Search NASA⌕ Search

SEARCH · Search NASA

Results for “translational invariance”

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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Ab initio leading order effective potential for elastic proton scattering based on the symmetry-adapted no-core shell model

Calculating microscopic optical potentials for elastic scattering at intermediate energies from light nuclei in an ab initio fashion within the Watson expansion has been established within the last few years. Based on the Watson expansion of the multiple scattering series, we employ a nonlocal translationally invariant nuclear density derived within the symmetry-adapted no-core shell model (SA-NCSM) framework from a chiral next-to-next-to-leading order (NNLO) nucleon-nucleon interaction and the very same interaction for a consistent full-folding calculation of the effective (optical) potential for nucleon-nucleus scattering for medium-heavy nuclei. The leading order effective (optical) folding potential is computed by integrating over a translationally invariant SA-NCSM one-body scalar density, spin-projected momentum distribution, and the Wolfenstein amplitudes 𝐴, 𝐶, and 𝑀. The resulting nonlocal potentials serve as input for a momentum space Lippmann-Schwinger equation. In the SA-NCSM, the model space is systematically up-selected using Sp⁡(3,ℝ) symmetry considerations. For the light nucleus of 6 He, we establish a systematic selection scheme in the SA-NCSM for scattering observables. Then, we apply this scheme to calculations of scattering observables, such as differential cross sections, analyzing powers, and spin rotation functions for elastic proton scattering from 20 Ne and 40 Ca in the energy regime between 65 and 200 MeV, and compare to available data. Furthermore, our calculations show that the leading order effective nucleon-nucleus potential in the Watson expansion of multiple scattering theory obtained from an up-selected SA-NCSM model space describes 40 Ca elastic scattering observables reasonably well to about 60 degrees in the center-of-mass frame, which coincides roughly with the validity of the NNLO chiral interaction used to calculate both the nucleon-nucleon amplitudes and the one-body scalar and spin nuclear densities.

Ab initio calculations↗
DOE OSTI2021

Accurate and scalable graph neural network force field and molecular dynamics with direct force architecture

Abstract Recently, machine learning (ML) has been used to address the computational cost that has been limiting ab initio molecular dynamics (AIMD). Here, we present GNNFF, a graph neural network framework to directly predict atomic forces from automatically extracted features of the local atomic environment that are translationally-invariant, but rotationally-covariant to the coordinate of the atoms. We demonstrate that GNNFF not only achieves high performance in terms of force prediction accuracy and computational speed on various materials systems, but also accurately predicts the forces of a large MD system after being trained on forces obtained from a smaller system. Finally, we use our framework to perform an MD simulation of Li 7 P 3 S 11 , a superionic conductor, and show that resulting Li diffusion coefficient is within 14% of that obtained directly from AIMD. The high performance exhibited by GNNFF can be easily generalized to study atomistic level dynamics of other material systems.

Chemistry↗
NASA NTRS1990

Connectivity strategies for higher-order neural networks applied to pattern recognition

Different strategies for non-fully connected HONNs (higher-order neural networks) are discussed, showing that by using such strategies an input field of 128 x 128 pixels can be attained while still achieving in-plane rotation and translation-invariant recognition. These techniques allow HONNs to be used with the larger input scenes required for practical pattern-recognition applications. The number of interconnections that must be stored has been reduced by a factor of approximately 200,000 in a T/C case and about 2000 in a Space Shuttle/F-18 case by using regional connectivity. Third-order networks have been simulated using several connection strategies. The method found to work best is regional connectivity. The main advantages of this strategy are the following: (1) it considers features of various scales within the image and thus gets a better sample of what the image looks like; (2) it is invariant to shape-preserving geometric transformations, such as translation and rotation; (3) the connections are predetermined so that no extra computations are necessary during run time; and (4) it does not require any extra storage for recording which connections were formed.

