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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 OSTI2024

Gauge invariance of radiative jet functions in the position-space formulation of SCET

In subleading powers of soft-collinear effective theory (SCET), the Lagrangian contains couplings between soft quarks and hard-collinear quarks. Matrix elements of the hard-collinear parts of these couplings are radiative jet functions. In the position-space formulation of SCET, the Lagrangians are constructed from operators that appear to be gauge invariant. Nevertheless, we find violations of gauge invariance arise in the hard-collinear sector because gauge transformations can shift the momentum of a hard-collinear quark field from the hard-collinear sector to the soft sector, where the hard-collinear fields, by definition, have no support. The violations of gauge invariance are manifested in perturbation theory in the hard-collinear sector through the absence of certain Feynman diagrams that would be present in full QCD. A consequence of the absence of these diagrams is that the radiative jet functions that follow directly from the position-space Lagrangians are not gauge invariant, and we demonstrate this through explicit calculations in lower-order perturbation theory. We obtain gauge-invariant Lagrangians by adding to existing position-space Lagrangians terms that are proportional to the soft-quark equation of motion. These gauge-invariant Lagrangians are valid for nonzero, as well as zero, quark masses. We also remark briefly on the gauge invariance of certain Lagrangians that have been constructed in the label-momentum formulation of SCET. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

Wall-crossing invariants: from quantum mechanics to knots

We offer a pedestrian-level review of the wall-crossing invariants. The story begins from the scattering theory in quantum mechanics where the spectrum reshuffling can be related to permutations of S-matrices. In nontrivial situations, starting from spin chains and matrix models, the S-matrices are operatorvalued and their algebra is described in terms of R- and mixing (Racah) U-matrices. Then the Kontsevich-Soibelman (KS) invariants are nothing but the standard knot invariants made out of these data within the Reshetikhin-Turaev-Witten approach. The R and Racah matrices acquire a relatively universal form in the semiclassical limit, where the basic reshufflings with the change of moduli are those of the Stokes line. Natural from this standpoint are matrices provided by the modular transformations of conformal blocks (with the usual identification R = T and U = S), and in the simplest case of the first degenerate field (2, 1), when the conformal blocks satisfy a second-order Shrödinger-like equation, the invariants coincide with the Jones (N = 2) invariants of the associated knots. Another possibility to construct knot invariants is to realize the cluster coordinates associated with reshufflings of the Stokes lines immediately in terms of check-operators acting on solutions of the Knizhnik-Zamolodchikov equations. Then the R-matrices are realized as products of successive mutations in the cluster algebra and are manifestly described in terms of quantum dilogarithms, ultimately leading to the Hikami construction of knot invariants.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Asymmetries of various P- and T-parities in angular distributions of products of cold-polarized-neutron-induced binary and ternary fission of oriented nuclei and T-invariance

It is shown that a quantum system whose Hamiltonian is independent of time is T -invariant if this Hamiltonian contains only those terms that do not change sign upon time reversal. It is also shown that the coincidence of the amplitudes for multistep direct and statistical nuclear reactions with the timereversed amplitudes for the reactions being studied is a condition that ensures the T -invariance of the amplitudes in question, the transition from the original amplitudes to their time-reversed counterparts being accomplished, first, upon introducing the inverse-reactionmatrices T instead of the original-reaction matrix T and, second, upon replacing the wave functions for the initial, final, and intermediate states of the system by the respective time-reversed functions. It is found that the T -even (T -odd) asymmetries in cross sections for nuclear reactions stem from the interference between the amplitudes characterizing these reactions and having identical (opposite) T -parities. It is shown that the T -invariance condition for the above T -even (T -odd) asymmetries is related to the conservation of (change in) the sign of these asymmetries upon going over from original to inverse nuclear reactions. Mechanisms underlying the appearance of possible T -even and T-odd asymmetries in the cross sections for the cold-polarizedneutron- induced binary and ternary fission of oriented target nuclei are analyzed for the case of employing T -invariant Hamiltonians for the systems under study. It is also shown that the asymmetries in question satisfy the T -invariance condition if the reactions being considered have a sequential multistep statistical character. It is concluded that T -invariance is violated in the limiting case where, in ternary nuclear fission, the emission of a light third particle froma fissile compound nucleus formed upon incident-neutron capture by a target nucleus and its separation to two fission fragments are simultaneous events.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2016

