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At least 1,063 records · Page 59

Dynamics of Quantum Adiabatic Evolution Algorithm for Number Partitioning

We have developed a general technique to study the dynamics of the quantum adiabatic evolution algorithm applied to random combinatorial optimization problems in the asymptotic limit of large problem size n. We use as an example the NP-complete Number Partitioning problem and map the algorithm dynamics to that of an auxiliary quantum spin glass system with the slowly varying Hamiltonian. We use a Green function method to obtain the adiabatic eigenstates and the minimum excitation gap. g min, = O(n 2(exp -n/2), corresponding to the exponential complexity of the algorithm for Number Partitioning. The key element of the analysis is the conditional energy distribution computed for the set of all spin configurations generated from a given (ancestor) configuration by simultaneous flipping of a fixed number of spins. For the problem in question this distribution is shown to depend on the ancestor spin configuration only via a certain parameter related to 'the energy of the configuration. As the result, the algorithm dynamics can be described in terms of one-dimensional quantum diffusion in the energy space. This effect provides a general limitation of a quantum adiabatic computation in random optimization problems. Analytical results are in agreement with the numerical simulation of the algorithm.

Smelyanskiy, V. N.↗

Modelling of monovacancy diffusion in W over wide temperature range

The diffusion of monovacancies in tungsten is studied computationally over a wide temperature range from 1300 K until the melting point of the material. Our modelling is based on Molecular Dynamics technique and Density Functional Theory. The monovacancy migration barriers are calculated using nudged elastic band method for nearest and next-nearest neighbour monovacancy jumps. The diffusion pre-exponential factor for monovacancy diffusion is found to be two to three orders of magnitude higher than commonly used in computational studies, resulting in attempt frequency of the order 10{sup 15} Hz. Multiple nearest neighbour jumps of monovacancy are found to play an important role in the contribution to the total diffusion coefficient, especially at temperatures above 2/3 of T{sub m}, resulting in an upward curvature of the Arrhenius diagram. The probabilities for different nearest neighbour jumps for monovacancy in W are calculated at different temperatures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Real-time spin systems from lattice field theory

We construct a lattice field theory method for computing the real-time dynamics of spin systems in a thermal bath. This is done by building on previous work of Takano with Schwinger-Keldysh and functional differentiation techniques. We derive a Schwinger-Keldysh path integral for generic spin Hamiltonians, then demonstrate the method on a simple system. Our path integral has a sign problem, which generally requires exponential run time in the system size, but requires only linear storage. The latter may place this method at an advantage over exact diagonalization, which is exponential in both. Our path integral is amenable to contour deformations, a technique for reducing sign problems.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

