ShantanuT01/DACTYL-Pretraining huggingface dataset:
The Coulomb potential produced by an ultrarelativistic particle (such as a heavy ion) in uniform motion is shown in the appropriate gauge to factorize into a longitudinal Dirac delta function of (z - t) times the simple two dimensional potential solution in the transverse direction. This form makes manifest the source of the energy independence of the interaction.
We combine the analyses for flavor changing neutral current processes and dark matter solutions in minimal-type supersymmetric grand unified theory (GUT) models, SO(10) and SU(5), with a large B_s - anti-B_s mixing phase and large tan beta. For large tan beta, the double penguin diagram dominates the SUSY contribution to the B_s - anti-B_s mixing amplitude. Also, the Br(B_s -> mu mu) constraint becomes important as it grows as tan^6 beta, although it can still be suppressed by large pseudoscalar Higgs mass m_A. We investigate the correlation between B_s -> mu mu and the dark matter direct detection cross-section through their dependence on m_A. In the minimal-type of SU(5) with type I seesaw, the large mixing in neutrino Dirac couplings results in large lepton flavor violating decay process tau to mu gamma, which in turn sets upper bound on m_A. In the SO(10) case, the large mixing can be chosen to be in the Majorana couplings instead, and the constraint from Br(tau -> mu gamma) can be avoided. The heavy Higgs funnel region turns out to be an interesting possibility in both cases and the direct dark matter detection should be possible in the near future in these scenarios.
Physically admissible choice of the "essential" coordinates identified with components of the metric tensor and co-moving frame of reference reduced to the formulation of the stationary axisymmetric GR problem. Such nontraditional approach allows to obtain new 4-parametric vacuum solution. In special static case this solution becomes the set well-known GR exact solutions for degenerate vacuum gravitational fields, in some special stationary case, after transformations coincides with Kerr solution. In other special stationary case the founded solution turn into modified NUT solution.
Optical quantum circuits can be optimized using gradient descent methods, as the gates in a circuit can be parametrized by continuous parameters. However, the parameter space as seen by the cost function is not Euclidean, which means that the Euclidean gradient does not generally point in the direction of steepest ascent. In order to retrieve the steepest ascent direction, in this work we implement Natural Gradient descent in the optical quantum circuit setting, which takes the local metric tensor into account. In particular, we adapt the Natural Gradient approach to a complex-valued parameter space. We then compare the Natural Gradient approach to vanilla gradient descent and to Adam over two state preparation tasks: a single-photon source and a Gottesman-Kitaev-Preskill state source. We observe that the NG approach has a faster convergence (due in part to the possibility of using larger learning rates) and a significantly smoother decay of the cost function throughout the optimization.
This paper is a survey of finiteness results in hyperk\"ahler geometry. We review some classical theorems by Sullivan, Koll\'ar-Matsusaka, Huybrechts, as well as theorems in the recent literature by Charles, Sawon, and joint results of the author with Verbitsky. We also strengthen a finiteness theorem of the author. These are extended notes of the author's talk during the closing conference of the Simons Semester in the Banach Center in B\c{e}dlewo, Poland.
In this article we study measurement circuit effects in three-terminal electrical transport measurements arising from finite line impedances. We provide exact expressions relating the measured voltages and differential conductances to their values at the device under test, which allow for spurious voltage divider effects to be corrected. Finally, we test the implementation of these corrections with experimental measurements.
We present an analytic derivation of Hawking radiation for an arbitrary (spatial) dispersion relation $\omega(k)$ as a model for ultra-high energy deviations from general covariance. It turns out that the Hawking temperature is proportional to the product of the group $d\omega/dk$ and phase $\omega/k$ velocities evaluated at the frequency $\omega$ of the outgoing radiation far away, which suggests that Hawking radiation is basically a low-energy phenomenon. Nevertheless, a group velocity growing too fast at ultra-short distances would generate Hawking radiation at ultra-high energies (``ultra-violet catastrophe'') and hence should not be a realistic model for the microscopic structure of quantum gravity.
