ShantanuT01/DACTYL-Pretraining huggingface dataset:
We investigate convolution semigroups of probability measures with continuous densities on locally compact abelian groups, which have a discrete subgroup such that the factor group is compact. Two interesting examples of the quotient structure are the $d$--dimensional torus, and the ad\`{e}lic circle. Our main result is to show that the Poisson summation formula for the density can be interpreted as a probabilistic trace formula, linking values of the density on the factor group to the trace of the associated semigroup on $L^{2}$-space. The Gaussian is a very important example. For rotationally invariant $\alpha$-stable densities, the trace formula is valid, but we cannot verify the Poisson summation formula. To prepare to study semistable laws on the ad\`{e}les, we first investigate these on the $p$--adics, where we show they have continuous densities which may be represented as series expansions. We use these laws to construct a convolution semigroup on the ad\`{e}les whose densities fail to satisfy the probabilistic trace formula.
The dd -> alpha X reaction is studied in a model where each pair of nucleons in the projectile and target deuterons undergoes pion production through the NN -> d pi reaction. The condition that the two deuterons fuse to form an alpha-particle then leads to peaks at small missing masses, the well-known ABC enhancement, but also a broad structure around the maximum missing mass. With a simplified input amplitude the model gives a quantitative description of both the alpha-particle momentum and angular distributions for a deuteron beam energy of 1250 MeV.
We investigate the occurrence of exact zero modes in one-dimensional quantum magnets of finite length that possess edge states. Building on conclusions first reached in the context of the spin-1/2 XY chain in a field, then for the spin-1 $J_1-J_2$ Heisenberg model, we show that the development of incommensurate correlations in the bulk invariably leads to oscillations in the sign of the coupling between edge states, hence to exact zero energy modes at the crossing points where the coupling between the edge states rigorously vanishes. This is true regardless of the origin of the frustration (e.g. next-nearest neighbor coupling or biquadratic coupling for the spin-1 chain), of the value of the bulk spin (we report on spin-1/2, spin-1 and spin-2 examples), and of the value of the edge-state emergent spin (spin-1/2 or spin-1).
F.-H. Lin studied minimal graphs of the Dirichlet problem in the hyperbolic space and proved that any such minimal graph has the same global regularity as the boundary if the dimension of the minimal graph is even and that there is an obstacle to the higher regularity if the dimension is odd. We discuss the odd dimension case and study how the higher regularity is obstructed. We introduce the logarithm of the distance to the boundary as an additional independent self-variable and establish concise boundary regularity for the minimal graph.
A solid with larger sound speeds exhibits higher lattice thermal conductivity (k_{lat}). Diamond is a prominent instance where its mean sound speed is 14400 m s-1 and k_{lat} is 2300 W m-1 K-1. Here, we report an extreme exception that CuP2 has quite large mean sound speeds of 4155 m s-1, comparable to GaAs, but the single crystals show a very low lattice thermal conductivity of about 4 W m-1 K-1 at room temperature, one order of magnitude smaller than GaAs. To understand such a puzzling thermal transport behavior, we have thoroughly investigated the atomic structure and lattice dynamics by combining neutron scattering techniques with first-principles simulations. Cu atoms form dimers sandwiched in between the layered P atomic networks and the dimers vibrate as a rattling mode with frequency around 11 meV. This mode is manifested to be remarkably anharmonic and strongly scatters acoustic phonons to achieve the low k_{lat}. Such a dimer rattling behavior in layered structures might offer an unprecedented strategy for suppressing thermal conduction without involving atomic disorder.
Magnetic moment of the Fe2+ ion in FeBr2 has been calculated to be 4.32 mB in the magnetically-ordered state at 0 K. It is composed from the spin moment of 3.52 mB and the orbital moment of +0.80 mB. These calculations show that for the meaningful analysis of e-m properties of FeBr2 the spin-orbit coupling is essentially important and that the orbital moment is largely unquenched.
