Search NASA⌕ Search

SEARCH · Search NASA

Results for “generalized perturbation theory”

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 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Gauge invariance and Ward identities in nonlinear response theory

We present a formal analysis of nonlinear response functions in terms of correlation functions in real- and imaginary-time domains. In particular, we show that causal nonlinear response functions, expressed in terms of nested commutators in real time, can be obtained from the analytic continuation of time-ordered response functions, which are more easily amenable to diagrammatic calculation. This generalizes the well-known result of linear response theory. We then use gauge invariance arguments to derive exact relations between second-order response functions in density and current channels. These identities, which are non-perturbative in the strength of inter-particle interactions, allow us to establish exact connections between nonlinear optics calculations done in different electromagnetic gauges.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

The five-point bootstrap

We study five-point correlation functions of scalar operators in d-dimensional conformal field theories. We develop a new approach to computing the five-point conformal blocks for exchanged primary operators of arbitrary spin by introducing a generalization of radial coordinates, using an appropriate ansatz, and perturbatively solving two quadratic Casimir differential equations. We then study five-point correlators 〈σσϵσσ〉 in the critical 3d Ising model. We truncate the operator product expansions (OPEs) in the correlator by including a finite number of primary operators with conformal dimension below a cutoff ∆ ⩽ ∆ cutoff . We then compute several OPE coefficients involving ϵ and two spinning operators by demanding that the truncated correlator approximately satisfies the crossing relation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Microemulsions in the driven Widom-Rowlinson lattice gas

An investigation of the two-dimensional Widom-Rowlinson lattice gas under an applied drive uncovered a remarkable nonequilibrium steady state in which uniform stripes (reminiscent of an equilibrium lamellar phase) form perpendicular to the drive direction [R. Dickman and R. K. P. Zia, Phys. Rev. E 97, 062126 (2018)]. Here we study this model at low particle densities in two and three dimensions, where we find a disordered phase with a characteristic length scale (a “microemulsion”) along the drive direction. Further we develop a continuum theory of this disordered phase to derive a coarse-grained field-theoretic action for the nonequilibrium dynamics. The action has the form of two coupled driven diffusive systems with different characteristic velocities, generated by an interplay between the particle repulsion and the drive. We then show how fluctuation corrections in the field theory may generate the characteristic features of the microemulsion phase, including a peak in the static structure factor corresponding to the characteristic length scale. This work lays the foundation for understanding the stripe phenomenon more generally.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Spatiotemporal spread of perturbations in power-law models at low temperatures: Exact results for classical out-of-time-order correlators

Here, we present exact results for the classical version of the out-of-time-order commutator (OTOC) for a family of power-law models consisting of N particles in one dimension and confined by an external harmonic potential. These particles are interacting via power-law interaction of the form ∝ $Σ_{i,j=(i≠j)}^{N}$ |x i -x j | -k for every k>1 where x i is the position of the i th particle. We present numerical results for the OTOC for finite N at low temperatures and short enough times so that the system is well approximated by the linearized dynamics around the many-body ground state. In the large-N limit, we compute the ground-state dispersion relation in the absence of external harmonic potential exactly and use it to arrive at analytical results for OTOC. We find excellent agreement between our analytical results and the numerics. We further obtain analytical results in the limit where only linear and leading nonlinear (in momentum) terms in the dispersion relation are included. The resulting OTOC is in agreement with numerics in the vicinity of the edge of the “light cone.” We find remarkably distinct features in OTOC below and above k=3 in terms of going from non-Airy behavior (1 < k < 3) to an Airy universality class (k>3). We present certain additional rich features for the case k=2 that stem from the underlying integrability of the Calogero-Moser model. We present a field theory approach that also assists in understanding certain aspects of OTOC such as the sound speed. Our findings are a step forward towards a more general understanding of the spatiotemporal spread of perturbations in long-range interacting systems.