We consider a general brane construction for realizing chiral four-dimensional gauge theories. The advantage of the construction is the simplicity and the possibility of realizing a large class of models existing in the literature. We start the study of these models by determining the matter content and the superpotential which naturally arise in the brane construction.
While diverse fracture characteristics have been observed in liquid metal embrittlement (LME) depending on the solid-liquid metal pairs, the penetration of nanometer-thick liquid metal films along the grain boundary has been identified as one of the key mechanisms for embrittlement in many classical LME systems, such as Al-Ga, Cu-Bi and Ni-Bi. For example, liquid Ga quickly penetrates deep into grain boundaries in Al, leading to intergranular fracture under very small stresses. We report on a series of molecular dynamics simulations of liquid Ga in contact with an Al bicrystal under a constant strain rate. We identify the grain boundary dislocations that are nucleated at the grain boundary groove tip and climb down along the grain boundary during Ga penetration and characterize their atomic structures based on topological method.
We investigate hadronic and leptonic scenarios for the GeV--TeV gamma-ray emission from jets of the microquasar SS 433. The emission region of the TeV photons coincides with the X-ray knots, where electrons are efficiently accelerated. On the other hand, the optical high-density filaments are also located close to the X-ray knots, which may support a hadronic scenario. We calculate multi-wavelength photon spectra of the extended jet region by solving the transport equations for the electrons and protons. We find that both hadronic and leptonic models can account for the observational data, including the latest {\it Fermi} LAT result. The hadronic scenarios predict higher-energy photons than the leptonic scenarios, and future observations such as with the Cherenkov Telescope Array (CTA), the Large High-Altitude Air Shower Observatory (LHAASO), and the Southern Wide-field Gamma-ray Observatory (SWGO) may distinguish between these scenarios and unravel the emission mechanism of GeV--TeV gamma-rays. Based on our hadronic scenario, the analogy between microquasars and radio galaxies implies that the X-ray knot region of the radio-galaxy jets may accelerate heavy nuclei up to ultrahigh energies.
We study a two dimensional electron system in a parabolic confining potential and constant magnetic field for the case of harmonic electron-electron interaction. We present analytic results for the electrochemical potential versus magnetic field and discuss the effects of correlation in connection with the addition energy of a Quantum Dot with few electrons.
We present results from a survey of the internal kinematics of 49 star-forming galaxies at z$\,\sim\,$2 in the CANDELS fields with the Keck/MOSFIRE spectrograph (SIGMA, Survey in the near-Infrared of Galaxies with Multiple position Angles). Kinematics (rotation velocity $V_{rot}$ and integrated gas velocity dispersion $\sigma_g$) are measured from nebular emission lines which trace the hot ionized gas surrounding star-forming regions. We find that by z$\,\sim\,$2, massive star-forming galaxies ($\log\,M_*/M_{\odot}\gtrsim10.2$) have assembled primitive disks: their kinematics are dominated by rotation, they are consistent with a marginally stable disk model, and they form a Tully-Fisher relation. These massive galaxies have values of $V_{rot}/\sigma_g$ which are factors of 2-5 lower than local well-ordered galaxies at similar masses. Such results are consistent with findings by other studies. We find that low mass galaxies ($\log\,M_*/M_{\odot}\lesssim10.2$) at this epoch are still in the early stages of disk assembly: their kinematics are often supported by gas velocity dispersion and they fall from the Tully-Fisher relation to significantly low values of $V_{rot}$. This "kinematic downsizing" implies that the process(es) responsible for disrupting disks at z$\,\sim\,$2 have a stronger effect and/or are more active in low mass systems. In conclusion, we find that the period of rapid stellar mass growth at z$\,\sim\,$2 is coincident with the nascent assembly of low mass disks and the assembly and settling of high mass disks.
We determine the impact of electron solvation on D$_2$O structures adsorbed on Cu(111) with low temperature scanning tunneling microscopy, two-photon photoemission, and ab initio theory. UV photons generating solvated electrons lead not only to transient, but also to permanent structural changes through the rearrangement of individual molecules. The persistent changes occur near sites with a high density of dangling OH groups that facilitate electron solvation. We conclude that energy dissipation during solvation triggers permanent molecular rearrangement via vibrational excitation.