Spirkovska, Lilly↗
DOE OSTI2024

Physics and chemistry from parsimonious representations: image analysis via invariant variational autoencoders

Electron, optical, and scanning probe microscopy methods are generating ever increasing volume of image data containing information on atomic and mesoscale structures and functionalities. This necessitates the development of the machine learning methods for discovery of physical and chemical phenomena from the data, such as manifestations of symmetry breaking phenomena in electron and scanning tunneling microscopy images, or variability of the nanoparticles. Variational autoencoders (VAEs) are emerging as a powerful paradigm for the unsupervised data analysis, allowing to disentangle the factors of variability and discover optimal parsimonious representation. Here, we summarize recent developments in VAEs, covering the basic principles and intuition behind the VAEs. The invariant VAEs are introduced as an approach to accommodate scale and translation invariances present in imaging data and separate known factors of variations from the ones to be discovered. We further describe the opportunities enabled by the control over VAE architecture, including conditional, semi-supervised, and joint VAEs. Several case studies of VAE applications for toy models and experimental datasets in Scanning Transmission Electron Microscopy are discussed, emphasizing the deep connection between VAE and basic physical principles. Python codes and datasets discussed in this article are available at https://github.com/saimani5/VAE-tutorials and can be used by researchers as an application guide when applying these to their own datasets.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Bicrystallography-informed Frenkel–Kontorova model for interlayer dislocations in strained 2D heterostructures

In recent years, van der Waals (vdW) heterostructures and homostructures, which consist of stacks of two-dimensional (2D) materials, have risen to prominence due to their association with exotic quantum phenomena originating from correlated electronic states harbored by them. Atomistic scale relaxation effects play an extremely important role in the electronic scale quantum physics of these systems, providing means of manipulation of these materials and allowing them to be tailored for emergent technologies. We investigate such structural relaxation effects in this work using atomistic and mesoscale models, within the context of twisted bilayer graphene — a well-known heterostructure system that features moiré patterns arising from the lattices of the two graphene layers. For small twist angles, atomic relaxation effects in this system are associated with the natural emergence of interface dislocations or strain solitons, which result from the cyclic nature of the generalized stacking fault energy (GSFE), that measures the interface energy based on the relative movement of the two layers. Here, in this work, we first demonstrate using atomistic simulations that atomic reconstruction in bilayer graphene under a large twist also results from interface dislocations, although the Burgers vectors of such dislocations are considerably smaller than those observed in small-twist systems. To reveal the translational invariance of the heterointerface responsible for the formation of such dislocations, we derive the translational symmetry of the GSFE of a 2D heterostructure using the notions of coincident site lattices (CSLs) and displacement shift complete lattices (DSCLs). The workhorse for this exercise is a recently developed Smith normal form bicrystallography framework. Next, we construct a bicrystallography-informed and frame-invariant Frenkel–Kontorova model, which can predict the formation of strain solitons in arbitrary 2D heterostructures, and apply it to study a heterostrained, large-twist bilayer graphene system. Our mesoscale model is found to produce results consistent with atomistic simulations. We anticipate that the model will be invaluable in predicting structural relaxation and for providing insights into various heterostructure systems, especially in cases where the fundamental unit cell is large and therefore, atomistic simulations are computationally expensive.

2D heterostructures↗
DOE OSTI2020

Classical discrete time crystals

The spontaneous breaking of time-translation symmetry in periodically driven quantum systems leads to a new phase of matter: the discrete time crystal (DTC). This phase exhibits collective subharmonic oscillations that depend upon an interplay of non-equilibrium driving, many-body interactions and the breakdown of ergodicity. However, subharmonic responses are also a well-known feature of classical dynamical systems ranging from predator–prey models to Faraday waves and a.c.-driven charge density waves. This raises the question of whether these classical phenomena display the same rigidity characteristic of a quantum DTC. In this work, we explore this question in the context of periodically driven Hamiltonian dynamics coupled to a finite-temperature bath, which provides both friction and, crucially, noise. Focusing on one-dimensional chains, where in equilibrium any transition would be forbidden at finite temperature, we provide evidence that the combination of noise and interactions drives a sharp, first-order dynamical phase transition between a discrete time-translation invariant phase and an activated classical discrete time crystal (CDTC) in which time-translation symmetry is broken out to exponentially long timescales. Power-law correlations are present along a first-order line, which terminates at a critical point. We analyse the transition by mapping it to the locked-to-sliding transition of a d.c.-driven charge density wave. To conclude, building upon results from the field of probabilistic cellular automata, we conjecture the existence of classical time crystals with true long-range order, where time-translation symmetry is broken out to infinite times.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Operator dynamics in Floquet many-body systems

