ShantanuT01/DACTYL-Pretraining huggingface dataset:
Theory predicts that the currents in scanning tunneling microscopy (STM) and the attractive forces measured in atomic force microscopy (AFM) are directly related. Atomic images obtained in an attractive AFM mode should therefore be redundant because they should be \emph{similar} to STM. Here, we show that while the distance dependence of current and force is similar for graphite, constant-height AFM- and STM images differ substantially depending on distance and bias voltage. We perform spectroscopy of the tunneling current, the frequency shift and the damping signal at high-symmetry lattice sites of the graphite (0001) surface. The dissipation signal is about twice as sensitive to distance as the frequency shift, explained by the Prandtl-Tomlinson model of atomic friction.
A variety of two-dimensional materials possess a band structure with an energy extremal ridge along a ring in momentum space. Examples are biased bilayer graphene, and surfaces and interfaces with a Rashba spin-orbit interaction where at low doping the carriers fill an annulus. This topological feature causes an anomalous screening behavior, which we study using the Thomas-Fermi theory. Specifically, reducing the doping is predicted to enhance the linear screening response, while at zero doping the size of the screening cloud surrounding a Coulomb impurity is found to increase as the cube root of the impurity charge.
Recent measurements on MgV$_2$O$_4$ single crystal have reignited the debate on the role of spin-orbit (SO) coupling in dictating the orbital order in Vanadium spinel systems. Density functional theory calculations were performed using the full-potential linearized augmented-plane-wave method within the local spin density approximation (LSDA), Coulomb correlated LSDA+U, and with SO interaction (LSDA+U+SO) to study the magnetic and orbital ordering in low temperature phase of MgV$_2$O$_4$. It is observed that the spin-orbit coupling in the experimentally observed antiferromagnetic phase, affects the orbital order differently in alternate V-atom chains along c-axis. This observation is found to be consistent with the experimental prediction that the effect of spin-orbit coupling is intermediate between that in case of ZnV$_2$O$_4$ and MnV$_2$O$_4$.
Pair wave functions (PWF) which are eigenfunctions of the reduced density 2-matrix are considered for a homogeneous Bose liquid. With the Bogoliubov principle of the correlation weakening it is proved that the distribution of the "dissociated" pair states over momenta is exactly the product of the single-particle distribution functions. Thus, the "dissociated" pair states are naturally classified as condensate-condensate, condensate-supracondensate and supracondensate-supracondensate ones provided the Bose-Einstein condensate exists. The condensate-condensate as well as condensate-supracondensate PWF are expressed in terms of the averages of products of the creation and destruction Bose operators. This leads to the simple interpretation of the anomalous averages as the "scattering parts" of the condensate-condensate and condensate-supracondensate PWF. It is shown that in contrast to the Fermi liquid, the appearance of the anomalous averages for the Bose liquid does not necessarily mean that there exist bound states of pairs of particles. The PWF in the Hartree-Fock-Bogoliubov (HFB) approach are found. Given the density of the condensate is not zero, there are no bound pair states in the HFB scheme. The expansion of the pair correlation function in the set of PWF is very useful in order to take into account both short-range and long-range spatial correlations. Applications (possible and already realized) of the formalism developed are discussed.
