ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this article we deal with stochastic perturbation of degenerate parabolic partial differential equations (PDEs). The particular emphasise is on analysing the effect of multiplicative L\'{e}vy noise to such problems and establishing wellposedness by developing a suitable weak entropy solution framework. The proof of existence is based on the vanishing viscosity technique. The uniqueness is settled by interpreting Kruzkov's doubling technique in the presence noise.
We compute the near-horizon radiation of quantum black holes in the context of self-dual loop quantum gravity. For this, we first use the unitary spinor basis of $\text{SL}(2,\mathbb{C})$ to decompose states of Lorentzian spin foam models into their self-dual and anti self-dual parts, and show that the reduced density matrix obtained by tracing over one chiral component describes a thermal state at Unruh temperature. Then, we show that the analytically-continued dimension of the $\text{SU}(2)$ Chern-Simons Hilbert space, which reproduces the Bekenstein-Hawking entropy in the large spin limit in agreement with the large spin effective action, takes the form of a partition function for states thermalized at Unruh temperature, with discrete energy levels given by the near-horizon energy of Frodden-Gosh-Perez, and with a degenerate ground state which is holographic and responsible for the entropy.
There is a common understanding in quantum optics that nonclassical states of light are states that do not have a positive semidefinite and sufficiently regular Glauber-Sudarshan $P$ function. Almost all known nonclassical states have $P$ functions that are highly irregular which makes working with them difficult and direct experimental reconstruction impossible. Here we introduce classes of nonclassical states with regular, non-positive-definite $P$ functions. They are constructed by "puncturing" regular smooth positive $P$ functions with negative Dirac-delta peaks, or other sufficiently narrow smooth negative functions. We determine the parameter ranges for which such punctures are possible without losing the positivity of the state, as well as the regimes yielding antibunching of light. Finally, we propose some possible experimental realizations of such states.
Newtonian Cosmology is commonly used in astrophysical problems, because of its obvious simplicity when compared with general relativity. However it has inherent difficulties, the most obvious of which is the non-existence of a well-posed initial value problem. In this paper we investigate how far these problems are met by using the post-Newtonian approximation in cosmology.
The influence of relativistic contributions to deuteron electrodisintegration is systematically studied in various kinematic regions of energy and momentum transfer. As theoretical framework the equation-of-motion and the unitarily equivalent S-matrix approaches are used. In a (p/M)-expansion, all leading order relativistic $\pi$-exchange contributions consistent with the Bonn OBEPQ model are included. In addition, static heavy meson exchange currents including boost terms, $\gamma\pi\rho/\omega$-currents, and $\Delta$-isobar contributions are considered. Sizeable effects from the various relativistic two-body contributions, mainly from $\pi$-exchange, have been found in inclusive form factors and exclusive structure functions for a variety of kinematic regions.
We present a necessary and sufficient condition for a root greater than unity of a monic reciprocal polynomial of an even degree at least four, with integer coefficients, to be a Salem number. We determine the probability of fulfillment the condition for an arbitrary power of the root.
In a foregoing paper, gravity has been interpreted as the pressure force exerted on matter at the scale of elementary particles by a perfect fluid. Under the condition that Newtonian gravity must be recovered in the incompressible case, a scalar field equation has thus been proposed for gravity, giving a new theory in the compressible case. Here the theory is reinterpreted so as to describe the relativistic effects, by extending the Lorentz-Poincar\'e interpretation of special relativity which is first recalled. Gravitational space-contraction and time-dilatation are postulated, as a consequence of the principle of local equivalence between the effects of motion and gravitation. The space-time metric (expressing the proper time along a trajectory) is hence curved also in the proposed theory. As the result of a modified Newton law, it is proved that free test particles follow geodesic lines of this metric. In the spherical static situation, Schwarzschild's exterior metric is exactly recovered and with it the experimental support of general relativity, but the interior solution as well as the problematic of singularities are different in the proposed theory, e.g. the radius of the body cannot be smaller than the Schwarzschild radius.
