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DOE OSTI2021

Twisted bilayer graphene. VI. An exact diagonalization study at nonzero integer filling

Using exact diagonalization, we research the projected Hamiltonian with the Coulomb interaction in the eight flat bands of first magic angle twisted bilayer graphene. Employing the U(4) [U(4) × U(4)] symmetries in the nonchiral (chiral) flat band limit, we reduced the Hilbert space to an extent that allows for study around ν = ±3,±2,±1 fillings. In the first chiral limit w 0 /w 1 = 0, where w 0 (w 1 ) is the A A (AB) stacking hopping, we find that the ground states at these fillings are extremely well-described by Slater determinants in a so-called Chern basis, and the exactly solvable charge ±1 excitations found in Bernevig et al. [Phys. Rev. B 103, 205415 (2021)] are the lowest charge excitations up to system sizes 8 × 8 (for restricted Hilbert space) in the chiral-flat limit. We also find that the flat metric condition (FMC) used by Bernevig et al. [Phys. Rev. B 103, 205411 (2021)], Song et al. [Phys. Rev. B 103, 205412 (2021)], Bernevig et al. [Phys. Rev. B 103, 205413 (2021)], Lian et al. [Phys. Rev. B 103, 205414 (2021)], and Bernevig et al. [Phys. Rev. B 103, 205415 (2021)] for obtaining a series of exact ground states and excitations holds in a large parameter space. For ν = -3, the ground state is the spin and valley polarized Chern insulator with ν C = ±1 at w 0 /w 1 ≲ 0.9 (0.3) with (without) FMC. At ν = -2, we can only numerically access the valley polarized sector, and we find a spin ferromagnetic phase when w 0 /w 1 ≳ 0.5 t where t ϵ [0,1] is the factor of rescaling of the actual TBG bandwidth, and a spin singlet phase otherwise, confirming the perturbative calculation [Lian. et al., Phys. Rev. B 103, 205414 (2021), Bultinck et al., Phys. Rev. X 10, 031034 (2020)]. The analytic FMC ground state is, however, predicted in the intervalley coherent sector which we cannot access [Lian et al., Phys. Rev. B 103, 205414 (2021), Bultinck et al., Phys. Rev. X 10, 031034 (2020)]. For ν = -3 with/without FMC, when w 0 /w 1 is large, the finite-size gap Δ to the neutral excitations vanishes, leading to phase transitions. Further analysis of the ground state momentum sectors at ν = -3 suggests a competition among (nematic) metal, momentum M M (π) stripe and K M -CDW orders at large w 0 /w 1 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Infinite temperature at zero energy

We construct a family of static, geometrically local Hamiltonians that inherit eigenstate properties of periodically-driven (Floquet) systems. Our construction is a variation of the Feynman-Kitaev clock -- a well-known mapping between quantum circuits and local Hamiltonians -- where the clock register is given periodic boundary conditions. Assuming the eigenstate thermalization hypothesis (ETH) holds for the input circuit, our construction yields Hamiltonians whose eigenstates have properties characteristic of infinite temperature, like volume-law entanglement entropy, across the whole spectrum -- including the ground state. We then construct a family of exactly solvable Floquet quantum circuits whose eigenstates are shown to obey the ETH at infinite temperature. Combining the two constructions yields a new family of local Hamiltonians with provably volume-law-entangled ground states, and the first such construction where the volume law holds for all contiguous subsystems.

FOS: Physical sciences↗

NASA NTRS1991

Oxygen extraction from lunar soil by fluorination

Mining and processing of lunar material could possibly lead to more cost-efficient scenarios for permanent presence of man in space and on the Moon. Production of oxygen for use as propellant seems especially important. Different candidate processes for oxygen-extraction from lunar soil were proposed, of which the reduction of ilmenite by hydrogen was studied most. This process, however, needs the concentration of ilmenite from lunar regolith to a large extent and releases oxygen only with low efficiency. Another possibility - the fluorination method - which works with lunar bulk material as feedstock is discussed. Liberation of oxygen from silicate or oxide materials by fluorination methods has been applied in geoscience since the early sixties. The fact that even at moderate temperatures 98 to 100 percent yields can be attained, suggests that fluorination of lunar regolith could be an effective way of propellant production. Lunar soil contains about 50 percent oxygen by weight which is gained nearly completely through this process as O2 gas. The second-most element Si is liberated as gaseous SiF4. It could be used for production of Si-metal and fluorine-recycling. All other main elements of lunar soil will be converted into solid fluorides which also can be used for metal-production and fluorine-recycling. Preliminary results of small scale experiments with different materials are discussed, giving information on specific oxygen-yields and amounts of by-products as functions of temperature. These experiments were performed with an already existing fluorine extraction and collection device at the University of Bonn, normally used for determination of oxygen-isotopic abundances. Optimum conditions, especially concerning energy consumption, are investigated. Extrapolation of the experimental results to large industrial-type plants on the Moon is tried and seems to be promising at first sight. The recycling of the fluorine is, however, crucial for the process. It might be achieved by means of electrolysis. This needs further investigation. The technical problem of transport and handling of the toxic and corrosive fluorine seems to be solvable and could be done by inert storage vessels.

