ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study the security of a specific authentication procedure of interest in the context of Quantum Key Distribution (QKD). It works as follows: use a secret but fixed Strongly Universal$_2$ (SU$_2$) hash function and encrypt the output tag with a one-time pad (OTP). If the OTP is completely secret, the expected time for an adversary to create a tag for a chosen message is exponential in the tag length. If, however, the OTP is partially known in each authentication round, as is the case in practical QKD protocols, then the picture is different; the adversary's partial knowledge of the OTP in each authentication round gives partial information on the secret hash function, and this weakens the authentication in later rounds. The effect of this is that the lifetime of the system is linear in the length of the fixed key. This is supported by the composability theorem for QKD, that in this setting provides an upper bound to the security loss on the secret hash function, which is exponential in the number of authentication rounds. This needs to be taken into account when using the protocol, since the authentication gets weakened at each subsequent round and thus the QKD generated is key is not as strong as when the authentication is strong. Some countermeasures are discussed at the end of this paper.
We study the Crank-Nicolson scheme for stochastic differential equations (SDEs) driven by multidimensional fractional Brownian motion $(B^{1}, \dots, B^{m})$ with Hurst parameter $H \in (\frac 12,1)$. It is well-known that for ordinary differential equations with proper conditions on the regularity of the coefficients, the Crank-Nicolson scheme achieves a convergence rate of $n^{-2}$, regardless of the dimension. In this paper we show that, due to the interactions between the driving processes $ B^{1}, \dots, B^{m} $, the corresponding Crank-Nicolson scheme for $m$-dimensional SDEs has a slower rate than for the one-dimensional SDEs. Precisely, we shall prove that when $m=1$ and when the drift term is zero, the Crank-Nicolson scheme achieves the exact convergence rate $n^{-2H}$, while in the case $m=1$ and the drift term is non-zero, the exact rate turns out to be $n^{-\frac12 -H}$. In the general case when $m>1$, the exact rate equals $n^{\frac12 -2H}$. In all these cases the limiting distribution of the leading error is proved to satisfy some linear SDE driven by Brownian motions independent of the given fractional Brownian motions.
The source 4U 1702-429 (Ara X-1) is a low-mass X-ray binary system hosting a neutron star. Albeit the source is quite bright ( $\sim10^{37}$ erg s$^{-1}$) its broadband spectrum has never been studied. Neither dips nor eclipses have been observed in the light curve suggesting that its inclination angle is smaller than 60$^{\circ}$.We analysed the broadband spectrum of 4U 1702-429 in the 0.3-60 keV energy range, using XMM-Newton and INTEGRAL data, to constrain its Compton reflection component if it is present. After excluding the three time intervals in which three type-I X-ray bursts occurred, we fitted the joint XMM-Newton and INTEGRAL spectra obtained from simultaneous observations. A broad emission line at 6.7 keV and two absorption edges at 0.87 and 8.82 keV were detected. We found that a self-consistent reflection model fits the 0.3-60 keV spectrum well. The broadband continuum is composed of an emission component originating from the inner region of the accretion disc, a Comptonised direct emission coming from a corona with an electron temperature of $2.63 \pm 0.06$ keV and an optical depth $\tau=13.6 \pm 0.2$, and, finally, a reflection component. The best-fit indicates that the broad emission line and the absorption edge at 8.82 keV, both associated with the presence of \ion{Fe}{xxv} ions, are produced by reflection in the region above the disc with a ionisation parameter of $Log(\xi) \simeq 2.7$. We have inferred that the inner radius, where the broad emission line originates, is $64^{+52}_{-15}$ km, and the inner radius of the accretion disc is $39^{+6}_{-8}$ km. (Abridged)
A Zevatron is an accelerator scheme envisaged to accelerate particles to ZeV energies (1 ZeV = $10^{21}$ eV). Schemes, most notably the internal shock model, have been proposed to explain the acceleration of ultra-high-energy cosmic-ray (UHECR) particles that have been sporadically detected reaching Earth since 1962. Here, the cyclotron auto-resonance acceleration (CARA) mechanism is tailored and used to demonstrate possible acceleration of particles ejected as a result of violent astrophysical processes such as the merger of a binary system or a supernova explosion. Such events result in emission of highly-energetic particles and ultra-intense beamed radiation. In the simultaneous presence of a super-strong magnetic field, the condition for cyclotron auto-resonance may be met. Thus CARA can act like a {\it booster} for particles pre-accelerated inside their progenitor by shock waves, possibly among other means. As examples, it is shown that nuclei of hydrogen, helium, and iron-56, may reach ZeV energies by CARA, under which conditions the particles, while gyrating around the lines of an ultra-strong magnetic field, also surf on the waves of a super-intense radiation field. When radiation-reaction is taken into account, it is shown that the ZeV energy gained by a particle can fall off by less than an order-of-magnitude if the resonance condition is missed by roughly less than 20\%.