The slow advance of a crack in sodo-silicate glasses was studied at nanometer scale by in situ and real time atomic force microscopy (AFM) in a well controlled atmosphere. An enhanced diffusion of sodium ions in the stress gradient field at the submicrometric vicinity of the crack tip was revealed through several effects: growth of nodules in AFM height images, changes in the AFM tip/sample energy dissipation. The nodules patterns revealed a dewetting phenomenon evidenced by 'breath figures'. Complementary chemical micro-analyses were done. These experimental results were explained by a two-step process: i) a fast migration (typical time: few milliseconds) of sodium ions towards the fracture surfaces as proposed by Langford et al. [J. Mat. Res. 6 (1991) 1358], ii) a slow backwards diffusion of the cations as evidenced in these AFM experiments (typical time: few minutes). Measurements of the diffusion coefficient of that relaxing process were done at room temperature. Our results strengthen the theoretical concept of a near-surface structural relaxation due to the stress-gradient at the vicinity of the crack tip. The inhomogeneous migration of sodium ions might be a direct experimental evidence of the presence of sodium rich channels in the silicate structure [A. Meyer et al., Phys. Rev. Let. 93 (2004) 027801].
We consider the problem of approximating ground states of one-dimensional quantum systems within the two most common variational ansatzes, namely the mean field ansatz and Matrix Product States. We show that both for mean field and for Matrix Product States of fixed bond dimension, the optimal solutions can be found in a way which is provably efficient (i.e., scales polynomially). This implies that the corresponding variational methods can be in principle recast in a way which scales provably polynomially. Moreover, our findings imply that ground states of one-dimensional commuting Hamiltonians can be found efficiently.
We compute the number density of massive Black Holes (BHs) at the centre of galaxies at z=6 in different Dynamical Dark Energy (DDE) cosmologies, and compare it with existing observational lower limits, to derive constraints on the evolution of the Dark Energy equation of state parameter w. Our approach only assumes the canonical scenario for structure formation from the collapse of overdense regions of the Dark Matter dominated primordial density field on progressively larger scales; the Black Hole accretion and merging rate have been maximized in the computation so as to obtain robust constraints on w and on its look-back time derivative w_a. Our results provide independent constraints complementary to those obtained by combining Supernovae, Cosmic Microwave Background and Baryonic Acoustic Oscillations; while the latter concern combinations of w_0 and w_a leaving the time evolution of the state parameter w_a highly unconstrained, the BH abundance mainly provide upper limits on w_a, only weakly depending on w_0. Combined with the existing constraints, our results significantly restrict the allowed region in DDE parameter space, ruling out DDE models not providing cosmic time and fast growth factor large enough to allow for the building up of the observed abundance of BHs; in particular, models with -1.2 \leq w_0 \leq -1 and positive redshift evolution w_a > 0.8 - completely consistent with previous constraints - are strongly disfavoured by our independent constraints from BH abundance. Such range of parameters corresponds to "Quintom" DDE models, with w crossing -1 starting from larger values.
We study superstrings on AdS_3 x S^3 x T^4 supported by a combination of Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz three form fluxes, and construct a set of finite-gap equations that describe the classical string spectrum. Using the recently proposed all-loop S-matrix we write down the all-loop Bethe ansatz equations for the massive sector. In the thermodynamic limit the Bethe ansatz reproduces the finite-gap equations. As part of this derivation we propose expressions for the leading order dressing phases. These phases differ from the well-known Arutyunov-Frolov-Staudacher phase that appears in the pure Ramond-Ramond case. We also consider the one-loop quantization of the algebraic curve and determine the one-loop corrections to the dressing phases. Finally we consider some classical string solutions including finite size giant magnons and circular strings.
As sp carbon chains (carbynes) are relatively rigid molecular objects, can we exploit them as construction elements in nanomechanics? To answer this question, we investigate their remarkable mechanical properties by ab-initio total-energy simulations. In particular, we evaluate their linear response to small longitudinal and bending deformations and their failure limits for longitudinal compression and elongation.
