ShantanuT01/DACTYL-Pretraining huggingface dataset:
For a quantum theory that includes exponentially decaying states and Breit-Wigner resonances, which are related to each other by the lifetime-width relation $\tau=\frac{\hbar}{\Gamma}$, where $\tau$ is the lifetime of the decaying state and $\Gamma$ the width of the resonance, one has to go beyond the Hilbert space and beyond the Schwartz-Rigged Hilbert Space $\Phi\subset\mathcal{H}\subset\Phi^\times$ of the Dirac formalism. One has to distinguish between prepared states, using a space $\Phi_-\subset\mat hcal{H}$, and detected observables, using a space $\Phi_+\subset\mathcal{H}$, where $-(+)$ refers to analyticity of the energy wave function in the lower (upper) complex energy semiplane.   This differentiation is also justified by causality: A state needs to be prepared first, before an observable can be measured in it. The axiom that will lead to the lifetime-width relation is that $\Phi_+$ and $\Phi_-$ are Hardy spaces of the upper and lower semiplane, respectively. Applying this axiom to the relativistic case for the variable $\s=p_\mu p^\mu$ leads to semigroup transformations into the forward light cone (Einstein causality) and a precise definition of resonance mass and width.
There has been much discussion recently regarding entanglement transformations in terms of local filtering operations and whether the optimal entanglement for an arbitrary two-qubit state could be realised. We introduce an experimentally realisable scheme for manipulating the entanglement of an arbitrary state of two polarisation entangled qubits. This scheme is then used to provide some perspective to the mathematical concepts inherent in this field with respect to a laboratory environment. Specifically, we look at how to extract enhanced entanglement from systems with a fixed rank and in the case where the rank of the density operator for the state can be reduced, show how the state can be made arbitrarily close to a maximally entangled pure state. In this context we also discuss bounds on entanglement in mixed states.
Aims: To reveal the morphology, chemical composition, kinematics and to establish the main processes prevalent in the gas at the foot points of the giant molecular loops (GMLs) in the Galactic center region   Methods: Using the 22-m Mopra telescope, we mapped the M$-3.8+0.9$ molecular cloud, placed at the foot points of a giant molecular loop, in 3-mm range molecular lines. To derive the molecular hydrogen column density, we also observed the $^{13}$CO $(2-1)$ line at 1 mm using the 12-m APEX telescope. From the 3 mm observations 12 molecular species were detected, namely HCO$^+$, HCN, H$^{13}$CN, HNC, SiO, CS, CH$_3$OH, N$_2$H$^+$, SO, HNCO, OCS, and HC$_3$N.   Results: Maps revealing the morphology and kinematics of the M$-3.8+0.9$ molecular cloud in different molecules are presented. We identified six main molecular complexes. We derive fractional abundances in 11 selected positions of the different molecules assuming local thermodynamical equilibrium.   Conclusions: Most of the fractional abundances derived for the M$-3.8+0.9$ molecular cloud are very similar over the whole cloud. However, the fractional abundances of some molecules show significant difference with respect to those measured in the central molecular zone (CMZ). The abundances of the shock tracer SiO are very similar between the GMLs and the CMZ. The methanol emission is the most abundant specie in the GMLs. This indicates that the gas is likely affected by moderate $\sim $ 30 km s$^{-1}$ or even high velocity (50 km s$^{-1}$) shocks, consistent with the line profile observed toward one of the studied position. The origin of the shocks is likely related to the flow of the gas throughout the GMLs towards the foot points.
The recent report by the PAMELA team of the observed rise in the cosmic-ray positron fraction above a few GeV and the report of an excess of cosmic-ray electrons around a few hundred GeV by the ATIC collaboration has resulted in a flurry of publications interpreting these observations either as a possible signature from the decay of dark matter or as a contribution from isolated astrophysical sources. While those interpretations are scientifically exciting, the possibility that measurements are contaminated by misidentified cosmic ray protons can not be ignored.