It is shown that two electrons located in a quantum well near a metal electrode attract each other due to the spin-orbit interaction (SOI) of the Bychkov-Rashba type and the electrostatic image forces. Using the example of a simple model, it is shown that, with quite attainable values of the characteristic parameters of the system, the effective attraction caused by SOI prevails over the Coulomb repulsion, and the formation of a bielectron becomes possible.
We develop an analytical tool which is adept for detecting shapes of oscillatory functions, is useful in decomposing homogenization problems into limit-problems for kinetic equations, and provides an efficient framework for the validation of multi-scale asymptotic expansions. We apply it first to a hyperbolic homogenization problem and transform it to a hyperbolic limit problem for a kinetic equation. We establish conditions determining an effective equation and counterexamples for the case that such conditions fail. Second, when the kinetic decomposition is applied to the problem of enhanced diffusion, it leads to a diffusive limit problem for a kinetic equation that in turn yields the effective equation of enhanced diffusion.
The era of detailed asteroseismic analyses opened by space missions such as CoRoT and $\textit{Kepler}$ has highlighted the need for stellar models devoid of numerical inaccuracies, in order to be able to diagnose which physical aspects are being ignored or poorly treated in standard stellar modeling. We tackle here the important problem of fixing convective zones boundaries in the frame of the local mixing length theory. First we show that the only correct way to locate a convective zone boundary is to find, at each iteration step, through interpolations or extrapolations from points $\textit{within the convective zone}$, the mass where the radiative luminosity is equal to the total one. We then discuss two misuses of the boundary condition and the way they affect stellar modeling and stellar evolution. The first one consists in applying the neutrality condition for convective instability on the $\textit{radiative}$ side of the convective boundary. The second way of misusing the boundary condition comes from the process of fixing the convective boundary through the search for a change of sign of a possibly \textit{discontinuous} function. We show that these misuses can lead to completely wrong estimates of convective core sizes with important consequences for the following evolutionary phases. We point out the advantages of using a double mesh point at each convective zone boundaries. The specific problem of a convective shell is discussed and some remarks concerning overshooting are given.
We propose a new computational method for astrophysical reaction rate of radiative capture process. In the method, an evolution of a wave function is calculated along the imaginary-time axis which is identified as the inverse temperature. It enables direct evaluation of reaction rate as a function of temperature without solving any scattering problem. The method is tested for two-body radiative capture reaction, ${^{16}{\rm O}}(\alpha,\gamma){^{20}{\rm Ne}}$, showing that it gives identical results to that calculated by the ordinary procedure. The new method will be suited for calculation of triple-alpha radiative capture rate for which an explicit construction of the scattering solution is difficult.
We investigate the Non-Commutative Abelian Higgs model. We argue that it is possible to introduce a consistent renormalization method by imposing the Non-commutative BRST invariance of the theory and by introducing the Non-Commutative Quasi-Classical Action Principle.
The Schottky diode, BN/GaN layered composite contacting to bulk aluminum, is theoretically plausible to harvest wireless energy above X-band. According to our first principle calculation, the insertion of GaN layers dramatically influences the optical properties of the layered composite. The relative dielectric constant of BN/GaN layered composite as a function of layer-to-layer separation is investigated where the optimized dielectric constant is 3.1. Furthermore, we design another Schottky diode via nanostructuring. Our first principle calculation suggests that the relative dielectric constant of boron nitride monolayer can be minimized to 1.5 only if it is deposited on aluminum monolayer. It is rare to find a semiconductor with the dielectric constant close to 1 which may push the cut-off frequency of Al/BN-based rectenna to the high-band 5G network.
In star forming regions in our own Galaxy, the 14N/15N ratio is found to vary from $\sim$ 100 in meteorites, comets and protoplanetary disks up to $\sim$ 1000 in pre-stellar and star forming cores, while in external galaxies the very few single-dish large scale measurements of this ratio lead to values of 100-450. The extent of the contribution of isotopic fractionation to these variations is, to date, unknown. In this paper we present a theoretical chemical study of nitrogen fractionation in external galaxies in order to determine the physical conditions that may lead to a spread of the 14N/15N ratio from the solar value of $\sim$440 and hence evaluate the contribution of chemical reactions in the ISM to nitrogen fractionation. We find that the main cause of ISM enrichment of nitrogen fractionation is high gas densities, aided by high fluxes of cosmic rays.