Machine learning strategies for systems with invariance properties

Here, in many scientific fields, empirical models are employed to facilitate computational simulations of engineering systems. For example, in fluid mechanics, empirical Reynolds stress closures enable computationally-efficient Reynolds-Averaged Navier-Stokes simulations. Likewise, in solid mechanics, constitutive relations between the stress and strain in a material are required in deformation analysis. Traditional methods for developing and tuning empirical models usually combine physical intuition with simple regression techniques on limited data sets. The rise of high-performance computing has led to a growing availability of high-fidelity simulation data, which open up the possibility of using machine learning algorithms, such as random forests or neural networks, to develop more accurate and general empirical models. A key question when using data-driven algorithms to develop these models is how domain knowledge should be incorporated into the machine learning process. This paper will specifically address physical systems that possess symmetry or invariance properties. Two different methods for teaching a machine learning model an invariance property are compared. In the first , a basis of invariant inputs is constructed, and the machine learning model is trained upon this basis, thereby embedding the invariance into the model. In the second method, the algorithm is trained on multiple transformations of the raw input data until the model learns invariance to that transformation. Results are discussed for two case studies: one in turbulence modeling and one in crystal elasticity. It is shown that in both cases embedding the invariance property into the input features yields higher performance with significantly reduced computational training costs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Gauge-invariant gravitational waves in matter beyond linearized gravity

Modeling the propagation of gravitational waves (GWs) in media other than vacuum is complicated by the gauge freedom of linearized gravity in that, once nonlinearities are taken into consideration, gauge artifacts can cause spurious acceleration of the matter. To eliminate these artifacts, we propose how to keep the theory of dispersive GWs gauge-invariant beyond the linear approximation and, in particular, obtain an unambiguous gauge-invariant expression for the energy–momentum of a GW in a dispersive medium. Using analytic tools from plasma physics, we propose an exactly gauge-invariant 'quasilinear' theory, in which GWs are governed by linear equations and also affect the background metric on scales large compared to their wavelength. As a corollary, the gauge-invariant geometrical optics of linear dispersive GWs in a general background is formulated. As an example, we show how the well-known properties of vacuum GWs are naturally and concisely yielded by our theory in a manifestly gauge-invariant form. We also show how the gauge invariance can be maintained within a given accuracy to an arbitrary order in the GW amplitude. These results are intended to form a physically meaningful framework for studying dispersive GWs in matter.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Nonlocal discrete continuity and invariant currents in locally symmetric effective Schrödinger arrays

We develop a formalism relating nonlocal current continuity to spatial symmetries of subparts in discrete Schrödinger systems. Breaking of such local symmetries hereby generates sources or sinks for the associated nonlocal currents. The framework is applied to locally inversion-(time-) and translation-(time-) symmetric one-dimensional photonic waveguide arrays with Hermitian or non-Hermitian effective tight-binding Hamiltonians. For stationary states the nonlocal currents become translationally invariant within symmetric domains, exposing different types of local symmetry. They are further employed to derive a mapping between wave amplitudes of symmetry-related sites, generalizing also the global Bloch and parity mapping to local symmetry in discrete systems. In scattering setups, perfectly transmitting states are characterized by aligned invariant currents in attached symmetry domains, whose vanishing signifies a correspondingly symmetric density. For periodically driven arrays, the invariance of the nonlocal currents is retained on period average for quasi-energy eigenstates. The proposed theory of symmetry-induced continuity and local invariants may contribute to the understanding of wave structure and response in systems with localized spatial order. - Highlights: • Nonlocal current continuity related to subsystem symmetries in discrete Schrödinger arrays. • Application to 1D (non-) Hermitian bound and scattering tight-binding setups. • Local inversion/translation symmetries described by invariant nonlocal currents. • Generalized parity/Bloch mapping between local-symmetry-related sites via currents. • Time-averaged invariant currents of Floquet states in periodically driven arrays.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Effective rationality for local unitary invariants of mixed states of two qubits

Abstract We calculate the field of rational local unitary invariants for mixed states of two qubits, by employing methods from algebraic geometry. We prove that this field is rational (i.e. purely transcendental), and that it is generated by nine algebraically independent polynomial invariants. We do so by constructing a relative section, in the sense of invariant theory, whose Weyl group is a finite abelian group. From this construction, we are able to give explicit expressions for the generating invariants in terms of the Bloch matrix representation of mixed states of two qubits. We also prove similar rationality results for the local unitary invariants of symmetrically mixed states of two qubits. We also provide a sketch of how to generalize our results to the case of an arbitrary number of qubits. Our results apply to both complex-valued and real-valued invariants.

