ShantanuT01/DACTYL-Pretraining huggingface dataset:
Zurek's derivation of Born's rule using envariance (invariance due to entanglement) is considered to capture the probability in full generality, but only as applied to measurement of a quantum observable. Contrariwise, textbook formulations of Born's rule begin with a pure state of a closed, undivided system. The task of this study is to show that a rearrangement of the Zurek approach is possible in which the latter is viewed as giving the probabilities for Schmidt states of an arbitrary composite state vector, and afterwards it is extended to probabilities in a closed, undivided system. This is achieved by determining simultaneously probability and measurement based on the fact that the physical meaning of probability and that of measurement are inextricably dependent on each other.
We consider the hyperfine-mediated transition rate between Zeeman split spin states of the lowest orbital level in a GaAs quantum dot. We separate the hyperfine Hamiltonian into a part which is diagonal in the orbital states and another one which mixes different orbitals. The diagonal part gives rise to an effective (internal) magnetic field which, in addition to an external magnetic field, determines the Zeeman splitting. Spin-flip transitions in the dots are induced by the orbital mixing part accompanied by an emission of a phonon. We evaluate the rate for different regimes of applied magnetic field and temperature. The rates we find are bigger that the spin-orbit related rates provided the external magnetic field is sufficiently low.
Accreting black holes show characteristic 'reflection' features in their X-ray spectra, including the iron K$\alpha$ fluorescence line, which result from X-rays radiated by a compact central corona being reprocessed in the accretion disc atmosphere. The observed line profile is distorted by relativistic effects, providing a diagnostic for disc geometry. Nearly all previous X-ray reflection spectroscopy studies have made the simplifying assumption that the disc ionization state is independent of radius in order to calculate the restframe reflection spectrum. However, this is unlikely to be the case in reality, since the irradiating flux should drop off steeply with radius. Here we analyse a Nuclear Spectroscopic Telescope ARray observation of GRS 1915+105 that exhibits strong reflection features. We find that using a self-consistently calculated radial ionization profile returns a better fit than assuming constant ionization. Our results are consistent with the inner disc being radiation pressure dominated, as is expected from the high inferred accretion rate for this observation. We also find that the assumed ionization profile impacts on the best fitting disc inner radius. This implies that the black hole spin values previously inferred for active galactic nuclei and X-ray binaries by equating the disc inner radius with the innermost stable circular orbit may be changed significantly by the inclusion of a self-consistent ionization profile.
We present hydrodynamic simulations of the common envelope binary interaction between a giant star and a compact companion carried out with the adaptive mesh refinement code ENZO and the smooth particle hydrodynamics code PHANTOM. These simulations mimic the parameters of one of the simulations by Passy et al., but assess the impact of a larger, more realistic initial orbital separation on the simulation outcome. We conclude that for both codes the post-common envelope separation is somewhat larger and the amount of unbound mass slightly greater when the initial separation is wide enough that the giant does not yet overflow or just overflows its Roche lobe. PHANTOM has been adapted to the common envelope problem here for the first time and a full comparison with ENZO is presented, including an investigation of convergence as well as energy and angular momentum conservation. We also set our simulations in the context of past simulations. This comparison reveals that it is the expansion of the giant before rapid in-spiral and not spinning up of the star that causes a larger final separation. We also suggest that the large range in unbound mass for different simulations is difficult to explain and may have something to do with simulations that are not fully converged.
We study cohomology support loci and higher direct images of (log) pluricanonical bundles of smooth projective varieties or log canonical pairs. We prove that the 0-th cohomology support loci of log pluricanonical bundles are finite unions of torsion translates of subtori. We also construct an example of morphism from a smooth projective variety to an abelian variety such that a higher direct image of a pluricanonical bundle to the abelian variety is not a GV-sheaf.