THE VERTICAL MOTIONS OF MONO-ABUNDANCE SUB-POPULATIONS IN THE MILKY WAY DISK

We present the vertical kinematics of stars in the Milky Way's stellar disk inferred from Sloan Digital Sky Survey/Sloan Extension for Galactic Understanding and Exploration (SDSS/SEGUE) G-dwarf data, deriving the vertical velocity dispersion, {sigma}{sub z}, as a function of vertical height |z| and Galactocentric radius R for a set of 'mono-abundance' sub-populations of stars with very similar elemental abundances [{alpha}/Fe] and [Fe/H]. We find that all mono-abundance components exhibit nearly isothermal kinematics in |z|, and a slow outward decrease of the vertical velocity dispersion: {sigma}{sub z}(z, R | [{alpha}/Fe], [Fe/H]) Almost-Equal-To {sigma}{sub z}([{alpha}/Fe], [Fe/H]) Multiplication-Sign exp (- (R - R{sub 0})/7 kpc). The characteristic velocity dispersions of these components vary from {approx}15 km s{sup -1} for chemically young, metal-rich stars with solar [{alpha}/Fe], to {approx}> 50 km s{sup -1} for metal-poor stars that are strongly [{alpha}/Fe]-enhanced, and hence presumably very old. The mean {sigma}{sub z} gradient (d{sigma}{sub z}/dz) away from the mid-plane is only 0.3 {+-} 0.2 km s{sup -1} kpc{sup -1}. This kinematic simplicity of the mono-abundance components mirrors their geometric simplicity; we have recently found their density distribution to be simple exponentials in both the z- and R-directions. We find a continuum of vertical kinetic temperatures ({proportional_to}{sigma}{sup 2}{sub z}) as a function of ([{alpha}/Fe], [Fe/H]), which contribute to the total stellar surface-mass density approximately as {Sigma}{sub R{sub 0}}({sigma}{sup 2}{sub z}){proportional_to} exp(-{sigma}{sup 2}{sub z}). This and the existence of isothermal mono-abundance populations with intermediate dispersions (30-40 km s{sup -1}) reject the notion of a thin-thick-disk dichotomy. This continuum of disk components, ranging from old, 'hot', and centrally concentrated ones to younger, cooler, and radially extended ones, argues against models where the thicker disk portions arise from massive satellite infall or heating; scenarios where either the oldest disk portion was born hot, or where internal evolution plays a major role, seem the most viable. In addition, the wide range of {sigma}{sub z}([{alpha}/Fe], [Fe/H]) combined with a constant {sigma}{sub z}(z) for each abundance bin provides an independent check on the precision of the SEGUE-derived abundances: {delta}{sub [{alpha}/Fe]} Almost-Equal-To 0.07 dex and {delta}{sub [Fe/H]} Almost-Equal-To 0.15 dex. The slow radial decline of the vertical dispersion presumably reflects the decrease in disk surface-mass density. This measurement constitutes a first step toward a purely dynamical estimate of the mass profile of the stellar and gaseous disk in our Galaxy.

79 ASTRONOMY AND ASTROPHYSICS↗

Comments on the quantum field theory of the Coulomb gas formalism

The holomorphic Coulomb gas formalism, as developed by Feigin-Fuchs, Dotsenko-Fateev and Felder, is a set of rules for computing minimal model observables using free field techniques. We attempt to derive and clarify these rules using standard techniques of quantum field theory. We begin with a careful examination of the timelike linear dilaton. Although the background charge of the model breaks the scalar field’s continuous shift symmetry, the exponential of the action remains invariant under a discrete shift because the background charge is imaginary. Gauging this symmetry makes the dilaton compact and introduces winding modes into the spectrum. One of these winding operators corresponds to the anti-holomorphic completion of the BRST current first introduced by Felder, and the full left/right cohomology of this BRST charge isolates the irreducible representations of the Virasoro algebra within the degenerate Fock space of the linear dilaton. The “supertrace” in the BRST complex reproduces the minimal model partition function and exhibits delicate cancellations between states with both momentum and winding. The model at the radius $R=\sqrt{pp^{\prime }}$ has two marginal operators corresponding to the Dotsenko-Fateev “screening charges”. Deforming by them, we obtain a model that might be called a “BRST quotiented compact timelike Liouville theory”. The Hamiltonian of the zero-mode quantum mechanics of this model is not Hermitian, but it is PT -symmetric and exactly solvable. Its eigenfunctions have support on an infinite number of plane waves, suggesting an infinite reduction in the number of independent states in the full quantum field theory. Applying conformal perturbation theory to the exponential interactions reproduces the Coulomb gas calculations of minimal model correlation functions. In contrast to spacelike Liouville, these “resonance correlators” are finite because the zero mode is compact. We comment on subtleties regarding the reflection operator identification, as well as naive violations of truncation in correlators with multiple reflection operators inserted. This work is part of an attempt to understand the relationship between the JT model of two dimen- sional gravity and the worldsheet description of the (2 , p ) minimal string as suggested by Seiberg and Stanford.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Evolution of finite viscous disks with time-independent viscosity