Physics↗
DOE OSTI2019

Galilean invariance restoration on the lattice

We consider the breaking of Galilean invariance due to different lattice cutoff effects in moving frames and a nonlocal smearing parameter, which is used in the construction of the nuclear lattice interaction. The dispersion relation and neutron-proton scattering phase shifts are used to investigate the Galilean invariance breaking effects and ways to restore it. For S-wave channels, 1 S 0 and 3 S 1 , we present the neutron-proton scattering phase shifts in moving frames calculated using both Lüscher's formula and the spherical wall method, as well as the dispersion relation. For the P and D waves, we present the neutron-proton scattering phase shifts in moving frames calculated using the spherical wall method. Furthermore, we find that the Galilean invariance breaking effects stemming from the lattice artifacts partially cancel those caused by the nonlocal smearing parameter. Due to this cancellation, the Galilean invariance breaking effect is small, and the Galilean invariance can be restored by introducing Galilean invariance restoration operators.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Invariant Features for Accurate Predictions of Quantum Chemical UV-vis Spectra of Organic Molecules

Including invariance of global properties of a phys-ical system as an intrinsic feature in graph neural networks (GNNs) enhances the model's robustness and generalizability and reduces the amount of training data required to obtain a desired accuracy for predictions of these properties. Existing open source GNN libraries construct invariant features only for specific GNN architectures. This precludes the generalization of invariant features to arbitrary message passing neural network (MPNN) layers which, in turn, precludes the use of these libraries for new, user-specified predictive tasks. To address this limitation, we implement invariant MPNNs into the flexible and scalable HydraGNN architecture. HydraGNN enables a seamless switch between various MPNNs in a unified layer sequence and allows for a fair comparison between the predictive performance of different MPNNs. We trained this enhanced HydraGNN archi-tecture on the ultraviolet-visible (UV-vis) spectrum of GDB-9 molecules, a feature that describes the molecule's electronic exci-tation modes, computed with time-dependent density functional tight binding (TD-DFTB) and available open source through the GDB-9-Ex dataset. We assess the robustness (i.e., accuracy and generalizability) of the predictions obtained using different invariant MPNNs with respect to different values of the full width at half maximum (FWHM) for the Gaussian smearing of the theoretical peaks. Our numerical results show that incorporating invariance in the HydraGNN architecture significantly enhances both accuracy and generalizability in predicting UV-vis spectra of organic molecules.

Baker, Justin↗
DOE OSTI2018

Construction and applications of the manifestly gauge invariant expressions of the solutions of the cosmological perturbation theory

After giving how to construct the gauge invariant perturbation variable in an arbitrarily high order and in the arbitrary background spacetime, we consider the manifestly gauge invariant theory of the cosmological perturbations in the long wavelength limit with the spatially flat homogeneous isotropic universe being the background spacetime. In the previous paper, the physical laws, such as the evolution equations, the constraint equations and the junction conditions become manifestly gauge invariant, by writing them in terms of only the single time background/scalar like objects defined by our previous paper. In the present paper, by extending our definition of the background/scalar like objects from the single time case to the many time case and by writing the solution of the physical law in the form where many time background/scalar like objects are vanishing, the solutions become the manifestly gauge invariant. We derive the formula changing the bases of the many time background/scalar like objects by which we can change the time slices for many times appearing in the solution including the initial time and the final time. We use this formula to our treatment of the evolution of the several slow rolling scalar fields using the τ function introduced by our previous paper. In the manifestly gauge invariant manner, we discuss the solution of the many step reheating, that is, the reheating with the arbitrarily many energy transfer steps. Using the energy density ρ as the evolution parameter, we discuss how well the junction model in which the energy transfers from the oscillatory scalar field fluid to the radiation fluid are described by the metric junctions approximates the reheating process described by the differential equations with the decay terms. By using the useful parametrization of the many step reheating, we manifestly prove that in the many step reheating system where any initial perturbation of each component does not become extremely large compared with the initial perturbations of the other components, compared with the effects of the prominent fluctuation generation processes the nearest to the present time the effects of all the fluctuations generated by the previous fluctuation generation processes become negligibly small. Therefore it can be concluded that in order to know the first/second order Bardeen parameters at the present time it is sufficient to calculate only the effects of the fluctuation of the scalar field fluid which becomes energetically dominant lastly (the curvaton mechanism) and the fluctuation of the decay parameter by which this scalar field fluid decays into the radiation (the modulated reheating mechanism).