1-dimensional systems↗
DOE OSTI2023

New tools for dissecting the general $\mathrm{2HDM}$

Two Higgs doublet models (2HDM) provide the low energy effective theory (EFT) description in many well motivated extensions of the Standard Model. It is therefore relevant to study their properties, as well as the theoretical constraints on these models. In this article we concentrate on three relevant requirements for the validity of the 2HDM framework, namely the perturbative unitarity bounds, the bounded from below constraints, and the vacuum stability constraints. In this study, we concentrate on the most general renormalizable version of the 2HDM — without imposing any parity symmetry, which may be violated in many UV extensions. We derive novel analytical expressions that generalize those previously obtained in more restrictive scenarios to the most general case. We also discuss the phenomenological implications of these bounds, focusing on CP violation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Normalization of ZZ instanton amplitudes in minimal string theory

We use insights from string field theory to analyze and cure the divergences in the cylinder diagram in minimal string theory with both boundaries lying on a ZZ brane. We focus on theories with worldsheet matter consisting of the (2, p) minimal model plus Liouville theory, with total central charge 26, together with the usual bc-ghosts. The string field theory procedure gives a finite, purely imaginary normalization constant for non-perturbative effects in minimal string theory, or doubly non-perturbative effects in JT gravity. We find precise agreement with the prediction from the dual double-scaled one-matrix integral. We also make a few remarks about the extension of this result to the more general (p', p) minimal string.

2D gravity↗
DOE OSTI2024

Pion gravitational form factors in the QCD instanton vacuum. II

We revisit the hard QCD contributions to the pion gravitational form factors, in terms of the twist-2,3 pion distribution amplitudes (DAs), including novel semihard contributions from the instantons. The pion DAs are evaluated in the QCD instanton vacuum and then properly evolved to higher resolution. The results are compared to our recent results from the QCD instanton vacuum, as well as Bethe-Salpeter calculations and recent lattice data. The interpolated hard and soft contributions to the pion D form factor are used to derive the (gravitational) pressure and shear within the pion, with a clear delineation of their range.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1974

Subsonic and supersonic indicial aerodynamics and aerodynamic transfer function for complex configurations

A general theory for indicial-potential-compressible aerodynamics around complex configurations is presented. The motion is assumed to consist of constant subsonic or supersonic speed (steady state) and small perturbations around the steady state. Using the finite-element method to discretize the space problem, a set of differential-difference equations in time relating the potential to its normal derivative on the surface of the body was obtained. The aerodynamics transfer function was derived by using standard method of operational calculus.

Morino, L.↗
DOE OSTI2022

The SAGEX review on scattering amplitudes Chapter 15: The multi-Regge limit

We review the Regge and multi-Regge limit of scattering amplitudes in gauge theory, focusing on QCD and its maximally supersymmetric cousin, planar $\mathcal{N}=4$ super-Yang–Mills theory. We identify the large logarithms that are developed in these limits, and the progress that has been made in resumming them, towards next-to-next-to-leading logarithms for BFKL evolution in QCD, as well as all-orders proposals in planar $\mathcal{N}=4$ super-Yang–Mills theory and the perturbative checks of those proposals. We also cover the application of single-valued multiple polylogarithms to this important kinematical limit of particle scattering.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Simulating Effective QED on Quantum Computers

In recent years simulations of chemistry and condensed materials has emerged as one of the preeminent applications of quantum computing, offering an exponential speedup for the solution of the electronic structure for certain strongly correlated electronic systems. To date, most treatments have ignored the question of whether relativistic effects, which are described most generally by quantum electrodynamics (QED), can also be simulated on a quantum computer in polynomial time. Here we show that effective QED, which is equivalent to QED to second order in perturbation theory, can be simulated in polynomial time under reasonable assumptions while properly treating all four components of the wavefunction of the fermionic field. In particular, we provide a detailed analysis of such simulations in position and momentum basis using Trotter-Suzuki formulas. We find that the number of T -gates needed to perform such simulations on a 3 D lattice of n s sites scales at worst as O ( n s 3 / &#x03F5; ) 1 + o ( 1 ) in the thermodynamic limit for position basis simulations and O ( n s 4 + 2 / 3 / &#x03F5; ) 1 + o ( 1 ) in momentum basis. We also find that qubitization scales slightly better with a worst case scaling of O &#x007E; ( n s 2 + 2 / 3 / &#x03F5; ) for lattice eQED and complications in the prepare circuit leads to a slightly worse scaling in momentum basis of O &#x007E; ( n s 5 + 2 / 3 / &#x03F5; ) . We further provide concrete gate counts for simulating a relativistic version of the uniform electron gas that show challenging problems can be simulated using fewer than 10 13 non-Clifford operations and also provide a detailed discussion of how to prepare multi-reference configuration interaction states in effective QED which can provide a reasonable initial guess for the ground state. Finally, we estimate the planewave cutoffs needed to accurately simulate heavy elements such as gold.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

