ShantanuT01/DACTYL-Pretraining huggingface dataset:
Neutrino oscillations constitute the first experimental confirmation of new physics, as they require a new piece that is absent in the Standard Model, non-zero neutrino masses. Questions such as how these masses are generated or why they are so small compared to other masses, are still under investigation. In this thesis, we study radiative neutrino mass models, a class of models where small neutrino masses are generated naturally, while the energy scale at which new physics appears is still low enough to be tested by current and future experiments, offering a falsifiable window to test beyond the Standard Model physics. In these models, neutrino masses are forbidden at the tree-level, but allowed at a certain order in loops. Consequently, we get masses suppressed by loop factors without requiring a large new physics scale and/or small couplings. In particular, we study the systematic classifications of the $d=7$ Majorana neutrino mass operator at one-loop order, the Weinberg operator at three-loop order and the $d=4$ Dirac neutrino mass models at the two-loop level. We then move to more specific models and mechanisms, analysing the connection between the generation of radiative neutrino masses and the stability of dark matter from a model-independent point of view, and examine a particular realisation of the type-I seesaw which relies on the radiative generation of Dirac Yukawa coupling. Finally, we analyse the phenomenology of some of the models discussed in the classifications, as well as a very particular case of neutrinoless double-$\beta$ decay where electrons are emitted with opposite chiralities along with a light scalar (Majoron).
We give an algorithm to construct a translation-invariant transport kernel between ergodic stationary random measures $\Phi$ and $\Psi$ on $\mathbb R^d$, given that they have equal intensities. As a result, this yields a construction of a shift-coupling of an ergodic stationary random measure and its Palm version. This algorithm constructs the transport kernel in a deterministic manner given realizations $\varphi$ and $\psi$ of the measures. The (non-constructive) existence of such a transport kernel was proved in [8]. Our algorithm is a generalization of the work of [3], in which a construction is provided for the Lebesgue measure and an ergodic simple point process. In the general case, we limit ourselves to what we call constrained densities and transport kernels. We give a definition of stability of constrained densities and introduce our construction algorithm inspired by the Gale-Shapley stable marriage algorithm. For stable constrained densities, we study existence, uniqueness, monotonicity w.r.t. the measures and boundedness.
Implementations of known reductions of the Strong Real Jacobian Conjecture (SRJC), to the case of an identity map plus cubic homogeneous or cubic linear terms, and to the case of gradient maps, are shown to preserve significant algebraic and geometric properties of the maps involved. That permits the separate formulation and reduction, though not so far the solution, of the SRJC for classes of nonsingular polynomial endomorphisms of real n-space that exclude the Pinchuk counterexamples to the SRJC, for instance those that induce rational function field extensions of a given fixed odd degree.
The extended Hubbard model with an attractive density-density interaction, positive pair hopping, or both, is shown to host topological phases, with a doubly degenerate entanglement spectrum and interacting edge spins. This constitutes a novel instance of topological order which emerges from interactions. When the interaction terms combine in a charge-SU(2) symmetric fashion, a novel partially polarized pseudospin phase appears, in which the topological features of the spin degrees of freedom coexist with long-range $\eta$-wave superconductivity. Thus, our system provides an example of an interplay between spontaneous symmetry breaking and symmetry-protected topological order that leads to novel and unexpected properties.
We prove the existence of recurrent initial configurations for the rotor walk on many graphs, including Z^d, and planar graphs with locally finite embeddings. We also prove that recurrence and transience of rotor walks are invariant under changes in the starting vertex and finite changes in the initial configuration.
We are interested by the rate of growth of increasing positive self-similar Markov processes (ipssMp) such that the subordinator associated to it via Lamperti's transformation has infinite mean. We prove that the logarithm of an ipssMp normalized by the logarithm of the time converges weakly, as the time tends to infinity, if and only if the Laplace exponent of the underlying subordinator is regularly varying at zero. Moreover, we prove that the regular variation at zero of the Laplace exponent is essentially nasc for the existence of a function that normalizes the logarithm of an ipssMp. We obtain a law of iterated logarithm for the liminf of the logarithm of an ipssMp and an integral test to study the upper envelope of it. Furthermore, results concerning the rate of growth of the random clock appearing in Lamperti's transformation are obtained.
