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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 19 records

On the Trotter Error in Many-body Quantum Dynamics with Coulomb Potentials

Efficient simulation of many-body quantum systems is central to advances in physics, chemistry, and quantum computing, with a key question being whether the simulation cost scales polynomially with the system size. Here, in this work, we analyze many-body quantum systems with Coulomb interactions, which are fundamental to electronic and molecular systems. We prove that Trotterization for such unbounded Hamiltonians achieves a 1/4-order convergence rate, with explicit polynomial dependence on the number of particles. The result holds for all initial wavefunctions in the domain of the Hamiltonian, and the 1/4-order convergence rate is optimal, as previous work has numerically demonstrated that it can be saturated by a specific initial ground state. The main challenges arise from the many-body structure and the singular nature of the Coulomb potential. Our proof strategy differs from prior state-of-the-art Trotter analyses, addressing both difficulties in a unified framework. Our analysis treats the Coulomb potential as an unbounded operator without modification or regularization, and does not rely on spatial discretization, making it compatible with both first- and second-quantized circuit constructions.

Fang, Di [Duke Univ., Durham, NC (United States)]↗

Quantum Drude oscillators coupled with Coulomb potential as an efficient model for bonded and non-covalent interactions in atomic dimers

The quantum Drude oscillator (QDO) model has been widely used as an efficient surrogate to describe the electric response properties of matter as well as long-range interactions in molecules and materials. Most commonly, QDOs are coupled within the dipole approximation so that the Hamiltonian can be exactly diagonalized, which forms the basis for the many-body dispersion method [Phys. Rev. Lett. 108, 236402 (2012)]. The dipole coupling is efficient and allows us to study non-covalent many-body effects in systems with thousands of atoms. However, there are two limitations: (i) the need to regularize the interaction at short distances with empirical damping functions and (ii) the lack of multipolar effects in the coupling potential. In this work, we convincingly address both limitations of the dipole-coupled QDO model by presenting a numerically exact solution of the Coulomb-coupled QDO model by means of quantum Monte Carlo methods. We calculate the potential-energy surfaces of homogeneous QDO dimers, analyzing their properties as a function of the three tunable parameters: frequency, reduced mass, and charge. We study the coupled-QDO model behavior at short distances and show how to parameterize this model to enable an effective description of chemical bonds, such as the covalent bond in the H2 molecule.

Chemistry↗

Charged-Particle Bound States in Periodic Boxes

We consider the binding energy of a two-body system with a repulsive Coulomb interaction in a finite periodic volume. We define the finite-volume Coulomb potential as the usual Coulomb potential, except that the distance is defined the shortest separation between the two bodies in the periodic volume. We investigate this problem in one and three-dimensional periodic boxes and derive the asymptotic behavior of the volume dependence for bound states with zero angular momentum in terms of Whittaker functions. We benchmark our results against numerical calculations and show how the method can be used to extract asymptotic normalization coefficients for charged-particle bound states. Furthermore, the results we derive here have immediate applications for calculations of atomic nuclei in finite periodic volumes for the case where the leading finite-volume correction is associated with two charged clusters.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

A numerical Poisson solver with improved radial solutions for a self-consistent locally scaled self-interaction correction method

Abstract The universal applicability of density functional approximations is limited by self-interaction error made by these functionals. Recently, a novel one-electron self-interaction-correction (SIC) method that uses an iso-orbital indicator to apply the SIC at each point in space by scaling the exchange-correlation and Coulomb energy densities was proposed. The locally scaled SIC (LSIC) method is exact for the one-electron densities, and unlike the well-known Perdew–Zunger SIC (PZSIC) method recovers the uniform electron gas limit of the uncorrected density functional approximation, and reduces to PZSIC method as a special case when isoorbital indicator is set to the unity. Here, we present a numerical scheme that we have adopted to evaluate the Coulomb potential of the electron density scaled by the iso-orbital indicator required for the self-consistent LSIC calculations. After analyzing the behavior of the finite difference method (FDM) and the green function solution to the radial part of the Poisson equation, we adopt a hybrid approach that uses the FDM for the Coulomb potential due to the monopole and the GF for all higher-order terms. The performance of the resultant hybrid method is assessed using a variety of systems. The results show improved accuracy than earlier numerical schemes. We also find that, even with a generic set of radial grid parameters, accurate energy differences can be obtained using a numerical Coulomb solver in standard density functional studies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Anomalous ellipticity dependence of the generation of near-threshold harmonics in noble gases