The connection between nonzero density and spontaneous symmetry breaking for interacting scalars

We consider U(1)-symmetric scalar quantum field theories at zero temperature. At nonzero charge densities, the ground state of these systems is usually assumed to be a superfluid phase, in which the global symmetry is spontaneously broken along with Lorentz boosts and time translations. We show that, in d > 2 spacetime dimensions, this expectation is always realized at one loop for arbitrary non-derivative interactions, confirming that the physically distinct phenomena of nonzero charge density and spontaneous symmetry breaking occur simultaneously in these systems. We quantify this result by deriving universal scaling relations for the symmetry breaking scale as a function of the charge density, at low and high density. Moreover, we show that the critical value of μ above which a nonzero density develops coincides with the pole mass in the unbroken, Poincaré invariant vacuum of the theory. The same conclusions hold non-perturbatively for an O(N) theory with quartic interactions in d = 3 and 4, at leading order in the 1/N expansion. We derive these results by computing analytically the zero-temperature, finite-μ one-loop effective potential, paying special attention to subtle points related to the iε terms. We check our results against the one-loop low-energy effective action for the superfluid phonons in λΦ 4 theory in d = 4 previously derived by Joyce and ourselves, which we further generalize to arbitrary potential interactions and arbitrary dimensions. As a byproduct, we find analytically the one-loop scaling dimension of the lightest charge-n operator for the λΦ 6 conformal superfluid in d = 3, at leading order in 1/n, reproducing a numerical result of Badel et al. For a λΦ 4 superfluid in d = 4, we also reproduce the Lee-Huang-Yang relation and compute relativistic corrections to it. Finally, we discuss possible extensions of our results beyond perturbation theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Generalized entropy of gravitational fluctuations

The corrections to holographic entanglement entropy from bulk quantum fields in a classical gravitational background are now well understood. They lead, in particular, to unitary Page curves for evaporating black holes. However, the correct treatment of quantum fluctuations of the metric, including graviton excitations, is a longstanding problem. We provide a gauge-invariant prescription for the generalized entropy of gravitons in anti-de Sitter space in terms of areas and bulk entanglement entropy, generalizing the quantum extremal surface prescription to accommodate fluctuations in the semiclassical spacetime geometry. This task requires a careful treatment of the area operator on the graviton Hilbert space and the definition of a “quantum extremal gauge” in which the extremal surface is unperturbed. It also requires us to determine the correct vacuum modular Hamiltonian for the graviton field, which we fix by requiring that it doesn’t contain a boundary term in extremal gauge. We check our prescription with an explicit computation of the vacuum-subtracted generalized entropy of states containing a graviton in an AdS-Rindler background. Our results exactly match vacuum-subtracted von Neumann entropies for stress-tensor excited states in holographic conformal field theory with d > 2 dimensions. We also use covariant phase space techniques to give a partial proof of our prescription when the entanglement wedge for the background spacetime has a bifurcate Killing horizon. Along the way, we identify a class of perturbative graviton states that have parametrically larger generalized entropy, in the small G N expansion, than any low-energy excitations of an ordinary quantum field.