We prove that a compact complex analytic variety is algebraizable if and only if its bounded derived dg-category of coherent sheaves is saturated.
We show that introducing an extended Heisenberg algebra in the context of the Weyl-Wigner-Groenewold-Moyal formalism leads to a deformed product of the classical dynamical variables that is inherited to the level of quantum field theory, and that allows us to relate the operator space noncommutativity in quantum mechanics to the quantum group inspired algebra deformation noncommutativity in field theory.
The abstract theory of critical spaces developed in [22] and [20] is applied to the Navier-Stokes equations in bounded domains with Navier boundary conditions as well as no-slip conditions. Our approach unifies, simplifies and extends existing work in the $L_p$-$L_q$ setting, considerably. As an essential step, it is shown that the strong and weak Stokes operators with Navier conditions admit an $\mathcal{H}^\infty$-calculus with $\mathcal{H}^\infty$-angle 0, and the real and complex interpolation spaces of these operators are identified.
Neutrino Deep Inelastic Scattering on nuclei is an essential process to constrain the strange quark parton distribution functions in the proton. The critical component on the way to using the neutrino DIS data in a proton PDF analysis is understanding the nuclear effects in parton distribution functions. We parametrize these effects by nuclear parton distribution functions. Here we compare results from two analysis of NPDF both done at next-to-leading order in QCD. The first uses neutral current charged-lepton lA Deeply Inelastic Scattering and Drell-Yan data for several nuclear targets and the second uses neutrino-nucleon DIS data. We compare the nuclear corrections factors F_2^Fe/F_2^D for the charged-lepton data with other results from the literature. In particular, we compare and contrast fits based upon the charged-lepton DIS data with those using neutrino-nucleon DIS data.
We show that it is both observationally allowable and theoretically possible to have large fluctuations in the dark energy equation of state as long as they occur at ultra-low redshifts z<0.02. These fluctuations would masquerade as a local transition in the Hubble rate of a few percent or less and escape even future, high precision, high redshift measurements of the expansion history and structure. Scalar field models that exhibit this behavior have a sharp feature in the potential that the field traverses within a fraction of an e-fold of the present. The equation of state parameter can become arbitrarily large if a sharp dip or bump in the potential causes the kinetic and potential energy of the field to both be large and have opposite sign. While canonical scalar field models can decrease the expansion rate at low redshift, increasing the local expansion rate requires a non-canonical kinetic term for the scalar field.
Although the spatial curvature has been precisely determined via the cosmic microwave background (CMB) observation by Planck satellite, it still suffers from the well-known cosmic curvature tension. As a standard siren, gravitational waves (GWs) from binary neutron star mergers provide a direct way to measure the luminosity distance. In addition, the accelerating expansion of the universe may cause an additional phase shift in the gravitational waveform, which allows us to measure the acceleration parameter. This measurement provides an important opportunity to determine the curvature parameter $\Omega_k$ in the GW domain based on the combination of two different observables for the same objects at high redshifts. In this study, we investigate how such an idea could be implemented with future generation of space-based DECi-hertz Interferometer Gravitational-wave Observatory (DECIGO) in the framework of two model-independent methods. Our results show that DECIGO could provide a reliable and stringent constraint on the cosmic curvature at a precision of $\Delta\Omega_k$=0.12, which is comparable to existing results based on different electromagnetic data. Our constraints are more stringent than the traditional electromagnetic method from the Pantheon SNe Ia sample, which shows no evidence for the deviation from the flat universe at $z\sim 2.3$. More importantly, with our model-independent method, such a second-generation space-based GW detector would also be able to explore the possible evolution $\Omega_k$ with redshifts, through direct measurements of cosmic curvature at different redshifts ($z\sim 5$). Such a model-independent $\Omega_k$ reconstruction to the distance past can become a milestone in gravitational-wave cosmology.
