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NASA NTRS1983

Unsteady behavior of a reattaching shear layer

A detailed investigation of the unsteadiness in a reattaching, turbulent shear layer is reported. Laser-Doppler velocimeter measurements were conditionally sampled on the basis of instantaneous flow direction near reattachment. Conditions of abnormally short reattachment and abnormally long reattachment were considered. Ensemble-averaging of measurements made during these conditions was used to obtain mean velocities and Rreynolds stresses. In the mean flow, conditional streamlines show a global change in flow pattern which correlates with wall-flow direction. This motion can loosely be described as a 'flapping' of the shear layer. Tuft probes show that the flow direction reversals occur quite randomly and are shortlived. Streses shown also vary with the change in flow pattern. Yet, the global'flapping' motion does not appear to contribute significantly to the stress in the flow. A second type of unsteady motion was identified. Spectral analysis of both wall static pressure and streamwise velocity shows that most of the energy in the flow resides in frequencies that are significantly lower than that of the turbulence. The dominant frequency is at a Strouhal number equal to 0.2, which is the characteristic frequency of roll-up and pairing of vortical structure seen in free shear layers. It is conjectured that the 'flapping' is a disorder of the roll-up and pairing process occurring in the shear layer.

Driver, D. M.↗

NASA NTRS1996

Dynamics of Disorder-Order Transitions in Hard Sphere Colloidal Dispersions in micro-g

We performed a series of experiments on 0.518 millimeter PMMA spheres suspended in an index matching mixture of decalin and tetralin the microgravity environment provided by the Shuttle Columbia on mission STS-73. The samples ranged in concentration from 0.49 to 0.62. volume fraction (phi) of spheres, which covers the range in which liquid, coexistence, solid and glass phases are expected from Earth bound experiments. Light scattering was used to probe the static structure, and the particle dynamics. Digital and 35 mm photos provided information on the morphology of the crystals. In general, the crystallites grew considerably larger (roughly an order of magnitude larger) than the same samples with identical treatment in 1 g. The dynamic light scattering shows the typical short time diffusion and long time caging effects found in 1 g. The surprises that were encountered in microgravity include the preponderance of random hexagonal close packed (RHCP) structures and the complete absence of the expected face centered cubic (FCC) structure, existence of large dendritic crystals floating in the coexistence samples (where liquid and solid phases coexist) and the rapid crystallization of samples which exist only in glass phase under the influence of one g. These results suggest that colloidal crystal growth is profoundly effected by gravity in yet unrecognized ways. We suspect that the RCHP structure is related to the nonequilibrium growth that is evident from the presence of dendrites. An analysis of the dendritic growth instabilities is presented within the framework of the Ackerson-Schatzel equation.

Zhu, J. X.↗

NASA NTRS2024

Expanding Ketamine Application for Treatment of Acute Suicidality in Long-Duration Spaceflight

Introduction. The transition to exploration missions places a heightened risk on behavioral health in spaceflight. Although serious psychiatric emergencies during spaceflight have been rare, longer duration missions increase the possibility of emergence in latent mental health disorders due to genetic predisposition, increased autonomy, isolation, helplessness, loss of family member, or catastrophic events. Complicated grief and bereavement have the highest rate of suicidal ideation. Recently, ketamine has been used as an emergent intervention for acute suicidality, promoting its stability, ease of administration, favorable safety profile, and outcomes for reduction of suicidal intent. The goal of this study was to review current literature and collate the understanding of ketamine as a safe, effective pharmacological adjunct for acute suicidality in spaceflight. Methods. This literature review was conducted to collate data on ketamine use for acute suicidality and inform on stability, limitations and utilization of ketamine within extreme environments. Results. 122 publications were reviewed for relevance including 23 randomized-control trials for ketamine use in behavioral emergencies. Discussion. Ketamine is a diverse pharmaceutical with multiple advantageous indications, including acute suicidality, pain, and sedation. Terrestrial use of ketamine suggests a rapidly efficacious medication for reduction in acute suicidality. As behavioral stressors expand related to extended missions, contingencies for behavioral emergencies become increasingly important. Although this review is not intended to re-develop current International Space Station (ISS) protocols, it is the first to discuss the benefits of ketamine in spaceflight as a potential safe, effective multifaceted tool for future exploration missions and treatment for acute suicidal ideation.

