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At least 127 records · Page 7

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DOE OSTI2022

Detailed analysis of excited-state systematics in a lattice QCD calculation of 𝑔 𝐴

Excited state contamination remains one of the most challenging sources of systematic uncertainty to control in lattice QCD calculations of nucleon matrix elements and form factors: early time separations are contaminated by excited states and late times suffer from an exponentially bad signal-to-noise problem. High-statistics calculations at large time separations ≳ 1 fm are commonly used to combat these issues. In this work, focusing on g A , we explore the alternative strategy of utilizing a large number of relatively low-statistics calculations at short to medium time separations (0.2–1 fm), combined with a multistate analysis. On an ensemble with a pion mass of approximately 310 MeV and a lattice spacing of approximately 0.09 fm, we find this provides a more robust and economical method of quantifying and controlling the excited state systematic uncertainty. A quantitative separation of various types of excited states enables the identification of the transition matrix elements as the dominant contamination. The excited state contamination of the Feynman-Hellmann correlation function is found to reduce to the 1% level at approximately 1 fm while, for the more standard three-point functions, this does not occur until after 2 fm. Critical to our findings is the use of a global minimization, rather than fixing the spectrum from the two-point functions and using them as input to the three-point analysis. We find that the ground state parameters determined in such a global analysis are stable against variations in the excited state model, the number of excited states, and the truncation of early-time or late-time numerical data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Many-fermion simulation from the contracted quantum eigensolver without fermionic encoding of the wave function

Quantum computers potentially have an exponential advantage over classical computers for the quantum simulation of many-fermion quantum systems. Nonetheless, fermions are more expensive to simulate than bosons due to the fermionic encoding—a mapping by which the qubits are encoded with fermion statistics. Here we generalize the contracted quantum eigensolver (CQE) to avoid fermionic encoding of the wave function. In contrast to the variational quantum eigensolver, the CQE solves for a many-fermion stationary state by minimizing the contraction (projection) of the Schrödinger equation onto two fermions. We avoid fermionic encoding of the wave function by contracting the Schrödinger equation onto an unencoded pair of particles. Solution of the resulting contracted equation by a series of unencoded two-body exponential transformations generates an unencoded wave function from which the energy and two-fermion reduced density matrix (2-RDM) can be computed. We apply the unencoded and the encoded CQE algorithms to the hydrogen fluoride molecule, the dissociation of oxygen O 2 , and a series of hydrogen chains. Both algorithms show comparable convergence towards the exact ground-state energies and 2-RDMs, but the unencoded algorithm has computational advantages in terms of state preparation and tomography.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2020

Characterization of quantum chaos by two-point correlation functions

In this work, we propose a characterization of quantum many-body chaos: given a collection of simple operators, the set of all possible pair correlations between these operators can be organized into a matrix with a random-matrix-like spectrum. This approach is particularly useful for locally interacting systems, which do not generically show exponential Lyapunov growth of out-of-time-ordered correlators. We demonstrate the validity of this characterization by numerically studying the Sachdev-Ye-Kitaev model and a one-dimensional spin chain with random magnetic field (XXZ model).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Slow scrambling and hidden integrability in a random rotor model

In this work, we analyze the out-of-time-order correlation functions of a solvable model of a large number $\textit{N}$ of $\textit{M}$-component quantum rotors coupled by Gaussian-distributed random, infinite-range exchange interactions. We focus on the growth of commutators of operators at a temperature $\textit{T}$ above the zero temperature quantum critical point separating the spin-glass and paramagnetic phases. In the large $\textit{N, M}$ limit, the squared commutators of the rotor fields do not display any exponential growth of commutators, in spite of the absence of any sharp quasiparticlelike excitations in the disorder-averaged theory. We show that in this limit, the problem is integrable and points out interesting connections to random-matrix theory. At leading order in 1/$\textit{M}$, there are no modifications to the critical behavior but an irrelevant term in the fixed-point action leads to a small exponential growth of the squared commutator. We also introduce and comment on a generalized model involving $\textit{p}$-pair rotor interactions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2026

Comparison between explicit and implicit discretization strategies for a dissipative thermal environment