We use the SPace Infrared telescope for Cosmology and Astrophysics (SPICA) project as a template to demonstrate how deep spectrophotometric surveys covering large cosmological volumes over extended fields (1-15 square degrees) with a mid-IR imaging spectrometer (17-36 micron) in conjunction with deep 70 micron photometry with a far-IR camera, at wavelengths which are not affected by dust extinction can answer the most crucial questions in current galaxy evolution studies. A SPICA-like mission will be able for the first time to provide an unobscured three dimensional (3-D, i.e. x, y and redshift z) view of galaxy evolution back to an age of the Universe of less than ~2 Gyrs, in the mid-IR rest-frame. This survey strategy will produce a full census of the Star formation Rate (SFR) in the Universe, using Polycyclic Aromatic Hydrocarbons (PAH) bands and fine-structure ionic lines, reaching the characteristic knee of the galaxy luminosity function, where the bulk of the population is distributed, at any redshift up to z ~3.5. Deep follow-up pointed spectroscopic observations with grating spectrometers { onboard the satellite}, across the full IR spectral range (17-210 micron), would simultaneously measure Black Hole Accretion Rate (BHAR), from high-ionization fine-structure lines, and SFR, from PAH and low- to mid-ionization lines in thousands of galaxies from solar to low metallicities, down to the knee of their luminosity functions. The analysis of the resulting atlas of IR spectra will reveal the physical processes at play in evolving galaxies across cosmic time, especially its heavily dust-embedded phase during the activity peak at the cosmic noon (z ~1-3), through IR emission lines and features that are insensitive to the dust obscuration.
Partial generalizations of virtual polyhedra theory (sometimes under different names) appeared recently in the theory of torus manifolds. These generalizations look very different from the original virtual polyhedra theory. They are based on simple arguments from homotopy theory while the original theory is based on integration over Euler characteristic. In the paper we explain how these generalizations are related to the classical theory of convex bodies and to the original virtual polyhedra theory. The paper basically contains no proofs: all proofs and all details can be found in the cited literature. The paper is based on my talk dedicated to V. I. Arnold's 85-th anniversary at the International Conference on Differential Equations and Dynamical Systems 2022 (Suzdal).
We investigate two-quark correlations in hot and dense quark matter. To this end we use the light front field theory extended to finite temperature $T$ and chemical potential $\mu$. Therefore it is necessary to develop quantum statistics formulated on the light front plane. As a test case for light front quantization at finite $T$ and $\mu$ we consider the NJL model. The solution of the in-medium gap equation leads to a constituent quark mass which depends on $T$ and $\mu$. Two-quark systems are considered in the pionic and diquark channel. We compute the masses of the two-body system using a $T$-matrix approach.
A series of tensile relaxation tests is performed on isotactic polypropylene in the sub-yield and post-yield regions at room temperature. Constitutive equations are derived for the time-dependent response of a semicrystalline polymer at isothermal loading with small strains. Adjustable parameters in the stress-strain relations are found by fitting experimental data. It is demonstrated that the growth of the longitudinal strain results in an increase in the relaxation rate in a small interval of strains in the sub-yield domain. When the strain exceeds some critical value which is substantially less than the apparent yield strain, the relaxation process becomes strain-independent.
The unusual and interesting physical properties of rare earth intemetallic compounds have their origin in the combination of strongly correlated 4f states and their hybridization with the conduction electron sea, which gives rise to their complex low temperature Kondo behavior. In particular, Ce compounds are very sensitive to the crystalline and chemical environment, as compared to other rare earth systems. The interaction of the 4f state with the conduction band plays an important role in the determination of the different magnetic, structural and transport properties of these systems. Among the cerium compounds, those of the type CeX, which crystallize in the rock salt structure, exhibit extremely unusual magnetic properties. By making use of the mixed LDA-NCA calculation technique we analyse the crystal-field splittings of CeX compounds (X=N, P, As, Sb, Bi). The obtained ab-initio hybridization functions are taken as imputs to calculate the crystal-field splittings within NCA (non crossing approximation) and the tendencies are contrasted with experiments. KEY WORDS: Highly correlated systems, crystal fields, p-electron.