The high redshift sub-mm sources discovered by SCUBA are widely believed to represent the dust-enshrouded formation of massive elliptical galaxies. Given the strong evidence for a link between the formation of the spheroid and the growth of the central black hole, one might expect to see a luminous quasar at the nucleus of every SCUBA source. Somewhat surprisingly, however, only a very small fraction (~5%) are detected by Chandra with quasar luminosities. In this paper I discuss some of the implications of these results and discuss the accumulating evidence that sub-mm sources and quasars may represent different stages in the evolutionary sequence of a massive proto-spheroid.
We consider a variant of self-repelling random walk on the integer lattice Z where the self-repellence is defined in terms of the local time on oriented edges. The long-time asymptotic scaling of this walk is surprisingly different from the asymptotics of the similar process with self-repellence defined in terms of local time on unoriented edges. We prove limit theorems for the local time process and for the position of the random walker. The main ingredient is a Ray-Knight-type of approach. At the end of the paper, we also present some computer simulations which show the strange scaling behaviour of the walk considered.
These notes are a writeup of lectures given at the twelfth Oporto meeting on ``Geometry, Topology, and Physics,'' and at the Adelaide workshop ``Strings and Mathematics 2003,'' primarily geared towards a physics audience. We review current work relating boundary states in the open string B model on Calabi-Yau manifolds to sheaves. Such relationships provide us with a mechanism for counting open string states in situations where the physical spectrum calculation is nearly intractable -- after translating to mathematics, such calculations become easy. We describe several different approaches to these models, and also describe how these models are changed by varying physical circumstances -- flat B field backgrounds, orbifolds, and nonzero Higgs vevs. We also discuss mathematical interpretations of operator products, and how such mathematical interpretations can be checked physically. One of the motivations for this work is to understand the precise physical relationship between boundary states in the open string B model and derived categories in mathematics, and we outline what is currently known of the relationship.
We are studying the motion of a random walker in two and three dimensional continuum with uniformly distributed jump-length. This is different from conventional Lavy flight. In 2D and 3D continuum, a random walker can move in any direction, with equal probability and with any step-length(l) varying randomly between 0 to 1 with equal probability. A random walker, who starts his journey from a particular point (taken as origin), walks through the region, centered around the origin. Here, in this paper, we studied the probability distribution of end-to-end distances and the probability of return for the first time within a circular zone of finite radius, centered about the initial point, of a random walker. We also studied the same when a random walker moves with constant step-length, unity. The probability distribution of the time of first return (within a specified zone) is also studied.
The surface rotation rates of young solar-type stars vary rapidly with age from the end of the pre-main sequence through the early main sequence. Important changes in the dynamos operating in these stars may result from this evolution, which should be observable in their surface magnetic fields. Here we present a study aimed at observing the evolution of these magnetic fields through this critical time period. We observed stars in open clusters and stellar associations of known ages, and used Zeeman Doppler Imaging to characterize their complex magnetic large-scale fields. Presented here are results for 15 stars, from 5 associations, with ages from 20 to 250 Myr, masses from 0.7 to 1.2 solar masses, and rotation periods from 0.4 to 6 days. We find complex large-scale magnetic field geometries, with global average strengths from 14 to 140 G. There is a clear trend towards decreasing average large-scale magnetic field strength with age, and a tight correlation between magnetic field strength and Rossby number. Comparing the magnetic properties of our zero-age main sequence sample to those of both younger and older stars, it appears that the magnetic evolution of solar-type stars during the pre-main sequence is primarily driven by structural changes, while it closely follows the stars' rotational evolution on the main sequence.
We study the in-medium propagation of low-lying charmonium states: $J/\Psi$, $\Psi$(3686), and $\Psi$(3770) in a $\bar p$ Au $10$ GeV collision. This energy regime will be available for the PANDA experiment. The time evolution of the spectral functions of the charmonium states is studied with a BUU type transport model. We observe a substantial effect of the medium in the dilepton spectrum.