Given a class of graphs F, we say that a graph G is universal for F, or F-universal, if every H in F is contained in G as a subgraph. The construction of sparse universal graphs for various families F has received a considerable amount of attention. One is particularly interested in tight F-universal graphs, i.e., graphs whose number of vertices is equal to the largest number of vertices in a graph from F. Arguably, the most studied case is that when F is some class of trees.   Given integers n and \Delta, we denote by T(n,\Delta) the class of all n-vertex trees with maximum degree at most \Delta. In this work, we show that every n-vertex graph satisfying certain natural expansion properties is T(n,\Delta)-universal or, in other words, contains every spanning tree of maximum degree at most \Delta. Our methods also apply to the case when \Delta is some function of n. The result has a few very interesting implications. Most importantly, we obtain that the random graph G(n,p) is asymptotically almost surely (a.a.s.) universal for the class of all bounded degree spanning (i.e., n-vertex) trees provided that p \geq c n^{-1/3} \log^2n where c > 0 is a constant. Moreover, a corresponding result holds for the random regular graph of degree pn. In fact, we show that if \Delta satisfies \log n \leq \Delta \leq n^{1/3}, then the random graph G(n,p) with p \geq c \Delta n^{-1/3} \log n and the random r-regular n-vertex graph with r \geq c\Delta n^{2/3} \log n are a.a.s. T(n,\Delta)-universal. Another interesting consequence is the existence of locally sparse n-vertex T(n,\Delta)-universal graphs. For constant \Delta, we show that one can (randomly) construct n-vertex T(n,\Delta)-universal graphs with clique number at most five. Finally, we show robustness of random graphs with respect to being universal for T(n,\Delta) in the context of the Maker-Breaker tree-universality game.
Spatial persistent large deviations probability of surface growth processes governed by the Edwards-Wilkinson dynamics, $P_x(x,s)$, with $-1 \leq s \leq 1$ is mapped isomorphically onto the temporal persistent large deviations probability $P_t(t,s)$ associated with the stochastic Markovian random walk problem. We show using numerical simulations that the infinite family of spatial persistent large deviations exponents $\theta_x(s)$ characterizing the power law decay of $P_x(x,s)$ agrees, as predicted on theoretical grounds by Majumdar and Bray [Phys. Rev. Lett. {\bf 86}, 3700 (2001)] with the numerical measurements of $\theta_t(s)$, the continuous family of exponents characterizing the long time power law behavior of $P_t(t,s)$. We also discuss the simulations of the spatial persistence probability corresponding to a discrete model in the Mullins-Herring universality class, where our discrete simulations do not agree well with the theoretical predictions perhaps because of the severe finite-size corrections which are known to strongly inhibit the manifestation of the asymptotic continuum behavior in discrete models involving large values of the dynamical exponent and the associated extremely slow convergence to the asymptotic regime.
We test the nonrelativistic QCD factorization conjecture for inclusive quarkonium production at two loops by carrying out a covariant calculation of the nonrelativistic quantum chromodynamics (NRQCD) long-distance matrix element (LDME) for a heavy-quark pair in an $S$-wave, color-octet state to fragment into a heavy-quark pair in a color-singlet state of arbitrary orbital angular momentum. The NRQCD factorization conjecture for the universality of the LDME requires that infrared divergences that it contains be independent of the direction of the Wilson line that appears in its definition. We find this to be the case in our calculation. The results of our calculation differ in some respects from those of a previous calculation that was carried out by Nayak, Qiu, and Sterman using light-cone methods. We have identified the sources of some of these differences. The results of both calculations are consistent with the NRQCD factorization conjecture. However, the general principle that underlies this confirmation of NRQCD factorization at two-loop order has yet to be revealed.
We review some basic natural geometric objects on null hypersurfaces. Gauss-Codazzi constraints are given in terms of the analog of canonical ADM momentum which is a well defined tensor density on the null surface. Bondi cones are analyzed with the help of this object.
