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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Dyson maps and unitary evolution for Maxwell equations in tensor dielectric media

The propagation and scattering of electromagnetic waves in dielectric media is of theoretical and experimental interest in a wide variety of fields. An understanding of observational results generally requires a numerical solution of Maxwell equations—usually implemented on conventional computers using sophisticated numerical algorithms. In recent years, advances in quantum information science and in the development of quantum computers have piqued curiosity about taking advantage of these resources for an alternate numerical approach to Maxwell equations. This requires a reformulation of the classical Maxwell equations into a form suitable for quantum computers which, unlike conventional computers, are limited to unitary operations. In this paper, a unitary framework is developed for the propagation of electromagnetic waves in a spatially inhomogeneous, passive, nondispersive, and anisotropic dielectric medium. For such a medium, generally, the evolution operator in the combined Faraday-Ampere equations is not unitary. There are two steps needed to convert this equation into a unitary evolution equation. In the first step, a weighted Hilbert space is formulated in which the generator of dynamics is a pseudo-Hermitian operator. In the second step, a Dyson map is constructed which maps the weighted-physical-Hilbert space to the original Hilbert space. Furthermore, the resulting evolution equation for the electromagnetic wave fields is unitary. Utilizing the framework developed in these steps, a unitary evolution equation is derived for electromagnetic wave propagation in a uniaxial dielectric medium. The resulting form is suitable for quantum computing.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Diquark correlations in hadron physics: Origin, impact and evidence

The last decade has seen a marked shift in how the internal structure of hadrons is understood. Modern experimental facilities, new theoretical techniques for the continuum bound-state problem and progress with lattice-regularised QCD have provided strong indications that soft quark+quark (diquark) correlations play a crucial role in hadron physics. For example, theory indicates that the appearance of such correlations is a necessary consequence of dynamical chiral symmetry breaking, viz. a corollary of emergent hadronic mass that is responsible for almost all visible mass in the universe; experiment has uncovered signals for such correlations in the flavour-separation of the proton's electromagnetic form factors; and phenomenology suggests that diquark correlations might be critical to the formation of exotic tetra- and penta-quark hadrons. Therefore, a broad spectrum of such information is evaluated herein, with a view to consolidating the facts and therefrom moving toward a coherent, unified picture of hadron structure and the role that diquark correlations might play.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Nemchinov-Dyson Solutions of the Two-Dimensional Axisymmetric Inviscid Compressible Flow Equations [Review]

We investigate the two-dimensional (2D) inviscid compressible flow equations in axisymmetric coordinates, constrained by an ideal gas equation of state (EOS). Beginning with the assumption that the 2D velocity field is space-time separable and linearly variable in each corresponding spatial coordinate, we proceed to derive an in nite family of elliptic or hyperbolic, uniformly expanding or contracting \gas cloud" solutions. Construction of specific example solutions belonging to this family is dependent on the solution of a system of nonlinear, coupled, second-order ordinary differential equations, and the prescription of an additional physical process of interest (e.g., uniform temperature or uniform entropy flow). The physical and computational implications of these solutions as pertaining to quantitative code verification or model qualification studies are discussed in some detail.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Timelike form factor for the anomalous process γ⁎π → ππ

The form factor 𝐹 3𝜋 (𝑠, 𝑡, 𝑢) for the anomalous process 𝛾∗𝜋 → 𝜋𝜋 is calculated in the isospin limit for several values of the light current-quark mass (i.e., the pion mass) using Dyson–Schwinger and Bethe–Salpeter equations. Beyond a quark interaction kernel representing gluon-mediated interactions, leading beyond-rainbow-ladder effects at low energies are incorporated by back-coupling pions as explicit degrees of freedom. Building upon an earlier calculation of the quark-photon vertex that captures the branch cut associated with the two-pion threshold and the ρ-meson resonance, the form factor 𝐹 3𝜋 (𝑠, 𝑡, 𝑢) is determined for timelike Mandelstam s. In particular, predictions are made for the kinematics relevant to the Primakoff reaction studied with COMPASS/AMBER at CERN.

