ShantanuT01/DACTYL-Pretraining huggingface dataset:
We prove a proposition that the entropy of the system composed of finite $N$ molecules of ideal gas is the $q$-entropy or Havrda-Charv\'at-Tsallis entropy, which is also known as Tsallis entropy, with the entropic index $q=\frac{D(N-1)-4}{D(N-1)-2}$ in $D$-dimensional space. The indispensable infinity assumption used by Boltzmann and others in their derivation of entropy formulae is not involved in our derivation, therefore our derived formula is exact. The analogy of the $N$-body system brings us to obtain the entropic index of a combined system $q_C$ formed from subsystems having different entropic indexes $q_A$ and $q_B$ as $\frac{1}{1-q_C}=\frac{1}{1-q_A}+\frac{1}{1-q_B}+\frac{D+2}{2}$. It is possible to use the number $N$ for the physical measure of deviation from Boltzmann entropy.
We exploit the parquet formalism to derive exact flow equations for the two-particle-reducible four-point vertices, the self-energy, and typical response functions, circumventing the reliance on higher-point vertices. This includes a concise, algebraic derivation of the multiloop flow equations, which have previously been obtained by diagrammatic considerations. Integrating the multiloop flow for a given input of the totally irreducible vertex is equivalent to solving the parquet equations with that input. Hence, one can tune systems from solvable limits to complicated situations by variation of one-particle parameters, staying at the fully self-consistent solution of the parquet equations throughout the flow. Furthermore, we use the resulting differential form of the Schwinger-Dyson equation for the self-energy to demonstrate one-particle conservation of the parquet approximation and to construct a conserving two-particle vertex via functional differentiation of the parquet self-energy. Our analysis gives a unified picture of the various many-body relations and exact renormalization group equations.
We construct four-center bubbled BPS solutions with a Gibbons-Hawking base space. We give a systematic procedure to build scaling solutions: starting from three-supertube configurations and using generalized spectral flows and gauge transformations to extend to solutions with four Gibbons-Hawking centers. This allows us to construct very large families of smooth horizonless solutions that have the same charges and angular momentum as supersymmetric black holes with a macroscopically large horizon area. Our construction reveals that all scaling solutions with four Gibbons Hawking centers have an angular momentum at around 99% of the cosmic censorship bound. We give both an analytical and a numerical explanation for this unexpected feature.
In this paper, we mainly investigate the Cauchy problem of the non-resistive MHD equation. We first establish the local existence in the homogeneous Besov space $\dot{B}^{\frac{d}{p}-1}_{p,1}\times \dot{B}^{\frac{d}{p}}_{p,1}$ with $p<\infty$, and give a lifespan $T$ of the solution which depends on the norm of the Littlewood-Paley decomposition of the initial data. Then, we prove that if the initial data $(u^n_0,b^n_0)\rightarrow (u_0,b_0)$ in $\dot{B}^{\frac{d}{p}-1}_{p,1}\times \dot{B}^{\frac{d}{p}}_{p,1}$, then the corresponding existence times $T_n\rightarrow T$, which implies that they have a common lower bound of the lifespan. Finally, we prove that the data-to-solutions map depends continuously on the initial data when $p\leq 2d$. Therefore the non-resistive MHD equation is local well-posedness in the homogeneous Besov space in the Hadamard sense. Our obtained result improves considerably the recent results in \cite{Li1,chemin1,Feffer2}.
The very simple product of the number of particles by the number of holes appearing in the expression of the reduced B(E2: 0+1 -> 2+1) (B(E2)^) transition probability of even-even nuclei obtained from the extension of the seniority scheme is used to analyze in a same time the experimental B(E2)^ values of 56-68 Ni and those of 62-72Zn. The evolution of these B(E2)^ values with neutron number fits in with a scenario involving p-n interaction.