We describe the effect of AGN light on host galaxy optical and UV-optical colours, as determined from X-ray-selected AGN host galaxies at z~1, and compare the AGN host galaxy colours to those of a control sample matched to the AGN sample in both redshift and stellar mass. We identify as X-ray-selected AGNs 8.7 +4/-3 per cent of the red-sequence control galaxies, 9.8 +/-3 per cent of the blue-cloud control galaxies, and 14.7 +4/-3 per cent of the green-valley control galaxies. The nuclear colours of AGN hosts are generally bluer than their outer colours, while the control galaxies exhibit redder nuclei. AGNs in blue-cloud host galaxies experience less X-ray obscuration, while AGNs in red-sequence hosts have more, which is the reverse of what is expected from general considerations of the interstellar medium. Outer and integrated colours of AGN hosts generally agree with the control galaxies, regardless of X-ray obscuration, but the nuclear colours of unobscured AGNs are typically much bluer, especially for X-ray luminous objects. Visible point sources are seen in many of these, indicating that the nuclear colours have been contaminated by AGN light and that obscuration of the X-ray radiation and visible light are therefore highly correlated. Red AGN hosts are typically slightly bluer than red-sequence control galaxies, which suggests that their stellar populations are slightly younger. We compare these colour data to current models of AGN formation. The unexpected trend of less X-ray obscuration in blue-cloud galaxies and more in red-sequence galaxies is problematic for all AGN feedback models, in which gas and dust is thought to be removed as star formation shuts down. [See paper for full abstract.]
We analyze features of mixed biphoton polarization states which arise from pure states of polarization-frequency biphoton ququarts after averaging over frequencies of photons. For mixed states we find their concurrence C, Schmidt parameter K and degree of polarization P, as well as the von Neumann mutual information I. In some simple cases we find also the relative entropy S_{rel} and the degree of classical correlations C_{cl}. We show that in mixed states the Schmidt parameter does not characterize anymore the degree of entanglement, as it does in pure states. Nevertheless, the Schmidt parameter remains useful even in the case of mixed states because it remains directly related to the degree of polarization. We compare results occurring in the cases of full pure polarization-frequency states of ququarts, mixed states (averaged over frequencies) and states with separated high- and low-frequency parts. Differences between these results can be seen in experiments with and without a dichroic beam-splitter, as well as with and without frequency filters in front of detector.
In this paper, some new forms of the Cheeger's inequalities are established for general (maybe unbounded) symmetric forms, the resulting estimates improve and extend the ones obtained by Lawler and Sokal (1988) for bounded jump processes. Furthermore, some existence criteria for spectral gap of general symmetric forms or general reversible Markov processes are presented, based on the Cheeger's inequalities and a relationship between the spectral gap and the first Dirichlet and Neumann eigenvalues on local region.
We discuss possible variations of the effective gravitational constant with length scale, predicted by most of alternative theories of gravity and unified models of physical interactions. After a brief general exposition, we review in more detail the predicted corrections to Newton's law of gravity in diverse brane world models. We consider various configurations in 5 dimensions (flat, de Sitter and AdS branes in Einstein and Einstein-Gauss-Bonnet theories, with and without induced gravity and possible incomplete graviton localization), 5D multi-brane systems and some models in higher dimensions. A common feature of all models considered is the existence of corrections to Newton's law at small radii comparable with the bulk characteristic length: at such radii, gravity on the brane becomes effectively multidimensional. Many models contain superlight perturbation modes, which modify gravity at large scale and may be important for astrophysics and cosmology.
We report growth, electronic structure and superconductivity of ultrathin epitaxial CoSi2 films on Si(111). At low coverages, preferred islands with 2, 5 and 6 monolayers height develop, which agrees well with the surface energy calculation. We observe clear quantum well states as a result of electronic confinement and their dispersion agrees well with density functional theory calculations, indicating weak correlation effect despite strong contributions from Co 3d electrons. Ex-situ transport measurements show that superconductivity persists down to at least 10 monolayers, with reduced Tc but largely enhanced upper critical field. Our study opens up the opportunity to study the interplay between quantum confinement, interfacial symmetry breaking and superconductivity in an epitaxial silicide film, which is technologically relevant in microelectronics.
