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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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DOE OSTI2026

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)]↗
DOE OSTI2018

The Connection between Resonances and Bound States in the Presence of a Coulomb Potential

The connection between resonant metastable states and bound states with changing potential strength in the presence of a Coulomb potential is fundamentally different from the case of short-range potentials. This phenomenon is central to the physics of dissociative recombination of electrons with molecular cations. In this paper, it is verified computationally that there is no direct connection between the resonance pole of the S-matrix and any pole in the bound state spectrum. A detailed analysis is presented of the analytic structure of the scattering matrix, in which the resonance pole remains distinct in the complex k-plane while a new state appears in the bound state spectrum. A formulation of quantum-defect theory is developed based on the scattering matrix, which nonetheless exposes a close analytic relation between the resonant and bound state poles and thereby reveals the connection between quantum-defect theory and analytic S-matrix theory in the complex energy and momentum planes. One-channel and multichannel versions of the expressions with numerical examples for simple models are given, and the formalism is applied to give a unified picture of ab initio electronic structure and scattering calculations for e-O 2 + and e-H 2 + scattering.

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

Dynamics of atoms in strong laser fields I: A quasi analytical model in momentum space based on a Sturmian expansion of the interacting nonlocal Coulomb potential

In this study we present a model that we have formulated in the momentum space to describe atoms interacting with intense laser fields. As a further step, it follows our recent theoretical approach in which the kernel of the reciprocal-space time-dependent Schrödinger equation (TDSE) is replaced by a finite sum of separable potentials, each of them supporting one bound state of atomic hydrogen (Tetchou Nganso et al. 2013). The key point of the model is that the nonlocal interacting Coulomb potential is expanded in a Coulomb Sturmian basis set derived itself from a Sturmian representation of Bessel functions of the first kind in the position space. As a result, this decomposition allows a simple spectral treatment of the TDSE in the momentum space. In order to illustrate the credibility of the model, we have considered the test case of atomic hydrogen driven by a linearly polarized laser pulse, and have evaluated analytically matrix elements of the atomic Hamiltonian and dipole coupling interaction. For various regimes of the laser parameters used in computations our results are in very good agreement with data obtained from other time-dependent calculations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

A comparative study of two-electron systems with screened Coulomb potentials

Highlights: • A comparison criterion for screened potentials is conjectured for two-electron atoms. • The limits of validity of the correlation hypothesis are discussed. • Independent Hylleraas and Lagrange mesh calculations verify the comparison criterion. - Abstract: The relative ordering of energy levels is investigated for bound two-electron systems with potentials of the form V(r{sub 1},r{sub 2},r{sub 12})=Z(v(r{sub 1})+v(r{sub 2}))-v(r{sub 12}). Given the two one-body binding potentials v{sup (1)}(r) and v{sup (2)}(r), it is argued that if f(r)≡v{sup (1)}(r)-v{sup (2)}(r) is positive and monotonically decreasing upon increasing r then the corresponding eigenvalues of the two-electron Hamiltonians H{sub i}=-(1/2)(∇{sub 1}{sup 2}+∇{sub 2}{sup 2})+Z(v{sup (i)}(r{sub 1})+v{sup (i)}(r{sub 2}))-v{sup (i)}(r{sub 12}) , i=1,2are highly likely to be pairwise ordered, i.e., E{sub n}{sup (1)}≥E{sub n}{sup (2)}, n=1,2,…, where E{sub 1}{sup (i)}≤E{sub 2}{sup (i)}≤⋯≤E{sub k}{sup (i)}≤⋯ , for both i=1 and i=2. This conjecture certainly holds at sufficiently large Z. The range of n may be finite or infinite, depending on the nature of the potentials. In fact, the range of values of n for v{sup (1)}(r) may be shorter than that of v{sup (2)}(r) (which is more binding). The one-electron potentials specifically considered are: v(r)={ v_C(r) =-(1/r) Coulomb v_D(r) =-(1/r)exp(-λr) Debye (Yukawa) v_H_u(r) =-(λ/(exp(λr)-1)) Hulthén v_E_C_S_C(r) =-(1/r)exp(-λr)cos(λr) ECSC}{sup ∗} , ){sup ∗}Exponential-Cosine-Screened-Coulomb where λ is the screening parameter. For each of the λ-dependent potentials we compare one- and two-electron spectra corresponding to distinct values of λ. This is followed by pairwise comparison of distinct potentials.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

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↗
DOE OSTI2016

Analytical solutions of the Dirac equation under Hellmann–Frost–Musulin potential

The approximate analytical solutions of the Dirac equation with Hellmann–Frost–Musulin potential have been studied by using the generalized parametric Nikiforov–Uvarov (NU) method for arbitrary spin–orbit quantum number k under the spin and pseudospin symmetries. The Hellmann–Frost–Musulin potential is a superposition potential that consists of Yukawa potential, Coulomb potential, and Frost–Musulin potential. As a particular case, we found the energy levels of the non-relativistic limit of the spin symmetry. The energy equation of Yukawa potential, Coulomb potential, Hellmann potential and Frost–Musulin potential are obtained. Energy values are generated for some diatomic molecules.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Stabilizing potentials in bound state analytic continuation methods for electronic resonances in polyatomic molecules

The computation of Siegert energies by analytic continuation of bound state energies has recently been applied to shape resonances in polyatomic molecules by several authors. Here, we critically evaluate a recently proposed analytic continuation method based on low order (type III) Padé approximants as well as an analytic continuation method based on high order (type II) Padé approximants. We compare three classes of stabilizing potentials: Coulomb potentials, Gaussian potentials, and attenuated Coulomb potentials. These methods are applied to a model potential where the correct answer is known exactly and to the 2 Π g shape resonance of N 2 - which has been studied extensively by other methods. Both the choice of stabilizing potential and method of analytic continuation prove to be important to the accuracy of the results. We then conclude that an attenuated Coulomb potential is the most effective of the three for bound state analytic continuation methods. With the proper potential, such methods show promise for algorithmic determination of the positions and widths of molecular shape resonances.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Comparison between Coulomb and Hulthèn potentials behaviors in γ-rigid nuclei within a generalized uncertainty principle

In the present paper, we study the effect of the minimal length on two well-known potentials: Coulomb and Hulthèn in transitional nuclei near the critical point symmetry X(3). Albeit these two potentials have mathematically similar behaviors at small deformations and give the same results for energy spectra and electromagnetic transition rates of nuclei, they behave differently in the presence of a minimal length. It appears that this latter acts on the intrinsic structure of the potential allowing both potentials’ actions to be differentiated.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

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↗
DOE OSTI2019

Influences of the impurity and magnetic field on the probability density and the period of the asymmetric Gaussian potential qubit

The eigenenergies and eigenfunctions of the ground and first-excited states of an electron, which is coupled to an LO-phonon in a quantum dot with an asymmetric Gaussian (AG) potential, Coulomb bound potential and the magnetic field was studied by using Lee-Low-Pines transformation and Pekar variation method. A single qubit can be realized in this two-level quantum system. Numerical results show that the probability density of electrons in the qubit oscillates with changing the time, the well width and the well depth the AG potential. The probability density obviously fluctuates with changes in the magnetic-field cyclotron (MFC) frequency, the dielectric constant (DC) ratio and the electron–phonon coupling (EPC) strength, respectively, which is not conducive to constructing a suitable qubit. The oscillation period of the qubit decreases with increasing the DC ratio, EPC strength and the MFC frequency, respectively, which has an adverse effect on the survival time of qubit.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