We use density functional theory to determine the equilibrium shape of graphene flakes, through the calculation of the edge orientation dependence of the edge energy and edge stress of graphene nanoribbons. The edge energy is a nearly linear function of edge orientation angle; increasing from the armchair orientation to the zigzag orientation. Reconstruction of the zigzag edge lowers its energy to less than that of the armchair edge. The edge stress for all edge orientations is compressive, however, reconstruction of the zigzag edge reduces this edge stress to near zero. Hydrogen adsorption is favorable for all edge orientations; dramatically lowering all edge energies and all edge stresses. It also removes the reconstruction of the zigzag edge. Using the new edge energy data, we determine the equilibrium shape of a graphene sheet (with unreconstructed edges) to be hexagonal with straight armchair edges in the presence and absence of hydrogen. However, zigzag edge reconstruction produces graphene flakes with a six-fold symmetry, but with rounded edges. This shape is dominated by near zigzag edges. The compressive edge stresses will lead to edge buckling (out-of-the-plane of the graphene sheet) for all edge orientations, in the absence of hydrogen. Exposing the graphene flake to hydrogen dramatically decreases the buckling amplitude.
In order to reveal many-body interactions in the three-dimensional (3D) perovskite manganite, we have performed an $in$ $situ$ angle-resolved photoemission spectroscopy (ARPES) on La$_{0.6}$Sr$_{0.4}$MnO$_3$ (LSMO) and investigated the behaviors of quasiparticles. We observe quasiparticle peaks around the Fermi momentum, both in the electron and the hole bands, and clear kinks throughout the hole Fermi surface in the ARPES band dispersion. The isotropic behavior sharply contrasts to the strong anisotropic quasiparticle excitation observed in layered manganites. These results suggest that polaronic quasiparticles by coupling of the electrons with Jahn-Teller phonons play an important role in the physical properties of the ferromagnetic metallic phase in 3D manganite LSMO.
Recent de Haas-van Alphen (dHvA) experiments on high-Tc compounds have been interpreted using Lifshitz-Kosevich (LK) theory, which ignores many-body effects. However in quasi-2d systems, interactions plus Landau level quantization give strong singularities in the self-energy $\Sigma$ and the thermodynamic potential $\Omega$. These are rapidly suppressed as one increases the c-axis tunneling amplitude $t_\perp$ and/or impurity scattering. We show that 2d-3d crossover and interaction effects should show up in these experiments, and that they can lead to strong deviations from LK behaviour. Moreover, dHvA experiments in quasi-2d systems should clearly distinguish between Fermi liquid and non-Fermi liquid states, for sufficiently weak impurity scattering.
In this paper, we introduce the idea of stochastic integrals with respect to an increasing process in the $G$-framework and extend $G$-It\^o's formula. Moreover, we study the solvability of the scalar valued stochastic differential equations driven by $G$-Brownian motion with reflecting boundary conditions (RGSDEs).
Young tidal dwarf galaxies (TDGs) are observed in the tidal debris of gas-rich interacting galaxies. In contrast to what is generally assumed to be the case for isolated dwarf galaxies, TDGs are not embedded in their own dark matter (DM) sub-halo. Hence, they are more sensitive to stellar feedback and could be disrupted on a short time-scale. Detailed numerical and observational studies demonstrate that isolated DM-dominated dwarf galaxies can have lifetimes of more than 10 Gyr. For TDGs that evolve in a tidal field with compressing accelerations equal to the gravitational acceleration within a DM sub-halo typical of an isolated dwarf galaxy, a similar survival time is expected. The tidal acceleration profile depends on the virial mass of the host galaxy and the distance between the TDG and its host. We analytically compare the tidal compression to the gravitational acceleration due to either cuspy or cored DM sub-halos of various virial masses. For example, the tidal field at a distance of 100 kpc to a host halo of 10^13 Msol can be as stabilizing as a 10^9 Msol DM sub-halo. By linking the tidal field to the equivalent gravitational field of a DM sub-halo, we can use existing models of isolated dwarfs to estimate the survivability of TDGs. We show that part of the unexpectedly high dynamical masses inferred from observations of some TDGs can be explained by tidal compression and hence TDGs require to contain less unobservable matter to understand their rotation curves.
Results on particle creation from vacuum by the gravitational field of the expanding Friedmann Universe are presented. Finite results for the density of particles and the energy density for created particles are given for different exact solutions for different regimes of the expansion of the Universe. The results are obtained as for conformal as for nonconformal particles. The hypothesis of the origination of visible matter from the decay of created from vacuum superheavy particles identified with the dark matter is discussed.