We study stochastic acceleration models for the Fermi bubbles. Turbulence is excited just behind the shock front via Kelvin--Helmholtz, Rayleigh--Taylor, or Richtmyer--Meshkov instabilities, and plasma particles are continuously accelerated by the interaction with the turbulence. The turbulence gradually decays as it goes away from the shock fronts. Adopting a phenomenological model for the stochastic acceleration, we explicitly solve the temporal evolution of the particle energy distribution in the turbulence. Our results show that the spatial distribution of high-energy particles is different from those for a steady solution. We also show that the contribution of electrons that escaped from the acceleration regions significantly softens the photon spectrum. The photon spectrum and surface brightness profile are reproduced by our models. If the escape efficiency is very high, the radio flux from the escaped low-energy electrons can be comparable to that of the WMAP haze. We also demonstrate hadronic models with the stochastic acceleration, but they are unlikely in the viewpoint of the energy budget.
We report on our investigation of the electrical properties of metal/Al2O3/GaN metal-insulator-semiconductor (MIS) capacitors. We determined the conduction band offset and interface charge density of the alumina/GaN interface by analyzing capacitance-voltage characteristics of atomic layer deposited Al2O3 films on GaN substrates. The conduction band offset at the Al2O3/GaN interface was calculated to be 2.13 eV, in agreement with theoretical predications. A non-zero field of 0.93 MV/cm in the oxide under flat-band conditions in the GaN was inferred, which we attribute to a fixed net positive charge density of magnitude 4.60x1012 cm-2 at the Al2O3/GaN interface. We provide hypotheses to explain the origin of this charge by analyzing the energy band line-up.
An elementary proof that certain pairs of $2\times 2$ matrices with nonnegative real coordinates generate free monoids.
We study the structure and properties of hot MHD accretion onto a Kerr black hole. In such a system, the hole is magnetically coupled to the inflowing gas and exerts a torque onto the accretion flow. A hot settling flow can form around the hole and transport the angular momentum outward, to the outer edge of the flow. Unlike other hot flows, such as advection- and convection-dominated flows and inflow-outflow solutions (ADAFs, CDAFs, and ADIOS), the properties of the hot settling flow are determined by the spin of the central black hole, but are insensitive to the mass accretion rate. Therefore, it may be possible to identify rapidly spinning BHs simply from their broad-band spectra.   Observationally, the hot settling flow around a Kerr hole is somewhat similar to other hot flows in that they all have hard, power-law spectra and relatively low luminosities. Thus, most black hole candidates in the low/hard and, perhaps, intermediate X-ray state may potentially accrete via the hot settling flow. However, a settling flow will be somewhat more luminous than ADAFs/CDAFs/ADIOS, will exhibit high variability in X-rays, and may have relativistic jets. This suggests that galactic microquasars and active galactic nuclei may be powered by hot settling flows. We identify several galactic X-ray sources as the best candidates.
We analyze archival Chandra HRC observations of the ultra luminous accreting pulsar M82-X2 (NuSTAR J095551+6940.8), and determine an upper limit of $< 1.7\times 10^{38}$~erg/s to its luminosity at an epoch at which it was undetected. Combined with other recent measurements, this confirms that the source X-ray emission has been highly variable during the last 15 years, ranging from a maximum of $10^{40}$ erg/s through intermediate values $\sim$ a few $\times 10^{39}$ erg/s, and down to a minimum that must be below the current detection threshold $\sim (2-3) \times 10^{38}$ erg/s . We interpret these results by means of a magnetically-threaded disk model: when at peak luminosity, the neutron star (NS) is close to spin equilibrium, its inner disk edge r_m ~ 10^8 cm is approximately half the corotation radius r_{co}, and radiation pressure dominates the disk out to r_{tr} ~ 10^9 cm. In the radiation pressure-dominated regime, r_m grows very slowly as the mass inflow rate drops: as a result, r_m < r_{co} remains valid until the mass accretion rate becomes ~ the Eddington accretion rate, allowing a wide range of accretion luminosities to the NS. Once the mass accretion rate is below Eddington, accretion onto the NS is inhibited because r_m > r_{co}, and the source luminosity is expected to drop by a large factor. We conclude that a magnetically threaded, radiation pressure-dominated disk, around a highly magnetized NS (B~10^{13} G) offers the best intepretation for all the currently observed properties of NuSTAR J095551+6940.8. This source offers an unprecedented opportunity to study the disk-magnetosphere interaction in a new regime of supercritical accretion, and across the transition between-radiation pressure and gas-pressure dominance inside the disk.