The high polarization observed in the prompt phase of some gamma-ray bursts (GRBs) arouses extensive studies on the emission mechanism. In this paper, we investigate the polarization properties of the synchrotron-self-Compton (SSC) process from a highly relativistic jet. A magnetic-dominated, baryon-loaded jet ejected from the central engine travels with a large Lorentz factor. Shells with slightly different velocities collide with each other and produce shocks. The shocks accelerate electrons to power-law distribution, and at the same time, magnify the magnetic field. Electrons move in the magnetic field and produce synchrotron photons. The synchrotron photons suffer from the Compton scattering (CS) process and then are detected by an observer locating slightly off-axis. We derive analytically the formulae of photon polarization in the SSC process in two magnetic configurations: magnetic field in the shock plane and perpendicular to the shock plane. We show that photons induced by the SSC process can be highly polarized, with the maximum polarization $\Pi \sim 24\%$ in the energy band $[0.5,5]$ MeV. The polarization depends on the viewing angles, peaking in the plane perpendicular to the magnetic field. In the energy band $[0.05,0.5]$ MeV, in which most $\gamma$-ray polarimeters are active, the polarization is about twice of that in the Thomson limit, reaching to $\Pi\sim 20\%$. This implies that the Klein-Nishina effect, which is often neglected in literatures, should be carefully considered.
In 1969, H. Davenport and W. Schmidt established a measure of simultaneous approximation for a real number \xi and its square by rational numbers with the same denominator, assuming only that \xi is not rational nor quadratic over Q. Here, we show by an example, that this measure is optimal. We also indicate several properties of the numbers for which this measure is optimal, in particular with respect to approximation by algebraic integers of degree at most three.
Existing approaches for unsupervised metric learning focus on exploring self-supervision information within the input image itself. We observe that, when analyzing images, human eyes often compare images against each other instead of examining images individually. In addition, they often pay attention to certain keypoints, image regions, or objects which are discriminative between image classes but highly consistent within classes. Even if the image is being transformed, the attention pattern will be consistent. Motivated by this observation, we develop a new approach to unsupervised deep metric learning where the network is learned based on self-supervision information across images instead of within one single image. To characterize the consistent pattern of human attention during image comparisons, we introduce the idea of transformed attention consistency. It assumes that visually similar images, even undergoing different image transforms, should share the same consistent visual attention map. This consistency leads to a pairwise self-supervision loss, allowing us to learn a Siamese deep neural network to encode and compare images against their transformed or matched pairs. To further enhance the inter-class discriminative power of the feature generated by this network, we adapt the concept of triplet loss from supervised metric learning to our unsupervised case and introduce the contrastive clustering loss. Our extensive experimental results on benchmark datasets demonstrate that our proposed method outperforms current state-of-the-art methods for unsupervised metric learning by a large margin.
The purpose of the paper is to find the joint distribution of the hitting time and place of two-dimensional Brownian motion hitting the negative horizontal axis. We provide various formulas for Green functions as well as for the conditional distributions. In the end we treat an analogous problem for the case when vertical component has a negative drift.
We propose a scalable approach to building cluster states of matter qubits using coherent states of light. Recent work on the subject relies on the use of single photonic qubits in the measurement process. These schemes can be made robust to detector loss, spontaneous emission and cavity mismatching but as a consequence the overhead costs grow rapidly, in particular when considering single photon loss. In contrast, our approach uses continuous variables and highly efficient homodyne measurements. We present a two-qubit scheme, with a simple bucket measurement system yielding an entangling operation with success probability 1/2. Then we extend this to a three-qubit interaction, increasing this probability to 3/4. We discuss the important issues of the overhead cost and the time scaling. This leads to a "no-measurement" approach to building cluster states, making use of geometric phases in phase space.
The recent discovery of an eclipsing hierarchical triple system with two low-mass stars in a close orbit (KOI-126) by Carter et al. (2011) appeared to reinforce the evidence that theoretical stellar evolution models are not able to reproduce the observational mass-radius relation for low-mass stars. We present a set of stellar models for the three stars in the KOI-126 system that show excellent agreement with the observed radii. This agreement appears to be due to the equation of state implemented by our code. A significant dispersion in the observed mass-radius relation for fully convective stars is demonstrated; indicative of the influence of physics currently not incorporated in standard stellar evolution models. We also predict apsidal motion constants for the two M-dwarf companions. These values should be observationally determined to within 1% by the end of the Kepler mission.
MnGe has been grown as a thin film on Si(111) substrates by molecular beam epitaxy. A 10 \AA\ layer of MnSi was used as seedlayer in order to establish the B20 crystal structure. Films of a thickness between 45 and 135 \AA\ have been prepared and structually characterized by RHEED, AFM and XRD. These techniques give evidence that MnGe forms in the cubic B20 crystal structure as islands exhibiting a very smooth surface. The islands become larger with increasing film thickness. A magnetic characterization reveals that the ordering temperature of MnGe thin films is enhanced compared to bulk material. The properties of the helical magnetic structure obtained from magnetization and magnetoresistivity measurements are compared with films of the related compound MnSi. The much larger Dzyaloshinskii-Moriya interaction in MnGe results in a higher rigidness of the spin helix.