In arbitrary dimension, we consider the Einstein-Maxwell Lagrangian supplemented by the more general quadratic-curvature corrections. For this model, we derive four classes of charged Lifshitz black hole solutions for which the metric function is shown to depend on a unique integration constant. The masses of these solutions are computed using the quasilocal formalism based on the relation established between the off-shell ADT and Noether potentials. Among these four solutions, three of them are interpreted as extremal in the sense that their mass vanishes identically. For the last family of solutions, the quasilocal mass and the electric charge both are shown to depend on the integration constant. Finally, we verify that the first law of thermodynamics holds for each solution and a Smarr formula is also established for the four solutions.
We consider the asymptotic behaviour of the second-order correlation function of the characteristic polynomial of a real symmetric random matrix. Our main result is that the existing result for a random matrix from the Gaussian Orthogonal Ensemble essentially continues to hold for a general real symmetric Wigner matrix.
In this article we investigate the properties of Bernstein processes generated by infinite hierarchies of forward-backward systems of decoupled linear deterministic parabolic partial differential equations defined in Rd, where d is arbitrary. An important feature of those systems is that the elliptic part of the parabolic operators may be realized as an unbounded Schr\"odinger operator with compact resolvent in standard L2-space. The Bernstein processes we are interested in are in general non-Markovian, may be stationary or non-stationary and are generated by weighted averages of measures naturally associated with the pure point spectrum of the operator. We also introduce time-dependent trace-class operators which possess most of the attributes of density operators in Quantum Statistical Mechanics, and prove that the statistical averages of certain bounded self-adjoint observables usually evaluated by means of such operators coincide with the expectation values of suitable functions of the underlying processes. In the particular case where the given parabolic equations involve the Hamiltonian of an isotropic system of quantum harmonic oscillators, we show that one of the associated processes is identical in law with the periodic Ornstein-Uhlenbeck process.
We present Quantum Monte Carlo calculations of magnetic moments and M1 transitions in $A\le 9$ nuclei which take into account contributions of two-body electromagnetic currents. The Hamiltonian utilized to generate the nuclear wave functions includes the realistic Argonne-{\it v}$_{18}$ two-nucleon and the Illinois-7 three-nucleon interactions. The nuclear two-body electromagnetic currents are derived from a pionful chiral effective field theory including up to one-loop corrections. These currents involve unknown Low Energy Constants which have been fixed so as to reproduce a number of experimental data for the two- and three-nucleon systems, such as $np$ phase shifts and deuteron, triton, and $^3$He magnetic moments. This preliminary study shows that two-body contributions provide significant corrections which are crucial to bring the theory in agreement with the experimental data in both magnetic moments and M1 transitions.
We investigate the evolution of holographic entanglement entropy (HEE) and holographic complexity (HC) under a thermal quench in Einstein-Maxwell-Axion theory (EMA), which is dual to a field theory with momentum relaxation on the boundary. A strip-shaped boundary geometry is utilized to calculate HEE and HC via `entropy=surface' and `complexity=volume' conjecture, respectively. By fixing other parameters we claim that either large enough black hole charge or width of the strip will introduce swallow-tail behaviors in HEE and multi-values in HC due to the discontinuity of the minimum Hubeny-Rangamani-Takayanagi (HRT) surface. Meanwhile, we explore the effects of momentum relaxation on the evolution of HEE and HC. The results present that the momentum relaxation will suppress the discontinuity to occur as it increases. For large enough momentum relaxation the continuity of HEE and HC will be recovered.
For relativistic closed systems, an operator is explained which has as stationary eigenvalues the squares of the total cms energies, while the wave function has only half as many components as the corresponding Dirac wave function. The operator's time dependence is generalized to a Klein-Gordon equation. It ensures relativistic kinematics in radiative decays. The new operator is not hermitian.
