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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 541 records · Page 30
All sourcesNASA NTRSDOE OSTI
NASA NTRS2012

TEM Observation of the Ti Interlayer Between SiC Substrates During Diffusion Bonding

Diffusion bonding was carried out to join SiC to SiC substrates using titanium interlayers. In this study, 10 m and 20 m thick physical vapor deposited (PVD) Ti surface coatings, and 10 and 20 m thick Ti foils were used. Diffusion bonding was performed at 1250 C for PVD Ti coatings and 1200 C for Ti foil. This study investigates the microstructures of the phases formed during diffusion bonding through TEM and selected-area diffraction analysis of a sample prepared with an FIB, which allows samples to be taken from the reacted area. In all samples, Ti3SiC2, Ti5Si3Cx and TiSi2 phases were identified. In addition, TiC and unknown phases also appeared in the samples in which Ti foils were used as interlayers. Furthermore, Ti3SiC2 phases show high concentration and Ti5Si3Cx formed less when samples were processed at a higher temperature and thinner interlayer samples were used. It appears that the formation of microcracks is caused by the presence of intermediate phase Ti5Si3Cx, which has anisotropic thermal expansion, and by the presence of an unidentified Ti-Si-C ternary phase with relatively low Si content.

Tsuda, Hiroshi↗
DOE OSTI2016

Characteristic energy range of electron scattering due to plasmaspheric hiss

In this paper, we investigate the characteristic energy range of electron flux decay due to the interaction with plasmaspheric hiss in the Earth's inner magnetosphere. The Van Allen Probes have measured the energetic electron flux decay profiles in the Earth's outer radiation belt during a quiet period following the geomagnetic storm that occurred on 7 November 2015. The observed energy of significant electron decay increases with decreasing L shell and is well correlated with the energy band corresponding to the first adiabatic invariant μ = 4–200 MeV/G. The electron diffusion coefficients due to hiss scattering are calculated at L = 2–6, and the modeled energy band of effective pitch angle scattering is also well correlated with the constant μ lines and is consistent with the observed energy range of electron decay. Using the previously developed statistical plasmaspheric hiss model during modestly disturbed periods, we perform a 2-D Fokker-Planck simulation of the electron phase space density evolution at L = 3.5 and demonstrate that plasmaspheric hiss causes the significant decay of 100 keV–1 MeV electrons with the largest decay rate occurring at around 340 keV, forming anisotropic pitch angle distributions at lower energies and more flattened distributions at higher energies. Finally, our study provides reasonable estimates of the electron populations that can be most significantly affected by plasmaspheric hiss and the consequent electron decay profiles.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Planck intermediate results: XXX. The angular power spectrum of polarized dust emission at intermediate and high Galactic latitudes

The polarized thermal emission from diffuse Galactic dust is the main foreground present in measurements of the polarization of the cosmic microwave background (CMB) at frequencies above 100 GHz. In this study we exploit the uniqueness of the Planck HFI polarization data from 100 to 353 GHz to measure the polarized dust angular power spectra C ℓ EE and C ℓ BB over the multipole range 40 <ℓ< 600 well away from the Galactic plane. These measurements will bring new insights into interstellar dust physics and allow a precise determination of the level of contamination for CMB polarization experiments. Despite the non-Gaussian and anisotropic nature of Galactic dust, we show that general statistical properties of the emission can be characterized accurately over large fractions of the sky using angular power spectra. The polarization power spectra of the dust are well described by power laws in multipole, C ℓ ∝ ℓ α , with exponents α EE,BB = -2.42 ± 0.02. The amplitudes of the polarization power spectra vary with the average brightness in a way similar to the intensity power spectra. The frequency dependence of the dust polarization spectra is consistent with modified blackbody emission with β d = 1.59 and T d = 19.6 K down to the lowest Planck HFI frequencies. We find a systematic difference between the amplitudes of the Galactic B- and E-modes, C ℓ BB /C ℓ EE = 0.5. We verify that these general properties are preserved towards high Galactic latitudes with low dust column densities. We show that even in the faintest dust-emitting regions there are no “clean” windows in the sky where primordial CMB B-mode polarization measurements could be made without subtraction of foreground emission. Finally, we investigate the level of dust polarization in the specific field recently targeted by the BICEP2 experiment. Extrapolation of the Planck 353 GHz data to 150 GHz gives a dust power D ℓ BB ≡ ℓ(ℓ+1)C ℓ BB /(2π) of 1.32 × 10 -2 μK CMB 2 over the multipole range of the primordial recombination bump (40 <ℓ< 120); the statistical uncertainty is ± 0.29 × 10 -2 μK CMB 2 and there is an additional uncertainty (+0.28, -0.24) × 10 -2 μK CMB 2 from the extrapolation. Finally, this level is the same magnitude as reported by BICEP2 over this ℓ range, which highlights the need for assessment of the polarized dust signal even in the cleanest windows of the sky.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1984

