Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Hamiltonian”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 577 records · Page 32
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Correlated Dirac–Coulomb–Breit multiconfigurational self-consistent-field methods

The fully correlated frequency-independent Dirac–Coulomb–Breit Hamiltonian provides the most accurate description of electron–electron interaction before going to a genuine relativistic quantum electrodynamics theory of many-electron systems. In this work, we introduce a correlated Dirac–Coulomb–Breit multiconfigurational self-consistent-field method within the frameworks of complete active space and density matrix renormalization group. In this approach, the Dirac–Coulomb–Breit Hamiltonian is included variationally in both the mean-field and correlated electron treatment. Here, we also analyze the importance of the Breit operator in electron correlation and the rotation between the positive- and negative-orbital space in the no-virtual-pair approximation. Atomic fine-structure splittings and lanthanide contraction in diatomic fluorides are used as benchmark studies to understand the contribution from the Breit correlation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

DFT-based insight into finite-temperature properties of ferroelectric perovskites with lone-pair: the case of CsGeX 3 (X = Cl, Br, I)

Ferroelectrics remain in the focus of scientific attention for decades owing to their fundamental and practical appeal. Recently, ferroelectricity has been demonstrated in semiconducting halide perovskites (Zhang et al 2022 Sci. Adv. 8 eabj5881), offering both a rare combination of ferroelectricity and semiconductivity in the same material and a possible alternative to the prevailing perovskite oxide ferroelectrics. We propose a route to simulating such materials at finite temperatures capable of reproducing key experimental and first-principle data, such as Curie temperature, phase transition sequence, spontaneous polarization, and soft mode frequencies. The key methodological finding is the superior performance of hybrid exchange correlation functionals in parametrization of effective Hamiltonians for ferroelectrics with lone pair. The parametrization for effective Hamiltonians for CsGeX 3 (X = Cl, Br, I) is reported. The application of methodology to study polarization reversal in CsGeX 3 allows for the development of a ‘minimalistic’ model for polarization reversal in ferroelectrics that provides an insight into the mechanisms of polarization reversal and its key features, such as the relationship between the coercive field, temperature, and AC field frequency. Importantly, the model reveals the origin of the well-known and ever-puzzling overestimation of coercive fields in computations. Furthermore, we report a variety of finite-temperature properties of CsGeX 3 ferroelectrics, such as dielectric susceptibility, pyroelectric coefficients, and energy storage density, which reveal that these halide perovskites possess properties comparable to their oxide counterparts. Here, we believe that our work provides significant methodological advancements, deepens fundamental understanding of ferroelectrics, and reveals the potential of halide perovskite ferroelectrics.

effective Hamiltonian↗
DOE OSTI2022

Quantum model learning agent: characterisation of quantum systems through machine learning

Accurate models of real quantum systems are important for investigating their behaviour, yet are difficult to distil empirically. Here, we report an algorithm—the quantum model learning agent (QMLA)—to reverse engineer Hamiltonian descriptions of a target system. We test the performance of QMLA on a number of simulated experiments, demonstrating several mechanisms for the design of candidate Hamiltonian models and simultaneously entertaining numerous hypotheses about the nature of the physical interactions governing the system under study. QMLA is shown to identify the true model in the majority of instances, when provided with limited a priori information, and control of the experimental setup. Our protocol can explore Ising, Heisenberg and Hubbard families of models in parallel, reliably identifying the family which best describes the system dynamics. We demonstrate QMLA operating on large model spaces by incorporating a genetic algorithm to formulate new hypothetical models. The selection of models whose features propagate to the next generation is based upon an objective function inspired by the Elo rating scheme, typically used to rate competitors in games such as chess and football. In all instances, our protocol finds models that exhibit F 1 score ≥ 0.88 when compared with the true model, and it precisely identifies the true model in 72% of cases, whilst exploring a space of over 250 000 potential models. By testing which interactions actually occur in the target system, QMLA is a viable tool for both the exploration of fundamental physics and the characterisation and calibration of quantum devices.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Optimized Quantum Program Execution Ordering to Mitigate Errors in Simulations of Quantum Systems

Simulating the time evolution of a physical system at quantum mechanical levels of detail - known as Hamiltonian Simulation (HS) - is an important and interesting problem across physics and chemistry. For this task, algorithms that run on quantum computers are known to be exponentially faster than classical algorithms; in fact, this application motivated Feynman to propose the construction of quantum computers. Nonetheless, there are challenges in reaching this performance potential. Prior work has focused on compiling circuits (quantum programs) for HS with the goal of maximizing either accuracy or gate cancellation. Our work proposes a compilation strategy that simultaneously advances both goals. At a high level, we use classical optimizations such as graph coloring and travelling salesperson to order the execution of quantum programs. Specifically, we group together mutually commuting terms in the Hamiltonian (a matrix characterizing the quantum mechanical system) to improve the accuracy of the simulation. We then rearrange the terms within each group to maximize gate cancellation in the final quantum circuit. Furthermore, these optimizations work together to improve HS performance and result in an average 40% reduction in circuit depth. This work advances the frontier of HS which in turn can advance physical and chemical modeling in both basic and applied sciences.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Strong Local Passivity in Unconventional Scenarios: A New Protocol for Amplified Quantum Energy Teleportation