This article is devoted to prove a stability result for two independent coefficients for a Schr\"odinger operator in an unbounded strip. The result is obtained with only one observation on an unbounded subset of the boundary and the data of the solution at a fixed time on the whole domain.
We develop a linear-response transport theory of diffusive spin and heat transport by magnons in magnetic insulators with metallic contacts. The magnons are described by a position dependent temperature and chemical potential that are governed by diffusion equations with characteristic relaxation lengths. Proceeding from a linearized Boltzmann equation, we derive expressions for length scales and transport coefficients. For yttrium iron garnet (YIG) at room temperature we find that long-range transport is dominated by the magnon chemical potential. We compare the model's results with recent experiments on YIG with Pt contacts [L.J. Cornelissen, et al., Nat. Phys. 11, 1022 (2015)] and extract a magnon spin conductivity of $\sigma_{m}=5\times10^{5}$ S/m. Our results for the spin Seebeck coefficient in YIG agree with published experiments. We conclude that the magnon chemical potential is an essential ingredient for energy and spin transport in magnetic insulators.
This work considers a stochastic model in which the uncertainty is driven by a multidimensional Brownian motion. The market price of risk process makes the transition between real world probability measure and risk neutral probability measure. Traditionally, the martingale representation formulas under the risk neutral probability measure requires the market price of risk process to be bounded. However, in several financial models the boundedness assumption of the market price of risk fails. One example is a stock price model with the market price of risk following an Ornstein-Uhlenbeck process. This work extends Clark-Haussmann formula to underlying stochastic processes which fail to satisfy the standard requirements. Our result can be applied to hedging and optimal investment in stock markets with unbounded market price of risk.
We report the discovery of X-ray periodicity of ~265.3 ms from a deep XMM-Newton observation of the radio-quiet gamma-ray pulsar, PSR J2021+4026, located at the edge of the supernova remnant G78.2+2.1 (gamma-Cygni).The detected frequency is consistent with the gamma-ray pulsation determined by the observation of Fermi Gamma-ray Space Telescope at the same epoch. The X-ray pulse profile resembles the modulation of hot spot on the surface of the neutron star. The phase-averaged spectral analysis also suggests that the majority of the observed X-rays have a thermal origin. This is the third member in the class of radio-quiet pulsars with the significant pulsations detected from both X-rays and gamma-ray regimes.
We compute the symbol of the first two-loop amplitudes in planar ${\cal N}=4$ SYM with algebraic letters, the eight-point NMHV amplitude (or the dual octagon Wilson loops). We show how to apply $\bar{Q}$ equations for computing the differential of two-loop $n$-point NMHV amplitudes and present the result for n=8 explicitly. The symbol alphabet for octagon consists of 180 independent rational letters and 18 algebraic ones involving Gram-determinant square roots. We comment on all-loop predictions for final entries and aspects of the result valid for all multiplicities.
One of Demailly's characterizations of Seshadri constants on ample line bundles works with Lelong numbers of certain positive singular hermitian metrics. In this note sections of multiples of the line bundle are used to produce such metrics and then to deduce another formula for Seshadri constants. It is applied to compute Seshadri constants on blown up products of curves, to disprove a conjectured characterization of maximal rationally connected quotients and to introduce a new approach to Nagata's conjecture.