We study operator dynamics in many-body quantum systems, focusing on generic features of systems that are ergodic, spatially extended, and lack conserved densities. Quantum circuits of various types provide simple models for such systems. We focus on Floquet quantum circuits, comparing their behavior with what has been found previously for circuits that are random in time. Floquet circuits, which have discrete time-translation symmetry, represent an intermediate case between circuits that are random in time and lack any symmetry, and systems with a time-independent Hamiltonian and continuous time-translation invariance. By making this comparison, one of our aims is to identify signatures of time-translation symmetry in Floquet operator dynamics. To characterize behavior we examine a variety of quantities in solvable models and numerically: operator autocorrelation functions; the partial spectral form factor; the out-of-time-order correlator (OTOC); and the paths in operator space that make the dominant contributions to the ensemble-averaged autocorrelation functions. Our most striking result is that ensemble-averaged autocorrelation functions show behavior that is distinctively different in Floquet systems compared to systems in which successive time-steps are independent. Specifically, while average autocorrelation functions decay on a microscopic timescale for circuits that are random in time, in Floquet systems they have a late-time tail with a duration that grows parametrically with the size of the operator support. In the simplest models this tail is separated from the initial decay by a minimum, so that the average autocorrelation function has an intermediate-time peak. The existence of these tails provides a way to understand deviations of the spectral form factor from random matrix behavior at times shorter than the Thouless time. In contrast to this feature in autocorrelation functions, we find no new aspects to the behavior of OTOCs for Floquet models compared to random-in-time circuits. We show that this difference between averaged autocorrelation functions and OTOCs can be understood in terms of the paths in operator space that contribute to the two quantities: paths for the former retain a limited support at late times, while paths for the latter are dominated by operator spreading. Published by the American Physical Society 2025

Yoshimura, Takato (ORCID:0000000309159846)↗
DOE OSTI2023

Energy cost of localization of relational quantum information

Entanglement of spatially separated quantum states is usually defined with respect to a reference frame provided by some external observer. Thus, if one wishes to localize the quantum information within a spatially separated entangled state, one must enact an entanglement extraction protocol also defined with respect to that external frame. Entanglement extraction for Gaussian ground states in such an external frame construction has been shown to require a minimum energy and is hence an interesting process for gravitational physics, where examinations of localization vs energy cost have a long history. General covariance, however, precludes dependence on external frames. In order to enact an extraction protocol in a generally covariant theory, dependence on the external reference frame must first be removed and the states made relational. Here, we examine the implementation of an extraction protocol for Gaussian states, whose center of mass and relational degrees of freedom are entangled, in a relational toy model where translation invariance stands in for full diffeomorphism invariance. Constructing fully relational states and the corresponding extraction/localization can, in principle, be done in two ways. External frame position information can be removed through 𝐺-twirling over translations or one can spontaneously break the translation symmetry via the gradient of an auxiliary field, or 𝑍-model. We determine the energetics of quantum information localization after the states have been made fully relational via both the 𝐺-twirl and 𝑍-model. We also show one can obtain the 𝐺-twirl construction from a 𝑍-model as a limit of positive operator valued measurements.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1990

Learning receptor positions from imperfectly known motions

An algorithm is described for learning image interpolation functions for sensor arrays whose sensor positions are somewhat disordered. The learning is based on failures of translation invariance, so it does not require knowledge of the images being presented to the visual system. Previously reported implementations of the method assumed the visual system to have precise knowledge of the translations. It is demonstrated that translation estimates computed from the imperfectly interpolated images can have enough accuracy to allow the learning process to converge to a correct interpolation.