Ketamine, Suicidality, Spaceflight↗

DOE OSTI2025

Bottlebrush Block Copolymer Thin Films

The self-assembly of block copolymers (BCPs) in thin films is governed by interfacial interactions (enthalpy) between the blocks and interfaces (at both the substrate and the surface). Advantage can also be taken of entropy to control the polymer orientation. Here, we synthesized a series of bottlebrush block copolymers (BBCPs), with deuterated polystyrene (DPS) as the core block and poly(solketal acrylate) (PSA) as the corona block, where the backbone length (N BB) and grafting densities (GDs) were varied. The hydrophobic PSA block was converted to a hydrophilic poly(glyceryl acrylate) (PGA) block by solid-state hydrolysis, bringing the BBCP from a disordered state into an ordered state with a lamellar microdomain morphology. The orientation of the morphology as a function of distance from the interfaces was systematically investigated by atomic force microscopy (AFM), interference microscopy, grazing-incidence small-angle X-ray scattering (GISAXS), and grazing-incidence small angle neutron scattering (GISANS). For N BB = 1 (diblock BCP), a mixed lamellar orientation was found. For N BB = 5 (star-like BBCP), a vertical orientation of the lamellar microdomains was found dominantly at the interfaces that propagated into the bulk of the film due to the entropic penalty associated with constraints on the junction points. Increasing the N BB to 50 (rod-like BBCP) and 100 (worm-like BBCP) yielded a random orientation, as the side chains became overcrowded when aligned in the same direction. By reducing the grafting density (GD) of a N BB = 50 BBCP from 100% to 75% and 50% by the incorporation of spacers into the backbone, the steric hindrance of side chains is reduced markedly, facilitating a vertical orientation of the lamellar microdomains. However, the vertical orientation becomes more random within the bulk of the thin film for different BBCP architectures. By modifying the substrate with a layer of PS, the preferential interactions between the core block of the BBCP and the interfaces induce a reconfiguration of the BBCP, drawing the core block out to contact substrate directly driven by enthalpy. Under these conditions, N BB = 5 showed a predominantly parallel orientation of the lamellar microdomains with the corona block minimizing contact with the substrate. Higher N BB values of 50 and 100 showed a more random orientation of the lamellar microdomains at different depths on the PS-modified substrate. Overall, thin-film morphology was regulated by tuning the configuration of the BBCP, varying the entropic contribution to the microdomain orientation.

Chen, Zhan↗

DOE OSTI2022

Particle transport in Markov stochastic mixtures with spatial gradients

Markov geometries are a prototype class of stochastic media that are widely used to model complex disordered systems. In a series of recent works, we have shown that spatially homogeneous (but possibly non-isotropic) Poisson tessellations can be conveniently used in order to generate three-dimensional realizations of Markov media and thus characterize the features of particle transport e.g. in fragmented fuel elements following severe nuclear accidents or Rayleigh-Taylor turbulent mixing for inertial confinement fusion. In this paper we show that Poisson tessellations can be extended to take into account the presence of spatial gradients, which commonly occur in real-world applications due to material stratification. For this purpose, we will provide an explicit construction of spatially-non-homogeneous Poisson tessellations, fully characterize their statistical properties, and finally illustrate the behaviour of particle transport in such random media. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Entropy-Driven Structural Evolution in Ceramic Oxides

High-entropy ceramics, with five or more elements randomly occupying the same cation crystallographic sites, offer vast compositional diversity and unique properties for material design and applications. However, for many dissimilar elements, entropic stabilization cannot overcome the enthalpic barrier to cation substitution. As a result, most high-entropy ceramics incorporate only a few similar elements, limiting the in-depth exploration of the effect of entropy on ceramic properties. Here, we first use density functional theory to model fluorite crystal structures composed of 1-10 elements and then experimentally present practical fluorite oxide nanostructures containing 1, 3, 8, and 15 metals, as well as a record-breaking 25-element high-entropy ceramic incorporating a diverse palette of rare-earth, transition, alkaline, p-block, and noble metals. As entropy increases, structural and configurational disorder in the solid solution rises, altering structural features such as lattice distortion, crystallinity, homogeneity, defect density, and thermal stability. This research provides new insights and understanding of the role of entropy in stabilizing compositionally complex ceramics.