Seboldt, W.↗

NASA NTRS1926

A resume of the advances in theoretical aeronautics made by Max M. Munk

In order to apply profitably the mathematical methods of hydrodynamics to aeronautical problems, it is necessary to make simplifications in the physical conditions of the latter. To begin with, it is allowable in many problems, as Prandtl has so successfully shown, to treat the air as having constant density and as free of viscosity. But this is not sufficient. It is also necessary to specify certain shapes for the solid bodies whose motion through the air is discussed, shapes suggested by the actual solids - airships or airfoils - it is true, but so chosen that they lead to solvable problems. In a valuable paper presented by Dr. Max M. Munk, of the National Advisory Committee for Aeronautics, Washington, to the Delft Conference in April, 1924, these necessary simplifying assumptions are discussed in detail. It is the purpose of the present paper to present in as simple a manner as possible some of the interesting results obtained by Dr. Munk's methods.

Ames, Joseph S↗

NASA NTRS1983

Space radiation interaction mechanisms in materials

Models of charged-particle impact under conditions typical of the space environment are reported, with a focus on impact excitation and nuclear reactions, especially for heavy ions. Impact excitation is studied by using a global model for electronic excitation based on formal relations through the classical dielectric function to derive an approximation related to the local plasma (electron density distribution) within the atoms and molecules; and corrections to the model resulting from the nonfluid nature of this plasma are discussed. Nuclear reactions are studied by reducing quantum-mechanical treatment of this general N-body problem to an equivalent two-body problem that is solvable, and by comparing the results with experimental data. The equations for heavy-charged-particle transport are derived and solution techniques demonstrated. Finally, these methods of analysis are applied to study the change in the electrical properties of a GaAs semiconductor for photovoltaic applications; proton damage to GaAs crystals is found to arise from stable replacement defects and to be nonannealable, in contrast to electron-induced damage.

Wilson, J. W.↗

DOE OSTI2022

Analysis of nonlinear features associated with radio-frequency sheaths

An analytic study is conducted of nonlinear features that arise when radio-frequency (RF) sheath boundary conditions are solved self-consistently with the electromagnetic fields in a magnetized plasma. An instability associated with RF sheath–plasma interactions is identified and shown to be closely linked with sheath–plasma resonance and the occurrence of multiple solutions. It is proposed that this instability serves as a physical mechanism that enables jumping from one solution branch to another, providing a physical basis for the prediction of an RF sheath hysteresis in the time domain. It is further shown that this instability can lead to non-intuitive features such as spontaneous symmetry breaking in an otherwise completely symmetric problem. In plane-stratified geometry, two analytically solvable examples are considered for the cases of an unbounded half-space and a bounded domain

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Scrambling Dynamics with Imperfections in a Solvable Model

We study how probes of quantum scrambling dynamics respond to two kinds of imperfections -- unequal forward and backward evolutions and decoherence -- in a solvable Brownian circuit model. We calculate a ``renormalized'' out-of-time-order correlator (ROTOC) in the model with $N$ qubits, and we show that the circuit-averaged ROTOC is controlled by an effective probability distribution in operator weight space which obeys a system of $N$ non-linear equations of motion. These equations can be easily solved numerically for large system sizes which are beyond the reach of exact methods. Moreover, for an operator initially concentrated on weight one $w_0=1$, we provide an exact solution to the equations in the thermodynamic limit of many qubits that is valid for all times, all non-vanishing perturbation strengths $p\gtrsim 1/\sqrt{N}$, and all decoherence strengths. We also show that a generic initial condition $w_0 >1$ leads to a metastable state that eventually collapses to the $w_0=1$ case after a lifetime $\sim \log(N/w_0)$. Our results highlight situations where it is still possible to extract the unperturbed chaos exponent even in the presence of imperfections, and we comment on the applications of our results to existing experiments with nuclear spins and to future scrambling experiments.