We report a precise experimental study on the shot noise of a quantum point contact (QPC) fabricated in a GaAs/AlGaAs based high-mobility two-dimensional electron gas (2DEG). The combination of unprecedented cleanliness and very high measurement accuracy has enabled us to discuss the Fano factor to characterize the shot noise with a precision of 1 %. We observed that the shot noise at zero magnetic field exhibits a slight enhancement exceeding the single particle theoretical prediction, and that it gradually decreases as a perpendicular magnetic field is applied. We also confirmed that this additional noise completely vanishes in the quantum Hall regime. These phenomena can be explained by the electron heating effect near the QPC, which is suppressed with increasing magnetic field.
We show that all $n$-qubit entangled states, with the exception of tensor products of single-qubit and bipartite maximally-entangled states, admit Hardy-type proofs of non-locality without inequalities or probabilities. More precisely, we show that for all such states, there are local, one-qubit observables such that the resulting probability tables are logically contextual in the sense of Abramsky and Brandenburger, this being the general form of the Hardy-type property. Moreover, our proof is constructive: given a state, we show how to produce the witnessing local observables. In fact, we give an algorithm to do this. Although the algorithm is reasonably straightforward, its proof of correctness is non-trivial. A further striking feature is that we show that $n+2$ local observables suffice to witness the logical contextuality of any $n$-qubit state: two each for two for the parties, and one each for the remaining $n-2$ parties.
35 Eclipsing binaries presenting unambiguous total eclipses were selected from a subsample of the list of Wyrzykowski et al. (2003). The photometric elements are given for the I curve in DiA photometry, as well as approximate Teff and masses of the components. The interest of these systems is stressed in view of future spectroscopic observations.
In this paper we propose a conjecture about integer solutions to any equations, based on Primal algebra specifically this conjecture is a corollary of the Acu\~na Theorem in that article. Also some problems are proposed which, if the conjecture is correct, could be solved.
In statistical physics, the XY model in two dimensions provides the paradigmatic example of phase transitions mediated by topological defects (vortices). Over the years, a variety of analytical and numerical methods have been deployed in an attempt to fully understand the nature of its transition, which is of the Berezinskii-Kosterlitz-Thouless type. These met with only limited success until it was realized that subtle effects (logarithmic corrections) that modify leading behaviour must be taken into account. This realization prompted renewed activity in the field and significant progress has been made. This paper contains a review of the importance of such subtleties, the role played by vortices and of recent and current research in this area. Directions for desirable future research endeavours are outlined.
We study properties of stable, strictly stable and locally outermost marginally outer trapped surfaces in spacelike hypersurfaces of spacetimes possessing certain symmetries such as isometries, homotheties and conformal Killings. We first obtain results for general diffeomorphisms in terms of the so-called metric deformation tensor and then particularize to different types of symmetries. In particular, we find restrictions at the surfaces on the vector field generating the symmetry. Some consequences are discussed. As an application we present a result on non-existence of stable marginally outer trapped surfaces in slices of FLRW.
The vector-tensor multiplet is coupled off-shell to an N=2 vector multiplet such that its central charge transformations are realized locally. A gauged central charge is a necessary prerequisite for a coupling to supergravity and the strategy underlying our construction uses the potential for such a coupling as a guiding principle. The results for the action and transformation rules take a nonlinear form and necessarily include a Chern-Simons term. After a duality transformation the action is encoded in a homogeneous holomorphic function consistent with special geometry.
We are engaged in a multi-wavelength study of several Galactic HII regions that exhibit signposts of triggered star formation on their borders, and where the collect and collapse process could be at work. When addressing the question of triggered star formation it is critically important to ensure the real association between the ionized gas and the neutral material observed nearby. In this paper we stress this point, and present CO observations of the RCW 82 star forming region. The velocity distribution of the molecular gas is combined with the study of young stellar objects (YSOs) detected in the direction of RCW 82. We discuss the YSO's evolutionary status using near- and mid-IR data. The spatial and velocity distributions of the molecular gas are used to discuss the possible scenarios for the star formation around RCW 82.