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Gauge invariants of linearized gravity with a general background metric

In linearized gravity with distributed matter, the background metric has no generic symmetries, and decomposition of the metric perturbation into global normal modes is generally impractical. This complicates the identification of the gauge-invariant part of the perturbation, which is a concern, for example, in the theory of dispersive gravitational waves (GWs) whose energy–momentum must be gauge-invariant. Here, we propose how to identify the gauge-invariant part of the metric perturbation and the six independent gauge invariants per se for an arbitrary background metric. For the Minkowski background, the operator that projects the metric perturbation on the invariant subspace is proportional to the well-known dispersion operator of linear GWs in vacuum. For a general background, this operator is expressed in terms of the Green’s operator of the vacuum wave equation. Further, if the background is smooth, it can be found asymptotically using the inverse scale of the background metric as a small parameter.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

Uniqueness of the gauge invariant action for cosmological perturbations

In second order perturbation theory different definitions are known of gauge invariant perturbations in single field inflationary models. Consequently the corresponding gauge invariant cubic actions do not have the same form. Here we show that the cubic action for one choice of gauge invariant variables is unique in the following sense: the action for any other, non-linearly related variable can be brought to the same bulk action, plus additional boundary terms. These boundary terms correspond to the choice of hypersurface and generate extra, disconnected contributions to the bispectrum. We also discuss uniqueness of the action with respect to conformal frames. When expressed in terms of the gauge invariant curvature perturbation on uniform field hypersurfaces the action for cosmological perturbations has a unique form, independent of the original Einstein or Jordan frame. Crucial is that the gauge invariant comoving curvature perturbation is frame independent, which makes it extremely helpful in showing the quantum equivalence of the two frames, and therefore in calculating quantum effects in nonminimally coupled theories such as Higgs inflation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Generating Einstein gravity, cosmological constant and Higgs mass from restricted Weyl invariance

It has previously been pointed out that dimensionless actions in four-dimensional curved spacetime possess a symmetry which goes beyond scale invariance but is smaller than full Weyl invariance. This symmetry was dubbed restricted Weyl invariance. We show that starting with a restricted Weyl invariant action that includes a Higgs sector with no explicit mass, one can generate the Einstein–Hilbert action with cosmological constant and a Higgs mass. Furthermore, the model contains an extra massless scalar field which couples to the Higgs field (and gravity). If the coupling of this extra scalar field to the Higgs field is negligibly small, this fixes the coefficient of the nonminimal coupling RΦ 2 between the Higgs field and gravity. Besides the Higgs sector, all the other fields of the Standard Model can be incorporated into the original restricted Weyl invariant action.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

An alternative to the Λcdm model: the case of scale invariance

The hypothesis is made that, at large scales where general relativity may be applied, empty space is scale invariant. This establishes a relation between the cosmological constant and the scale factor λ of the scale-invariant framework. This relation brings major simplifications in the scale-invariant equations for cosmology, which contain a new term, depending on the derivative of the scale factor, that opposes gravity and produces an accelerated expansion. The displacements due to the acceleration term make a high contribution Ω{sub λ} to the energy density of the universe, satisfying an equation of the form Ω{sub m}+Ω{sub k}+Ω{sub λ}=1. The models do not demand the existence of unknown particles. There is a family of flat models with different density parameters Ω{sub m}<1. Numerical integrations of the cosmological equations for different values of the curvature and density parameter k and Ω{sub m} are performed. The presence of even tiny amounts of matter in the universe tends to kill scale invariance. The point is that for Ω{sub m}=0.3 the effect is not yet completely killed. Models with non-zero density start explosively with a braking phase followed by a continuously accelerating expansion. Several observational properties are examined, in particular the distances, the m–z diagram, and the Ω{sub m} versus Ω{sub λ} plot. Comparisons with observations are also performed for the Hubble constant H{sub 0} versus Ω{sub m}, for the expansion history in the plot H(z)/(z+1) versus redshift z, and for the transition redshift from braking to acceleration. These first dynamical tests are satisfied by scale-invariant models, which thus deserve further study.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Extending the thermodynamic form factor bootstrap program: multiple particle-hole excitations, crossing symmetry, and reparameterization invariance