Ahumada, Albert J., Jr.↗
DOE OSTI2021

Nondispersing Wave Packets in Lattice Floquet Systems

We show that in a one-dimensional translationally invariant tight binding chain, nondispersing wave packets can in general be realized as Floquet eigenstates—or linear combinations thereof—using a spatially inhomogeneous drive, which can be as simple as modulation on a single site. The recurrence time of these wave packets (their “round-trip” time) locks in at rational ratios sT/r of the driving period T, where s, r are coprime integers. Wave packets of different s / r can coexist under the same drive, yet travel at different speeds. They retain their spatial compactness either infinitely (s/r = 1) or over a long time (s/r ≠ 1). Discrete time translation symmetry is manifestly broken for s ≠ 1, reminiscent of integer and fractional Floquet time crystals. We further demonstrate how to reverse engineer a drive protocol to reproduce a target Floquet micromotion, such as the free propagation of a wave packet, as if coming from a strictly linear energy spectrum. The variety of control schemes open up a new avenue for Floquet engineering in quantum information sciences.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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 OSTI2022

$T\overline{T}$ deformations and the width of fundamental particles

We provide a simple geometric meaning for deformations of so-called $T\overline{T}$ type in relativistic and non-relativistic systems. Deformations by the cross products of energy and momentum currents in integrable quantum field theories are known to modify the thermodynamic Bethe ansatz equations by a “CDD factor”. In turn, CDD factors may be interpreted as additional, fixed shifts incurred in scattering processes: a finite width added to the fundamental particles (or, if negative, to the free space between them). We suggest that this physical effect is a universal way of understanding $T\overline{T}$ deformations, both in classical and quantum systems. We first show this in non-relativistic systems, with particle conservation and translation invariance, using the deformation formed out of the densities and currents of particles and momentum. This holds at the level of the equations of motion, and for any interaction potential, integrable or not. We then argue, and show by similar techniques in free relativistic particle systems, that $T\overline{T}$ deformations of relativistic systems produce the equivalent phenomenon, accounting for length contractions. We also show that, in both the relativistic and non-relativistic cases, the width of particles is equivalent to a state-dependent change of metric, where the distance function discounts the particles’ widths, or counts the additional free space. This generalises and explains the known field-dependent coordinate change describing $T\overline{T}$ deformations. The results connect such deformations with generalised hydrodynamics, where the relations between scattering shifts, widths of particles and state-dependent changes of metric have been established.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Exact Ground State of Interacting Electrons in Magic Angle Graphene

One of the most remarkable theoretical findings in magic angle twisted bilayer graphene (TBG) is the emergence of ferromagnetic Slater determinants as exact ground states for the interacting Hamiltonian at the chiral limit. This discovery provides an explanation for the correlated insulating phase which has been experimentally observed at half filling. This work is the first mathematical study of interacting models in magic angle graphene systems. These include not only TBG but also TBG-like systems featuring four flat bands per valley, and twisted trilayer graphene systems with equal twist angles. We identify symmetries of the chiral limit of the Bistritzer-MacDonald Hamiltonian that are responsible for characterizing the Hartree-Fock ground states as zero energy many-body ground states. Furthermore, for a general class of Hamiltonian, we establish criteria that the ferromagnetic Slater determinants are the unique ground states within the class of uniformly half-filled, translation invariant Slater determinants. We then demonstrate that these criteria can be explicitly verified for TBG and TBG-like systems at the chiral limit, using properties of Jacobi-θ$${\theta }$$ and Weierstrass-℘$${\wp }$$ functions.