We present a numerical study of the order-parameter probability density function (PDF) of the square Ising model for lattices with linear sizes $L=80-140$. A recent efficient entropic sampling scheme, combining the Wang-Landau and broad histogram methods and based on the high-levels of the Wang-Landau process in dominant energy subspaces is employed. We find that for large lattices there exists a stable window of the scaled order-parameter in which the full ansatz including the pre-exponential factor for the tail regime of the universal PDF is well obeyed. This window is used to estimate the equation of state exponent and to observe the behavior of the universal constants implicit in the functional form of the universal PDF. The probability densities are used to estimate the universal Privman-Fisher coefficient and to investigate whether one could obtain reliable estimates of the universal constants controlling the asymptotic behavior of the tail regime.
We study the low-temperature behaviour of spin ice when uniaxial pressure induces a tetragonal distortion. There is a phase transition between a Coulomb liquid and a fully magnetised phase. Unusually, it combines features of discontinuous and continuous transitions: the order parameter exhibits a jump, but this is accompanied by a divergent susceptibility and vanishing domain wall tension. All these aspects can be understood as a consequence of an emergent SU(2) symmetry at the critical point. We map out a possible experimental realisation.
The prism over a graph $G$ is the cartesian product $G \Box K_2$. It is known that the property of having a Hamiltonian prism (prism-Hamiltonicity) is stronger than that of having a $2$-walk (spanning closed walk using every vertex at most twice) and weaker than that of having a Hamilton path. For a graph $G$, it is known that $\alpha(G) \leq 2 \kappa(G)$, where $\alpha(G)$ is the independence number and $\kappa(G)$ is the connectivity, imples existence of a $2$-walk in $G$, and the bound is sharp. West asked for a bound on $\alpha (G)$ in terms of $\kappa (G)$ guaranteeing prism-Hamiltonicity. In this paper we answer this question and prove that $\alpha(G) \leq 2 \kappa(G)$ implies the stronger condition, prism-Hamiltonicity of $G$.
For a $G$-variety $X$ with an open orbit, we define its boundary $\partial X$ as the complement of the open orbit. The action sheaf $S_X$ is the subsheaf of the tangent sheaf made of vector fields tangent to $\partial X$. We prove, for a large family of smooth spherical varieties, the vanishing of the cohomology groups $H^i(X,S_X)$ for $i>0$, extending results of F. Bien and M. Brion.   We apply these results to study the local rigidity of the smooth projective varieties with Picard number one classified in a previous paper of the first author.
The process of top quark pair production at the ILC with subsequent decays of one of the top quarks to a charged Higgs boson and b-quark is considered. The charged Higgs decays to tau leptons whose polarization is the opposite to those coming from W bosons. This difference is reflected in the energy distributions of the tau decay products in the top quark rest frame, which can be reconstructed at the ILC using the recoil mass technique. We present an analysis including spin correlations, backgrounds, ISR/FSR and beamstrahlung, and show that a fit of the shape of the pion energy spectrum yields the charged Higgs boson mass with an accuracy of about 1 GeV.
The metric dimension (MD) of a graph is a combinatorial notion capturing the minimum number of landmark nodes needed to distinguish every pair of nodes in the graph based on graph distance. We study how much the MD can increase if we add a single edge to the graph. The extra edge can either be selected adversarially, in which case we are interested in the largest possible value that the MD can take, or uniformly at random, in which case we are interested in the distribution of the MD. The adversarial setting has already been studied by [Eroh et. al., 2015] for general graphs, who found an example where the MD doubles on adding a single edge. By constructing a different example, we show that this increase can be as large as exponential. However, we believe that such a large increase can occur only in specially constructed graphs, and that in most interesting graph families, the MD at most doubles on adding a single edge. We prove this for $d$-dimensional grid graphs, by showing that $2d$ appropriately chosen corners and the endpoints of the extra edge can distinguish every pair of nodes, no matter where the edge is added. For the special case of $d=2$, we show that it suffices to choose the four corners as landmarks. Finally, when the extra edge is sampled uniformly at random, we conjecture that the MD of 2-dimensional grids converges in probability to $3+\mathrm{Ber}(8/27)$, and we give an almost complete proof.
