ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper we consider diffusions on the half line (0, $\infty$) such that the expectation of the arrival time at the origin is uniformly bounded in the initial point. This implies that there is a well defined diffusion process starting from infinity, which takes finite values at positive times. We study the behaviour of hitting times of large barriers and in a dual way, the behaviour of the process starting at infinity for small time. In particular we prove that the process coming down from infinity is in small time governed by a specific deterministic function. Suitably normalized fluctuations of the hitting times are asymptotically Gaussian. We also derive the tail of the distribution of the hitting time of the origin and a Yaglom limit for the diffusion starting from infinity. We finally prove that the distribution of this process killed at the origin is absolutely continuous with respect to the speed measure. The density is expressed in terms of the eigenvalues and eigenfunctions of the generator of the killed diffusion.
Electronic states in silicon quantum dots are examined theoretically, taking into account a multivalley structure of the conduction band. We find that (i) exchange interaction hardly works between electrons in different valleys. In consequence electrons occupy the lowest level in different valleys in the absence of Hund's coupling when the dot size is less than 10 nm. High-spin states are easily realized by applying a small magnetic field. (ii) When the dot size is much larger, the electron-electron interaction becomes relevant in determining the electronic states. Electrons are accommodated in a valley, making the highest spin, to gain the exchange energy. (iii) In the presence of intervalley scattering, degenerate levels in different valleys are split. This could result in low-spin states. These spin states in multivalley artificial atoms can be observed by looking at the magnetic-field dependence of peak positions in the Coulomb oscillation.
The spin-orbit -induced spin splitting of energy bands in low symmetry compounds (the Rashba Effect) has a long-standing relevance to spintronic applications and to the fundamental understanding of symmetry breaking in solids, yet the knowledge of what controls its magnitude in different materials is difficult to anticipate. Indeed, rare discoveries of compounds with large Rashba coefficients are invariably greeted as pleasant surprises. We advance the understanding of the "Rashba Scale" using the "inverse design" approach by formulating theoretically the relevant design principle and then identifying compounds that satisfy it. We show that the presence of energy band anti-crossing provides a causal design principle of compounds with large Rashba coefficients, leading to the identification via first-principles calculations of 34 rationally designed strong-Rashba compounds. Since topological insulators must have band anti crossing, this leads us to establish an interesting cross functionality of "Topological Rashba Insulators" (TRI) that may provide a platform for the simultaneous control of spin splitting and spin-polarization.
The study of scattering encounters continues to provide new insights into the general relativistic two-body problem. The local-in-time conservative dynamics of an aligned-spin binary, for both unbound and bound orbits, is fully encoded in the gauge-invariant scattering-angle function, which is most naturally expressed in a post-Minkowskian (PM) expansion, and which exhibits a remarkably simple dependence on the masses of the two bodies (in terms of appropriate geometric variables). This dependence links the PM and small-mass-ratio approximations, allowing gravitational self-force results to determine new post-Newtonian (PN) information to all orders in the mass ratio. In this paper, we exploit this interplay between relativistic scattering and self-force theory to obtain the third-subleading (4.5PN) spin-orbit dynamics for generic spins, and the third-subleading (5PN) spin$_1$-spin$_2$ dynamics for aligned spins. We further implement these novel PN results in an effective-one-body framework, and demonstrate the improvement in accuracy by comparing against numerical-relativity simulations.
It was recently proposed that the globular cluster system of the very low surface-brightness galaxy NGC1052-DF2 is dynamically very cold, leading to the conclusion that this dwarf galaxy has little or no dark matter. Here, we show that a robust statistical measure of the velocity dispersion of the tracer globular clusters implies a mundane velocity dispersion and a poorly constrained mass-to-light ratio. Models that include the possibility that some of the tracers are field contaminants do not yield a more constraining inference. We derive only a weak constraint on the mass-to-light ratio of the system within the half-light radius (M/L_V<6.7 at the 90% confidence level) or within the radius of the furthest tracer (M/L_V<8.1 at the 90% confidence level). This limit may imply a mass-to-light ratio on the low end for a dwarf galaxy but many Local Group dwarf galaxies fall well within this contraint. With this study, we emphasize the need to reliably account for measurement uncertainties and to stay as close as possible to the data when determining dynamical masses from very small data sets of tracers.