We find Green functions for the accretion disk with fixed outer radius and time-independent viscosity. With the Green functions, a viscous evolution of the disk with any initial conditions can be described. Two types of inner boundary conditions are considered: the zero stress tensor and the zero accretion rate. The variable mass inflow at the outer radius can also be included. The well-known exponential decline of the accretion rate is a part of the solution with the inner zero stress tensor. The solution with the zero central accretion rate is applicable to disks around stars whose magnetosphere's boundary exceeds the corotation radius. Using the solution, the viscous evolution of disks in some binary systems can be studied. We apply the solution with zero inner stress tensor to outbursts of short-period X-ray transients during the time around the peak. It is found that for the Kramers’ regime of opacity and the initial surface density proportional to the radius, the rise time to the peak is t{sub rise}≈0.15 r{sub out}{sup 2}/ν{sub out} and the e-folding time of the decay is t{sub exp}≈0.45 r{sub out}{sup 2}/ν{sub out}. Comparison to non-stationary α-disks shows that both models with the same value of viscosity at the outer radius produce similar behavior on the viscous time-scale. For six bursts in X-ray novae, which exhibit fast-rise–exponential-decay and are fitted by the model, we find a way to restrict the turbulent parameter α.

79 ASTRONOMY AND ASTROPHYSICS↗

Probing universalities in d > 2 CFTs: from black holes to shockwaves

Gravitational shockwaves are insensitive to higher-curvature corrections in the action. Recent work found that the OPE coefficients of lowest-twist multi-stress-tensor operators, computed holographically in a planar black hole background, are insensitive as well. In this paper, we analyze the relation between these two limits. We explicitly evaluate the two-point function on a shockwave background to all orders in a large central charge expansion. In the geodesic limit, we find that the ANEC exponentiates in the multi-stress-tensor sector. To compare with the black hole limit, we obtain a recursion relation for the lowest-twist products of two stress tensors in a spherical black hole background, letting us efficiently compute their OPE coefficients and prove their insensitivity to higher curvature terms. After resumming the lowest-twist stress-tensors and analytically continuing their contributions to the Regge limit, we find a perfect agreement with the shockwave computation. We also discuss the role of double-trace operators, global degenerate states, and multi-stress-tensor conformal blocks. These holographic results suggest the existence of a larger universal structure in higher-dimensional CFTs.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Magnus method for electronic structure calculations at extreme conditions

We present the application of Magnus based methods to the solution of first order coupled ordinary differential equations in High Energy Density (HED) physics applications. Our focus is on the application to quantum mechanical methods, specifically on the solution of the radial Dirac equation for real and complex energies. HED applications require accurate solutions across a wide range of spatial and energy domains, including regimes where the solutions exhibit pronounced oscillatory behavior. Such cases pose significant computational challenges. We demonstrate that Magnus-based integrators can efficiently and accurately address these challenges. We discuss the implementation of the Magnus method for the solution of the radial Dirac equation, including practical considerations such as the evaluation of matrix exponentials, numerical integration, error estimation, and adaptive step size control. We also discuss the application of these methods to complex energy Green’s function techniques and the efficient approximation of integrals of the solutions relevant to HED electronic structure calculations. Here, we demonstrate the accuracy and robustness of the resulting method in applications to the free-particle case, for which analytic solutions are available for comparison, as well as the challenging case of gold at HED conditions.

general physics↗

Collective coherence in nearest neighbor coupled metamaterials: A metasurface ruler equation

The collective coherent interactions in a meta-atom lattice are the key to myriad applications and functionalities offered by metasurfaces. We demonstrate a collective coherent response of the nearest neighbor coupled split-ring resonators whose resonance shift decays exponentially in the strong near-field coupled regime. This occurs due to the dominant magnetic coupling between the nearest neighbors which leads to the decay of the electromagnetic near fields. Based on the size scaling behavior of the different periodicity metasurfaces, we identified a collective coherent metasurface ruler equation. From the coherent behavior, we also show that the near-field coupling in a metasurface lattice exists even when the periodicity exceeds the resonator size. The identification of a universal coherence in metasurfaces and their scaling behavior would enable the design of novel metadevices whose spectral tuning response based on near-field effects could be calibrated across microwave, terahertz, infrared, and the optical parts of the electromagnetic spectrum.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DFT + DMFT calculations of the complex band and tunneling behavior for the transition metal monoxides MnO, FeO, CoO, and NiO