A finite set $X$ in some Euclidean space $R^n$ is called Ramsey if for any $k$ there is a $d$ such that whenever $R^d$ is $k$-coloured it contains a monochromatic set congruent to $X$. This notion was introduced by Erdos, Graham, Montgomery, Rothschild, Spencer and Straus, who asked if a set is Ramsey if and only if it is spherical, meaning that it lies on the surface of a sphere. This question (made into a conjecture by Graham) has dominated subsequent work in Euclidean Ramsey theory. In this paper we introduce a new conjecture regarding which sets are Ramsey; this is the first ever `rival' conjecture to the conjecture above. Calling a finite set transitive if its symmetry group acts transitively---in other words, if all points of the set look the same---our conjecture is that the Ramsey sets are precisely the transitive sets, together with their subsets. One appealing feature of this conjecture is that it reduces (in one direction) to a purely combinatorial statement. We give this statement as well as several other related conjectures. We also prove the first non-trivial cases of the statement. Curiously, it is far from obvious that our new conjecture is genuinely different from the old. We show that they are indeed different by proving that not every spherical set embeds in a transitive set. This result may be of independent interest.
We revisit the reliability of metallicity estimates of high velocity clouds with the help of hydrodynamical simulations. We quantify the effect of accretion and viewing angle on metallicity estimates derived from absorption lines. Model parameters are chosen to provide strong lower limits on cloud contamination by ambient gas. Consistent with previous results, a cloud traveling through a stratified halo is contaminated by ambient material to the point that <10% of its mass in neutral hydrogen consists of original cloud material. Contamination progresses nearly linearly with time, and it increases from head to tail. Therefore, metallicity estimates will depend on the evolutionary state of the cloud, and on position. While metallicities change with time by more than a factor of 10, well beyond observational uncertainties, most lines-of-sight range only within those uncertainties at any given time over all positions. Metallicity estimates vary with the cloud's inclination angle within observational uncertainties. The cloud survives the infall through the halo because ambient gas continuously condenses and cools in the cloud's wake and thus appears in the neutral phase. Therefore, the cloud observed at any fixed time is not a well-defined structure across time, since material gets constantly replaced. The thermal phases of the cloud are largely determined by the ambient pressure. Internal cloud dynamics evolve from drag gradients caused by shear instabilities, to complex patterns due to ram-pressure shielding, leading to a peloton effect, in which initially lagging gas can catch up to and even overtake the head of the cloud.
Dense and cold clouds seem to populate the broad line region surrounding the central black hole in AGNs. These clouds could interact with the AGN jet base and this could have observational consequences. We want to study the gamma-ray emission produced by these jet-cloud interactions, and explore under which conditions this radiation would be detectable. We investigate the hydrodynamical properties of jet-cloud interactions and the resulting shocks, and develop a model to compute the spectral energy distribution of the emission generated by the particles accelerated in these shocks. We discuss our model in the context of radio-loud AGNs, with applications to two representative cases, the low-luminous Centaurus A, and the powerful 3C 273. Some fraction of the jet power can be channelled to gamma-rays, which would be likely dominated by synchrotron self-Compton radiation, and show typical variability timescales similar to the cloud lifetime within the jet, which is longer than several hours. Many clouds can interact with the jet simultaneously leading to fluxes significantly higher than in one interaction, but then variability will be smoothed out. Jet-cloud interactions may produce detectable gamma-rays in non-blazar AGNs, of transient nature in nearby low-luminous sources like Cen A, and steady in the case of powerful objects of FR II type.