Spectral fitting of the spin a in the microquasar GRS 1915+105 estimate values higher than a=0.98. However, there are certain doubts about this (nearly) extremal number. Confirming a high value of a>0.9 would have significant concequences for the theory of high-frequency quasiperiodic oscillations (HF QPOs). Here we discuss its possible implications assuming several commonly used orbital models of 3:2 HF QPOs. We show that the estimate of a>0.9 is almost inconsistent with two hot-spot (relativistic precession and tidal disruption) models and the warped disc resonance model. In contrast, we demonstrate that the epicyclic resonance and discoseismic models assuming the c- and g- modes are favoured. We extend our discussion to another two microquasars that display the 3:2 HF QPOs. The frequencies of these QPOs scale roughly inversely to the microquasar masses, and the differences in the individual spins, such as a=0.9 compared to a=0.7, represent a generic problem for most of the discussed geodesic 3:2 QPO models. To explain the observations of all the three microquasars by one unique mechanism, the models would have to accommodate very large non-geodesic corrections.
We report the discovery of large elephant trunk (ET)-like objects, named giant elephant trunk (GET), of molecular gas in star forming complexes in the Scutum and Norma arms using the $^{12}$CO(J=1-0)-line survey data with the Nobeyama 45-m telescope. In comparison with the CO maps of ETs in M16 as derived from the same data, we discuss physical properties of the GETs. Their lengths are $\sim 20$ to 50 pc, an order of magnitude larger than ETs. GETs show a cometary structure coherently aligned parallel to the galactic plane, and emerge from bow-shaped concave surface of giant molecular clouds (GMC) facing the HII regions, and point down-stream of the gas flow in the spiral arms. The molecular masses of the head clumps are $\sim 10^3 -10^4 M_\odot$, about 3 to 4 times the virial masses, indicating that the clumps are gravitationally stable. Jeans masses calculated for the derived density and assumed kinetic temperature are commonly sub-solar. We suggest that the GET heads are possible birth sites of stellar clusters, similarly to ETs' globules, but at much greater scale. We discuss the origin of the GETs by Rayleigh-Taylor instability due to deceleration of GMCs by low density gas stagnated in the galactic shock waves as well as by pressure of the HII regions.
Spins of single donor atoms are attractive candidates for large scale quantum information processing in silicon, since quantum computation can be realized through the manipulation of electron and/or nuclear spins. We here report on two-pulse electron spin echo experiments on phosphorus shallow donors in natural and 28Si-enriched silicon epilayers doped with 10^16 cm-3 P donors. The experiments address the spin-spin relaxation times and mechanisms and provide, through the electron spin echo envelope modulation (ESEEM) effect, information on the donor electron wave function. Experiments performed as a function of the pulse turning angle allowed us to measure the exponential relaxation and spectral diffusion times depurated by instantaneous diffusion. According to these results, isotopically purified samples are necessary to reduce the spectral diffusion contribution and the P shallow donors concentration plays a fundamental role in determining the intrinsic phase memory time. ESEEM peaks have been assigned to hyperfine-coupled silicon-29 nuclei at specific crystallographic positions on the basis of a spectral fit procedure including instrumental distortions.
We address the relation between star formation and AGN activity in a sample of 231 nearby ($0.0002<z<0.0358$) early type galaxies by carrying out a multi-wavelength study using archival observations in the UV, IR and radio. Our results indicate that early type galaxies in the current epoch are rarely powerful AGNs, with $P<10^{22}\,WHz^{-1}$ for a majority of the galaxies. Only massive galaxies are capable of hosting powerful radio sources while less massive galaxies are hosts to lower radio power sources. Evidence of ongoing star formation is seen in approximately 7% of the sample. The SFR of these galaxies is less than 0.1 $M_{\odot}yr^{-1}$. They also tend to be radio faint ($P<10^{22}\,WHz^{-1}$). There is a nearly equal fraction of star forming galaxies in radio faint ($P<10^{22}\,WHz^{-1}$) and radio bright galaxies ($P\geq10^{22}\,WHz^{-1}$) suggesting that both star formation and radio mode feedback are constrained to be very low in our sample. We notice that our galaxy sample and the Brightest Cluster Galaxies (BCGs) follow similar trends in radio power versus SFR. This may be produced if both radio power and SFR are related to stellar mass.