Accretion by magnetic neutron stars. II - Plasma entry into the magnetosphere via diffusion, polar cusps, and magnetic field reconnection

A variety of entry modes were investigated to determine whether most of the accreting plasma enters the magnetosphere as a result of hydromagnetic instability or via other means. It is shown that diffusion is never important under the conditions of interest, nor is the loss-cone entry through the polar cusps when the plasma is collisionless. Although the loss-cone entry rate can be significantly increased if the plasma in the cusps cools and becomes collisional, this cannot stabilize the magnetosphere. The descent of the cusps cannot be the dominant entry process if the star has a persistent luminosity greater than about 10 to the 36th erg/s and a substantial fraction of the magnetosphere is illuminated. This, however, can be a significant entry process for much lower luminosities or strongly anisotropic illumination. The possibility that plasma entry via reconnection can stabilize the magnetosphere is also unlikely.

Elsner, R. F.↗
DOE OSTI2015

EVIDENCE OF LANDAU AND CYCLOTRON RESONANCE BETWEEN PROTONS AND KINETIC WAVES IN SOLAR WIND TURBULENCE

The wave–particle interaction processes occurring in the solar wind provide crucial information to understand the wave dissipation and simultaneous particle heating in plasma turbulence. One requires observations of both wave fluctuations and particle kinetics near the dissipation range, which have, however, not yet been analyzed simultaneously. Here we show new evidence of wave–particle interactions by combining the diagnosis of wave modes with the analysis of particle kinetics on the basis of measurements from the WIND spacecraft with a high cadence of about 3 s. Solar wind protons appear to be highly dynamic in their velocity distribution consisting of varying anisotropic core and beam components. The basic scenario of solar wind proton heating through wave–particle interaction is suggested to be the following. Left-handed cyclotron resonance occurs continuously, and is evident from the observed proton core velocity distribution and the concurrent quasi-parallel left-handed Alfvén cyclotron waves. Landau and right-handed cyclotron resonances are persistent and indicated by the observed drifting anisotropic beam and the simultaneous quasi-perpendicular right-handed kinetic Alfvén waves in a general sense. The persistence of non-gyrotropic proton distributions may cast new light on the nature of the interaction between particles and waves near and beyond the proton gyro-frequency.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Anisotropic hot deformed magnets prepared from Zn-coated MRE-Fe-B ribbon powder

Milled melt-spun ribbon flake of MRE-Fe-B coated with Zn coating using a vapor transport technique was found to have significant increase in coercivity without degrading the magnetization when the Zn thickness and heat treatment were optimized. Magnetic measurements show that 0.5–1 wt. % Zn coating increases the coercivity about 1 kOe over the initial ribbon powder. After vacuum hot deformation (VHD), the VHD magnet with Zn coating of 0.5 wt. % results in a nearly 3 kOe higher coercivity than an un-coated alloy magnet. An optimized VHD magnet with 0.5 wt. % Zn coating obtains a coercivity of 11.2 kOe and (BH)max of 23.0 MGOe, respectively. SEM and TEM microstructures analysis demonstrates that the Zn coating on the surface of ribbon powder has diffused along the intergranular boundaries after the ribbon powder was annealed at 750 °C for 30 min or was hot deformed at 700–750 °C.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Electrochemical characteristics of nanostructured silicon anodes for lithium-ion batteries