First, we consider Kolmogorov flow (a shear flow with a sinusoidal velocity profile) for 2D Navier-Stokes equation on a torus. Such flows, also called bar states, have been numerically observed as one type of metastable states in the study of 2D turbulence. For both rectangular and square tori, we prove that the non-shear part of perturbations near Kolmogorov flow decays in a time scale much shorter than the viscous time scale. The results are obtained for both the linearized NS equations with any initial vorticity in L^2, and the nonlinear NS equation with initial L^2 norm of vorticity of the size of viscosity. In the proof, we use the Hamiltonian structure of the linearized Euler equation and RAGE theorem to control the low frequency part of the perturbation. Second, we consider two classes of shear flows for which a sharp stability criterion is known. We show the inviscid damping in a time average sense for non-shear perturbations with initial vorticity in L^2. For the unstable case, the inviscid damping is proved on the center space. Our proof again uses the Hamiltonian structure of the linearized Euler equation and an instability index theory recently developed by Lin and Zeng for Hamiltonian PDEs.
We examine the behavior of the diffusion coefficient of the ST2 model of water over a broad region of the phase diagram via molecular dynamics simulations. The ST2 model has an accessible liquid-liquid transition between low-density and high-density phases, making the model an ideal candidate to explore the impacts of the liquid-liquid transition on dynamics. We locate characteristic dynamical loci in the phase diagram and compare them with the previously investigated thermodynamic loci. The low-density liquid phase shows a crossover from non-Arrhenius to Arrhenius behavior, signaling the onset of a crossover from fragile-to-strong behavior. We explain this crossover in terms of the asymptotic approach of the low-density liquid to a random tetrahedral network, and show that the temperature dependence of the diffusion coefficient over a wide temperature range can be simply related to the concentration of defects in the network. Our findings thus confirm that the low-density phase of ST2 water is a well-defined metastable liquid.
Higgs bosons pair production is well known for its sensitivity to probing the sign and size of Higgs boson self coupling, providing a way to determine whether there is an extended Higgs sector. The Georgi-Machacek (GM) model extends the Standard Model (SM) with an $SU(2)_L$ triplet scalar field that has one real and one complex components. The Higgs self coupling now has a wider range than that in the SM, with even the possibility of a sign flip. The new heavy singlet Higgs boson $H^{0}_{1}$ can contribute to s-channel production of the $hh$ pairs. In this work, we study non-resonant/resonant Higgs boson pair productions $p p \rightarrow hh$ and $p p \rightarrow H^{0}_{1} \rightarrow hh$, focusing exclusively on the contribution of $H^0_1$. We show the sensitivity for Higgs boson pair production searches at the 13-TeV LHC with the luminosities of $3.2,\ 30$ and $100$~fb$^{-1}$.
We have analyzed the Chandra archival data of NGC 1132, a well-known fossil group, i.e. a system expected to be old and relaxed long after the giant elliptical galaxy assembly. Instead, the Chandra data reveal that the hot gas morphology is disturbed and asymmetrical, with a cold front following a possible bow shock. We discuss possible origins of the disturbed hot halo, including sloshing by a nearby object, merger, ram pressure by external hotter gas and nuclear outburst. We consider that the first two mechanisms are likely explanations for the disturbed hot halo, with a slight preference for a minor merger with a low impact parameter because of the match with simulations and previous optical observations. In this case, NGC 1132 may be a rare example of unusual late mergers seen in recent simulations. Regardless of the origin of the disturbed hot halo, the paradigm of the fossil system needs to be reconsidered.