We investigate strategies for simulating open quantum systems coupled to dissipative baths by comparing explicit wave function-based discretization [via multi-layer multi-configuration time-dependent Hartree (ML-MCTDH)] and the implicit density matrix-based master equation method [via tree tensor network hierarchical equations of motion (TTN-HEOM)]. For dissipative baths characterized by exponentially decaying bath correlation functions, the implicit discretization approach of HEOM—rooted in bath correlation function decompositions—proves significantly more efficient than explicit discretization of the bath into discrete harmonic modes. Explicit methods, like ML-MCTDH, require extensive mode discretization to approximate continuum baths, leading to computational bottlenecks. Case studies for two-level systems and a Fenna–Matthews–Olson complex model highlight TTN-HEOM’s superiority in capturing dissipative dynamics with relaxations with a minimal number of auxiliary modes, while the explicit methods are as exact as the HEOM in pure dephasing regimes. This comparison is enabled by the TENSO package, which has both ML-MCTDH and TTN-HEOM implemented using the same computational structure and propagation strategy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Phenomenology of the Prethermal Many-Body Localized Regime

The dynamical phase diagram of interacting disordered systems has seen substantial revision over the past few years. Theory must now account for a large prethermal many-body localized regime in which thermalization is extremely slow, but not completely arrested. We derive a quantitative description of these dynamics in short-ranged one-dimensional systems using a model of successive many-body resonances. Here, the model explains the decay timescale of mean autocorrelators, the functional form of the decay—a stretched exponential—and relates the value of the stretch exponent to the broad distribution of resonance timescales. The Jacobi method of matrix diagonalization provides numerical access to this distribution, as well as a conceptual framework for our analysis. The resonance model correctly predicts the stretch exponents for several models in the literature. Successive resonances may also underlie slow thermalization in strongly disordered systems in higher dimensions, or with long-range interactions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1991

Post-glacial relaxation of a viscously stratified compressible mantle

The postglacial relaxation phenomenon of a viscously compressible nonself-gravitating spherical-shell model is investigated. Analytical solutions to an exponentially depth-dependent viscosity are developed with various types of compressible density models such as those with an exponential dependence of the radius and an algebraic-root dependence of the radius. The solutions of a viscously compressible multilayered model with constant thermodynamic properties and viscosity are developed by the propagator matrix method. The results show that inferences of deep mantle viscosity from postglacial rebound would be hampered by mantle compressibility for long-wavelength harmonics because of the smaller excitation of compressible eigenfunctions in the lower mantle. The relaxation times and velocity fields are more sensitive to higher viscosity contrast for the exponentially varying viscosity than for models with discrete jumps in the viscosity structure.

Wu, J.↗

DOE OSTI2021

Adiabatic quantum decoherence in many non-interacting subsystems induced by the coupling with a common boson bath

Highlights: • System–environment quantum correlation: a main solid state NMR decoherence channel. • Non-separable system–environment model yields realistic spin decoherence rates. • New open quantum system approach explains irreversible decay of refocused NMR echoes. • Adiabatic quantum decoherence is inherently irreversible and eigen-selective. This work addresses adiabatic quantum decoherence of many-body spin systems coupled with a boson field in the framework of open quantum systems theory. We generalize the traditional spin-boson model by considering a system–environment interaction Hamiltonian that represents a partition of non-interacting subsystems and highlights the collective correlation that appears exclusively due to the coupling with a common environment. Remarkably, this simple, exactly solvable model encompasses relevant aspects of a many-body open quantum system and features the subtle quantum effects that arise when the size scales up to a macroscopic level. We derive an analytical expression for the time dependence of the density matrix elements (in the preferred basis) without assuming coarse-graining. The resulting decoherence function is eigen-selective and is a complex exponential whose exponent has a real part that introduces a decay similar to that in the spin-boson model. On the contrary, the imaginary part depends on the quantum numbers and geometry of the whole partition and does not reflect the system temperature. Motivated by decoherence in solid-state NMR, and in search of realistic numerical estimations, we apply the theoretical results to a partition of dipole-coupled spin pairs in contact with a common phonon bath, using typical parameters of hydrated salts. The proposal allows estimating the decoherence time scale in terms of the system physical constants: sound velocity and eigenvalue distribution width. As a significant novelty, the decoherence function phase depends on the eigenvalue distribution throughout the sample. It plays the leading role, overshadowing the mechanism associated with the bath thermal state. Finally, we apply the formalism to describe decoherence in the “magic echo” NMR reversal experiment. We find that the system–environment correlation explains the origin of irreversibility, and both the decoherence rate value and its dependence on the dipolar frequency, are remarkably similar to the experiment.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1990