High-aspect periodic structures with thin vertical walls are studied as regards their applicability as negative electrodes of lithium-ion batteries. The nanostructures are fabricated from single-crystal silicon using photolithography, electrochemical anodization, and subsequent anisotropic shaping. The capacity per unit of the visible surface area of the electrode and the specific internal surface area are compared for structures of varied architecture: 1D (wires), 2D (zigzag walls), and 3D structures (walls forming a grid). Main attention is given to testing the endurance of anodes based on zigzag and grid structures, performed by galvanostatic cycling in half-cells with a lithium counter electrode. The influence exerted by the geometric parameters of the structures and by the testing mode on the degradation rate is determined. It is shown that the limiting factor of the lithiation and delithiation processes is diffusion. The endurance of an electrode dramatically increases when the charging capacity is limited to ∼1000 mA h/g. In this case, nanostructures with 300-nm-thick walls, which underwent cyclic testing at a rate of 0.36C, retain a constant discharge capacity and a Coulomb efficiency close to 100% for more than 1000 cycles.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Anisotropic Synthesis of Armchair Graphene Nanoribbon Arrays from Sub-5 nm Seeds at Variable Pitches on Germanium

At widths below 10 nm, armchair graphene nanoribbons become semiconductors. One interesting route to synthesize nanoribbons is chemical vapor deposition (CVD) of hydrocarbons on Ge(001), and synthesis from seeds reduces nanoribbon polydispersity. In this contribution, we advance the seed-initiated synthesis of nanoribbons and explore the impact of seed size and nanoribbon spacing on growth kinetics. Periodic arrays of graphene seeds are lithographically patterned and etched to reduce their diameter. The viability of initiating synthesis from sub-5 nm seeds is demonstrated, and the pitch between nanoribbons is reduced from 500 to 50 nm to show that crowding effects do not perturb nanoribbon growth kinetics. The invariance of kinetics with pitch in combination with density functional theory (DFT) calculations suggest that (1) the growth species for synthesis has a diffusion length of &#x226a;50 nm and/or (2) the kinetics are strongly attachment-limited. These results demonstrate that seed-initiated synthesis on Ge(001) is a promising path for creating dense arrays of armchair graphene nanoribbons for semiconductor electronics applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Comparison of the telegraph and hyperdiffusion approximations in cosmic-ray transport

The telegraph equation and its generalizations have been repeatedly considered in the models of diffusive cosmic-ray transport. Yet the telegraph model has well-known limitations, and analytical arguments suggest that a hyperdiffusion model should serve as a more accurate alternative to the telegraph model, especially on the timescale of a few scattering times. We present a detailed side-by-side comparison of an evolving particle density profile, predicted by the telegraph and hyperdiffusion models in the context of a simple but physically meaningful initial-value problem, compare the predictions with the solution based on the Fokker–Planck equation, and discuss the applicability of the telegraph and hyperdiffusion approximations to the description of strongly anisotropic particle distributions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Rotational Dynamics and Transition Mechanisms of Surface-Adsorbed Proteins

Assembly of biomolecules at solid-water interfaces requires molecules to traverse complex orientation-dependent energy landscapes through processes that are poorly understood, largely due to the dearth of in-situ single molecule measurements and statistical analyses of the rotational dynamics that define directional selection. Emerging capabilities in high-speed atomic force microscopy and machine learning have allowed us to directly determine the orientational energy landscape and observe and quantify the rotational dynamics for protein nanorods on the surface of muscovite mica under a variety of conditions. Comparisons with kinetic Monte Carlo simulations show that the transition rates between adjacent orientation-specific energetic minima can largely be understood through traditional models of in-plane Brownian rotation across a biased energy landscape, with resulting transition rates that are exponential in the energy-barriers between states. However, transitions between more distant angular states are decoupled from barrier height, with jump-size distributions showing a power-law decay that is characteristic of a non-classical Levy-flight random walk, indicating that large jumps are enabled by alternative modes of motion via activated states. The findings provide new insights into the dynamics of biomolecules at solid-liquid interfaces that lead to self-assembly, epitaxial matching and other orientationally anisotropic outcomes and define a general procedure for exploring such dynamics with implications for hybrid biomolecular-inorganic materials design.