Liu, Shuo↗

DOE OSTI2022

Efficiency and Forward Voltage of Blue and Green Lateral LEDs with V-shaped Defects and Random Alloy Fluctuation in Quantum Wells

For nitride-based blue and green light-emitting diodes (LEDs), the forward voltage V for is larger than expected, especially for green LEDs. This is mainly due to the large barriers to vertical carrier transport caused by the total polarization discontinuity at multiple quantum well and quantum barrier interfaces. The natural random alloy fluctuation in quantum wells has proven to be an important factor reducing V for . However, this does not suffice in the case of green LEDs because of their larger polarization-induced barrier. V-shaped defects (V-defects) have been proposed as another key factor in reducing V for to allow lateral injection into multiple quantum wells, thus bypassing the multiple energy barriers incurred by vertical transport. In this paper, to model carrier transport in the whole LED, we consider both random-alloy and V-defect effects. A fully two-dimensional drift-diffusion charge-control solver is used to model both effects. The results indicate that the turn-on voltages for blue and green LEDs are both affected by random alloy fluctuations and the V-defect density. For green LEDs, V for decreases more due to V-defects, where the smaller polarization barrier at the V-defect sidewall is the major path for lateral carrier injection. Then, we discuss how the V-defect density and size affects the results.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Visualizing band selective enhancement of quasiparticle lifetime in a metallic ferromagnet

Abstract Electrons navigate more easily in a background of ordered magnetic moments than around randomly oriented ones. This fundamental quantum mechanical principle is due to their Bloch wave nature and also underlies ballistic electronic motion in a perfect crystal. As a result, a paramagnetic metal that develops ferromagnetic order often experiences a sharp drop in the resistivity. Despite the universality of this phenomenon, a direct observation of the impact of ferromagnetic order on the electronic quasiparticles in a magnetic metal is still lacking. Here we demonstrate that quasiparticles experience a significant enhancement of their lifetime in the ferromagnetic state of the low-density magnetic semimetal EuCd 2 As 2 , but this occurs only in selected bands and specific energy ranges. This is a direct consequence of the magnetically induced band splitting and the multi-orbital nature of the material. Our detailed study allows to disentangle different electronic scattering mechanisms due to non-magnetic disorder and magnon exchange. Such high momentum and energy dependence quasiparticle lifetime enhancement can lead to spin selective transport and potential spintronic applications.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Driven superconducting vortex dynamics in systems with twofold anisotropy in the presence of pinning

Abstract We examine the dynamics of superconducting vortices with twofold anisotropic interaction potentials driven over random pinning, and compare the behavior under drives applied along the hard and the soft anisotropy directions. As the driving force increases, the number of topological defects reaches a maximum near the depinning threshold, and then decreases as the vortices form one-dimensional (1D) chains. This coincides with a transition from a pinned nematic to a moving smectic aligned with the soft anisotropy direction. The system is generally more ordered when the drive is applied along the soft direction of the anisotropy. For driving along the hard direction, there is a critical value of the twofold anisotropy above which the system remains aligned with the soft direction. Hysteretic behavior appears upon cycling the driving force, with 1D vortex chains persisting during the decreasing leg below the threshold for chain formation for increasing drive. More anisotropic systems have a greater amount of structural disorder in the moving state. For lower anisotropy, the system forms a moving smectic-A state, while at higher anisotropy, a moving nematic state appears instead.

36 MATERIALS SCIENCE↗

DOE OSTI2026

One-dimensional neutron diffraction from layered graphite: Reciprocal space structure and grating behavior

In this work we report observations of one-dimensional neutron diffraction from highly oriented pyrolytic graphite (HOPG), where the scattering angle varies continuously with incident angle following classical grating-like behavior. The 2D polycrystalline structure of HOPG—with highly aligned layers along the 𝑐 axis but random in-plane rotations—creates planes of scattering intensity in reciprocal space at 𝑄 𝑐 =𝑛⁢(2⁢𝜋/𝑑) where 𝑑=3.35Å is the interlayer spacing. As the Ewald sphere sweeps through reciprocal space during sample rotation, it continuously intersects these planes, producing the observed angular dispersion. We observe both first-order (𝑛=1) and second-order (𝑛=2) diffraction at conventional scattering angles (25°–70°), with peak positions that remain temperature-independent between 10 K and 294 K and follow quantitative agreement with momentum conservation 𝑄 𝑐 =𝑘⁢[sin⁡𝜓−sin⁡𝜓 𝑓 ]=𝑛⁢(2⁢𝜋/𝑑). X-ray diffraction under similar conditions shows no comparable behavior, confirming that sharp nuclear-vacuum contrast is essential. While diffraction intensities are weak (∼10 −6 of Bragg peaks), the observations demonstrate how the interplay of atomic-scale periodicity, nuclear contrast, and structural disorder enables observation of continuous diffraction curves at thermal neutron wavelengths, illustrating how HOPG's unique microstructure determines its scattering properties beyond conventional Bragg diffraction.