Quantum energy teleportation (QET) has been proposed to overcome the restrictions of strong local passivity (SLP) and to facilitate energy transfer in quantum systems. Traditionally, QET has only been considered under strict constraints, including the requirements that the initial state be the ground state of an interacting Hamiltonian, that Alice’s measurement commute with the interaction terms, and that entanglement be present. These constraints have significantly limited the broader applicability of QET protocols. In this work, we demonstrate that SLP can arise beyond these conventional constraints, establishing the necessity of QET in a wider range of scenarios for local energy extraction. This leads to a more flexible and generalized framework for QET. Furthermore, we introduce the concept of a “local effective Hamiltonian,” which eliminates the need for optimization techniques in determining Bob’s optimal energy extraction in QET protocols. As an additional advantage, the amount of energy that can be extracted using our new protocol is amplified to be 7.2 times higher than that of the original protocol. These advancements enhance our understanding of QET and extend its broader applications to quantum technologies. To support our findings, we implement the protocol on quantum hardware, confirming its theoretical validity and experimental feasibility.

amplified energy extraction↗
DOE OSTI2020

Secular Resonances in Nonrestricted Hierarchical Triple Systems

In this paper, the averaged Hamiltonian of a nonrestricted hierarchical triple system truncated at the third order is investigated. First, each secular resonant term is studied. For the well-studied secular quadrupole theory, it is analytically reformulated in a different manner in our work. The resonance width is numerically determined and displayed on the √(1−e{sub 1}{sup 2})−√(1−e{sub 2}{sup 2}) plane (also denoted as the e-tilde {sub 1}− e-tilde {sub 2} plane). In terms of the octupole terms, we show that for a near-planar configuration of the system, considerable variations of both the eccentricities of the inner and outer orbits can be generated by a single resonant term. The resonance width for every secular resonant angle from the octupole terms is also numerically determined and displayed on the e-tilde {sub 1}− e-tilde {sub 2} plane. The results show that an orbit flip with a near-perpendicular initial mutual inclination is possible for each secular resonance. By displaying the resonance widths of different resonant terms on the same e-tilde {sub 1}− e-tilde {sub 2} plane, we intuitively show the overlap of different secular resonances. Then, the full averaged Hamiltonian with both quadrupole and octupole terms is investigated using the Poincaré surface of section, with a special focus on the orbit flip. For the cases we exploited, we find that the near-planar flip of the inner orbit can be either regular or chaotic while the outer orbit flip is generally chaotic.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRSDate not supplied

A Numerical Method for Computing the State Transition Matrix Using Poincare Integral Invariants

The Poincare integral invariants describe the volumes of sets in Hamiltonian phase space. We use these invariants to derive a new numerical procedure for obtaining the state transition matrix (STM), which can be applied to both conservative and nonconservative systems. The method is analogous to a finite difference approximation of the STM, where perturbed states are numerically propagated along with the reference trajectory. We discuss the mathematical similarities between this new STM and existing methods, show numerical results for orbital motion and uncertainty propagation, and discuss new insights afforded by the Hamiltonian properties of phase flow.

state transition matrix↗
DOE OSTI2022

Physics-Informed Machine Learning of Dynamical Systems for Efficient Bayesian Inference

Although the no-u-turn sampler (NUTS) is a widely adopted method for performing Bayesian inference, it requires numerous posterior gradients which can be expensive to compute in practice. Recently, there has been a significant interest in physics-based machine learning of dynamical (or Hamiltonian) systems and Hamiltonian neural networks (HNNs) is a noteworthy architecture. But these types of architectures have not been applied to solve Bayesian inference problems efficiently. We propose the use of HNNs for performing Bayesian inference efficiently without requiring numerous posterior gradients. We introduce latent variable outputs to HNNs (L-HNNs) for improved expressivity and reduced integration errors. We integrate L-HNNs in NUTS and further propose an online error monitoring scheme to prevent sampling degeneracy in regions where L-HNNs may have little training data. We demonstrate L-HNNs in NUTS with online error monitoring consider several complex high-dimensional posterior densities and compare its performance to NUTS.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Unconventional Spintronics from Chiral Perovskites