Orientational energy landscapes, Rotational dynami↗
DOE OSTI2013

Structure and electrochemical properties of nanometer Cu substituted α-nickel hydroxide

Graphical abstract: Display Omitted Highlights: ► Cu substituted α-nickel hydroxide was prepared by ultrasonic assisted precipitation. ► The XRD peaks are anisotropic broadening. ► The electrode for 0.9 wt.% Cu has the highest capacity of 310 mAh/g at 0.2 C. -- Abstract: Nanometer Cu-substituted α-nickel hydroxide was synthesized by means of ultrasonic-assisted precipitation. Particle size distribution (PSD) measurement, X-ray diffraction (XRD), and high-resolution transmission electron microscope (HR-TEM) were used to characterize the physical properties of the synthesized samples. The results indicate that the average particle size of the samples is about 96–110 nm and the XRD diffraction peaks are anisotropic broadening. The crystal grains are mainly polycrystal structure with columnar or needle-like morphology, containing many defects. With increase of Cu content, the shape of primary particles transform from columnar to needle-like. The influences of doping amounts of Cu on the electrochemical performance were investigated through constant current charge/discharge and cyclic voltammetric measurements. The specific capacity increases initially and then decreases with increasing Cu-doping ratio, the electrode C containing 0.9 wt.% Cu shows the maximum discharge capacity of 310 mAh/g at 0.2 C, and it has the lowest charging voltage, higher discharge voltage plateau, better cycle performance and larger proton diffusion coefficient than the other electrodes.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Morphological analysis of the polarized synchrotron emission with WMAP and Planck

The bright polarized synchrotron emission, away from the Galactic plane, originates mostly from filamentary structures. We implement a filament finder algorithm which allows the detection of bright elongated structures in polarized intensity maps. We analyse the sky at 23 and 30 GHz as observed respectively by WMAP and Planck. We identify 19 filaments, 13 of which have been previously observed. For each filament, we study the polarization fraction, finding values typically larger than for the areas outside the filaments, excluding the Galactic plane, and a fraction of about 30% is reached in two filaments. We study the polarization spectral indices of the filaments, and find a spectral index consistent with the values found in previous analysis (about -3.1) for more diffuse regions. Decomposing the polarization signals into the E and B families, we find that most of the filaments are detected in P E , but not in P B . We then focus on understanding the statistical properties of the diffuse regions of the synchrotron emission at 23 GHz. Using Minkowski functionals and tensors, we analyse the non-Gaussianity and statistical isotropy of the polarized intensity maps. For a sky coverage corresponding to 80% of the fainter emission, and on scales smaller than 6 degrees (ℓ > 30), the deviations from Gaussianity and isotropy are significantly higher than 3σ. The level of deviation decreases for smaller scales, however, it remains significantly high for the lowest analised scale (~ 1.5°). When 60% sky coverage is analysed, we find that the deviations never exceed 3σ. Finally, we present a simple data-driven model to generate non-Gaussian and anisotropic simulations of the synchrotron polarized emission. The simulations are fitted in order to match the spectral and statistical properties of the faintest 80% sky coverage of the data maps.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Response of 11 B enriched ZrB 2 ultra-high temperature ceramic to neutron irradiation at elevated temperatures

ZrB 2 , an ultra-high temperature ceramic (UHTC) is being considered for use in fusion reactor first-wall structures, yet its response to irradiation remains poorly understood. This study employed scanning/transmission electron microscopy (S/TEM), synchrotron X-ray diffraction (XRD), finite element calculations, and thermal property measurements to thoroughly investigate the neutron-irradiation effects on 11 B-enriched ZrB 2 . Neutron irradiations were conducted at 220 °C and 620 °C, with a neutron fluence of 2.2 × 10 25 neutron/m 2 (energy > 0.1 MeV), resulting in 3.9 dpa and 4200 appm He. The study revealed the unusual prevalence of prism loops and a > c anisotropic lattice swelling, likely linked to the low c/a ratio of ZrB 2 , leading to grain boundary microcracking. Reducing the grain sizes was effective in reducing intergranular cracking and macroscopic swelling. The observation of cavities in ZrB 2 irradiated at 620 °C, as opposed to 220 °C, prompts questions about the temperature at which vacancies in ZrB 2 become mobile, and the role of neutron absorption by 10 B in elevating irradiation temperatures. Isotopic enrichment in 11 B proves to be a viable strategy for mitigating helium production in transition-metal diborides, which is a critical consideration for nuclear applications. Irradiation-induced defects reduce the thermal diffusivity and conductivity of ZrB 2 by a factor of 4–9, which has important implications for its role as a plasma-facing material in fusion reactors that drive high heat fluxes through first-wall materials. Here, this comprehensive study lays the foundation for understanding ZrB 2 behavior under neutron irradiation and highlights important phenomena to consider for various material applications.