Here, we report complex band structure (CBS) calculations for the four late transition metal monoxides MnO, FeO, CoO, and NiO in their paramagnetic phase. The CBS is obtained from density functional theory plus dynamical mean field theory (DMFT) calculations to take into account correlation effects. The so-called β parameters, governing the exponential decay of the transmission probability in the nonresonant tunneling regime of these oxides, are extracted from the CBS. Different model constructions are examined in the DMFT part of the calculation. The calculated β parameters provide theoretical estimation for the decay length in the evanescent channel, which would be useful for tunnel junction applications of these materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Clarifying remotely-retrieved precipitation of shallow marine clouds from the NSF/NCAR Gulfstream V

Precipitation is a key process within the shallow cloud lifecycle. The Cloud System Evolution in the Trades (CSET) campaign included the first deployment of a 94 GHz Doppler radar and 532 nm lidar. Despite a larger sampling volume, initial mean radar/lidar retrieved rain rates (Schwartz et al. 2019) based on the upward-pointing remote sensor datasets are systematically less than those measured by in-situ precipitation probes in the cumulus regime. Subsequent retrieval improvements produce rainrates that compare better to in-situ values, but still underestimate. Retrieved shallow cumulus drop sizes can remain too small and too few, with an overestimated shape parameter narrowing the raindrop size distribution too much. Three potential causes for the discrepancy are explored: the gamma functional fit to the dropsize distribution, attenuation by rain and cloud water, and an underaccounting of Mie dampening of the reflectivity. A truncated exponential fit may represent the dropsizes below a showering cumulus cloud more realistically, although further work would be needed to fully evaluate the impact of a different dropsize representation upon the retrieval. The rain attenuation is within the measurement uncertainty of the radar. Mie dampening of the reflectivity is shown to be significant, in contrast to previous stratocumulus campaigns with lighter rain rates, and may be difficult to constrain well with the remote measurements. An alternative approach combines an a priori determination of the dropsize distribution width based on the in-situ data with the mean radar Doppler velocity and reflectivity. This can produce realistic retrievals, although a more comprehensive assessment is needed to better characterize the retrieval errors.

54 ENVIRONMENTAL SCIENCES↗

Turbulent dynamo in a conducting fluid and a partially ionized gas

By following the Kazantsev theory and taking into account both microscopic and turbulent diffusion of magnetic fields, we develop a unified treatment of the kinematic and nonlinear stages of a turbulent dynamo process, and we study the dynamo process for a full range of magnetic Prandtl number P {sub m} and ionization fractions. We find a striking similarity between the dependence of dynamo behavior on P {sub m} in a conducting fluid and R (a function of ionization fraction) in a partially ionized gas. In a weakly ionized medium, the kinematic stage is largely extended, including not only exponential growth but a new regime of dynamo characterized by a linear-in-time growth of magnetic field strength, and the resulting magnetic energy is much higher than the kinetic energy carried by viscous-scale eddies. Unlike the kinematic stage, the subsequent nonlinear stage is unaffected by microscopic diffusion processes and has a universal linear-in-time growth of magnetic energy with the growth rate as a constant fraction 3/38 of the turbulent energy transfer rate, showing good agreement with earlier numerical results. Applying the analysis to the first stars and galaxies, we find that the kinematic stage is able to generate a field strength only an order of magnitude smaller than the final saturation value. But the generation of large-scale magnetic fields can only be accounted for by the relatively inefficient nonlinear stage and requires longer time than the free-fall time. It suggests that magnetic fields may not have played a dynamically important role during the formation of the first stars.