Consider compound Poisson processes with negative drift and no negative jumps, which converge to some spectrally positive L\'evy process with non-zero L\'evy measure. In this paper we study the asymptotic behavior of the local time process, in the spatial variable, of these processes killed at two different random times: either at the time of the first visit of the L\'evy process to 0, in which case we prove results at the excursion level under suitable conditionings; or at the time when the local time at 0 exceeds some fixed level. We prove that finite-dimensional distributions converge under general assumptions, even if the limiting process is not c\`adl\`ag. Making an assumption on the distribution of the jumps of the compound Poisson processes, we strengthen this to get weak convergence. Our assumption allows for the limiting process to be a stable L\'evy process with drift.   These results have implications on branching processes and in queueing theory, namely, on the scaling limit of binary, homogeneous Crump-Mode-Jagers processes and on the scaling limit of the Processor-Sharing queue length process.
We consider a Hamiltonian chain of weakly coupled anharmonic oscillators. It is well known that if the coupling is weak enough then the system admits families of periodic solutions exponentially localized in space (breathers). In this paper we prove asymptotic stability in energy space of such solutions. The proof is based on two steps: first we use canonical perturbation theory to put the system in a suitable normal form in a neighborhood of the breather, second we use dispersion in order to prove asymptotic stability. The main limitation of the result rests in the fact that the nonlinear part of the on site potential is required to have a zero of order 8 at the origin. From a technical point of view the theory differs from that developed for Hamiltonian PDEs due to the fact that the breather is not a relative equilibrium of the system.
We obtain non-asymptotic Gaussian concentration bounds for the difference between the invariant measure $\nu$ of an ergodic Brownian diffusion process and the empirical distribution of an approximating scheme with decreasing time step along a suitable class of (smooth enough) test functions f such that f -- $\nu$(f) is a coboundary of the infinitesimal generator. We show that these bounds can still be improved when the (squared) Fr{\"o}benius norm of the diffusion coefficient lies in this class. We apply these bounds to design computable non-asymptotic confidence intervals for the approximating scheme. As a theoretical application, we finally derive non-asymptotic deviation bounds for the almost sure Central Limit Theorem.
We propose a procedure of constructing new block designs starting from a given one by looking at the intersections of its blocks with various sets and grouping those sets according to the structure of the intersections.   We introduce a symmetric relationship of friendship between block designs built on a set $V$ and consider families of block designs where all designs are friends of each other, the so-called friendly families. We show that a friendly family admits a partial ordering. Furthermore, we exhibit a map from the power set of $V$, partially ordered by inclusion, to a friendly family of a particular type which preserves the partial order.
We show that space- and time-correlated single-qubit rotation errors can lead to high-weight errors in a quantum circuit when the rotation angles are drawn from heavy-tailed distributions. This leads to a breakdown of quantum error correction, yielding reduced or in some cases no protection of the encoded logical qubits. While heavy-tailed phenomena are prevalent in the natural world, there is very little research as to whether noise with these statistics exist in current quantum processing devices. Furthermore, it is an open problem to develop tomographic or noise spectroscopy protocols that could test for the existence of noise with such statistics. These results suggest the need for quantum characterization methods that can reliably detect or reject the presence of such errors together with continued first-principles studies of the origins of space- and time-correlated noise in quantum processors. If such noise does exist, physical or control-based mitigation protocols must be developed to mitigate this noise as it would severely hinder the performance of fault-tolerant quantum computers.