In this paper we further study the relationship between convexity and additive growth, building on the work of Schoen and Shkredov (\cite{SS}) to get some improvements to earlier results of Elekes, Nathanson and Ruzsa (\cite{ENR}). In particular, we show that for any finite set $A\subset{\mathbb{R}}$ and any strictly convex or concave function $f$, \[|A+f(A)|\gg{\frac{|A|^{24/19}}{(\log|A|)^{2/19}}}\] and \[\max\{|A-A|,\ |f(A)+f(A)|\}\gg{\frac{|A|^{14/11}}{(\log|A|)^{2/11}}}.\] For the latter of these inequalities, we go on to consider the consequences for a sum-product type problem.
Future cosmological measurements should enable the sum of neutrino masses to be determined indirectly through their effects on the expansion rate of the Universe and the clustering of matter. We consider prospects for the gravitationally lensed Cosmic Microwave Background anisotropies and Baryon Acoustic Oscillations in the galaxy distribution, examining how the projected uncertainty of $\approx15$ meV on the neutrino mass sum (a 4$\sigma$ detection of the minimal mass) might be reached over the next decade. The current 1$\sigma$ uncertainty of $\approx 103$ meV (Planck-2015+BAO-15) will be improved by upcoming 'Stage-3' CMB experiments (S3+BAO-15: 44 meV), then upcoming BAO measurements (S3+DESI: 22 meV), and planned next-generation 'Stage 4' CMB experiments (S4+DESI: 15-19 meV, depending on angular range). An improved optical depth measurement is important: the projected neutrino mass uncertainty increases to $26$ meV if S4 is limited to $\ell>20$ and combined with current large-scale polarization data. Looking beyond $\Lambda$CDM, including curvature uncertainty increases the forecast mass error by $\approx$ 50% for S4+DESI, and more than doubles the error with a two-parameter dark energy equation of state. Complementary low-redshift probes including galaxy lensing will play a role in distinguishing between massive neutrinos and a departure from a $w=-1$, flat geometry.
In this contributed paper I review our current knowledge of the local Black Hole (BH) scaling relations, and their impact on the determination of the local BH mass function. I particularly emphasize the remaining systematic uncertainties impinging upon a secure determination of the BH mass function and how progress can be made. I then review and discuss the evidence for a different time evolution for separate BH-galaxy scaling relations, and how these independent empirical evidences can be reconciled with the overall evolution of the structural properties of the host galaxies. I conclude discussing BH demography in the context of semi-empirical continuity accretion models, as well as more complex evolutionary models, emphasizing the general constraints we can set on them.
In the early 1980s, Erd\H{o}s and S\'os initiated the study of the classical Tur\'an problem with a uniformity condition: the uniform Tur\'an density of a hypergraph $H$ is the infimum over all $d$ for which any sufficiently large hypergraph with the property that all its linear-size subhyperghraphs have density at least $d$ contains $H$. In particular, they raise the questions of determining the uniform Tur\'an densities of $K_4^{(3)-}$ and $K_4^{(3)}$. The former question was solved only recently in [Israel J. Math. 211 (2016), 349-366] and [J. Eur. Math. Soc. 20 (2018), 1139-1159], while the latter still remains open for almost 40 years. In addition to $K_4^{(3)-}$, the only $3$-uniform hypergraphs whose uniform Tur\'an density is known are those with zero uniform Tur\'an density classified by Reiher, R\"odl and Schacht [J. London Math. Soc. 97 (2018), 77-97] and a specific family with uniform Tur\'an density equal to $1/27$.   We develop new tools for embedding hypergraphs in host hypergraphs with positive uniform density and apply them to completely determine the uniform Tur\'an density of a fundamental family of $3$-uniform hypergraphs, namely tight cycles $C_\ell^{(3)}$. The uniform Tur\'an density of $C_\ell^{(3)}$, $\ell\ge 5$, is equal to $4/27$ if $\ell$ is not divisible by three, and is equal to zero otherwise. The case $\ell=5$ resolves a problem suggested by Reiher.
Singlet scalar Dark Matter can naturally arise in composite Higgs models as an additional stable pseudo-Nambu-Goldstone boson. We study the properties of such a candidate in a model based on $SU(6)/SO(6)$, with the light quark masses generated by 4-fermion interactions. The presence of non-linearities in the couplings allows to saturate the relic density for masses $400 < m_{\rm DM} < 1000$ GeV, and survive the bound from Direct Detection and Indirect Detection. The viable parameter regions are in reach of the sensitivities of future upgrades, like XENONnT and LZ.