We propose a new method to obtain the K -> pi pi amplitude from K -> pi which allows one to fully account for the effects of final state interactions. The method is based on a set of dispersion relations for the K -> pi pi amplitude in which the weak Hamiltonian carries momentum. The soft pion theorem, which relates this amplitude to the K -> pi amplitude, can be used to determine one of the two subtraction constants - the second constant is at present known only to leading order in chiral perturbation theory.
We calculate the deuteron charge, electric quadrupole, and magnetic form factors up to next-to-next-to-leading order in chiral effective field theory, treating subleading corrections, especially that of chiral nuclear forces, in perturbation theory. We examine the power counting based on naive dimensional analysis by investigating the ultraviolet cutoff variation of these form factors. We find that the N${}^2$LO magnetic form factor shows significant cutoff dependence, suggesting the contact current operator responsible be enhanced. After promotion to N${}^2$LO, it indeed renormalizes the magnetic form factor. This is in agreement with a previous work based on renormalization-group analysis. For the charge and quadrupole moments, perturbative calculation allows us to study how they scale with multiple low-energy parameters such as the pion mass, deuteron binding momentum, and momentum transfer.
We prove that for a Hecke cuspform $f\in S_k(\Gamma_0(N),\chi)$ and a prime $l>\max\{k,6\}$ such that $l\nmid N$, there exists an infinite family $\{k_r\}_{r\geq 1}\subseteq\mathbb{Z}$ such that for each $k_r$, there is a cusp form $f_{k_r}\in S_{k_r}(\Gamma_0(N),\chi)$ such that the Deligne representation $\rho_{f_{k_r,l}}$ is a crystaline and potentially diagonalizable lift of $\overline{\rho}_{f,l}$. When $f$ is $l$-ordinary, we base our proof on the theory of Hida families, while in the non-ordinary case, we adapt a local-to-global argument due to Khare and Wintenberger in the setting of their proof of Serre's modularity conjecture, together with a result on existence of lifts with prescribed local conditions over CM fields, a flatness result due to B\"ockle and a local dimension result by Kisin. We discuss the motivation and tentative future applications of our result in ongoing research on the automorphy of $\mathrm{GL}_{2n}$-representations in the higher level case.
The nearest known binary brown dwarf WISE J104915.57-531906.1AB (LUH 16) is a well-studied benchmark for our understanding of substellar objects. Previously published astrometry of LUH 16 obtained with FORS2 on the Very Large Telescope was affected by errors that limited its use in combination with other datasets, thereby hampering the determination of its accurate orbital parameters and masses. We improve upon the calibration and analysis of the FORS2 astrometry with the help of Gaia DR2 to generate a high-precision dataset that can be combined with present and future LUH 16 astrometry. We demonstrate its use by combining it with available measurements from the Hubble Space Telescope (HST) and Gemini/GeMS and deriving updated orbital and mass parameters. Using Gaia DR2 as astrometric reference field, we derived the absolute proper motion and updated the absolute parallax of the binary to 501.557 +/- 0.082 mas. We refined the individual dynamical masses of LUH 16 to 33.5 +/- 0.3 M[Jupiter] (component A) and 28.6 +/- 0.3 M[Jupiter] (component B), which corresponds to a relative precision of ~1% and is three to four times more precise than previous estimates. We found that these masses show a weak dependence on one datapoint extracted from a photographic plate from 1984. The exact determination of a residual mass bias, if any, will be possible when more high-precision data can be incorporated in the analysis.
We use coupling to study the time taken until the distribution of a statistic on a Markov chain is close to its stationary distribution. Coupling is a common technique used to obtain upper bounds on mixing times of Markov chains, and we explore how this technique may be used to obtain bounds on the mixing of a statistic instead.