Becker, Simon↗
DOE OSTI2022

On the closedness and geometry of tensor network state sets

Tensor network states (TNS) are a powerful approach for the study of strongly correlated quantum matter. The curse of dimensionality is addressed by parametrizing the many-body state in terms of a network of partially contracted tensors. These tensors form a substantially reduced set of effective degrees of freedom. In practical algorithms, functionals like energy expectation values or overlaps are optimized over certain sets of TNS. Concerning algorithmic stability, it is important whether the considered sets are closed because, otherwise, the algorithms may approach a boundary point that is outside the TNS set and tensor elements diverge. Here we discuss the closedness and geometries of TNS sets, and we propose regularizations for optimization problems on non-closed TNS sets. We show that sets of matrix product states (MPS) with open boundary conditions, tree tensor network states, and the multiscale entanglement renormalization ansatz are always closed, whereas sets of translation-invariant MPS with periodic boundary conditions (PBC), heterogeneous MPS with PBC, and projected entangled pair states are generally not closed. The latter is done using explicit examples like the W state, states that we call two-domain states, and fine-grained versions thereof.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

New data-driven approach to bridging power system protection gaps with deep learning

Protection is a critical function in power systems to avoid equipment damage, maintain personnel safety, and support system reliability. However, current protective relay technology cannot adequately protect equipment and personnel from effects of some events; these deficiencies are termed protection gaps. In this paper, a data-driven approach is proposed to complement traditional protection technology and distinguish fault conditions from transients caused by normal operations. A combined convolutional neural network and long short-term memory (CNN-LSTM) network is implemented to achieve data translation invariance and capture the temporal correlation of the time-series input data. As a result, the data-driven method can accurately detect system faults despite variation and noise in the input data. In addition, using the CNN-LSTM--based method avoids the complicated, manual feature extraction procedure required by many traditional data-driven methods. The effectiveness of the proposed approach is tested on two kinds of protection gaps: high-impedance faults and transformer inter-turn faults. Lastly, a transfer learning method is also proposed to address the common issue of data-driven methods for which real-world training data are scarce. Extensive study results demonstrate that the proposed approach can accurately bridge power system protection gaps.

42 ENGINEERING↗
DOE OSTI2024

Scalable semidefinite programming approach to variational embedding for quantum many-body problems

In quantum embedding theories, a quantum many-body system is divided into localized clusters of sites which are treated with an accurate ‘high-level’ theory and glued together self-consistently by a less accurate ‘low-level’ theory at the global scale. The recently introduced variational embedding approach for quantum many-body problems combines the insights of semidefinite relaxation and quantum embedding theory to provide a lower bound on the ground-state energy that improves as the cluster size is increased. The variational embedding method is formulated as a semidefinite program (SDP), which can suffer from poor computational scaling when treated with black-box solvers. Here, we exploit the interpretation of this SDP as an embedding method to develop an algorithm which alternates parallelizable local updates of the high-level quantities with updates that enforce the low-level global constraints. Moreover, we show how translation invariance in lattice systems can be exploited to reduce the complexity of projecting a key matrix to the positive semidefinite cone.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Momentum-independent magnetic excitation continuum in the honeycomb iridate H 3 LiIr 2 O 6

Understanding the interplay between the inherent disorder and the correlated fluctuating-spin ground state is a key element in the search for quantum spin liquids. H 3 LiIr 2 O 6 is considered to be a spin liquid that is proximate to the Kitaev-limit quantum spin liquid. Its ground state shows no magnetic order or spin freezing as expected for the spin liquid state. However, hydrogen zero-point motion and stacking faults are known to be present. The resulting bond disorder has been invoked to explain the existence of unexpected low-energy spin excitations, although data interpretation remains challenging. Here, we use resonant X-ray spectroscopies to map the collective excitations in H 3 LiIr 2 O 6 and characterize its magnetic state. In the low-temperature correlated state, we reveal a broad bandwidth of magnetic excitations. The central energy and the high-energy tail of the continuum are consistent with expectations for dominant ferromagnetic Kitaev interactions between dynamically fluctuating spins. Furthermore, the absence of a momentum dependence to these excitations are consistent with disorder-induced broken translational invariance. Our low-energy data and the energy and width of the crystal field excitations support an interpretation of H 3 LiIr 2 O 6 as a disordered topological spin liquid in close proximity to bond-disordered versions of the Kitaev quantum spin liquid.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