Miramontes, Angel S. [Univ. of Valencia (Spain)] (↗
DOE OSTI2024

Electromagnetic and two-photon transition form factors of the pseudoscalar mesons: An algebraic model computation

We compute electromagnetic and two-photon transition form factors of ground-state pseudoscalar mesons: π , K , η c , η b . To this end, we employ an algebraic model based upon the coupled formalism of Schwinger-Dyson and Bethe-Salpeter equations. Within this approach, the dressed quark propagator and the relevant Bethe-Salpeter amplitude encode the internal structure of the corresponding meson. Electromagnetic properties of the meson are probed via the quark-photon interaction. The algebraic model employed by us unifies the treatment of all ground-state pseudoscalar mesons. Its parameters are carefully fitted performing a global analysis of existing experimental data including the knowledge of the charge radii of the mesons studied. We then compute and predict electromagnetic and two-photon transition form factors for a wide range of probing photon momentum-squared which is of direct relevance to the experimental observations carried out thus far or planned at different hadron physics facilities such as the Thomas Jefferson National Accelerator Facility (JLab) and the forthcoming Electron-Ion Collider. We also present comparisons with other theoretical models and approaches and lattice quantum chromodynamics. Published by the American Physical Society 2024

Higuera-Angulo, I. M. (ORCID:0000000256008875)↗
DOE OSTI2024

Lyapunov exponent as a signature of dissipative many-body quantum chaos

A distinct feature of Hermitian quantum chaotic dynamics is the exponential increase of certain out-of-time-order correlation (OTOC) functions around the Ehrenfest time with a rate given by a Lyapunov exponent. Physically, the OTOCs describe the growth of quantum uncertainty that crucially depends on the nature of the quantum motion. Here, we employ the OTOC in order to provide a precise definition of dissipative quantum chaos. For this purpose, we compute analytically the Lyapunov exponent for the vectorized formulation of the large- q limit of a q -body Sachdev-Ye-Kitaev model coupled to a Markovian bath. These analytic results are confirmed by an explicit numerical calculation of the Lyapunov exponent for several values of q ≥ 4 based on the solutions of the Schwinger-Dyson and Bethe-Salpeter equations. We show that the Lyapunov exponent decreases monotonically as the coupling to the bath increases and eventually becomes negative at a critical value of the coupling signaling a transition to a dynamics which is no longer quantum chaotic. Therefore, a positive Lyapunov exponent is a defining feature of dissipative many-body quantum chaos. The observation of the breaking of the exponential growth for sufficiently strong coupling suggests that dissipative quantum chaos may require in certain cases a sufficiently weak coupling to the environment. Published by the American Physical Society 2024

García-García, Antonio M.↗
DOE OSTI2023

Qubit Lattice Algorithms Based on the Schrödinger-Dirac Representation of Maxwell Equations and Their Extensions

It is well known that Maxwell equations can be expressed in a unitary Schrodinger-Dirac representation for homogeneous media. However, difficulties arise when considering inhomogeneous media. A Dyson map points to a unitary field qubit basis, but the standard qubit lattice algorithm of interleaved unitary collision-stream operators must be augmented by some sparse non-unitary potential operators that recover the derivatives on the refractive indices. Here, the effect of the steepness of these derivatives on two-dimensional scattering is examined with simulations showing quite complex wavefronts emitted due to transmissions/reflections within the dielectric objects. Maxwell equations are extended to handle dissipation using Kraus operators. Then, our theoretical algorithms are extended to these open quantum systems. A quantum circuit diagram is presented as well as estimates on the required number of quantum gates for implementation on a quantum computer.

2D electromagnetic scattering↗
DOE OSTI2023

Qubit Lattice Algorithms based on the Schrodinger-Dirac representation of Maxwell Equations and their Extensions

It is well known that Maxwell equations can be expressed in a unitary Schrodinger-Dirac representation for homogeneous media. However, difficulties arise when considering inhomoge- neous media. A Dyson map points to a unitary field qubit basis, but the standard qubit lattice algorithm of interleaved unitary collision-stream operators must be augmented by some sparse non-unitary potential operators that recover the derivatives on the refractive indices. The effect of the steepness of these derivatives on two dimensional scattering is examined with simulations showing quite complex wavefronts emitted due to transmissions/reflections within the dielectric objects. Maxwell equations are extended to handle dissipation using Kraus operators. Then, our theoretical algorithms are extended to these open quantum systems. A quantum circuit diagram is presented as well as estimates on the required number of quantum gates for implementation on a quantum computer.