We present a new measurement of the systemic proper motion of the Small Magellanic Cloud (SMC), based on an expanded set of 30 fields containing background quasars and spanning a $\sim$3 year baseline, using the \textit{Hubble Space Telescope} (\textit{HST}) Wide Field Camera 3. Combining this data with our previous 5 \textit{HST} fields, and an additional 8 measurements from the \textit{Gaia}-Tycho Astrometric Solution Catalog, brings us to a total of 43 SMC fields. We measure a systemic motion of $\mu_{W}$ = $-0.82$ $\pm$ 0.02 (random) $\pm$ 0.10 (systematic) mas yr$^{-1}$ and $\mu_{N}$ = $-1.21$ $\pm$ 0.01 (random) $\pm$ 0.03 (systematic) mas yr$^{-1}$. After subtraction of the systemic motion, we find little evidence for rotation, but find an ordered mean motion radially away from the SMC in the outer regions of the galaxy, indicating that the SMC is in the process of tidal disruption. We model the past interactions of the Clouds with each other based on the measured present-day relative velocity between them of $103 \pm 26$ km s$^{-1}$. We find that in 97\% of our considered cases, the Clouds experienced a direct collision $147 \pm 33$ Myr ago, with a mean impact parameter of $7.5 \pm 2.5$ kpc.
The recent discovery of two-dimensional magnetic insulators has generated a great deal of excitement over their potential for nanoscale manipulation of spin or magnetism. One intriguing use for these materials is to put them in contact with graphene, with the goal of making graphene magnetic while maintaining its unique electronic properties. Such a system could prove useful in applications such as magnetic memories, or could serve as a host for exotic states of matter. Proximity to a magnetic insulator will alter the spin transport properties of graphene, and the strength of this interaction can be probed with Hanle spin precession experiments. To aid in the analysis of such experiments, in this work we derive an explicit expression for Hanle spin precession in graphene interfaced with a ferromagnetic insulator whose magnetization points perpendicular to the graphene plane. We find that this interface results in a shifted and asymmetric Hanle response, and we discuss how this behavior can be used to interpret measurements of spin transport in these systems.
With the advances in high resolution and spin-resolved scanning tunneling microscopy as well as atomic-scale manipulation, it has become possible to create and characterize quantum states of matter bottom-up, atom-by-atom. This is largely based on controlling the particle- or wave-like nature of electrons, as well as the interactions between spins, electrons, and orbitals and their interplay with structure and dimensionality. We review the recent advances in creating artificial electronic and spin lattices that lead to various exotic quantum phases of matter, ranging from topological Dirac dispersion to complex magnetic order. We also project future perspectives in non-equilibrium dynamics, prototype technologies, engineered quantum phase transitions and topology, as well as the evolution of complexity from simplicity in this newly developing field.
In nonadaptive group testing, the main research objective is to design an efficient algorithm to identify a set of up to $t$ positive elements among $n$ samples with as few tests as possible. Disjunct matrices and separable matrices are two classical combinatorial structures while one provides a more efficient decoding algorithm and the other needs fewer tests, i.e., larger rate. Recently, a notion of strongly separable matrix has been introduced, which has the same identifying ability as a disjunct matrix, but has larger rate. In this paper, we use a modified probabilistic method to improve the lower bounds for the rate of strongly separable matrices. Using this method, we also improve the lower bounds for some well-known combinatorial structures, including locally thin set families and cancellative set families.
We propose the concept of global temperature for spatially non-uniform heat conduction systems. With this novel quantity, we present an extended framework of thermodynamics for the whole system such that the fundamental relation of thermodynamics holds, which we call "global thermodynamics" for heat conduction systems. Associated with this global thermodynamics, we formulate a variational principle for determining thermodynamic properties of the liquid-gas phase coexistence in heat conduction, which corresponds to the natural extension of the Maxwell construction for equilibrium systems. We quantitatively predict that the temperature of the liquid-gas interface deviates from the equilibrium transition temperature. This result indicates that a super-cooled gas stably appears near the interface.