We measured the ellipticity dependence of the harmonic yield of He, Ne, Ar, Kr, and Xe. It is found that the harmonic yield in general decreases monotonically with increasing laser ellipticity but anomalous dependence does occur for each atom for some harmonic orders. Additionally, we found that the degree of anomaly is weakest in helium but is stronger for the heavier atoms. The anomaly also depends on laser intensity. To explain these features, we developed a quantum trajectory Monte Carlo (QTMC) model based on the quantum path integral theory to study high-order harmonic generation (HHG). The model includes the effect of Coulomb potential from the target ion, thus it is capable of calculating near-threshold harmonics quantitatively. This model reveals that the presence of Coulomb potential would generate orbiting trajectories which are responsible for the anomalous ellipticity dependence near the threshold.

74 ATOMIC AND MOLECULAR PHYSICS↗

Excited Rydberg states in MoSe 2 /WSe 2 heterostructures

The functional form of Coulomb interactions in the transition metal dichalcogenides (TDMs) and other van der Waals solids is critical to many of their unique properties, e.g. strongly-correlated electron states, superconductivity and emergent ferromagnetism. This paper presents measurements of key excitonic energy levels in MoSe 2 /WSe 2 heterostructures. These measurements are obtained from resonance Raman experiments on specific Raman peaks only observed at excited states of the excitons. This data is used to validate a model of the Coulomb potential in these structures which predicts the exciton energies to within ~5 meV. This model is used to determine the effect of heterostructure formation on the single-particle band gaps of the layers and will have a wide applicability in designing the next generation of more complex TDM structures.

Materials Science↗

Tunable discrete scale invariance in transition-metal pentatelluride flakes

Log-periodic quantum oscillations discovered in transition-metal pentatelluride give a clear demonstration of discrete scale invariance (DSI) in solid-state materials. The peculiar phenomenon is convincingly interpreted as the presence of two-body quasi-bound states in a Coulomb potential. However, the modifications of the Coulomb interactions in many-body systems having a Dirac-like spectrum are not fully understood. Here, we report the observation of tunable log-periodic oscillations and DSI in ZrTe 5 and HfTe 5 flakes. By reducing the flakes thickness, the characteristic scale factor is tuned to a much smaller value due to the reduction of the vacuum polarization effect. The decreasing of the scale factor demonstrates the many-body effect on the DSI, which has rarely been discussed hitherto. Furthermore, the cut-offs of oscillations are quantitatively explained by considering the Thomas-Fermi screening effect. Finally, our work clarifies the many-body effect on DSI and paves a way to tune the DSI in quantum materials.

36 MATERIALS SCIENCE↗

A method to predict texture effect on ion beam channeling analysis of polycrystals and the application to study the mosaic spreading effect in highly oriented pyrolytic graphite

We propose a method to convert the channeling Rutherford backscattering spectrum yield map of a single crystal to a polycrystal through a matrix rotation technique. The rotation matrix is determined by the deviation of the crystal axial direction from the original z axis. The final yield map is created after averaging the rotated yields using the texture function as the weight factor. For highly oriented pyrolytic graphite (HOPG) exhibiting mosaic spread, the method leads to a Gaussian kernel averaging of the map obtained from a single crystal. The yield map of a single crystal is obtained by a simulation of ion trajectories in a potential field described by Moliere screened Coulomb potentials. Yield maps are calculated under various σ values (standard deviations of mosaic spread). The simulated results are compared with experimental results obtained using 1.2 MeV alpha particle. σ is extracted through the best fitting, demonstrating that the method can be used to obtain texture details. The effects of mosaic spread on minimum yield χ min and the half-width at half maximum of angular scans ψ ½ are systematically modeled and compared with previous theoretical equations. The study also shows that previous theoretical equations are valid only at small σ values. The proposed method can be applied to any type of polycrystal and is not limited to HOPG. It provides near-surface mosaic spread and crystallography information with a longitudinal depth resolution of tens of nanometers and is not influenced by grain shapes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Collaborative Research: Unravelling the Physics Associated with the Production of Extremely Dense Plasma States of Microscale (Final Report) Nanosecond-pulsed Discharges