We study dynamics of incoherent exciton formation under interband photoexcitation in Cu$_2$O using time-and angle-resolved photoemission spectroscopy at 90 K. Hot electrons injected by allowed optical transitions with 3.40-eV photons show ultrafast relaxation to the conduction-band minimum (CBM), surviving up to 500 fs after excitation. While hot-electron states with high excess energy show a rapid population decay of ~25 fs, an abrupt increase to 130 fs is observed for states with excess energies of 0.15 eV. This latter is interpreted in terms of phonon bottleneck dynamics characteristic of LO-phonon mediated energy relaxation. Excitons, having a small binding energy of 60 meV, are formed below the CBM quasi-instantaneously and subsequently relax to the 1S-exciton state of the yellow series within 1.5 ps. We find that, together with possible plasma screening for electron-hole interaction, the cooling of exciton center-of-mass motion plays an important role in the exciton relaxation dynamics. The characteristic features of exciton photoionization process are critically discussed based on the detailed analysis of angle-resolved photoemission results for the 1S excitons formed 1.5 ps after excitation.
We measure the evolution of the luminous red galaxy (LRG) luminosity function in the redshift range 0.1<z<0.9 using samples of galaxies from the Sloan Digital Sky Survey as well as new spectroscopy of high-redshift massive red galaxies. Our high-redshift sample of galaxies is largest spectroscopic sample of massive red galaxies at z~0.9 collected to date and covers 7 square deg, minimizing the impact of large scale structure on our results. We find that the LRG population has evolved little beyond the passive fading of its stellar populations since z~0.9. Based on our luminosity function measurements and assuming a non-evolving Salpeter stellar initial mass function, we find that the most massive (L>3L*) red galaxies have grown by less than 50% (at 99% confidence), since z=0.9, in stark contrast to the factor of 2-4 growth observed in the L* red galaxy population over the same epoch. We also investigate the evolution of the average LRG spectrum since z~0.9 and find the high-redshift composite to be well-described as a passively evolving example of the composite galaxy observed at low-redshift. From spectral fits to the composite spectra, we find at most 5% of the stellar mass in massive red galaxies may have formed within 1Gyr of z=0.9. While L* red galaxies are clearly assembled at z<1, 3L* galaxies appear to be largely in place and evolve little beyond the passive evolution of their stellar populations over the last half of cosmic history.
Quantum error correction protocols will play a central role in the realisation of quantum computing; the choice of error correction code will influence the full quantum computing stack, from the layout of qubits at the physical level to gate compilation strategies at the software level. As such, familiarity with quantum coding is an essential prerequisite for the understanding of current and future quantum computing architectures. In this review, we provide an introductory guide to the theory and implementation of quantum error correction codes. Where possible, fundamental concepts are described using the simplest examples of detection and correction codes, the working of which can be verified by hand. We outline the construction and operation of the surface code, the most widely pursued error correction protocol for experiment. Finally, we discuss issues that arise in the practical implementation of the surface code and other quantum error correction codes.
FaCE is a self contained programme, with namelist input, that solves the three body Faddeev equations. It enables the inclusion of excitation of one of the three bodies, whilst the other two remain inert. It is particularly useful for obtaining the binding energies and bound state structure compositions of light exotic nuclei treated as three-body systems, given the three effective two body interactions. A large variety of forms for these interactions may be defined, and supersymmetric transformations of these potentials may be calculated whenever two body states need to be removed due to Pauli blocking.
We investigate occupation time statistics for random walks on a comb with ramified teeth. This is achieved through the relation between the occupation time and the first passage times. Statistics of occupation times in half space follows Lamperti's distribution, i.e. the generalized arcsine law holds. Transitions between different behaviors are observed, which are controlled by the size of the backbone and teeth of the comb, as well as bias. Occupation time on a non-simply connected domain is analyzed with a mean-field theory and numerical simulations. In that case, the generalized arcsine law isn't valid.