Spintronic devices typically employ heterostructures with ferromagnets which break time-reversal symmetry and have non-vanishing magnetization. With the growing class of materials that support spin-polarized carriers, current, and excitations, it is possible to envision emerging spintronic applications that are not limited to magnetoresistance. Here, chiral perovskites with no net magnetization are considered, where the space-inversion and mirror symmetries are broken to induce chiral structure. The known importance of these perovskites is further expanded by the demonstration of the chiral-induced spin selectivity (CISS). However, the generation of the spin-polarized carriers across the interface with these chiral perovskites remains to be fully understood. These first-principles studies for 2D PbBr4-based chiral perovskites provide their electronic structure and an orbital-based symmetry analysis, which allows to establish an effective Hamiltonian to elucidate the underlying origin of their chirality. The same analysis is used for the Edelstein effect, responsible for electrical generation of the nonequilibrium spin polarization in many materials, which in chiral perovskites can be a mechanism contributing to CISS. Furthermore, by examining optical properties of chiral perovskites and the opportunity to use them to realize tunable altermagnets, another class of zero-magnetization spintronic materials, a versatile materials platform is put forth for unconventional spintronics.

14 SOLAR ENERGY↗
DOE OSTI2021

Entanglement and confinement in coupled quantum systems

We study some general properties of coupled quantum systems. We consider simple interactions between two copies of identical Hamiltonians such as the SYK model, Pauli spin chains with random magnetic field and harmonic oscillators. Such couplings make the ground states close to the thermofield double states of the uncoupled Hamiltonians. For the coupled SYK model, we push the numerical computation further towards the thermodynamic limit so that an extrapolation in the size of the system is possible. We find good agreement between the extrapolated numerical result and the analytic result in the large-q limit. We also consider the coupled gauged matrix model and vector model, and argue that the deconfinement is associated with the loss of the entanglement, similarly to the previous observation for the coupled SYK model. The understanding of the microscopic mechanism of the confinement/deconfinement transition enables us to estimate the quantum entanglement precisely, and backs up the dual gravity interpretation which relates the deconfinement to the disappearance of the wormhole. Our results demonstrate the importance of the entanglement between the color degrees of freedom in the emergence of the bulk geometry from quantum field theory via holography.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

On running coupling in the JIMWLK evolution and its Langevin formulation

Abstract Various conventional running coupling prescriptions reproducingβ 0 -dependent terms of NLO JIMWLK are reviewed and found to be theoretically inconsistent: the JIMWLK evolution Hamiltonian with running coupling violates the requirement of positive semidefiniteness. This requirement appears to be tightly related to the possibility of having a Langevin formulation for the evolution. We also review the scheme that attributes a part ofβ 0 -dependent terms to the DGLAP evolution of the projectile. The remainingβ 0 -dependent contributions sum up into so-called “daughter dipole” prescription, which leads to a manifestly positive semidefinite Hamiltonian.

Physics↗
DOE OSTI2026

Infinite matrix product states for (1 + 1)-dimensional gauge theories

We present a matrix product operator construction that allows us to represent the lattice Hamiltonians of (abelian or non-abelian) gauge theories in a local and manifestly translation-invariant form. In particular, we use symmetric matrix product states and introduce link-enhanced matrix product operators (LEMPOs) that can act on both the physical and virtual spaces of the matrix product states. This construction allows us to study Hamiltonian lattice gauge theories on infinite lattices. As examples, we show how to implement this method to study the massless and massive one-flavor Schwinger model and adjoint QCD 2 .

confinement↗
DOE OSTI2023

Towards a nonperturbative construction of the S-matrix

We present a nonperturbative recipe for directly computing the S-matrix in strongly-coupled QFTs. The method makes use of spectral data obtained in a Hamiltonian framework and can be applied to a wide range of theories, including potentially QCD. We demonstrate the utility of this prescription in the specific example of the 2+1d O(N) model at large N, using energy eigenstates computed with Hamiltonian truncation to reproduce the full 2 → 2 scattering amplitude for arbitrary (complex) center-of-mass energy.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Linear growth of circuit complexity from Brownian dynamics

How rapidly can a many-body quantum system generate randomness? Using path integral methods, we demonstrate that Brownian quantum systems have circuit complexity that grows linearly with time. In particular, we study Brownian clusters of N spins or fermions with time-dependent all-to-all interactions, and calculate the Frame Potential to characterize complexity growth in these models. In both cases the problem can be mapped to an effective statistical mechanics problem which we study using path integral methods. Within this framework it is straightforward to show that the kth Frame Potential comes within ϵ of the Haar value after a time of order t ~ kN + k log k + log ϵ –1 . Using a bound on the diamond norm, this implies that such circuits are capable of coming very close to a unitary k-design after a time of order t ~ kN. We also consider the same question for systems with a time-independent Hamiltonian and argue that a small amount of time-dependent randomness is sufficient to generate a k-design in linear time provided the underlying Hamiltonian is quantum chaotic. These models provide explicit examples of linear complexity growth that are analytically tractable and are directly applicable to practical applications calling for unitary k-designs.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Holography and unitarity