We consider a model Hamiltonian describing the interaction of a single-mode radiation field with the atoms of a nonlinear medium, and study the dynamics of entanglement for specific non-entangled initial states of interest: namely, those in which the field mode is initially in a Fock state, a coherent state, or a photon-added coherent state. The counterparts of near-revivals and fractional revivals are shown to be clearly identifiable in the entropy of entanglement. The ``overlap fidelity'' of the system is another such indicator, and its behaviour corroborates that of the entropy of entanglement in the vicinity of near-revivals. The expectation values and higher moments of suitable quadrature variables are also examined, with reference to possible squeezing and higher-order squeezing.
Igusa noted that the Hasse invariant of the Legendre family of elliptic curves over a finite field of odd characteristic is a solution mod $p$ of a Gaussian hypergeometric equation. We show that any family of exponential sums over a finite field has a Hasse invariant which is a sum of products of mod $p$ solutions of $A$-hypergeometric systems.
We present an algorithm for estimating consistent dense depth maps and camera poses from a monocular video. We integrate a learning-based depth prior, in the form of a convolutional neural network trained for single-image depth estimation, with geometric optimization, to estimate a smooth camera trajectory as well as detailed and stable depth reconstruction. Our algorithm combines two complementary techniques: (1) flexible deformation-splines for low-frequency large-scale alignment and (2) geometry-aware depth filtering for high-frequency alignment of fine depth details. In contrast to prior approaches, our method does not require camera poses as input and achieves robust reconstruction for challenging hand-held cell phone captures containing a significant amount of noise, shake, motion blur, and rolling shutter deformations. Our method quantitatively outperforms state-of-the-arts on the Sintel benchmark for both depth and pose estimations and attains favorable qualitative results across diverse wild datasets.
By restricting the motion of high-mobility 2D electron gas to a network of channels with smooth confinement, we were able to trace, both classically and quantum-mechanically, the interplay of backscattering, and of the bending action of a weak magnetic field. Backscattering limits the mobility, while bending initiates quantization of the Hall conductivity. We demonstrate that, in restricted geometry, electron motion reduces to two Chalker-Coddington networks, with opposite directions of propagation along the links, which are weakly coupled by disorder. Interplay of backscattering and bending results in the quantum Hall transition in a non-quantizing magnetic field, which decreases with increasing mobility. This is in accord with scenario of floating up delocalized states.
We analyze the lepton sector of a Left-Right Model based on the gauge group SU(2)_L x SU(2)_R x U(1), concentrating mainly on neutrino properties. Using the seesaw mechanism and a horizontal symmetry, we keep the right-handed symmetry breaking scale relatively low, while simultaneously satisfying phenomenological constraints on the light neutrino masses. We take the right-handed scale to be of order 10's of TeV and perform a full numerical analysis of the model's parameter space, subject to experimental constraints on neutrino masses and mixings. The numerical procedure yields results for the right-handed neutrino masses and mixings and the various CP-violating phases. We also discuss phenomenological applications of the model to neutrinoless double beta decay, lepton-flavor-violating decays (including decays such as \tau \to 3\mu) and leptogenesis.
In these lectures we give a concise introduction to the ideas of renormalon calculus in QED and QCD. We focus in particular on the example of the Adler D function of vacuum polarization, and on relations between perturbative renormalon ambiguities and corresponding non-perturbative Operator Product Expansion (OPE) ambiguities. Recent work on infrared freezing of Euclidean observables is also discussed.
We study real elliptic surfaces and trigonal curves (over a base of an arbitrary genus) and their equivariant deformations. We calculate the real Tate-Shafarevich group and reduce the deformation classification to the combinatorics of a real version of Grothendieck's {\it dessins d'enfants}. As a consequence, we obtain an explicit description of the deformation classes of $M$- and $(M-1)$- (i.e., maximal and submaximal in the sense of the Smith inequality) curves and surfaces.
In this paper, by explicitly calculating the principal symbols of pseudodifferential operators and by applying H\"omander's spectral function theorem, we obtain the Weyl-type asymptotic formulas with sharp remainder estimates for the counting functions of the two classes of biharmonic Steklov eigenvalues $\lambda_k$ and $\mu_k$ in a smooth bounded domain of a Riemannian manifold. This solves a longstanding challenging problem.