We present an ongoing study of 18 nearby galaxy groups, chosen for the availability of Chandra and/or XMM-Newton data and evidence for AGN/hot intragroup gas interaction. We have obtained 235 and 610 MHz observations at the GMRT for all the groups, and 327 and 150 MHz for a few. We discuss two interesting cases - NGC 5044 and AWM 4 - which exhibit different kinds of AGN/hot gas interaction. With the help of these examples we show how joining low-frequency radio data (to track the history of AGN outbursts through emission from aged electron populations) with X-ray data (to determine the state of hot gas, its disturbances, heating and cooling) can provide a unique insight into the nature of the feedback mechanism in galaxy groups.
A very simple wormhole geometry is considered as a model of a mode of topological fluctutation in Planck-scale spacetime foam. Quantum dynamics of the hole reduces to quantum mechanics of one variable, throat radius, and admits a WKB analysis. The hole is quantum-mechanically unstable: It has no bound states. Wormhole wave functions must eventually leak to large radii. This suggests that stability considerations along these lines may place strong constraints on the nature and even the existence of spacetime foam.
The measured B -> pi pi, pi K branching ratios exhibit puzzling patterns. We point out that the B -> pi pi hierarchy can be nicely accommodated in the Standard Model (SM) through non-factorizable hadronic interference effects, whereas the B -> pi K system may indicate new physics (NP) in the electroweak (EW) penguin sector. Using the B -> pi pi data and the SU(3) flavour symmetry, we may fix the hadronic B -> pi K parameters, which allows us to show that any currently observed feature of the B -> pi K system can be easily explained through enhanced EW penguins with a large CP-violating NP phase. Restricting ourselves to a specific scenario, where NP enters only through Z^0 penguins, we derive links to rare K and B decays, where an enhancement of the K_L-> pi^0 nu nu_bar rate by one order of magnitude, with BR(K_L -> pi^0 nu nu_bar) > BR(K^+ -> pi^+ nu nu_bar), BR(K_L -> pi^0 e^+ e^-)=O(10^{-10}), (\sin2\beta)_{pi nu nu_bar}<0, and a large forward-backward CP asymmetry in B_d -> K* mu^+ mu^-, are the most spectacular effects. We address also other rare K and B decays, epsilon'/epsilon and B_d -> phi K_S.
This is a comment on a reply (gr-qc/9601040) to a comment (gr-qc/9606045) on a paper of Hellaby & Dray (gr-qc/9404001), repeating the identification of an important mistake which is still being denied by the authors: their proposed solutions do not satisfy the Einstein- Klein-Gordon equations at a change of signature. Substitution of the proposed solutions into the Einstein-Klein-Gordon equations in unit normal coordinates yields Dirac delta terms describing source layers at the junction. Hellaby & Dray's criticisms of this straightforward calculation are absurd: it does not involve "imaginary time", it does not involve a "modified form" of the field equations, and it is "purely classical". Moreover, Hellaby & Dray's latest attempt to lose the delta terms is mathematically invalid, involving division by zero and products of distributions, hinging on an identity whose incorrectness may be checked by substitution.
An analytical solution of the Dirac equation with a Cornell potential, with identical scalar and vectorial parts, is presented. The solution is obtained by using the linear potential solution, related to Airy functions, multiplied by another function to be determined. The energy levels are obtained and we notice that they obey a band structure.