We construct the explicit boundary state description of the vortex-type (codimension two) tachyon condensation in brane-antibrane systems generalizing the known result of the kink-type (Frau et al. hep-th/9903123). In this description we show how the RR-charge of the lower dimensional D-branes emerges. We also investigate the tachyon condensation in T^4/Z_2 orbifold and find that the twisted sector can be treated almost in the same way as the untwisted sector from the viewpoint of the boundary state. Further we discuss the higher codimension cases.
The spectroscopic factors for the low-lying quasi-hole states observed in the 16O(e,e'p)15N reaction are reinvestigated with a variational Monte Carlo calculation for the structure of the initial and final nucleus. A computational error in a previous report is rectified. It is shown that a proper treatment of center-of-mass motion does not lead to a reduction of the spectroscopic factor for $p$-shell quasi-hole states, but rather to a 7% enhancement. This is in agreement with analytical results obtained in the harmonic oscillator model. The center-of-mass effect worsens the discrepancy between present theoretical models and the experimentally observed single-particle strength. We discuss the present status of this problem, including some other mechanisms that may be relevant in this respect.
We compute the zero bias conductance of electrons through a single ballistic channel weakly coupled to a side quantum dot with Coulomb interaction. In contrast to the standard setup which is designed to measure the transport through the dot, the channel conductance reveals Coulomb blockade dips rather then peaks due to the Fano-like backscattering. At zero temperature the Kondo effect leads to the formation of broad valleys of small conductance corresponding to an odd number of electrons on the dot. By applying a magnetic field in the dot region we find two dips corresponding to a total suppression in the conductance of spins up and down separated by an energy of the order of the Coulomb interaction. This provides a possibility of a perfect spin filter.
Background: The nuclear kinetic density is one of many fundamental quantities in density functional theory (DFT) dependent on the nonlocal nuclear density. Often, approximations may be made when computing the density that may result in spurious contributions in other DFT quantities. With the ability to compute the nonlocal nuclear density from ab initio wave functions, it is now possible to estimate effects of such spurious contributions. Purpose: We derive the kinetic density using ab initio nonlocal scalar one-body nuclear densities computed within the no-core shell model (NCSM) approach, utilizing two- and three-nucleon chiral interactions as the sole input. With the ability to compute translationally invariant nonlocal densities, it is possible to directly gauge the impact of the spurious center-of-mass (COM) contributions in DFT quantities such as the kinetic density. Methods: The nonlocal nuclear densities are derived from the NCSM one-body densities calculated in second quantization. We present a review of COM contaminated and translationally invariant nuclear densities. We then derive an analytic expression for the kinetic density using these nonlocal densities, producing an ab initio kinetic density. Results: The ground state nonlocal densities of \textsuperscript{4,6,8}He, \textsuperscript{12}C, and \textsuperscript{16}O are used to compute the kinetic densities of the aforementioned nuclei. The impact of the COM removal technique in the densities is discussed. The results of this work can be extended to other fundamental quantities in DFT. Conclusions: The use of a general nonlocal density allows for the calculation of fundamental quantities taken as input in theories such as DFT. This allows benchmarking of procedures for COM removal in different many-body techniques.
We study SUSY models in which Bino contributions solve the muon g-2 anomaly. The contributions are enhanced by large left-right mixing of the smuons. However, it is constrained by the vacuum stability condition of the slepton--Higgs potential. Therefore, there are upper bounds on masses of sleptons and Bino. When the slepton soft masses are universal, the upper bound on the smuon mass becomes 330 (460)GeV in order to solve the g-2 anomaly at the 1 sigma (2 sigma) level. It is within the reach of LHC and ILC. If the stau is heavier than the smuon, the bound can be as large as 1.4 (1.9)TeV. Such non-universal slepton mass spectrum generically predicts too large LFV/CPV. We show that the models are expected to be probed by LHC/ILC and LFV/CPV complementarily in future.