2-dimensional systems↗

DOE OSTI2021

Resolving Chemical and Spatial Heterogeneities at Complex Electrochemical Interfaces in Li-Ion Batteries

The high specific capacities of Ni-rich transition metal oxides have garnered immense interest for improving the energy density of Li-ion batteries (LIBs). Despite the potential of these materials, Ni-rich cathodes suffer from interfacial instabilities that lead to crystallographic rearrangement of the active material surface as well as the formation of a cathode electrolyte interphase (CEI) layer on the composite during electrochemical cycling. While changes in crystallographic structure can be detected with diffraction-based methods, probing the chemistry of the disordered, heterogeneous CEI layer is challenging. In this work, we use a combination of ex situ solid-state nuclear magnetic resonance (SSNMR) spectroscopy and X-ray photoemission electron microscopy (XPEEM) to provide chemical and spatial information, on the nanometer length scale, on the CEI deposited on LiNi 0.8 Mn 0.1 Co 0.1 O 2 (NMC811) composite cathode films. XPEEM elemental maps offer insight into the lateral arrangement of the electrolyte decomposition products that comprise the CEI and paramagnetic interactions (assessed with electron paramagnetic resonance (EPR) and relaxation measurements) in 13 C SSNMR provide information on the radial arrangement of the CEI from the NMC811 particles outward. Using this approach, here we find that LiF, Li 2 CO 3 , and carboxy-containing structures are directly appended to NMC811 active particles, whereas soluble species detected during in situ 1 H and 19 F solution NMR experiments (e.g., alkyl carbonates, HF, and vinyl compounds) are randomly deposited on the composite surface. We show that the combined approach of ex situ SSNMR and XPEEM, in conjunction with in situ solution NMR, allows spatially-resolved, molecular-level characterization of paramagnetic surfaces and new insights into electrolyte oxidation mechanisms in porous electrode films.

36 MATERIALS SCIENCE↗

DOE OSTI2020

In-situ re-crystallization of heavily-irradiated Gd 2 Ti 2 O 7

Gadolinium titanate (Gd 2 Ti 2 O 7 , or GTO) and other lanthanide pyrochlores are interesting candidates for actinide waste disposal and fast ion conduction because the relevant material properties are intimately dependent on local cation structure. Therefore, a deep understanding of the kinetics associated with cation ordering and disordering is required if such material properties are to be tuned for specific device designs. To this end, single crystals of GTO were irradiated with 190 keV helium ions to a total fluence of 1 × 10 17 ions/cm 2 , amorphizing the sample surface to a depth of ~1 μm and resulting in significant He bubble accumulation. FIB lamellae lifted out from the irradiated sections were examined during heat treatment in the (scanning) transmission electron microscope. Two distinct stages of the re-crystallization of the amorphized material were observed. The material near the end of the ions’ range transformed first and with the same orientation as the pristine material. This was due to the close proximity of the pristine material and the presence of small defect fluorite seeds, but the propagation of this growth front was frustrated by the large pores (formerly bubbles) in the He accumulation layer. This was followed by heterogeneous nucleation of new crystallites at random orientations at the top of the He accumulation layer, which is attributed to the high surface area associated with the many small He bubbles in that region. Finally, it is inferred that the kinetics of grain growth in this material are significantly faster than the kinetics of grain nucleation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Commensuration effects on skyrmion Hall angle and drag for manipulation of skyrmions on two-dimensional periodic substrates