Including the vacuum effects, the compressional properties of nuclear matter are studied in the cutoff field theory. Under the Hartree approximation, the low-energy effective Lagrangian is derived in the framework of the renormalization group methods. The coefficients are determined in a way where the physical results hardly depend on the value of the cutoff which is conveniently introduced into the theory. It is shown that, to reproduce the empirical data of the nucleus incompressibility, the compressibility of the nuclear matter is favorable to be 250$\sim$350MeV.
Convergence of directed forests, spanning on random subsets of lattices or on point processes, towards the Brownian web has made the subject of an abundant literature, a large part of which relies on a criterion proposed by Fontes, Isopi, Newman and Ravishankar (2004). One of their convergence condition, called (B2), states that the probability of the event that there exists three distinct paths for a time interval of length $t(>0)$, all starting within a segment of length $\varepsilon$, is of small order of $\varepsilon$. This condition is often verified by applying an FKG type correlation inequality together with a coalescing time tail estimate for two paths. For many models where paths have complex interactions, it is hard to establish FKG type inequalities. In this article, we show that for a non-crossing path model, with certain assumptions, a suitable upper bound on expected first collision time among three paths can be obtained directly using Lyapunov functions. This, in turn, provides an alternate verification of Condition (B2). We further show that in case of independent simple symmetric one dimensional random walks or in case of independent Brownian motions, the expected value can be computed explicitly. We apply this alternate method of verification of (B2) to several models in the basin of attraction of the Brownian web studied earlier in the literature ([S67], [H71], [FLT04]).
A new proof is given for the explicit formulae for the non-archimedean canonical height on an elliptic curve. This arises as a direct calculation of the Haar integral in the elliptic Jensen formula.
The influence of the Hall effect on the global stability of cool Kepler disks under the influence of an axial magnetic field is considered. For sufficiently large magnetic Reynolds numbers Rm the magnetorotational instability (MRI) exists in a finite interval of magnetic field amplitudes, $B$_{min} < $B$ < $B$_{max}. For Kepler disks the pure MRI needs both rather high Rm (representing the needed electrical conductivity) as well as $B$_{min} of order 0.1 G. The magnetic field pattern resulting from our global and linear calculations is of quadrupolar parity. For magnetic fields $antiparallel$ to the rotation axis the Hall effect reduces the minimum magnetic Reynolds number by about one order of magnitude. The $B$_{min}, however, is even (sightly) increased (see Fig. 6). For magnetic fields $parallel$ to the rotation axis the Hall effect drives its own instability without the action of the Lorentz force. The corresponding critical magnetic Reynolds number proves to be larger with Hall effect (Rm ~ 10) than without Hall effect (Rm ~ 7) so that the Hall effect for parallel fields even disturbs the formation of MHD-instability in cool protoplanetary disks. If the disk is supercritical then the main result of the Hall effect for positive fields is the strong reduction of the minimum magnetic field amplitude which is necessary to start the instability. Observations must show whether in star-forming regions the rotation axis and the magnetic field orientation are correlated or are anticorrelated. If the magnetic fields are high enough then our model predicts the dominance of fields antiparallel to the rotation axis.
We present the new preliminary MRST parton distributions at NLO and NNLO. The analysis includes some new data and there is an improvement in the theoretical treatment at NNLO. Essentially complete NNLO partons are presented for the first time, together with uncertainties.
We report on the behaviour of two-level quantum systems, or qubits, in the background of rotating and non-rotating metrics and provide a method to derive the related spin currents and motions. The calculations are performed in the external field approximation.
Considering the five-dimensional warped spacetime AdS_5 with the D3-brane, we derive a potential in the fifth dimension, according to which ordinary particles are initially confined on the D3-brane. It is estimated, however, that the lightest neutrino with mass m_1 is tunneling away into the extra dimension. Hence there is a possibility that no neutrinos with mass m_1 exist in cosmicbackground neutrinos, but surviving neutrinos are those with heavier masses m_2 and m_3. The other possibilities are also discussed.