1/N expansion↗
DOE OSTI2022

Tunable band gaps and optical absorption properties of bent MoS2 nanoribbons

Abstract The large tunability of band gaps and optical absorptions of armchair MoS 2 nanoribbons of different widths under bending is studied using density functional theory and many-body perturbation GW and Bethe–Salpeter equation approaches. We find that there are three critical bending curvatures, and the non-edge and edge band gaps generally show a non-monotonic trend with bending. The non-degenerate edge gap splits show an oscillating feature with ribbon width n , with a period $$\Delta n=3$$ Δ n = 3 , due to quantum confinement effects. The complex strain patterns on the bent nanoribbons control the varying features of band structures and band gaps that result in varying exciton formations and optical properties. The binding energy and the spin singlet–triplet split of the exciton forming the lowest absorption peak generally decrease with bending curvatures. The large tunability of optical properties of bent MoS 2 nanoribbons is promising and will find applications in tunable optoelectronic nanodevices.

36 MATERIALS SCIENCE↗
NASA NTRS1983

Celestial mechanics with geometric algebra

Geometric algebra is introduced as a general tool for Celestial Mechanics. A general method for handling finite rotations and rotational kinematics is presented. The constants of Kepler motion are derived and manipulated in a new way. A new spinor formulation of perturbation theory is developed.

Hestenes, D.↗
DOE OSTI2020

Shell-model study of calcium isotopes toward their drip line

Here, we report in this paper a study in terms of the nuclear shell model about the location of the calcium isotopes drip line. The starting point is considering the realistic two-body potential derived by Entem and Machleidt within chiral perturbation theory at next-to-next-to-next-to-leading order (N 3 LO), as well as a chiral three-body force at next-to-next-to-leading order (N 2 LO) whose structure and low-energy constants are consistent with the two-body potential. Then we construct the effective single-particle energies and residual interaction needed to diagonalize the shell-model Hamiltonian. The calculated two-neutron separation energies agree nicely with experiment until 56 Ca, which is the heaviest isotope whose mass has been measured, and do not show any sign of two-neutron emission until 70 Ca . We discuss the role of the choice of the model space in determining the neutron drip line, and also the dependence of the results on the parameters of the shell-model Hamiltonian.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Polarizabilities of neutral atoms and atomic ions with a noble gas electron configuration

Atomic polarizabilities play an important role in the development of force fields for molecular simulations, as well as for the development of qualitative concepts of atomic and molecular behavior. Coupled cluster theory at the coupled cluster singles doubles triples level with very large correlation-consistent basis sets with extended diffuse functions has been used to predict the polarizabilities of the atomic neutrals, mono-cations and mono-anions with a noble gas configuration. Additional corrections for scalar relativistic and spin–orbit effects were also included for the electron configurations of Kr, Xe, and Rn. The results are in excellent agreement with experiment or with other high level calculations where available. The current results for most of these species represent the best available values for the polarizabilities. The results show that the polarizability of H - is very difficult to calculate without extremely diffuse functions. The polarizability of H - is the largest value, 34.05 Å 3 , calculated for all species in the current study. The polarizabilities of the remaining halogen anions are also the best available values. The polarizabilities of the halogen anions (excluding F - ) and H - have a linear correlation with the electron affinity of the neutral atom. Spin– orbit effects, even for closed shell species, cannot be ignored for quantitative accuracy, and the inclusion of spin–orbit effects for Fr + , Rn, and At - increases the polarizability by 4%, 6%, and 15%, respectively.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

A theory for colors of strongly correlated electronic systems

Many strongly correlated transition metal insulators are colored, even though they have band gaps much larger than the highest energy photons from the visible light. An adequate explanation for the color requires a theoretical approach able to compute subgap excitons in periodic crystals, reliably and without free parameters—a formidable challenge. The literature often fails to disentangle two important factors: what makes excitons form and what makes them optically bright. We pick two archetypal cases as examples: NiO with green color and MnF 2 with pink color, and employ two kinds of ab initio many body Green’s function theories; the first, a perturbative theory based on low-order extensions of the $GW$ approximation, is able to explain the color in NiO, while the same theory is unable to explain why MnF 2 is pink. We show its color originates from higher order spin-flip transitions that modify the optical response, which is contained in dynamical mean-field theory (DMFT). We show that symmetry lowering mechanisms may determine how ‘bright’ these excitons are, but they are not fundamental to their existence.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