If holography is an equivalence between quantum theories, one might expect it to be described by a map that is a bijective isometry between bulk and boundary Hilbert spaces, preserving the hamiltonian and symmetries. Holography has been believed to be a property of gravitational (or string) theories, but not of non-gravitational theories; specifically Marolf has argued that it originates from the gauge symmetries and constraints of gravity. These observations suggest study of the assumed holographic map as a function of the gravitational coupling G . The zero coupling limit gives ordinary quantum field theory, and is therefore not necessarily expected to be holographic. This, and the structure of gravity at non-zero G , raises important questions about the full map. In particular, construction of a holographic map appears to require as input a solution of the nonperturbative analog of the bulk gravitational constraints, that is, the unitary bulk evolution. Moreover, examination of the candidate boundary algebra, including the boundary hamiltonian, reveals commutators that don’t close in the usual fashion expected for a boundary theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Post-Minkowskian effective field theory for conservative binary dynamics

We develop an Effective Field Theory (EFT) formalism to solve for the conservative dynamics of binary systems in gravity via Post-Minkowskian (PM) scattering data. Our framework combines a systematic EFT approach to compute the deflection angle in the PM expansion, together with the ‘Boundary-to-Bound’ (B2B) dictionary introduced. Due to the nature of scattering processes, a remarkable reduction of complexity occurs both in the number of Feynman diagrams and type of integrals, compared to a direct EFT computation of the potential in a PM scheme. We provide two illustrative examples. Firstly, we compute all the conservative gravitational observables for bound orbits to 2PM, which follow from only one topology beyond leading order. The results agree with those, obtained through the ‘impetus formula’ applied to the classical limit of the one loop amplitude. For the sake of comparison we reconstruct the conservative Hamiltonian to 2PM order, which is equivalent to the one derived from a matching calculation. Secondly, we compute the scattering angle due to tidal effects from the electric- and magnetic-type Love numbers at leading PM order. Using the B2B dictionary we then obtain the tidal contribution to the periastron advance. We also construct a Hamiltonian including tidal effects at leading PM order. Although relying on (relativistic) Feynman diagrams, the EFT formalism developed here does not involve taking the classical limit of a quantum amplitude, neither integrals with internal massive fields, nor additional matching calculations, nor spurious (‘super-classical’) infrared singularities. By construction, the EFT approach can be automatized to all PM orders.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Dijet impact factor in DIS at next-to-leading order in the Color Glass Condensate

In this work, we compute the next-to-leading order impact factor for inclusive dijet production in deeply inelastic electron-nucleus scattering at small x Bj . Our computation, performed in the framework of the Color Glass Condensate effective field theory, includes all real and virtual contributions in the gluon shock wave background of all-twist lightlike Wilson line correlators. We demonstrate explicitly that the rapidity evolution of these correlators, to leading logarithmic accuracy, is described by the JIMWLK Hamiltonian. When combined with the next-to-leading order JIMWLK Hamiltonian, our results for the impact factor improve the accuracy of the inclusive dijet cross-section to \( \mathcal{O} \) ( \( {\alpha}_s^2 \) ln( x f /x Bj )), where x f is a rapidity factorization scale. These results are an essential ingredient in assessing the discovery potential of inclusive dijets to uncover the physics of gluon saturation at the Electron-Ion Collider.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Small circle expansion for adjoint QCD 2 with periodic boundary conditions

We study 1 + 1-dimensional SU(N) gauge theory coupled to one adjoint multiplet of Majorana fermions on a small spatial circle of circumference L. Using periodic boundary conditions, we derive the effective action for the quantum mechanics of the holonomy and the fermion zero modes in perturbation theory up to order (gL) 3 . When the adjoint fermion mass-squared is tuned to g 2 N/(2π), the effective action is found to be an example of supersymmetric quantum mechanics with a nontrivial superpotential. We separate the states into the ℤN center symmetry sectors (universes) labeled by p = 0, . . . , N – 1 and show that in one of the sectors the supersymmetry is unbroken, while in the others it is broken spontaneously. These results give us new insights into the (1, 1) supersymmetry of adjoint QCD 2 , which has previously been established using light-cone quantization. When the adjoint mass is set to zero, our effective Hamiltonian does not depend on the fermions at all, so that there are 2 N−1 degenerate sectors of the Hilbert space. This construction appears to provide an explicit realization of the extended symmetry of the massless model, where there are 2 2N−2 operators that commute with the Hamiltonian. We also generalize our results to other gauge groups G, for which supersymmetry is found at the adjoint mass-squared g 2 h ∨ /(2π), where h ∨ is the dual Coxeter number of G.

effective field theories↗