Here, we examine the dynamics of an individually driven skyrmion moving through a background lattice of skyrmions coupled to a 2D periodic substrate as we vary the ratio of the number of skyrmions to the number of pinning sites across commensurate and incommensurate conditions. As the skyrmion density increases, the skyrmion Hall angle is nonmonotonic, dropping to low or zero values in commensurate states and rising to an enhanced value in incommensurate states. Under commensuration, the driven skyrmion is channeled by a symmetry direction of the pinning array and exhibits an increased velocity. At fillings for which the skyrmion Hall angle is zero, the velocity has a narrow band noise signature, while for incommensurate fillings, the skyrmion motion is disordered and the velocity noise is broad band. Under commensurate conditions, multi-step depinning transitions appear and the skyrmion Hall angle is zero at low drives but becomes finite at higher drives, while at incommensurate fillings there is only a single depinning transition. As the gyrotropic component of the skyrmion dynamics, called the Magnus force, increases, peaks in the velocity that appear in commensurate regimes cross over to dips, and new types of directional locking effects can arise in which the skyrmion travels along other symmetry directions of the background lattice. At large Magnus forces, and particularly at commensurate fillings, the driven skyrmion can experience a velocity boost in which the skyrmion moves faster than the applied drive due to the alignment of the Magnus-induced velocity with the driving direction. In some cases, an increase of the Magnus force can produce regimes of enhanced pinning when the skyrmion is forced to move along a nonsymmetry direction of the periodic pinning array. This is in contrast to systems with random pinning, where increasing the Magnus force generally reduces the pinning effect. We demonstrate these dynamics for both square and triangular substrates and map out the different regimes as a function of filling fraction, pinning force, and the strength of the Magnus force in a series of dynamic phase diagrams.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Eminuscent phase in frustrated magnets: a challenge to quantum spin liquids

A geometrically frustrated (GF) magnet consists of localised magnetic moments, spins, whose orientation cannot be arranged to simultaneously minimise their interaction energies. Such materials may host novel fascinating phases of matter, such as fluid-like states called quantum spin-liquids. GF magnets have, like all solid-state systems, randomly located impurities whose magnetic moments may “freeze” at low temperatures, making the system enter a spin-glass state. We analyse the available data for spin-glass transitions in GF materials and find a surprising trend: the glass-transition temperature grows with decreasing impurity concentration and reaches a finite value in the impurity-free limit at a previously unidentified, “hidden”, energy scale. We propose a scenario in which the interplay of interactions and entropy leads to a crossover in the permeability of the medium that assists glass freezing at low temperatures. This low-temperature, “eminuscent”, phase may obscure or even destroy the widely-sought spin-liquid states in rather clean systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Effects on the Ocular Surface from Reading on Different Smartphone Screens: A Prospective Randomized Controlled Study

The purpose of this study was to investigate the influence of smartphone reading on the ocular surface and to compare the various effects of different screens and light conditions on the ocular surface. One hundred nineteen volunteers were randomly divided into: light + organic light‐emitting diode (OLED), light + electronic ink (eINK), dark + OLED, and dark + eINK. Ocular surface examinations, including noninvasive break‐up time (NIBUT), noninvasive keratograph tear meniscus height (NIKTMH), ocular redness, fluorescein break‐up time (FBUT), corneal fluorescein staining, meibomian gland assessment, Schirmer I Test, and blinking frequency, were performed before and after a reading task. Symptoms were evaluated using the Ocular Surface Disease Index (OSDI) and Computer Vision Syndrome Questionnaire (CVS‐Q). NIBUT and FBUT were decreased statistically significantly after participants read on an OLED screen for 2 hours compared with the baseline in light and dark environments, whereas no statistically significant decrease was observed on an eINK screen. NIKTMH was statistically significantly decreased after reading on an OLED screen in light and dark settings, and the eINK screen had a lesser effect on NIKTMH. An obvious increase in the ocular redness, OSDI and CVS‐Q scores was observed after reading on an OLED screen, whereas the eINK screen had a lesser effect on these indicators. Blink rate increased gradually in OLED subgroups during the reading task, whereas no statistically significant difference was observed in the eINK subgroups. Our research suggested that reading on an OLED screen can cause ocular surface disorder and obvious subjective discomfort, whereas reading on an eINK screen can minimize ocular surface disorder in both dark and light environments.