Spectral simulation of unsteady compressible flow past a circular cylinder

An unsteady compressible viscous wake flow past a circular cylinder was successfully simulated using spectral methods. A new approach in using the Chebyshev collocation method for periodic problems is introduced. It was further proved that the eigenvalues associated with the differentiation matrix are purely imaginary, reflecting the periodicity of the problem. It was been shown that the solution of a model problem has exponential growth in time if improper boundary conditions are used. A characteristic boundary condition, which is based on the characteristics of the Euler equations of gas dynamics, was derived for the spectral code. The primary vortex shedding frequency computed agrees well with the results in the literature for Mach = 0.4, Re = 80. No secondary frequency is observed in the power spectrum analysis of the pressure data.

Don, Wai-Sun↗

DOE OSTI2024

Spectral scheme for atomic structure calculations in density functional theory

In this study, we present a spectral scheme for atomic structure calculations in pseudopotential Kohn-Sham density functional theory. In particular, after applying an exponential transformation of the radial coordinates, we employ global polynomial interpolation on a Chebyshev grid, with derivative operators approximated using the Chebyshev differentiation matrix, and integrations using Clenshaw-Curtis quadrature. We demonstrate the accuracy and efficiency of the scheme through spin-polarized and unpolarized calculations for representative atoms, while considering local, semilocal, and hybrid exchange-correlation functionals. In particular, we find that $\mathcal{O}$(200) grid points are sufficient to achieve an accuracy of 1 microhartree in the eigenvalues for optimized norm conserving Vanderbilt pseudopotentials spanning the periodic table from atomic number Ζ = 1 to 83.

74 ATOMIC AND MOLECULAR PHYSICS↗

NASA NTRS1983

Slant path attenuation and cross-polarization prediction

The accuracy with which slant-path attenuation and cross-polarization are predicted using differential reflectivity (ZDR) radar data is discussed. Consideration is given to the use of generalized relationships between radar reflectivity (Z), ZDR, and rainfall rate (R); and between R, attenuation, and cross-polarization (XPD) on a slant path. The forward-scatter matrix which is used to calculate the slant path attenuation and XPD is described. It is shown that the use of a double exponential drop size distribution and forward-scatter matrices improves the accuracy of the prediction of slant-path attenuation and XPD. Data obtained with the VPI & SU S-band radar, using slow switching between orthorzonal polarizations is presented. The results are illustrated in graphs.

Pratt, T.↗

DOE OSTI2022

Variational quantum state eigensolver

Extracting eigenvalues and eigenvectors of exponentially large matrices will be an important application of near-term quantum computers. The variational quantum eigensolver (VQE) treats the case when the matrix is a Hamiltonian. Here, we address the case when the matrix is a density matrix ρ. We introduce the variational quantum state eigensolver (VQSE), which is analogous to VQE in that it variationally learns the largest eigenvalues of ρ as well as a gate sequence V that prepares the corresponding eigenvectors. VQSE exploits the connection between diagonalization and majorization to define a cost function C=Tr(ρ~H) where H is a non-degenerate Hamiltonian. Due to Schur-concavity, C is minimized when ρ~=VρV† is diagonal in the eigenbasis of H. VQSE only requires a single copy of ρ (only n qubits) per iteration of the VQSE algorithm, making it amenable for near-term implementation. We heuristically demonstrate two applications of VQSE: (1) Principal component analysis, and (2) Error mitigation.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Two-color polarization spectroscopy measurements of Zeeman state-to-state collision induced transitions of nitric oxide in binary gas mixtures