36 MATERIALS SCIENCE↗
NASA NTRS1998

Profile Evolution Simulation in Etching Systems Using Level Set Methods

Semiconductor device profiles are determined by the characteristics of both etching and deposition processes. In particular, a highly anisotropic etch is required to achieve vertical sidewalls. However, etching is comprised of both anisotropic and isotropic components, due to ion and neutral fluxes, respectively. In Ar/Cl2 plasmas, for example, neutral chlorine reacts with the Si surfaces to form silicon chlorides. These compounds are then removed by the impinging ion fluxes. Hence the directionality of the ions (and thus the ion angular distribution function, or IAD), as well as the relative fluxes of neutrals and ions determines the amount of undercutting. One method of modeling device profile evolution is to simulate the moving solid-gas interface between the semiconductor and the plasma as a string of nodes. The velocity of each node is calculated and then the nodes are advanced accordingly. Although this technique appears to be relatively straightforward, extensive looping schemes are required at the profile corners. An alternate method is to use level set theory, which involves embedding the location of the interface in a field variable. The normal speed is calculated at each mesh point, and the field variable is updated. The profile comers are more accurately modeled as the need for looping algorithms is eliminated. The model we have developed is a 2-D Level Set Profile Evolution Simulation (LSPES). The LSPES calculates etch rates of a substrate in low pressure plasmas due to the incident ion and neutral fluxes. For a Si substrate in an Ar/C12 gas mixture, for example, the predictions of the LSPES are identical to those from a string evolution model for high neutral fluxes and two different ion angular distributions.(2) In the figure shown, the relative neutral to ion flux in the bulk plasma is 100 to 1. For a moderately isotropic ion angular distribution function as shown in the cases in the left hand column, both the LSPES (top row) and rude's string method (bottom row) predict tapered profiles. The LSPES uses an AD with a FWHM = 13.5 degrees, and rude's model uses a ratio of sheath voltage to ion temperature of 50. The more anisotropic IADs produce profiles with more vertical sidewalls and a wider bottom surface, as shown in the right hand column. Here, the LSPES has an AD with a FWHM = 2 degrees, and rude's model uses a ratio of 500 of sheath voltage to ion temperature. The agreement between the LSPES and rude's model is excellent in both cases. We will present etching profiles generated by the LSPES, including calculations of the re-emitted fluxes of both neutrals and ions off of the profile walls. In addition, we will show the effect of geometric structures (overhangs, etc.) on the etching profiles. Other physical aspects, such as surface diffusion, will also be included in the model.

Hwang, Helen H.↗
DOE OSTI2021

Multipoint Observations of Quasiperiodic Emission Intensification and Effects on Energetic Electron Precipitation

The two Van Allen Probes simultaneously recorded a coherently modulated quasiperiodic (QP) emission that persisted for 3 h. The magnetic field pulsation at the locations of the two satellites showed a substantial difference, and their frequencies were close to but did not exactly match the repetition frequency of QP emissions for most of the time, suggesting that those coherent QP emissions probably originated from a common source, which then propagated over a broad area in the magnetosphere. The QP emissions were amplified by local anisotropic electron distributions, and their large-scale amplitudes were modulated by the plasma density. A novel observation of this event is that chorus waves at frequencies above QP emissions exhibit a strong correlation with QP emissions. Those chorus waves intensified when the QP emissions reach their peak frequency. This indicates that embryonic QP emissions may be critical for its own intensification as well as chorus waves under certain circumstances. A Low-Earth-Orbit POES satellite observed enhanced energetic electron precipitation in conjunction with the Van Allen Probes, providing direct evidence that QP emissions precipitate energetic electrons into the atmosphere. Finally, this scenario is quantitatively confirmed by our quasilinear diffusion simulation results.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Whistler waves generated by nongyrotropic and gyrotropic electron beams during asymmetric guide field reconnection