Let $R_n$ be a $n \times n$ random matrix with i.i.d. subgaussian entries. Let $M$ be a $n \times n$ deterministic matrix with norm $\lVert M \rVert \le n^\gamma$ where $1/2<\gamma<1$. The goal of this paper is to give a general estimate of the smallest singular value of the sum $R_n + M$, which improves an earlier result of Tao and Vu.
Felsner and Reuter introduced the linear extension diameter of a partially ordered set $\mathbf{P}$, denoted $\mbox{led}(\mathbf{P})$, as the maximum distance between two linear extensions of $\mathbf{P}$, where distance is defined to be the number of incomparable pairs appearing in opposite orders (reversed) in the linear extensions. In this paper, we introduce the reversal ratio $RR(\mathbf{P})$ of $\mathbf{P}$ as the ratio of the linear extension diameter to the number of (unordered) incomparable pairs. We use probabilistic techniques to provide a family of posets $\mathbf{P}_k$ on at most $k\log k$ elements for which the reversal ratio $RR(\mathbf{P}_k)\leq C/\log k$, where $C$ is a constant. We also examine the questions of bounding the reversal ratio in terms of order dimension and width.
In this work we study the dynamical generation of mass in the Lorentz-violating low-dimensional Super-Yang-Mills theory in the aether superspace coupled to a scalar matter. We also suggest that our studies can be applied for condensed matter systems, especially lower-dimensional superconductors and topological insulators. In low dimensional materials, the parameter $\Delta$ generated by presence of the aether term can be interpreted as a quantity that renormalizes the propagation velocity of the bosonic mode with respect to the Fermi velocity.
A new hierarchy of separability conditions for bipartite states is obtained. All the conditions in the hierarchy are necessary for separability. The conditions are expressed in terms of higher powers of the density operator of the bipartite system and the reduced density operators of the subsystems. Violation of any of the conditions in the hierarchy implies entanglement. As a consequence of the hierarchy, another separability condition, expressed in terms of the eigenvalues of the density operators of the total system and subsystems, is obtained.
Magnetic monopoles have eluded experimental detection since their prediction nearly a century ago by Dirac. Recently it has been shown that classical analogues of these enigmatic particles occur as excitations out of the topological ground state of a model magnetic system, dipolar spin ice. These quasi-particle excitations do not require a modification of Maxwell's equations, but they do interact via Coulombs law and are of magnetic origin. In this paper we present an experimentally measurable signature of monopole dynamics and show that magnetic relaxation measurements in the spin ice material $Dy_{2}Ti_{2}O_{7}$ can be interpreted entirely in terms of the diffusive motion of monopoles in the grand canonical ensemble, constrained by a network of "Dirac strings" filling the quasi-particle vacuum. In a magnetic field the topology of the network prevents charge flow in the steady state, but there is a monopole density gradient near the surface of an open system.
In this review we present the recent advances for calculations of the reactions $NN\to NN\pi$ using chiral effective field theory. Discussed are the next-to-next-to leading order loop contributions with nucleon and Delta-isobar for near threshold s-wave pion production. Results of recent experimental pion-production data for energies close to the threshold are analyzed. Several particular applications are discussed: (i) it is shown how the measured charge symmetry violating pion-production reaction can be used to extract the strong-interaction contribution to the proton-neutron mass difference; (ii) the role of $NN\to NN\pi$ for the extraction of the pion-nucleon scattering lengths from pionic atoms data is illuminated.
Broad band power density spectra offer a window to understanding turbulent behavior in the emission mechanism and, at the highest frequencies, in the putative inner engines powering long GRBs. We describe a chirp search method which steps aside Fourier analysis for signal detection in the Poisson noise-dominated 2 kHz sampled BeppoSAX light curves. An efficient numerical implementation is described in $O(Nn\log n)$ operations, where $N$ is the number of chirp templates and $n$ is the length of the light curve time series, suited for embarrassingly parallel processing. For detection of individual chirps of duration $\tau=1$ s, the method is one order of magnitude more sensitive in SNR than Fourier analysis. The Fourier-chirp spectra of GRB 010408 and GRB 970816 show a continuation of the spectral slope up to 1 kHz of turbulence identified in low frequency Fourier analysis. The same continuation is observed in an ensemble averaged spectrum of 40 bright long GRBs. An outlook on a similar analysis of upcoming gravitational wave data is included.