The reconstruction of the neutrino energy is crucial in oscillation experiments that use interactions with nuclei to detect the neutrino.   The common reconstruction procedure is based on the kinematics of the final-state lepton. The interpretation of the reconstructed energy in terms of the real neutrino energy must rely on a model for the neutrino-nucleus interaction. The Relativistic Fermi Gas (RFG) model is frequently used in these analyses. In the Hartree-Fock (HF) model for quasielastic nucleon knockout, the bound nucleon wave functions are obtained using an effective nucleon-nucleon force. The final-state wave function is constructed from continuum states in the same potential which have the correct asymptotic behavior. The Continuum Random Phase Approximation (CRPA) model extends the HF approach taking long range correlations into account in a self-consistent way. Considering only single-nucleon processes, the distributions of reconstructed neutrino energies obtained within the HF-CRPA approach are compared with the results of the RFG, an RPWIA calculation, and the RPA+np-nh model of Martini et al.   We find that the distributions of reconstructed energies for a fixed incoming energy in the HF-CRPA display additional strength in the low reconstructed energy tails compared to models without elastic distortion of the outgoing nucleon. This asymmetry redistributes strength from higher to lower values of the reconstructed energy. The mean field description of the nuclear dynamics results in a reshaping of the reconstructed energy distribution that cannot be accounted for in a plane wave impulse approximation model, even by modifying ad hoc parameters such as the binding energy. In particular it is shown that in the RFG calculations there is no value of the binding energy which is able to reproduce the entire T2K $\nu_\mu$ oscillated spectrum as calculated in HF-CRPA.
We study a holographic gauge theory dual to the D3/D5 intersection. We consider a pure gauge B-field flux through the internal two-sphere wrapped by the probe D5--brane, which corresponds to a non-commutative configuration of adjoint scalars. There is a domain wall separating the theory into regions with different ranks of the adjoint group. At zero temperature the theory is supersymmetric and at finite temperature there is a critical point of a second order phase transition. We study the corresponding critical exponents and find that the second derivatives of the free energy, with respect to the bare mass and the magnetic field, diverge with a critical exponent of -2/3.
We investigate charge pumping in carbon nanotube quantum dots driven by the electric field of a surface acoustic wave. We find that at small driving amplitudes, the pumped current reverses polarity as the conductance is tuned through a Coulomb blockade peak using a gate electrode. We study the behavior as a function of wave amplitude, frequency and direction and develop a model in which our results can be understood as resulting from adiabatic charge redistribution between the leads and quantum dots on the nanotube.
The paper is devoted to the study of two-parametric families of Dirichlet problems for systems of equations with $p, q$-Laplacians and indefinite nonlinearities. Continuous and monotone curves $\Gamma_f$ and $\Gamma_e$ on the parametric plane $\lambda \times \mu$, which are the lower and upper bounds for a maximal domain of existence of weak positive solutions are introduced. The curve $\Gamma_f$ is obtained by developing our previous work \cite{BobkovIlyasov} and it determines a maximal domain of the applicability of the Nehari manifold and fibering methods. The curve $\Gamma_e$ is derived explicitly via minimax variational principle of the extended functional method.
It has been argued that fluctuations of fermion parity are harmful for the demonstration of non-Abelian anyonic statistics. Here, we demonstrate a striking exception in which such fluctuations are actively used. We present a theory of coherent electron transport from a tunneling tip into a Corbino geometry Josephson junction where four Majorana bound states (MBSs) rotate. While the MBSs rotate, electron tunneling happens from the tip to one of the MBSs thereby changing the fermion parity of the MBSs. The tunneling events in combination with the rotation allow us to identify a novel braiding operator that does not commute with the braiding cycles in the absence of tunneling, revealing the non-Abelian nature of MBSs. The time-averaged tunneling current exhibits resonances as a function of the tip voltage with a period that is a direct consequence of the interference between the non-commuting braiding operations. Our work opens up a possibility for utilizing parity non-conserving processes to control non-Abelian states.
Within the framework of the isospin-dependent quantum molecular dynamics model along with the GEMINI model, the reaction of $^{86}$Kr+$^{181}$Ta at 80,120 and 160 MeV/nucleon and the reaction of $^{78}$Kr+$^{181}$Ta at 160 MeV/nucleon are studied, and the production cross sections of the generated fragments are calculated. More intermediate and large mass fragments can be produced in the reaction with a large range of impact parameter. The production cross sections of nuclei such as the isotopes of Si and P generally decrease with the increasing incident energy. The isotopes near the neutron drip line are produced more in the neutron-rich system $^{86}$Kr+$^{181}$Ta.