The 2s_{1/2} state of hydrogen is metastable and overpopulated in HII regions. In addition, the 2p states may be pumped by ambient Lyman-alpha radiation. Fine structure transitions between these states may be observable in HII regions at 1.1 GHz (2s_{1/2}-2p_{1/2}) and/or 9.9 GHz (2s_{1/2}-2p_{3/2}), although the details of absorption versus emission are determined by the relative populations of the 2s and 2p states. The n=2 level populations are solved with a parameterization that allows for Lyman-alpha pumping of the 2p states. The density of Lyman-alpha photons is set by their creation rate, easily determined from the recombination rate, and their removal rate. Here we suggest that the dominant removal mechanism of Lyman-alpha radiation in HII regions is absorption by dust. This circumvents the need to solve the Lyman-alpha transfer problem, and provides an upper limit to the rate at which the 2p states are populated by Lyman-alpha photons. In virtually all cases of interest, the 2p states are predominantly populated by recombination, rather than Lyman-alpha pumping. We then solve the radiative transfer problem for the fine structure lines in the presence of free-free radiation. In the likely absence of Lyman-alpha pumping, the 2s_{1/2}-2p_{1/2} lines will appear in stimulated emission and the 2s_{1/2}-2p_{3/2} lines in absorption. Searching for the 9.9 GHz lines in high emission measure HII regions offers the best prospects for detection. The lines are predicted to be weak; in the best cases, line-to-continuum ratios of several tenths of a percent might be expected with line strengths of tens to a hundred mK with the Green Bank Telescope.
In this paper we give a generalization of the main results in \cite{ab,ab1} about $b$-ary expansions of algebraic numbers. As a byproduct we get a large class of new transcendence criteria. One of our corollaries implies that $b$-ary expansions of linearly independent irrational algebraic numbers are quite independent. Motivated by this result, we propose a generalized Borel conjecture.
The processes regulating protoplanetary disk evolution are constrained by studying how mass accretion rates scale with stellar and disk properties. The spread in these relations can be used as a constraint to the models of disk evolution, but only if the impact of accretion variability is correctly accounted for. While the effect of variability might be substantial in the embedded phases of star formation, it is often considered limited at later stages. Here we report on the observed large variation in the accretion rate for one target, XX Cha, and we discuss the impact on population studies of classical T Tauri stars. The mass accretion rate determined by fitting the UV-to-near-infrared spectrum in recent X-Shooter observations is compared with the one measured with the same instrument 11 years before. XX Cha displays an accretion variability of almost 2 dex between 2010 and 2021. Although the timescales on which this variability happens are uncertain, XX Cha displays an extreme accretion variability for a classical T Tauri star. If such behavior is common among classical T Tauri stars, possibly on longer timescales than previously probed, it could be relevant for discussing the disk evolution models constrained by the observed spread in accretion rates. Finally, we remark that previous studies of accretion variability based on spectral lines may have underestimated the variability of some targets.
The deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) has been proved one of the best models to probe the exotic structures in deformed nuclei. In DRHBc, the potentials and densities are expressed in terms of the multipole expansion with Legendre polynomials, the dependence on which has only been touched for light nuclei so far. In this paper, taking a light nucleus $^{20}$Ne and a heavy nucleus $^{242}$U as examples, we investigated the dependence on the multipole expansion of the potentials and densities in DRHBc. It is shown that the total energy converges well with the expansion truncation both in the absence of and presence of the pairing correlation, either in the ground state or at a constrained quadrupole deformation. It is found that to reach a same accuracy of the total energy, even to a same relative accuracy by percent, a larger truncation is required by a heavy nucleus than a light one. The dependence of the total energy on the truncation increases with deformation. By decompositions of the neutron density distribution, it is shown that a higher-order component has a smaller contribution. With the increase of deformation, the high-order components get larger, while at the same deformation, the high-order components of a heavy nucleus play a more important role than that of a light one.
We investigate the collapse and internal structure of dark matter halos. We consider halo formation from initially scale-free perturbations, for which gravitational collapse is self-similar. Fillmore and Goldreich (1984) and Bertschinger (1985) solved the one dimensional (i.e. spherically symmetric) case. We generalize their results by formulating the three dimensional self-similar equations. We solve the equations numerically and analyze the similarity solutions in detail, focusing on the internal density profiles of the collapsed halos. By decomposing the total density into subprofiles of particles that collapse coevally, we identify two effects as the main determinants of the internal density structure of halos: adiabatic contraction and the shape of a subprofile shortly after collapse; the latter largely reflects the triaxiality of the subprofile. We develop a simple model that describes the results of our 3D simulations. In a companion paper, we apply this model to more realistic cosmological fluctuations, and thereby explain the origin of the nearly universal (NFW-like) density profiles found in N-body simulations.