We investigate the attempt using flavor violation gauge interaction in the up sector to explain the LHCb recently observed large $\Delta A_{CP}$ ($A_{CP}(D^{0}\to K^{+}K^{-})-A_{CP}(D^{0}\to \pi^{+}\pi^{-})$). We study an Abelian model that only right-handed up quarks is charged under it and the 1-3 coupling is maximized. The simultaneous 1-3 2-3 mixing is realized by a quark mixing of 1-2 generation. Given the easy identification of top quark, the model can be directly tested by $\Delta F=1$ and $\Delta F=2$ processes at the hadron colliders as associated top production $g c \to t Z^{\prime}$ or same-sign top scattering $u u\to t t$. The direct search bounds are still consistent with the assumption that $ut$ and $ct$ couplings are equal but the same-sign top scattering bound is expected to be reached very soon. However, since there is no CKM-like suppression, the corresponding parameter space for generating $\Delta A_{CP}$ is completely excluded by the $D^{0}-\bar{D}^{0}$ mixing. We conclude that the up FCNC type models cannot explain the $\Delta A_{CP}$ while to be consistent with the $D^{0}-\bar{D}^{0}$ mixing constraint at the same time. On the other hand, a model as SM with fourth family extension has better chance to explain the large $\Delta A_{CP}$ consistently.
We demonstrate a state reconstruction technique which provides either the Wigner function or the density matrix of a field mode and requires only avalanche photodetectors, without any phase or amplitude discrimination power. It represents an alternative, of simpler implementation, to quantum homodyne tomography.
In this paper we address the problem of representing solutions of a system of scalar linear partial difference equations akin to state space equations of 1-D systems theory. We first obtain a representation formula for a special class of autonomous systems. Then we show every autonomous system can be converted into the special ones by a coordinate transformation on n-d integer grid. Using this conversion we provide representation formula for general autonomous systems. The representation formula we present can be viewed as multidimensional flow operators acting on initial conditions. These initial conditions are required to satisfy certain compatibility conditions. We give a full description of the set of allowable initial conditions.   In our search for a general representation formula, one algebraic result plays a very crucial role. In this result we show that every quotient ring of the n-variable Laurent polynomial ring can be made a finitely generated faithful module over another Laurent polynomial ring of smaller dimension by doing a suitable change of coordinates. We call this result a discrete version of Noether's Normalization Lemma.
We study an evolving spatial network in which sequentially arriving vertices are joined to existing vertices at random according to a rule that combines preference according to degree with preference according to spatial proximity. We investigate phase transitions in graph structure as the relative weighting of these two components of the attachment rule is varied.   Previous work of one of the authors showed that when the geometric component is weak, the limiting degree sequence of the resulting graph coincides with that of the standard Barab\'asi--Albert preferential attachment model. We show that at the other extreme, in the case of a sufficiently strong geometric component, the limiting degree sequence coincides with that of a purely geometric model, the on-line nearest-neighbour graph, which is of interest in its own right and for which we prove some extensions of known results. We also show the presence of an intermediate regime, in which the behaviour differs significantly from both the on-line nearest-neighbour graph and the Barab\'asi--Albert model; in this regime, we obtain a stretched exponential upper bound on the degree sequence.   Our results lend some mathematical support to simulation studies of Manna and Sen, while proving that the power law to stretched exponential phase transition occurs at a different point from the one conjectured by those authors.
Magnetic resonance (muSR and NMR) studies of f-electron non-Fermi-liquid (NFL) materials give clear evidence that structural disorder is a major factor in NFL behavior. Longitudinal-field muSR relaxation measurements at low fields reveal a wide distribution of muon relaxation rates and divergences in the frequency dependence of spin correlation functions in the NFL systems UCu_{5-x}Pd_x and CePtSi_{1-x}Ge_x. These divergences seem to be due to slow dynamics associated with quantum spin-glass behavior, rather than quantum criticality as in a uniform system, for two reasons: the observed strong inhomogeneity in the muon relaxation rate, and the strong and frequency-dependent low-frequency fluctuation observed in U(Cu,Pd)_5 and CePt(Si,Ge). In the NFL materials CeCu_{5.9}Au_{0.1}, Ce(Ru_{0.5}Rh_{0.5})_2Si_2, CeNi_2Ge_2, and YbRh_2Si_2 the low-frequency weight of the spin fluctuation spectrum is much weaker than in the disordered NFL systems.