The aim of this project is to study and establish the physical mechanisms that contribute to the formation of anomalously dense plasmas in high-pressure nanosecond-pulsed discharges. These discharges have a broad range of applications such as plasma-assisted combustion, plasma flow actuators, biomedical sterilization and exotic materials synthesis. The structure and formation of these discharges, producing high plasma densities of ~10 14 -10 15 cm -3 , are well-studied and understood. Fast-pulsed microscale high-pressure discharges can be driven to even higher densities of > 10 19 cm -3 , approaching warm dense matter conditions. The mechanisms that generate these plasmas have not been understood. Analysis of the warm dense matter state under laboratory conditions is an expensive and non-trivial endeavor. For instance, dense plasmas can be generated by electrical explosions of metal foils and wires. Plasmas generated after the explosion have a short lifetime and often present difficult conditions for diagnostics. Generation of dense plasmas was also achieved during high-voltage nanosecond pulsed discharges when the so-called explosive electron emission is obtained. Unfortunately, this process is very difficult to control for the studies of warm dense matter. In our recent study, we have shown that additional heating of plasma by lasers can further increase the density of plasma and even lead to the fully ionized state. This method, potentially, allows better control of the plasma parameters. In this work, we studied a second stage laser-heated micro-discharge using a self-consistent one-dimensional particle-in-cell Monte Carlo-collision (1D PIC-MCC) model coupled with Maxwell’s equations. We predicted the generation of a fully ionized plasma on the picosecond time scale. However, this model considered the plasma as an ideal gas despite the high pressure and the nearly fully ionized state. The ideal plasma model assumes that the dilute gas approximation is valid, where the inter-particle interactions are negligible. For charged particles this assumption holds as long as the shielded Coulomb potential assumption is valid. For very high plasma densities, this concept breaks down since the Debye sphere surrounding each charged particle no longer contains enough electrons to statistically provide the shielding of the single particle Coulomb interaction potential. At such densities, the plasma can no longer be described as ideal and non-ideal coupling effects need to be considered. In this report, we elucidate our recent work of developing a PIC-MCC model with improvements for non-ideal plasma conditions due to Coulomb coupling at high densities. In particular, we study the interaction of green light radiation and a dense microplasma, and explore the non-ideal plasma effects in this interaction. In this computational model, we implement the two most important non-ideal effects: ionization potential depression (IPD) and enhanced collision cross sections. Our primary goal is to study the physics associated with electromagnetic (EM) wave heating, also called the second-stage wave-heating, and establish the role of plasma non-ideality in this phenomenon. Our secondary goal is to improve the chemistry mechanism of the 1D PIC-MCC model by including a more detailed excited species collision treatment. At high pressures, stepwise ionization from excited species might play an important role in the ionization process. Previously, this ionization mechanism was neglected due to the excitation collision cross section of xenon being smaller than that of ionization. However, a preliminary study showed that the excited species density in the initial microplasma was an order of magnitude higher than the electron density. Therefore, my aim is to determine the significance of this additional ionization pathway to the plasma generation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Proton radiation effects in indium oxide using cascade molecular dynamics simulations

Metal oxide (MO) semiconductors, characterized by their wide band gaps and notable charge transport properties, are promising candidates for electronic applications in extreme environments, including near-Earth space. However, atomistic simulations of radiation–matter interactions in MOs remain challenging due to the limitations of existing interatomic potentials, which often fail to capture both the short-range repulsive forces essential for radiation damage modeling and the long-range electrostatic effects governing defect evolution. In this work, we develop a customized interatomic potential tailored for radiation damage simulations in indium oxide (In 2 O 3 ) as a model system, a representative MO material. Our potential integrates the Ziegler-Biersack-Littmark potential to accurately describe short-range interactions with Buckingham and Coulombic potentials to account for long-range forces. We perform molecular dynamics simulations of low-energy proton irradiation using this custom potential. We employ the primary knock-on atom (PKA) cascade method to study atomic displacements and primary defect formation. Simulations were conducted for 1 keV proton irradiation in four randomly chosen directions, and PKA-driven defect analyses at 5, 10, and 15 keV to examine the effects of direction and energy level on damage generation. Our results provide insight into the impact of irradiation direction and energy level on the cascade evolution and defect formation mechanisms.