Reconstruction is becoming a crucial procedure of galaxy clustering analysis for future spectroscopic redshift surveys to obtain subpercent level measurement of the baryon acoustic oscillation scale. Most reconstruction algorithms rely on an estimation of the displacement field from the observed galaxy distribution. However, the displacement reconstruction degrades near the survey boundary due to incomplete data and the boundary effects extend to $\sim100\,\mathrm{Mpc}/h$ within the interior of the survey volume. We study the possibility of using radial velocities measured from the cosmic microwave background observation through the kinematic Sunyaev-Zel'dovich effect to improve performance near the boundary. We find that the boundary effect can be reduced to $\sim30-40\,\mathrm{Mpc}/h$ with the velocity information from Simons Observatory. This is especially helpful for dense low redshift surveys where the volume is relatively small and a large fraction of total volume is affected by the boundary.
A recent description of the motion of atoms in a classical monatomic system in liquid and supercooled liquid states divides the motion into two parts: oscillations within a given many-particle potential valley, and transit motion which carries the system from one many-particle valley to another. Building on this picture, we construct a model for the trajectory of an average atom in the system. The trajectory consists of oscillations at the normal-mode distribution of frequencies, representing motion within a fluctuating single-particle well, interspersed with position- and velocity-conserving transits to similar adjacent wells. For the supercooled liquid in nondiffusing states, the model gives velocity and displacement autocorrelation functions which exactly match those found in the many-particle harmonic approximation, and which are known to agree almost precisely with molecular dynamics (MD) simulations of liquid Na. At higher temperatures, by allowing transits to proceed at a temperature-dependent rate, the model gives velocity autocorrelation functions which are also in remarkably good agreement with MD simulations of Na at up to three times its melting temperature. Two independent processes in the model relax velocity autocorrelations: (a) dephasing due to the presence of many frequency components, which operates at all temperatures but which produces zero diffusion, and (b) the transit process, which increases with increasing temperature and which produces diffusion.
Suppose $\{ \lambda_d\}$ are Selberg's sieve weights and $1 \le w < y \le x$. Graham's estimate on the Barban-Vehov problem shows that $\sum_{1 \le n \le x} (\sum_{d|n} \lambda_d)^2 = \frac{x}{\log(y/w)} + O(\frac{x}{\log^2(y/w)})$. We prove an analogue of this estimate for a sum over ideals of an arbitrary number field $k$. Our asymptotic estimate remains the same; the only difference is that the effective error term may depend on arithmetics of $k$. Our innovation involves multiple counting results on ideals instead of integers. Notably, some of the results are nontrivial generalizations. Furthermore, we prove a corollary that leads to a new zero density estimate.
We present AC and DC magnetometry, heat capacity, muon spin relaxation ($\mu$SR) and resonant inelastic X-ray scattering (RIXS) studies of the pyrochlore osmate Y$_2$Os$_2$O$_7$. We observe a non-zero effective moment governed by $\sqrt{f}\mu_{\rm{eff}} = 0.417(1)\,\mu_{\rm{B}}$ where $f$ is the fraction of Os sites which exhibit a spin, and spin freezing at temperature $T_{\rm f} \simeq 5\,$K, consistent with previous results. The field dependence of magnetisation data shows that the paramagnetic moment is most likely due to large moments $\mu_{\rm eff} \simeq 3\,\mu_{\rm B}$ on only a small fraction $f \simeq 0.02$ of Os sites. Comparison of single-ion energy level calculations with the RIXS data yields a non-magnetic $J_{\rm eff} = 0$ ground state on the Os$^{4+}$ sites. The spin-orbit interaction, Hund's coupling and trigonal distortion of OsO$_{6}$ octahedra are all important in modelling the experimentally observed spectra. We are able to rule out impurity effects, leaving disorder-related effects such as oxygen non-stoichiometry or site interchange between Os and Y ions as the most plausible explanation for the magnetic response in this material.