Yuan, Kelan↗

DOE OSTI2024

Anomalous Hall effects in chiral superconductors

We report theoretical results for the electronic contribution to thermal and electrical transport for chiral superconductors belonging to even or odd-parity E 1 and E 2 representations of the tetragonal and hexagonal point groups. Chiral superconductors exhibit novel properties that depend on the topology of the order parameter and Fermi surface, and—as we highlight—the structure of the impurity potential. An anomalous thermal Hall effect is predicted and shown to be sensitive to the winding number, ν, of the chiral order parameter via Andreev scattering that transfers angular momentum from the chiral condensate to excitations that scatter off the random potential. For heat transport in a chiral superconductor with isotropic impurity scattering, i.e., point-like impurities, a transverse heat current is obtained for ν = ± 1, but vanishes for | ν | > 1. This is not a universal result. For finite-size impurities with radii of order or greater than the Fermi wavelength, R ≥ ℏ / p f, the thermal Hall conductivity is finite for chiral order with | ν | ≥ 2, and determined by a specific Fermi-surface average of the differential cross-section for electron-impurity scattering. Our results also provide quantitative formulae for analyzing and interpreting thermal transport measurements for superconductors predicted to exhibit broken time-reversal and mirror symmetries.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

NMR study of Ni 50+x ⁢Ti 50-x strain glasses

Here, we studied Ni 50+x ⁢Ti 50-x with compositions up to x = 2, performing 47 Ti and 49 Ti nuclear magnetic resonance (NMR) measurements from 4 to 400 K. For large x in this system, a strain glass appears in which frozen ferroelastic nanodomains replace the displacive martensite structural transition. Here, we demonstrate that NMR can provide an extremely effective probe of the strain-glass freezing process, with large changes in NMR line shape due to the effects of random strains which become motionally narrowed at high temperatures. At the same time with high-resolution x-ray diffraction we confirm the lack of structural changes in x ≥ 1.2 samples, while we show that there is little change in the electronic behavior across the strain-glass freezing temperature. NMR spin-lattice relaxation time (T 1 ) measurements provide a further measure of the dynamics of the freezing process, and indicate a predominantly thermally activated behavior both above and below the strain-glass freezing temperature. We show that the strain-glass results are consistent with a very small density of critically divergent domains undergoing a Vogel-Fulcher-type freezing process, coexisting with domains exhibiting faster dynamics and stronger pinning.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Avalanches and many-body resonances in many-body localized systems

Here we numerically study both the avalanche instability and many-body resonances in strongly disordered spin chains exhibiting many-body localization (MBL). Finite-size systems behave like MBL within the MBL regimes, which we divide into the asymptotic MBL phase and the finite-size MBL regime; the latter regime is, however, thermal in the limit of large systems and long times. In both Floquet and Hamiltonian models, we identify some landmarks within the MBL regimes. Our first landmark is an estimate of where the MBL phase becomes unstable to avalanches, obtained by measuring the slowest relaxation rate of a finite chain coupled to an infinite bath at one end. Our estimates indicate that the actual MBL-to-thermal phase transition occurs much deeper in the MBL regimes than has been suggested by most previous studies. Our other landmarks involve systemwide many-body resonances: We find that the effective matrix elements producing eigenstates with systemwide many-body resonances are enormously broadly distributed. This broad distribution means that the onset of such resonances in typical samples occurs quite deep in the MBL regimes, and the first such resonances typically involve rare pairs of eigenstates that are farther apart in energy than the minimum gap. Thus we find that the resonance properties define two landmarks that divide the MBL regimes of finite-size systems into three subregimes: (i) at strongest randomness, typical samples do not have any eigenstates that are involved in systemwide many-body resonances; (ii) there is a substantial intermediate subregime where typical samples do have such resonances but the pair of eigenstates with the minimum spectral gap does not, so the size of the minimum gap agrees with expectations from Poisson statistics; and (iii) in the weaker randomness subregime, the minimum gap is larger than predicted by Poisson level statistics because it is involved in a many-body resonance and thus subject to level repulsion. Nevertheless, even in this third subregime, all but a vanishing fraction of eigenstates remain nonresonant and the system thus still appears MBL in most respects. Based on our estimates of the location of the avalanche instability, it might be that the MBL phase is only part of subregime (i) and the other subregimes are entirely in the thermal phase, even though they look localized in most respects, so are in the finite-size MBL regime.

36 MATERIALS SCIENCE↗