A glitch of a pulsar is known as a sudden increase in the spin frequency and spin-down rate (frequency time derivative), and it can be caused by a sudden rel\ ease of the stress built up in the solid crust of the star or pinned vortices in the superfluid interior. PSR J2021+4026 is the first pulsar that shows a significant change in the gamma-ray flux and pulse profile at the glitch that occurred around 2011 October 16. We report the results of timing and spectral analysis of PSR~J2021+4026 using $\sim$ 8~yr Fermi-LAT data. We find that the pulsar stayed at a high spin-down rate ($\sim 4\%$ higher than the pre-glitch value) and a low gamma-ray state ($\sim 18\%$ lower) for about 3~yr after the glitch. Around 2014 December, the spin-down rate and gamma-ray flux gradually returned to pre-glitch values within a time scale of a few months. The phase-resolved spectra and pulse profiles after the relaxation are also consistent with those before the glitch. The observed long-term evolution of the spin-down rate and the gamma-ray flux indicates that the glitch triggered a mode change in the global magnetosphere. We speculate that the glitch changed the local magnetic field structure around the polar cap and/or the inclination angle of the dipole axis, leading to a change in the electric current circulating in the magnetosphere.
In this study, we have used a Zr-Nb alloy containing well-defined nano-precipitates as a model material in which to study imaging contrast inversions (atomic number or diffraction contrast) observed with the forescattered electron imaging system, ARGUSTM, in a scanning electron microscope (SEM) when imaging a thin foil in a transmission geometry. The study is based on Monte Carlo simulations and analysis of micrographs experimentally acquired under different imaging conditions. Based on the results, imaging conditions that enhance atomic number or diffraction contrast have been proposed. Data acquired from the ARGUSTM imaging system in SEM has also been compared with results from standard transmission electron microscopy and scanning transmission electron microscopy imaging of the same material. These results demonstrate the capability of the ARGUSTM system to investigate microstructures in nano-scale materials.
We consider pseudogap effects for electrons interacting with gapless modes. We study both generic 1D semiconductors with acoustic phonons and incommensurate charge density waves. We calculate the subgap absorption as it can be observed by means of the photo electron or tunneling spectroscopy. Within the formalism of functional integration and the adiabatic approximation, the probabilities are described by nonlinear configurations of an instanton type. Particularities of both cases are determined by the topological nature of stationary excited states (acoustic polarons or amplitude solitons) and by presence of gapless phonons which change the usual dynamics to the regime of the quantum dissipation. Below the free particle edge the pseudogap starts with the exponential (stretched exponential for gapful phonons) decrease of transition rates. Deeply within the pseudogap they are dominated by a power law, in contrast with nearly exponential law for gapful modes.
In this work we explore the sensitivity to the Higgs self-coupling $\lambda$ in the production of two Higgs bosons via vector boson scattering at the LHC. Although these production channels, concretely $W^+W^- \to HH$ and $ ZZ \to HH$, have lower rates than gluon-gluon fusion, they benefit from being tree level processes, being independent of top physics and having very distinctive kinematics that allow to obtain very clean experimental signatures. This makes them competitive channels concerning the sensitivity to the Higgs self-coupling. In order to give predictions for the sensitivity to this coupling, we first study the role of $\lambda$ at the subprocess level, both in and beyond the Standard Model, to move afterwards to the LHC scenario. We characterize the $pp\to HHjj$ case first and then provide quantitative results for the values of $\lambda$ that can be probed at the LHC in vector boson scattering processes after considering the Higgs boson decays. We focus mainly in $pp\to b\bar{b}b\bar{b}jj$, since it has the largest signal rates, and also comment on the potential of other channels, such as $pp\to b\bar{b}\gamma\gamma jj$, as they lead to cleaner, although smaller, signals. Our whole study is performed for a center of mass energy of $\sqrt{s}=14$ TeV and for various future expected LHC luminosities.