Recent IR surveys of the Galactic plane have revealed a large number of candidate Luminous Blue Variables. In order to verify these classifications we have been undertaking a long term spectroscopic and photometric monitoring campaign supplemented with tailored non-LTE model atmosphere analysis. Here we present a brief overview of selected aspects of this program, highlighting the prospects for identification, classification and quantitative analysis of LBVs in the near-IR spectral window.
Surveys in the 21cm line of neutral hydrogen are testing the completeness of the catalogs of nearby galaxies. The remarkable observational fact is that the potential wells that confine gas to sufficient density that it can remain neutral in the face of ionizing radiation also provide sites for star formation, so that there are no known cases of neutral intergalactic clouds without associated star light.
Let Cox(S) be the homogeneous coordinate ring of the blow-up S of P^2 in r general points, i.e., a smooth Del Pezzo surface of degree 9-r. We prove that for r=6 and 7, Proj(Cox(S)) can be embedded into G/P, where G is an algebraic group with root system given by the primitive Picard lattice of S and P is a certain maximal parabolic subgroup in G.
We show that quantum state discrimination sits neatly in the framework of Bayesian experimental design. In this setting, the two main branches of quantum state discrimination (minimal error and maximal confidence) simply correspond to two different utility functions. This view allows straightforward extensions and mixing of different discrimination tasks by examining the utility functions, and to describe multi-objective discrimination tasks. In addition, the probability of success and the total confidence are resource monotones quantifying the usefulness of measurements. We give general conditions under which utility functions lead to resource monotones in the resource theory of quantum measurement.
This short note clarifies that the "pinched hysteresis loop" fingerprint of a memristor, or a memristive device, must hold for all amplitudes, for all frequencies, and for all initial conditions, of any periodic testing waveform, such as sinusoidal or triangular signals, which assumes both positive and negative values over each period of the waveform. We proved that the systems presented in [1] are not memristive devices because their hysteresis loops are not pinched at the origin for all amplitudes, and for all initial conditions.
The quantization of closed cosmologies makes it necessary to study squared Dirac operators on closed intervals and the corresponding quantum amplitudes. This paper proves self-adjointness of these second-order elliptic operators.
We consider the mixed problem for the Laplace operator in a class of Lipschitz graph domains in two dimensions with Lipschitz constant at most 1. The boundary of the domain is decomposed into two disjoint sets D and N. We suppose the Dirichlet data, f_D has one derivative in L^p(D) of the boundary and the Neumann data is in L^p(N). We find conditions on the domain and the sets D and N so that there is a p_0>1 so that for p in the interval (1,p_0), we may find a unique solution to the mixed problem and the gradient of the solution lies in L^p.
Recent experimental observations of Weyl fermions in materials opens a new frontier of condensed matter physics. Based on first-principles calculations, we here discover Weyl fermions in a two-dimensional layered electride material Y$_2$C. We find that the Y 4$d$ orbitals and the anionic $s$-like orbital confined in the interstitial spaces between [Y$_2$C]$^{2+}$ cationic layers are hybridized to give rise to van Have singularities near the Fermi energy $E_{\rm F}$, which induce a ferromagnetic (FM) order via the Stoner-type instability. This FM phase with broken time-reversal symmetry hosts the rotation-symmetry protected Weyl nodal lines near $E_{\rm F}$, which are converted into the multiple pairs of Weyl nodes by including spin-orbit coupling (SOC). However, we reveal that, due to its small SOC effects, Y$_2$C has a topologically nontrivial drumhead-like surface state near $E_{\rm F}$ as well as a very small magnetic anisotropy energy with several ${\mu}$eV per unit cell, consistent with the observed surface state and paramagnetism at low temperatures below ${\sim}$2 K. Our findings propose that the Brillouin zone coordinates of Weyl fermions hidden in paramagnetic electride materials would fluctuate in momentum space with random orientations of the magnetization direction.