Atomistic simulations↗

Coulomb field correction due to virtual $e$ + $e$ - production in heavy ion collisions

The correction to the Coulomb energy due to virtual production of $e$ + $e$ - pairs, which is on the order of one percent of the Coulomb energy at nuclear scales is discussed. The effects of including a pair-production term in the semi-empirical mass formula and the correction to the Coulomb barrier for a handful of nuclear collisions using the Bass and Coulomb potentials are studied. Furthermore, with an eye toward future work using Constrained Molecular Dynamics (CoMD) model, we also calculate the correction to the Coulomb energy and force between protons after folding with a Gaussian spatial distribution.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Molecular dynamics simulation of hydrodynamic transport coefficients in plasmas

Molecular dynamics simulations are used to calculate transport coefficients in a two-component plasma interacting through a repulsive Coulomb potential. The thermal conductivity, electrical conductivity, electrothermal coefficient, thermoelectric coefficient, and shear viscosity are computed using the Green–Kubo formalism over a broad range of Coulomb coupling strength, 0.01 ≤ Γ ≤ 140. Emphasis is placed on testing standard results of the Chapman–Enskog solution in the weakly coupled regime (Γ ≪ 1) using these first-principles simulations. As expected, the results show good agreement for Γ ≲ 0.1. However, this agreement is only possible if careful attention is paid to the definitions of linear constitutive relations in each of the theoretical models, a point that is often overlooked. For example, the standard Green–Kubo expression for thermal conductivity is a linear combination of thermal conductivity, electrothermal, and thermoelectric coefficients computed in the Chapman–Enskog formalism. Meaningful results for electrical conductivity are obtained over the full range of coupling strengths explored, but it is shown that potential and virial components of the other transport coefficients diverge in the strongly coupled regime (Γ ≫ 1). In this regime, only the kinetic components of the transport coefficients are meaningful for a classical plasma.

Electrical conductivity↗

Stochastic evaluation of four-component relativistic second-order many-body perturbation energies: A potentially quadratic-scaling correlation method

A second-order many-body perturbation correction to the relativistic Dirac-Hartree-Fock energy is evaluated stochastically by integrating 13-dimensional products of four-component spinors and Coulomb potentials. The integration in the real space of electron coordinates is carried out by the Monte Carlo (MC) method with the Metropolis sampling, whereas the MC integration in the imaginary-time domain is performed by the inverse-CDF (cumulative distribution function) method. The computational cost to reach a given relative statistical error for spatially compact but heavy molecules is observed to be no worse than cubic and possibly quadratic with the number of electrons or basis functions. This is a vast improvement over the quintic scaling of the conventional, deterministic second-order many-body perturbation method. The algorithm is also easily and efficiently parallelized with demonstrated 92% strong scalability going from 64 to 4096 processors for a fixed job size.

74 ATOMIC AND MOLECULAR PHYSICS↗

Enabling attractive-repulsive potentials in binary-collision-approximation monte-carlo codes for ion-surface interactions

Abstract Binary Collision Approximation (BCA) codes for ion-material interactions, such as SRIM, Tridyn, F-TRIDYN, and SDtrimSP, have historically been limited to screened Coulomb potentials even at low energies due to the difficulty in numerically solving the Distance of Closest Approach (DOCA) problem for attractive-repulsive potentials. Techniques such as direct n-body simulation or modifications to Newton’s method are either prohibitively costly or not guaranteed to work for all potentials. Advanced rootfinding techniques, such as companion matrix solvers, offer a solution. For many attractive-repulsive potentials, however, a companion matrix cannot be used directly, because there is no way to put the associated functions into a monomial basis form. A complementary technique is proxy rootfinding—by finding the best-fit polynomial approximant of a function, the zeros of the approximant can be guaranteed to be close to the zeros of the function. Using the Chebyshev basis and grid offers additional guarantees with regards to the quality of the approximation, the speed of convergence, and the avoidance of Runge’s phenomenon. By finding Chebyshev interpolants and using the Chebyshev-Frobenius companion matrix, the zeros of any real function on a bounded domain can be found. Here we show that using an Adaptive Chebyshev Proxy Rootfinder with Automatic Subdivision (ACPRAS) with appropriate scaling functions, numerical issues presented by attractive-repulsive potentials, including those of scale, can be handled. Using these techniques, we show that it is possible to include any physically reasonable interatomic potential in a BCA code, and to guarantee correctness of the resulting scattering angle calculations.