79 ASTRONOMY AND ASTROPHYSICS↗

A new class of energy based control laws for revolute robot arms - Tracking control, robustness enhancement and adaptive control

A class of joint-level control laws for all-revolute robot arms is introduced. The analysis is similar to the recently proposed energy Liapunov function approach except that the closed-loop potential function is shaped in accordance with the underlying joint space topology. By using energy Liapunov functions with the modified potential energy, a much simpler analysis can be used to show closed-loop global asymptotic stability and local exponential stability. When Coulomb and viscous friction and model parameter errors are present, a sliding-mode-like modification of the control law is proposed to add a robustness-enhancing outer loop. Adaptive control is also addressed within the same framework. A linear-in-the-parameters formulation is adopted, and globally asymptotically stable adaptive control laws are derived by replacing the model parameters in the nonadaptive control laws by their estimates.

Wen, John T.↗

BRAINSTACK – A Platform for Artificial Intelligence & Machine Learning Collaborative Experiments on a Nano-Satellite

As the space economy continues to expand through increasingly easy access to advanced and inexpensive technology, space missions themselves have become more ambitious with exploration targets growing ever distant while simultaneously requiring larger guidance and communication budgets. These conflicting desires of distance and control drive the need for advanced on-board intelligent decision making to reduce communication and control limitations by automating as many mission functions as possible in-situ. While the amount of research on such Artificial Intelligence and Machine Learning (AI/ML) software modules has grown exponentially, the capacity to experimentally validate such software modules in space in a rapid and inexpensive format has not. To this end, the Nano Orbital Workshop (NOW) group at NASA Ames Research Center has been at the forefront of performing initial flight evaluation tests of ‘commercially’ available bleeding-edge computational platforms via what is programmatically referred to as the BrainStack on the TechEdSat (TES-n) flight series. This on-orbit computational platform provides an evaluation laboratory where advanced software experiments are pre-loaded into memory prior to launch, then executed as payloads during mission operations with results reported back and program tweaks or new training sets uploaded as needed. Processors selected as part of the BrainStack are of ideal size, packaging, and power consumption for easy integration into a cube satellite structure. These experiments have included the evaluation of small, high-performance GPUs and, more recently, neuromorphic processors, in LEO operations. Neuromorphic processors are of particular interest due to their superior power efficiency over GPUs in intelligent automation applications. The first TES-n flight test of an Intel first-generation Loihi neuromorphic processor launched on TES-13, January 13, 2022, and continues to operate in orbit despite no significant modifications to harden the processor against the space environment. The Intel Loihi Gen-1 on TES-13 is characterized by a 14nm 128-core Spiking Neural Network (SNN) able to support on-chip training. The processor is packaged in the Kapoho Bay USB module, providing a relatively straight-forward interface to the bus avionics system. The Kapoho Bay was in turn managed by an Intel Pentium single-board computer to handle scheduling of the software application payloads and communications with the satellite’s primary computer. The recently released Intel Loihi Gen-2, able to support integer-valued spike payloads and produced using 7nm process, will form part of the continually evolving BrainStack in the upcoming three TES-n/NOW flights. The Kapoho Point unit will incorporate eight Loihi-2 processors, enabling neural networks of up to one million neurons and one billion synapsis. Additionally, it is planned to measure the radiation environment these processors experience to understand any degradation or computational artifacts caused by long term space radiation exposure on these novel architectures. This evolving flexible and collaborative environment involving various research teams across NASA and other organizations is intended to be a convenient orbital test platform from which many anticipated future space automation applications may be initially tested.