We review the fundamentals and the recent developments in understanding of common envelope physics. We report specifically on the progress that was made by the consideration of the recombination energy. This energy is found to be responsible for the complete envelope ejection in the case of a prompt binary formation, for the delayed dynamical ejections in the case of a self-regulated spiral-in, and for the steady recombination outflows during the transition between the plunge-in and the self-regulated spiral-in. Due to different ways how the recombination affects the common envelope during fast and slow spiral-ins, the apparent efficiency of the orbital energy use can be different between the two types of spiral-ins by a factor of ten. We also discuss the observational signatures of the common envelope events, their link a new class of astronomical transients, Luminous Red Novae, and to a plausible class of very luminous irregular variables.
One important result from recent large integral field spectrograph (IFS) surveys is that the intrinsic velocity dispersion of galaxies traced by star-forming gas increases with redshift. Massive, rotation-dominated discs are already in place at z~2, but they are dynamically hotter than spiral galaxies in the local Universe. Although several plausible mechanisms for this elevated velocity dispersion (e.g. star formation feedback, elevated gas supply, or more frequent galaxy interactions) have been proposed, the fundamental driver of the velocity dispersion enhancement at high redshift remains unclear. We investigate the origin of this kinematic evolution using a suite of cosmological simulations from the FIRE (Feedback In Realistic Environments) project. Although IFS surveys generally cover a wider range of stellar masses than in these simulations, the simulated galaxies show trends between intrinsic velocity dispersion, SFR, and redshift in agreement with observations. In both the observed and simulated galaxies, intrinsic velocity dispersion is positively correlated with SFR. Intrinsic velocity dispersion increases with redshift out to z~1 and then flattens beyond that. In the FIRE simulations, intrinsic velocity dispersion can vary significantly on timescales of <100 Myr. These variations closely mirror the time evolution of the SFR and gas inflow rate. By cross-correlating pairs of intrinsic velocity dispersion, gas inflow rate, and SFR, we show that increased gas inflow leads to subsequent enhanced star formation, and enhancements in intrinsic velocity dispersion tend to temporally coincide with increases in gas inflow rate and SFR.
The density-dependent mobility of n-type HgTe quantum wells with inverted band ordering has been studied both experimentally and theoretically. While semiconductor heterostructures with a parabolic dispersion exhibit an increase in mobility with carrier density, high quality HgTe quantum wells exhibit a distinct mobility maximum. We show that this mobility anomaly is due to backscattering of Dirac fermions from random fluctuations of the band gap (Dirac mass). Our findings open new avenues for the study of Dirac fermion transport with finite and random mass, which so far has been hard to access.
Galaxies in the Las Campanas Redshift Survey are classified according to their spectra, and the resulting spectral types are analyzed to determine if local environment affects their properties. We find that the luminosity function of early-type objects varies as a function of local density. Our results suggest that early-type galaxies (presumably ellipticals and S0's) are, on average, fainter when they are located in high-density regions of the Universe. The same effect may operate for some, but not all, late-type galaxies. We discuss the implications of this result for theories of galaxy formation and evolution.
Nonequilibrium statistical physics is concerned with a fundamental problem in physics, the phenomenon of irreversibility, which is not rigorously solved yet. Different approaches to the statistical mechanics of nonequilibrium processes are based on empirical assumptions but a rigorous, first principle theory is missing. An important contribution to describe irreversible behavior starting from reversible Hamiltonian dynamics was given by Zubarev who invented the method of the nonequilibrium statistical operator (NSO). We discuss this approach, in particular the extended von Neumann equation and the entropy concept. The method of NSO proved to be a general and universal approach to different nonequilibrium phenomena. Typical applications are the quantum master equation, kinetic theory, and linear response theory which are outlined and illustrated solving standard examples for reaction and transport processes. Some open questions are emphasized.
Starting from the concept of the universal exterior algebra in non-commutative differential geometry we construct differential forms on the quantum phase-space of an arbitrary system. They bear the same natural relationship to quantum dynamics which ordinary tensor fields have with respect to classical hamiltonian dynamics.
The interplay of the tunneling transfer of charges and the emission and absorption of light can be investigated in a set-up, where a voltage-biased Josephson junction is placed in series to a microwave cavity. Here, we concentrate on the emission process and show that due to the inherent nonlinearity of the Josephson junction tunneling Cooper-pairs can create a variety of non-classical states of light. Depending on experimental parameters and tuning the device can be described by effective Hamiltonians, indicating specific photon creation mechanisms which lead to strongly bunched or anti-bunched light emission. We derive explicit analytical expressions for the photon correlation function $g^{(2)}(\tau=0)$ for these different processes and investigate their full crossover numerically. Photon distribution functions show squeezing and other interesting non-Poissonian behavior.