Using a two-dimensional particle-in-cell simulation of asymmetric reconnection with a guide field whose strength is 0.3 times the reconnecting magnetic field, we study electron distribution functions and wave intensities in the diffusion region, focusing on the electron diffusion region (EDR). Wave activities with frequencies below the electron cyclotron frequency are observed, and these are whistler waves propagating almost anti-parallel to the magnetic field. The waves are concentrated near the magnetospheric separatrix away from the X line, but the wave activity also spreads through the EDR near the X line. The reconnection outflows are asymmetric in the outflow direction in the magnetospheric side, and the wave intensity is stronger in the side of the faster electron outflow. We study the whistler waves using the fast Fourier transform, analyses of electron velocity distribution functions, and the dispersion solver calculation. Along the magnetospheric separatrix in the stronger outflow side, highly anisotropic electron beams exist with super-Alfvénic drift speeds. The dispersion analysis shows that there are two modes: a temperature anisotropy mode and a beam mode. Outside the EDR, the whistler wave intensity is highest near the separatrix, but the wave intensity decreases if we move away from the separatrix toward the magnetic neutral line because of the increase in the electron population near zero parallel velocity. In the EDR, in the velocity plane perpendicular to the magnetic field, ring/crescent electron distribution functions are observed. Near the X-line, the wave power is enhanced where nongyrotropic electrons contribute to increase the perpendicular temperature anisotropy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2022

Whistler Waves Generated by Nongyrotropic and Gyrotropic Electron Beams During Asymmetric Guide Field Reconnection

Using a two-dimensional particle-in-cell simulation of asymmetric reconnection with a guide field whose strength is 0.3 times the reconnecting magnetic field, we study electron distribution functions and wave intensities in the diffusion region, focusing on the electron diffusion region (EDR). Wave activities with frequencies below the electron cyclotron frequency are observed, and these are whistler waves propagating almost anti-parallel to the magnetic field. The waves are concentrated near the magnetospheric separatrix away from the X line, but the wave activity also spreads through the EDR near the X line. The reconnection outflows are asymmetric in the outflow direction in the magnetospheric side, and the wave intensity is stronger in the side of the faster electron outflow. We study the whistler waves using the fast Fourier transform, analyses of electron velocity distribution functions, and the dispersion solver calculation. Along the magnetospheric separatrix in the stronger outflow side, highly anisotropic electron beams exist with super-Alfvénic drift speeds. The dispersion analysis shows that there are two modes: a temperature anisotropy mode and a beam mode. Outside the EDR, the whistler wave intensity is highest near the separatrix, but the wave intensity decreases if we move away from the separatrix toward the magnetic neutral line because of the increase in the electron population near zero parallel velocity. In the EDR, in the velocity plane perpendicular to the magnetic field, ring/crescent electron distribution functions are observed. Near the X-line, the wave power is enhanced where nongyrotropic electrons contribute to increase the perpendicular temperature anisotropy.

magnetic reconnection↗
DOE OSTI2020

Universal spin dynamics in infinite-temperature one-dimensional quantum magnets

Here, we address the nature of spin dynamics in various integrable and non-integrable, isotropic and anisotropic quantum spin-$S$ chains, beyond the paradigmatic $S=1/2$ Heisenberg model. In particular, we investigate the algebraic long-time decay $\propto t^{-1/z}$ of the spin-spin correlation function at infinite temperature, using state-of-the-art simulations based on tensor network methods. We identify three universal regimes for the spin transport, independent of the exact microscopic model: (i) superdiffusive with $z=3/2$, as in the Kardar-Parisi-Zhang universality class, when the model is integrable with extra symmetries such as spin isotropy that drive the Drude weight to zero, (ii) ballistic with $z=1$ when the model is integrable with a finite Drude weight, and (iii) diffusive with $z=2$ with easy-axis anisotropy or without integrability, at variance with previous observations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