We investigated collision induced transitions in the (0, 0) band of the A2Σ+–X2Π electronic transition of nitric oxide (NO) using two-color polarization spectroscopy (TCPS). Two sets of TCPS spectra for 1% NO, diluted in different buffer gases at 295 K and 1 atm, were obtained with the pump beam tuned to the R11(11.5) and OP12(1.5) transitions. The buffer gases were He, Ar, and N2. The probe was scanned while the pump beam was tuned to the line center. Theoretical TCPS spectra, calculated by solving the density matrix formulation of the time-dependent Schrödinger wave equation, were compared with the experimental spectra. A collision model based on the modified exponential-gap law was used to model the rotational level-to-rotational level collision dynamics. A model for collisional transfer from an initial to a final Zeeman state was developed based on the difference in cosine of the rotational quantum number J projection angle with the z-axis for the two Zeeman states. Rotational energy transfer rates and Zeeman state collisional dynamics were varied to obtain good agreement between theory and experiment for the two different TCPS pump transitions and for the three different buffer gases. One key finding, in agreement with quasi-classical trajectory calculations, is that the spin-rotation changing transition rate in the A2Σ+ level of NO is almost zero for rotational quantum numbers ≥8. It was necessary to set this rate to near zero to obtain agreement with the TCPS spectra.

Chemistry↗

NASA NTRS1991

A class of least-squares filtering and identification algorithms with systolic array architectures

A unified approach is presented for deriving a large class of new and previously known time- and order-recursive least-squares algorithms with systolic array architectures, suitable for high-throughput-rate and VLSI implementations of space-time filtering and system identification problems. The geometrical derivation given is unique in that no assumption is made concerning the rank of the sample data correlation matrix. This method utilizes and extends the concept of oblique projections, as used previously in the derivations of the least-squares lattice algorithms. Exponentially weighted least-squares criteria are considered for both sliding and growing memory.

Kalson, Seth Z.↗

DOE OSTI2025

Gate-Based Quantum Simulation of Gaussian Bosonic Circuits on Exponentially Many Modes

We introduce a framework for simulating, on an ( n + 1 )-qubit quantum computer, the action of a Gaussian bosonic (GB) circuit on a state over 2 n modes. Specifically, we encode the initial bosonic state’s expectation values over quadrature operators (and their covariance matrix) as an input qubit state. This is then evolved by a quantum circuit that effectively implements the symplectic propagators induced by the GB gates. We find families of GB circuits and initial states leading to efficient quantum simulations. For this purpose, we introduce a dictionary that maps between GB and qubit gates such that particle- (non-particle-) preserving GB gates lead to real- (imaginary-) time evolutions at the qubit level. For the special case of particle-preserving circuits, we present a bounded-error-quantum-polynomial time (BQP)-complete GB decision problem, indicating that GB evolutions of Gaussian states on exponentially many modes are as powerful as universal quantum computers. We also perform numerical simulations of an interferometer on ∼ 8 × 10 9 modes, illustrating the power of our framework. Published by the American Physical Society 2025

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Emergence of many-body quantum chaos via spontaneous breaking of unitarity

It is suggested that many-body quantum chaos appears as the spontaneous symmetry breaking of unitarity in interacting quantum many-body systems. It has been shown that many-body level statistics, probed by the spectral form factor (SFF) defined as K(η,t)=$\langle$|Tr exp(-ηH+itH)| 2 $\rangle$, is dominated by a diffuson-type mode in a field theory analysis. The key finding of this Letter is that the “unitary” η = 0 case is different from the η → 0 ± limit, with the latter leading to a finite mass of these modes due to interactions. This mass suppresses a rapid exponential ramp in the SFF, which is responsible for the fast emergence of Poisson statistics in the noninteracting case, and gives rise to a nontrivial random matrix structure of many-body levels. The interaction-induced mass in the SFF shares similarities with the dephasing rate in the theory of weak localization and the Lyapunov exponent of the out-of-time-ordered correlators.

36 MATERIALS SCIENCE↗

NASA NTRS1973

On stability of discrete composite systems

Conditions are developed under which exponential stability of a composite discrete system is implied by exponential stability of its subsystems and the nature of their interactions. Stability of the system is determined by testing positive definiteness property of a real symmetric matrix the dimension of which is equal to the number of subsystems.

Grujic, L. T.↗

NASA NTRS1973

On stability of discrete composite systems.

Grujic, L. T.↗