Artificial Intelligence↗

Optimizing white light luminescence in Dy{sup 3+}-doped Lu{sub 3}Ga{sub 5}O{sub 12} nano-garnets

Trivalent dysprosium-doped Lu{sub 3}Ga{sub 5}O{sub 12} nano-garnets have been prepared by sol-gel method and characterized by X-ray powder diffraction, high-resolution transmission electron microscopy, dynamic light scattering, and laser excited spectroscopy. Under a cw 457 nm laser excitation, the white luminescence properties of Lu{sub 3}Ga{sub 5}O{sub 12} nano-garnets have been studied as a function of the optically active Dy{sup 3+} ion concentration and at low temperature. Decay curves for the {sup 4}F{sub 9/2} level of Dy{sup 3+} ion exhibit non-exponential nature for all the Dy{sup 3+} concentrations, which have been well-fitted to a generalized energy transfer model for a quadrupole-quadrupole interaction between Dy{sup 3+} ions without diffusion. From these data, a simple rate-equations model can be applied to predict that intense white luminescence could be obtained from 1.8 mol% Dy{sup 3+} ions-doped nano-garnets, which is in good agreement with experimental results. Chromaticity color coordinates and correlated color temperatures have been determined as a function of temperature and are found to be within the white light region for all Dy{sup 3+} concentrations. These results indicate that 2.0 mol% Dy{sup 3+} ions doped nano-garnet could be useful for white light emitting device applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

On the statistical theory of self-gravitating collisionless dark matter flow

Dark matter, if it exists, accounts for five times as much as the ordinary baryonic matter. Compared to hydrodynamic turbulence, the flow of dark matter might possess the widest presence in our universe. This paper presents a statistical theory for the flow of dark matter that is compared with N-body simulations. By contrast to hydrodynamics of normal fluids, dark matter flow is self-gravitating, long-range, and collisionless with a scale-dependent flow behavior. The peculiar velocity field is of constant divergence nature on small scale and irrotational on large scale. The statistical measures, i.e., correlation, structure, dispersion, and spectrum functions, are modeled on both small and large scales, respectively. Kinematic relations between statistical measures are fully developed for incompressible, constant divergence, and irrotational flow. Incompressible and constant divergence flow share the same kinematic relations for even order correlations. The limiting correlation of velocity $\mathrm{ρ_{L}=1/2}$ on the smallest scale ( r = 0) is a unique feature of collisionless flow (⁠$\mathrm{ρ_{L}=1}$ for incompressible flow). On large scale, transverse velocity correlation has an exponential form $T_{2}∝e^{–r/r_2}$ with a constant comoving scale r 2 =21.3 Mpc/h that may be related to the horizon size at matter–radiation equality. All other correlation, structure, dispersion, and spectrum functions for velocity, density, and potential fields are derived analytically from kinematic relations for irrotational flow. On small scale, longitudinal structure function follows one-fourth law of ${S}_{2}^{1}∝r^{1/4}$. All other statistical measures can be obtained from kinematic relations for constant divergence flow. Vorticity is negatively correlated for scale r between 1 and 7 Mpc/h. Divergence is negatively correlated for r > 30 Mpc/h that leads to a negative density correlation.

79 ASTRONOMY AND ASTROPHYSICS↗

Final state interactions and the Sivers function

The non-vanishing of naive T-odd parton distributions function can be explained by the existence of the gauge link which emerges from the factorized description of the deep inelastic scattering cross section into perturbatively calculable and non-perturbative factors. This path ordered exponential describes initial / final-state interactions of the active parton due to soft gluon exchanges with the target remnants. Although these interactions are non-perturbative, studies of final state interactions have been approximated by perturbative one-gluon exchange in Abelian models. We include higher-order gluonic contributions from the gauge link by applying non-perturbative eikonal methods, incorporating color degrees of freedom in a calculation of the Sivers function. In this context we study the effects of color by considering the FSIs with with Abelian and non-Abelian gluon interactions. We confirm the large N{sub c} QCD scaling behavior of Sivers functions and further uncover the deviations for finite N{sub c}. Within this framework of FSIs we perform a quantitative check of approximate relations between T-odd TMDs and GPD which goes beyond the discussion of overall signs.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