We study electron transport through single-electron spin-valve transistors in the presence of non-local exchange between the ferromagnetic leads and the central normal-metal island. The Coulomb interaction is described with the orthodox model for Coulomb blockade and we allow for noncollinear lead magnetization directions. Two distinct exchange mechanisms that have been discussed in the literature are shown to be of comparable strength and are taken into account on equal footing. We present results for the linear conductance as a function of gate voltage and magnetic configuration, and discuss the response of the system to applied magnetic fields.
Using Papadodimas and Raju construction of operators describing the interior of a black hole, we present a general relation between partition functions of operators describing inside and outside the black hole horizon. In particular for an eternal black hole the partition function of the interior modes may be given in terms those partition functions associated with the modes of left and right exteriors. By making use of this relation we observe that setting a finite UV cutoff will enforce us to have a cutoff behind the horizon whose value is fixed by the UV cutoff. The resultant cutoff is in agreement with what obtained in the context of holographic complexity.
Blazars from the first-three-months Fermi-AGN list were observed with the Urumqi 25m radio telescope at 5GHz in IDV (Intra-Day Variability) mode and inter-month observation mode. A significant correlation between the flux density at 5GHz and the gamma-ray intensity for the Fermi-LAT detected blazars is seen. There is a higher IDV detection rate in Fermi detected blazars than those reported for other samples. Stronger variability appears at lower Galactic latitudes; IDV appears to be stronger in weaker sources, indicating that the variability is affected by interstellar scintillation.
Two-time physics (2T) is a general reformulation of one-time physics (1T) that displays previously unnoticed hidden symmetries in 1T dynamical systems and establishes previously unknown duality type relations among them. This may play a role in displaying the symmetries and constructing the dynamics of little understood systems, such as M-theory. 2T physics describes various 1T dynamical systems as different d-dimensional ``holographic'' views of the same 2T system in $d+2$ dimensions. The ``holography'' is due to gauge symmetries that tend to reduce the number of effective dimensions. Different 1T evolutions (i.e. different Hamiltonians) emerge from the same 2T theory when gauge fixing is done with different embeddings of d dimensions inside d+2 dimensions. Thus, in the 2T setting, the distinguished 1T which we call ``time'' is a gauge dependent concept. The 2T action has also a global SO(d,2) symmetry in flat spacetime, or a more general d+2 symmetry in curved spacetime, under which all dimensions are on an equal footing. This symmetry is observable in many 1T systems, but it remained unknown until discovered in the 2T formalism. 2T physics has mainly been developed in the context of particles, including spin and supersymmetry, but some advances have also been made with strings and p-branes, and insights for M-theory have already emerged. In the case of particles, there exists a general worldline formulation with background fields, as well as a field theory formulation, both described in terms of fields that depend on d+2 coordinates. The Standard Model of particle physics can be regarded as a gauge fixed form of a 2T theory in 4+2 dimensions. These facts already provide evidence for a new type of higher dimensional unification.
We study the dynamics of inhomogeneous scalar and pseudoscalar chiral order parameters within the framework of the time-dependent Ginzburg-Landau equations. We utilize a nonlocal chiral quark model to obtain the phase diagram of the model as function of temperature and baryon chemical potential and study the formation of metastable spatial domains of matter where the order parameters acquire a spatial modulation in the course their dynamical evolution. We found that, before reaching the expected equilibrium homogeneous state, both scalar and pseudoscalar chiral condensates go through long-lived metastable inhomogeneous structures. For different initial configurations of the order parameters, the lifetimes of the inhomogeneous structures are compared to timescales in a relativistic heavy-ion collision.
A higher dimensional modified gravity theory with an action that includes dimensionally continued Euler-Poincar\'e forms up to second order in curvatures is considered. The variational field equations are derived. Matter in the universe at large scales is modeled by a fluid satisfying an equation of state with dimensional dichotomy. We study solutions that describe higher dimensional steady state cosmologies with constant volume for which the three dimensional external space is expanding at an accelerated rate while the (compact) internal space is contracting. We showed that the second order Euler-Poincar\'e term in the constructions of higher dimensional steady state cosmologies could be crucial.