In this study, we further the thermodynamic bootstrap program which involves a set of recently developed ideas used to determine thermodynamic form factors of local operators in integrable quantum field theories. These form factors are essential building blocks for dynamic correlation functions at finite temperatures or non-equilibrium stationary states. In this work we extend this program in three ways. Firstly, we demonstrate that the conjectured annihilation pole axiom is valid in the low energy particle-hole excitations. Secondly, we introduce a crossing relation, which establishes a connection between form factors with different excitation content. Typically, the crossing relation is a consequence of Lorentz invariance, but due to the finite energy density of the considered states, Lorentz invariance is broken. Nonetheless a crossing relation involving excitations with both particles and holes can established using the finite volume representation of the thermodynamic form factors. Finally, we demonstrate that the thermodynamic form factors satisfy a reparameterization invariance, an invariance which encompasses crossing. Reparameterization invariance exploits the fact that the details of the representation of the thermodynamic state are unimportant. In the course of developing these results, we demonstrate the internal consistency of the thermodynamic form factor bootstrap program in a number of ways. Finally, we provide explicit computations of form factors of conserved charges and densities with crossed excitations and show our results can be used to infer information about thermodynamic form factors in the Lieb-Liniger model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Shape invariant potentials in higher dimensions

In this paper we investigate the shape invariance property of a potential in one dimension. We show that a simple ansatz allows us to reconstruct all the known shape invariant potentials in one dimension. This ansatz can be easily extended to arrive at a large class of new shape invariant potentials in arbitrary dimensions. A reformulation of the shape invariance property and possible generalizations are proposed. These may lead to an important extension of the shape invariance property to Hamiltonians that are related to standard potential problems via space time transformations, which are found useful in path integral formulation of quantum mechanics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

General formulas for adiabatic invariants in nearly periodic Hamiltonian systems

While it is well known that every nearly periodic Hamiltonian system possesses an adiabatic invariant, extant methods for computing terms in the adiabatic invariant series are inefficient. The most popular method involves the heavy intermediate calculation of a non-unique near-identity coordinate transformation, even though the adiabatic invariant itself is a uniquely defined scalar. Here, a less well-known method, developed by S. Omohundro, avoids calculating intermediate sequences of coordinate transformations but is also inefficient as it involves its own sequence of complex intermediate calculations. In order to improve the efficiency of future calculations of adiabatic invariants, we derive generally applicable, readily computable formulas for the first several terms in the adiabatic invariant series. To demonstrate the utility of these formulas, we apply them to charged-particle dynamics in a strong magnetic field and magnetic field-line dynamics when the field lines are nearly closed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Permutationally Invariant Networks for Enhanced Sampling (PINES): Discovery of Multimolecular and Solvent-Inclusive Collective Variables

The typically rugged nature of molecular free energy landscapes can frustrate efficient sampling of the thermodynamically relevant phase space due to the presence of high free energy barriers. Enhanced sampling techniques can improve phase space exploration by accelerating sampling along particular collective variables (CVs). A number of techniques exist for data-driven discovery of CVs parameterizing the important large scale motions of the system. A challenge to CV discovery is learning CVs invariant to symmetries of the molecular system, frequently rigid translation, rigid rotation, and permutational relabeling of identical particles. Of these, permutational invariance has proved a persistent challenge in frustrating the data-driven discovery of multi-molecular CVs in systems of self-assembling particles and solvent-inclusive CVs for solvated systems. In this work, we integrate Permutation Invariant Vector (PIV) featurizations with autoencoding neural networks to learn nonlinear CVs invariant to translation, rotation, and permutation, and perform interleaved rounds of CV discovery and enhanced sampling to iteratively expand sampling of configurational phase space and obtain converged CVs and free energy landscapes. Here, we demonstrate the Permutationally Invariant Network for Enhanced Sampling (PINES) approach in applications to the self-assembly of a 13-atom Argon cluster, association/dissociation of a NaCl ion pair in water, and hydrophobic collapse of a C 45 H 92 n-pentatetracontane polymer chain. We make the approach freely available as a new module within the PLUMED2 enhanced sampling libraries.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