FOS: Physical sciences↗

DOE OSTI2022

Produced Water and Waste Heat-aided Blowdown Water Treatment: Using Chemical and Energy Synergisms for Value Creation

The project objective was to develop a cooling blowdown water (BDW) treatment process utilizing produced water (PW) and low-grade heat to maximize water reuse and saleable by-product generation while reducing chemical and energy footprints of the treatment. The proposed treatment process consists of mixing, softening, organics and suspended solids removal, reverse osmosis (RO), thermal desalination, and brine electrolysis. BDW samples collected from a local coal-fired power plant and PW samples from two shale gas production wells were used in this study. Each treatment unit was first designed and tested to quantify its treatment efficiency, and its chemical and energy requirements. In addition, a process model was developed and model simulations were conducted based on the experimental results and literature data to optimize the treatment process. A techno-economic analysis was conducted to quantify chemical and energy savings as well as production of 10-lb brine as a saleable product. With the field-collected BDW and PW samples, mixing experiments determined a volumetric mixing ratio 10:1 (BDW:PW) resulted in the best performance of multivalent ions removal and largest chemical savings for softening. Softening of the BDW/PW mixtures using alkaline chemicals (Na 2 CO 3 and NaOH) achieved 95%-100% removal of scaling-forming cations (Ca, Mg, Fe, Ba, Sr) and 60% of silicon, and 10% of total organic carbon (TOC). The mixing and softening treatments yielded an effluent with total dissolved solids (TDS) concentration of 23 g/L. Activated carbon (AC) filtration removed TOC to a low level (< 3 mg/L) and further removed remaining scale-forming divalent metals and silica from the softened water. The AC filtration resulted in a slight reduction of TDS from 23 g/L to 20 g/L, leaving behind only mostly monovalent ions (i.e., sodium and chloride) in the filtered water. These pretreatments yielded a feed water that met the criteria of the downstream reverse osmosis (RO) to prevent membrane fouling. A cross-flow RO system was used to further concentrate the TDS of the AC effluent. Various factors including TDS, pH, and applied pressure were examined and optimal conditions were determined for the co-treatment process. An integrated process consisting of mixing, softening, AC filtration and RO was used to treat a continuous flow (0.25 – 1.2 L/min, or 0.07 – 0.32 gpm) and successfully generated RO permeate as product water (TDS < 0.5 g/L) for reuse in cooling operation, and a concentrate (TDS ~ 45 g/L) to be further treated in a thermal desalination unit. These flow rates meet the FOA’s criterion of 0.01 – 1 gpm. Overall, the co-treatment of BDW/PW allowed shorter ramp-up time compared to treatment of BDW alone. It resulted in 40% and 55% savings of Na 2 CO 3(s) and NaOH, respectively, compared to treating the BDW and PW individually for the same level of softening. The co-treatment also resulted in a 29% energy saving compared to treatment of BDW only for the level of TDS concentration. A thermal desalination system was designed using CFD simulations and manufactured in the WVU Innovation Hub for further treatment of the RO concentrate to generate 10-lb brine. The system has a design flow rate of 2 gpm and has been successfully tested. A bench-scale brine electrolysis system was developed for on-site generation of chlorine/hypochlorite (Cl 2 /OCl - ) and caustic soda (NaOH) as useful chemicals for the co-treatment process. Using salt solutions (0.5 M and 1 M), the system achieved faradaic efficiencies of 93%-97% and 70%-77% for caustic soda and chlorine/hypochlorite generation, respectively. An economic analysis showed that the electricity costs for on-site generation of these chemicals were significantly lower than the chemical prices offered by suppliers. An industrial-scale process model consisting of mixing, softening, AC filtration, RO, thermal desalination, and brine electrolysis was developed using the Aspen Plus V9 in conjunction with Aspen Custom Modeler V9. The model serves as a solvable Aspen Plus model and as basis to form the costing infrastructure. In addition, techno-economic analysis considering capital, operating, and transportation costs was conducted. An optimization solution showed that produced water for mixing is still advantageous in low quantities. The optimum solution approaches a leveled cost of water (LCW) of 2 $/m 3 which becomes cost competitive with nominal water treatment prices.

20 FOSSIL-FUELED POWER PLANTS↗