Vahala, George↗
DOE OSTI2024

Open-closed string duality, branes, and topological recursion

We consider matrix models exhibiting open-closed string duality in two-dimensional string theories with various amounts of supersymmetry. In particular, a relationship between matrix models in the β = 2 Wigner-Dyson class and models in the (1 + 2Γ, 2) Altland-Zirnbauer class relates the perturbative solutions of the two systems’ string equations. Point-like operator insertions in the closed string theory are mapped to the topological expansion of the free energy in the open string theory. We compute correlation functions of macroscopic loop operators and FZZT branes in a general topological gravity background. The relationship between the topological recursion of moduli space volumes and branes is discussed by analyzing the Virasoro conditions in the matrix models.

2D Gravity↗
DOE OSTI2026

Influence of Markovianity and self-consistency on time-resolved spectral functions of driven quantum systems

We present a systematic comparison of the real-time Dyson expansion (RTDE) with established nonequilibrium Green's function (GF) approaches for simulating driven, interacting quantum systems. Focusing on density matrix dynamics, time-off-diagonal GFs, and time-resolved photoemission spectra, we benchmark RTDE against fully self-consistent Kadanoff-Baym equation (KBE) calculations, the generalized Kadanoff-Baym ansatz, and exact diagonalization for small systems using second-order many-body perturbation theory. Using a driven two-band Hubbard model, we show that mean-field single-particle density matrix trajectories provide a reliable baseline for RTDE across a broad range of interaction strengths and excited-carrier populations. Further, RTDE accurately captures correlation effects in the GFs, including long-lived oscillations and revivals that are strongly suppressed by the overdamping inherent to self-consistent KBE schemes. As a consequence, RTDE resolves rich nonequilibrium spectral structure in time-resolved photoemission, such as interaction- and population-dependent quasiparticle splittings and band gap renormalization, which are largely washed out in self-consistent approaches yet are present in exact solutions. Furthermore, our results demonstrate that RTDE bridges the gap between mean-field propagation and full two-time KBE simulations, retaining favorable linear scaling while capturing essential dynamical correlations relevant for ultrafast spectroscopy.

Electronic structure↗
DOE OSTI2026

Degenerate coupled-cluster theory

A size-extensive, converging, black-box, ab initio coupled-cluster (ΔCC) ansatz is introduced that computes the energies and wave functions of states from any degenerate or nondegenerate Slater-determinant references with any numbers of α- and β-spin electrons, any patterns of orbital occupancy, any spin multiplicities, and any spatial symmetries. For a nondegenerate reference, it reduces to the single-reference coupled-cluster ansatz. For a degenerate multireference, it is a natural coupled-cluster extension of degenerate Møller–Plesset perturbation (ΔMP) theory. For ionized and electron-attached references, it is a coupled-cluster Green’s function, although the present theory is convergent toward the full-configuration-interaction limits, while the Feynman–Dyson many-body Green’s function (MBGF) theory generally is not. Its single-excitation instance is a projection Hartree–Fock theory as per the Thouless theorem, which may be useful for core ionizations, high-spin states, and possibly electron affinities. Additionally, a new multireference coupled-cluster theory for a general model space is developed. This quasidegenerate coupled-cluster (QCC) theory is exactly converging, but not black-box, and intended for strong correlation. Determinant-based, general-order algorithms of ΔCC and QCC theories are implemented and compared with configuration-interaction (CI) and equation-of-motion coupled-cluster (EOM-CC) theories through octuple excitations and with ΔMP and MBGF theories up to the nineteenth order. An algebraic, optimal-scaling algorithm of the ΔCC theory is computer-synthesized at the levels of single excitations (ΔCCS) and of single and double excitations (ΔCCSD). As a result, the order of performance is QCC ≈ ΔCC > EOM-CC > CI at the same order or QCC ≈ ΔCC > ΔMP > MBGF at the same cost scaling.

Hirata, So [University of Illinois at Urbana-Champ↗