We study within the many-body Green's function GW and Bethe-Salpeter approaches the neutral singlet excitations of the zinctetraphenylporphyrin and C70 fullerene donor-acceptor complex. The lowest transition is a charge-transfer excitation between the donor and the acceptor with an energy in excellent agreement with recent constrained density functional theory calculations. Beyond the lowest charge-transfer state, of which the energy can be determined with simple electrostatic models that we validate, the Bethe-Salpeter approach provides the full excitation spectrum. We evidence the existence of hot electron-hole states which are resonant in energy with the lowest donor intramolecular excitation and show an hybrid intramolecular and charge-transfer character, favouring the transition towards charge separation. These findings support the recently proposed scenario for charge separation at donor-acceptor interfaces through delocalized hot charge-transfer states.
In the present work, higher-order mesonic interactions are included in the linear sigma model at a finite temperature. The effective potential is minimized in the calculations of the sigma and pion effective masses. The field equations have been solved in the mean-field approximation, by using the extended iteration method at a finite temperature. The order of chiral phase transition, the effective sigma and pion masses, and the effective mesonic potential are investigated as functions of the temperature. We find that the chiral phase transition satisfies the Goldstone theorem below the critical temperature point, when the minimization condition is satisfied in the chiral limit. The value of the critical temperature is reduced as compared with that of the original model in agreement with lattice QCD results. The modified model is compared to with models in other works.
Our goal in this paper is to examine the discovery potential of laboratory experiments searching for the oscillation $\nu_\mu(\nu_e) \rightarrow \nu_\tau$, in the light of recent data on solar and atmospheric neutrino experiments, which we analyse together with the most restrictive results from laboratory experiments on neutrino oscillations in a four-neutrino framework.}
It has been known for nearly 20 years that the pseudo phase-space density profile of equilibrium simulated dark matter halos, $\rho(r)/\sigma^3(r)$, is well described by a power law over 3 decades in radius, even though both the density $\rho(r)$, and the velocity dispersion $\sigma(r)$ deviate significantly from power laws. The origin of this scale-free behavior is not understood. It could be an inherent property of self-gravitating collisionless systems, or it could be a mere coincidence. To address the question we work with equilibrium halos, and more specifically, the second derivative of the Jeans equation, which, under the assumptions of (i) Einasto density profile, (ii) linear velocity anisotropy - density slope relation, and (iii) $\rho/\sigma^3\propto r^{-\alpha}$, can be transformed from a differential equation to a cubic algebraic equation. Relations (i)-(iii) are all observed in numerical simulations, and are well parametrized by a total of 4 or 6 model parameters. We do not consider dynamical evolution of halos; instead, taking advantage of the fact that the algebraic Jeans equation for equilibrium halos puts relations (i)-(iii) on the same footing, we study the (approximate) solutions of this equation in the 4 and 6 dimensional spaces. We argue that the distribution of best solutions in these parameter spaces is inconsistent with $\rho/\sigma^3\propto r^{-\alpha}$ being an fundamental property of gravitational evolution, and conclude that the scale-free nature of this quantity is likely to be a fluke.
The cut dominant of a graph is the unbounded polyhedron whose points are all those that dominate some convex combination of proper cuts. Minimizing a nonnegative linear function over the cut dominant is equivalent to finding a minimum weight cut in the graph. We give a forbidden-minor characterization of the graphs whose cut dominant can be defined by inequalities with integer coefficients and right-hand side at most 2. Our result is related to the forbidden-minor characterization of TSP-perfect graphs by Fonlupt and Naddef (Math. Prog., 1992). We prove that our result implies theirs, with a shorter proof. Furthermore, we establish general properties of forbidden minors for right-hand sides larger than 2.