Transient electron dynamics and the Fano resonance formation over time in transport through a two quantum dot system in a T-shape geometry (2QD-T) are analysed for free electrons. Time evolution of the transport characteristics are different for a weak and a strong inter-dot coupling with respect to the dot-electrode coupling. When the dot-dot coupling is weak, we find that transport dynamics is governed by two channel tunneling processes with two different relaxation times and buildup of the Fano resonance is developed much slower, with the longer relaxation time. In the opposite limit, the transmission evolves with a single relaxation time, from the single peak resonance structure into the structure with two asymmetric peaks. One observes large dot-electrode charge oscillations, which can temporarily change direction of transient currents. We find also that the time evolution of entanglement is different in both coupling regimes; in particular rapid Rabi oscillations caused by coherent electron transfer between the 2QD states can be seen for the strong dot-dot coupling.
We shall show that no reductive splitting of the spin group exists in dimension 3 \leq m \leq 20 other than in dimension m = 4. In dimension 4 there are reductive splittings in any signature. Euclidean and Lorentzian signatures are reviewed in particular and signature (2, 2) is investigated explicitly in detail. Reductive splittings allow to define a global SU(2)-connection over spacetime which encodes in an weird way the holonomy of the standard spin connection. The standard Barbero-Immirzi (BI) connection used in LQG is then obtained by restriction to a spacelike slice. This mechanism provides a good control on globality and covariance of BI connection showing that in dimension other than 4 one needs to provide some other mechanism to define the analogous of BI connection and control its globality.
We prove a generalization of the Davenport-Heilbronn theorem to quotients of ideal class groups of quadratic fields by the primes lying above a fixed set of rational primes $S$. Additionally, we obtain average sizes for the relaxed Selmer group $\mathrm{Sel}_3^S(K)$ and for $\mathcal{O}_{K,S}^\times/(\mathcal{O}_{K,S}^\times)^3$ as $K$ varies among quadratic fields with a fixed signature ordered by discriminant.
We have examined the local structure of PMN-PT and PZN-PT solid solutions using density functional theory. We find that the directions and magnitudes of cation displacement can be explained by an interplay of cation-oxygen bonding, electrostatic dipole-dipole interactions and short-range direct and through oxygen Pb-B-cation repulsive interactions. We find that the Zn ions off-center in the PZN-PT system, which also enables larger Pb and Nb/Ti displacements. The off-centering behavior of Zn lessens Pb-B-cation repulsion, leading to a relaxor to ferroelectric and a rhombohedral to tetragonal phase transition at low PbTiO$_3$ content in the PZN-PT system. We also show that a simple quadratic relationship exists between Pb and B-cation displacements and the temperature maximum of dielectric constant, thus linking the enhanced displacements in PZN-PT systems with the higher transition temperatures.
Continuum intensity images from PICARD/SODISM and SDO/HMI covering a 209 days period in 2011 are analyzed in order to extract mode parameters for spherical harmonics up to $l=100$. SODISM helioseismology signal is affected by the low orbit of PICARD and by important gaps and CCD persistence effects. SODISM intensity signal has a lower signal to noise ratio and duty cycle than HMI and less modes were successfully fitted over the same period. A comparison of the rotation profiles obtained from both sets of continuum images shows however that the results remain compatible within one standard deviation of HMI formal errors.
We calculate the spin temperature and 21 cm brightness of early \HII regions around the first stars. We use outputs from cosmological radiation-hydrodynamics simulations of the formation and evolution of early \HII regions. In the pre-reionization era, \HII regions around massive primordial stars have diameters of a few kpc. The gas within the \HII regions is almost fully ionized, but begins recombining after the central stars die off. The relic \HII regions are then seen as bright {\it emission} sources in hydrogen 21 cm. We make brightness temperature maps of the \HII regions, accounting for radiative coupling with Lyman-$\alpha$ photons in a simplified manner. The spin temperature in the relic \HII region is close to the gas kinetic temperature, generally several hundred to several thousand degrees. We show that the relic \HII region can be as bright as $\delta T_{\rm b} \sim 100$ mK in differential temperature against the cosmic microwave background for an angular resolution of sub-arcseconds. While individual early \HII patches will not be identified by currently planned radio telescopes, the collective fluctuations from early \HII regions might imprint signatures in the 21 cm background.