In the first part of this article we show how observations of the chemical evolution of the Galaxy: G- and K-dwarf numbers as functions of metallicity, and abundances of the light elements, D, Li, Be and B, in both stars and the interstellar medium (ISM), lead to the conclusion that metal poor HI gas has been accreting to the Galactic disc during the whole of its lifetime, and is accreting today at a measurable rate, ~2 Msun per year across the full disc. Estimates of the local star formation rate (SFR) using methods based on stellar activity, support this picture. The best fits to all these data are for models where the accretion rate is constant, or slowly rising with epoch. We explain here how this conclusion, for a galaxy in a small bound group, is not in conflict with graphs such as the Madau plot, which show that the universal SFR has declined steadily from z=1 to the present day. We also show that a model in which disc galaxies in general evolve by accreting major clouds of low metallicity gas from their surroundings can explain many observations, notably that the SFR for whole galaxies tends to show obvious variability, and fractionally more for early than for late types, and yields lower dark to baryonic matter ratios for large disc galaxies than for dwarfs. In the second part of the article we use NGC 1530 as a template object, showing from Fabry-Perot observations of its Halpha emission how strong shear in this strongly barred galaxy acts to inhibit star formation, while compression acts to stimulate it.
Scaling nature of absorbing critical phenomena is well understood for the directed percolation (DP) and the directed Ising (DI) systems. However, a full analysis of the crossover behavior is still lacking, which is of our interest in this study. There are three different routes from the DI to the DP classes by introducing a symmetry breaking field (SB), breaking a modulo 2 conservation (CB), or making channels connecting two equivalent absorbing states (CC). Each route can be characterized by a crossover exponent, which is found numerically as $\phi=2.1\pm 0.1$ (SB), $4.6\pm 0.2$ (CB), and $2.9\pm 0.1$ (CC), respectively. The difference between the SB and CB crossover can be understood easily in the domain wall language, while the CC crossover involves an additional critical singularity in the auxiliary field density with the memory effect to identify itself independent.
Let K be a field of characteristic zero, alpha algebraic of degree n over K. Given a proper parametrization psi of a rational curve C, we present a new algorithm to compute the hypercircle associated to the parametrization psi. As a consequence, we can decide if the curve C is defined over K and, if not, to compute the minimum field of definition of C containing K. The algorithm exploits the conjugate curves of C but avoids computation in the normal closure of K(alpha) over K.
We present a new library of synthetic spectra based on the stellar atmosphere code PHOENIX. It covers the wavelength range from 500{\AA} to 55000{\AA} with a resolution of R=500000 in the optical and near IR, R=100000 in the IR and {\Delta}{\lambda}=0.1{\AA} in the UV. The parameter space covers 2300K<=Teff<=8000K, 0.0<=log(g)<=6.0, -4.0<=[Fe/H]<=+1.0 and -0.3<=[{\alpha}/Fe]<=+0.8. The library is work-in-progress and going to be extended to at least Teff=25000K. We use a new self-consistent way of describing the microturbulence for our model atmospheres. The entire library of synthetic spectra will be available for download. Futhermore we present a method for fitting spectra, especially designed to work with the new 2nd generation VLT instrument MUSE. We show that we can determine stellar parameters (Teff, log(g), [Fe/H] and [{\alpha}/Fe]) and even single element abundances.
The highly luminous and variable prompt emission in Gamma-Ray Bursts (GRBs) arises in an ultra-relativistic outflow. The exact underlying radiative mechanism shaping its non-thermal spectrum is still uncertain, making it hard to determine the outflow's bulk Lorentz factor $\Gamma$. GRBs with spectral cutoff due to pair production ($\gamma\gamma\to e^+e^-$) at energies $E_c\gtrsim10\;$MeV are extremely useful for inferring $\Gamma$. We find that when the emission region has a high enough compactness, then as it becomes optically thick to scattering, Compton downscattering by non-relativistic $e^\pm$-pairs can shift the spectral cutoff energy well below the self-annihilation threshold, $E_{\rm sa}=\Gamma m_ec^2/(1+z)$. We treat this effect numerically and show that $\Gamma$ obtained assuming $E_c=E_{\rm sa}$ can under-predict its true value by as much as an order of magnitude.