Materials Science↗

Structural and Dynamic Disorder, Not Ionic Trapping, Controls Charge Transport in Highly Doped Conducting Polymers

Doped organic semiconductors are critical to emerging device applications, including thermoelectrics, bioelectronics, and neuromorphic computing devices. It is commonly assumed that low conductivities in these materials result primarily from charge trapping by the Coulomb potentials of the dopant counter-ions. Here, we present a combined experimental and theoretical study rebutting this belief. Using a newly developed doping technique, we find the conductivity of several classes of high-mobility conjugated polymers to be strongly correlated with paracrystalline disorder but poorly correlated with ionic size, suggesting that Coulomb traps do not limit transport. A general model for interacting electrons in highly doped polymers is proposed and carefully parameterized against atomistic calculations, enabling the calculation of electrical conductivity within the framework of transient localisation theory. Theoretical calculations are in excellent agreement with experimental data, providing insights into the disordered-limited nature of charge transport and suggesting new strategies to further improve conductivities.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Twisted bilayer graphene. V. Exact analytic many-body excitations in Coulomb Hamiltonians: Charge gap, Goldstone modes, and absence of Cooper pairing

We find exact analytic expressions for the energies and wave functions of the charged and neutral excitations above the exact ground states (at rational filling per unit cell) of projected Coulomb Hamiltonians in twisted bilayer graphene. Our exact expressions are valid for any form of the Coulomb interaction and any form of A A and A B / B A tunneling. The single charge excitation energy is a convolution of the Coulomb potential with a quantum geometric tensor of the TBG bands. The neutral excitations are (high-symmetry group) magnons, and their dispersion is analytically calculated in terms of the form factors of the active bands in TBG. The two-charge excitation energy and wave functions are also obtained, and a sufficient condition on the graphene eigenstates for obtaining a Cooper pair from Coulomb interactions is obtained. For the actual TBG bands at the first magic angle, we can analytically show that the Cooper pair binding energy is zero in all such projected Coulomb models, implying that either phonons and/or nonzero kinetic energy are needed for superconductivity. Since Vafek and Kang [Phys. Rev. Lett. 125, 257602 (2020)] showed that the kinetic energy bounds on the superexchange energy are less 10 -3 in Coulomb units, the phonon mechanism becomes then very likely. If nonetheless the superconductivity is due to kinetic terms which render the bands nonflat, one prediction of our theory is that the highest T c would not occur at the highest DOS.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Superconductivity in a doped valley coherent insulator in magic angle graphene: Goldstone-mediated pairing and Kohn-Luttinger mechanism

We consider magic angle graphene in the doping regime around charge neutrality and study the connection between a recently proposed inter-valley coherent insulator at zero doping and the neighboring superconducting domes. The breaking of the valley U(1) symmetry leads to massless Goldstone modes, which couple to the doped charge carriers. We derive the effective interaction between these Goldstone modes and the conduction electrons and study its role in mediating superconductivity. Combining it with the screened Coulomb potential, we find weak-coupling superconducting instabilities in the two-component p- and d-wave channels. The competition between the two channels is set by the distance between the bilayer graphene device and the metallic gates. We find that the p-wave instability originates from the attraction mediated by the Goldstone modes, while the d-wave pairing is caused purely by the screened Coulomb interaction, similarly to the Kohn-Luttinger mechanism.

Kozii, Vladyslav↗

A three-step model of high harmonic generation using complex classical trajectories

Highlights: • Rigorous trajectory formulation of strong field physics and high harmonic generation. • The Coulomb ground state is represented by an ensemble of complex trajectories. • Trajectories transition seamlessly from the ground state to ionization or recollision. • The ionized wavepacket is reproduced well from the complex trajectories. • Classically allowed and forbidden processes are treated in a single framework. We present a new trajectory formulation of high harmonic generation that treats classically allowed and classically forbidden processes within a single dynamical framework. Complex trajectories orbit the nucleus, producing the stationary Coulomb ground state. When the field is turned on, these complex trajectories continue their motion in the field-dressed Coulomb potential and therefore tunnel ionization, unbound evolution and recollision are described within a single, seamless framework. The new formulation can bring mechanistic understanding to a broad range of strong field physics effects.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