is observed, implying a gapful spin excitation; when $J_{d}/J_{t}>0.6$, the system exhibits a gapless excitation, in which the dimer-dimer correlation is found decaying in a power law, while the spin-spin and chiral-chiral correlation functions decay exponentially. At the isotropic point ($J_{d}/J_{t}=1$), we unveil that at low temperature ($T$) the specific heat depends linearly on $T$, and the susceptibility tends to a constant for $T\rightarrow 0$, giving rise to a Wilson ratio around unity, implying that the system under interest is a fermionic algebraic quantum spin liquid.
Computational searches for stable and metastable structures of water ice and other H:O compositions at TPa pressures have led us to predict that H$_2$O decomposes into H$_2$O$_2$ and a hydrogen-rich phase at pressures of a little over 5 TPa. The hydrogen-rich phase is stable over a wide range of hydrogen contents, and it might play a role in the erosion of the icy component of the cores of gas giants as H$_2$O comes into contact with hydrogen. Metallization of H$_2$O is predicted at a higher pressure of just over 6 TPa, and therefore H$_2$O does not have a thermodynamically stable low-temperature metallic form. We have also found a new and rich mineralogy of complicated water ice phases which are more stable in the pressure range 0.8--2 TPa than any predicted previously.
Under mild hypotheses on the residual representation, we prove the Equivariant Tamagawa Number Conjecture for modular motives with coefficients in universal deformation rings and Hecke algebras using a novel combination of the methods of Euler systems and Taylor-Wiles systems. We also prove the compatibility of this conjecture with specialization.
We explain the current excess seen at the Large Hadron Collider via the $gg\to H\to\gamma\gamma$ channel in the search for a neutral Higgs boson in terms of both singly (marginally) and doubly (predominantly) charged Higgs bosons predicted by the Higgs Triplet Model.