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Results for “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.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Gauge invariance in the theoretical description of time-resolved angle-resolved pump/probe photoemission spectroscopy

Nonequilibrium calculations in the presence of an electric field are usually performed in a gauge, and need to be transformed to reveal the gauge-invariant observables. In this work, we discuss the issue of gauge invariance in the context of time-resolved angle-resolved pump/probe photoemission. If the probe is applied while the pump is still on, one must ensure that the calculations of the observed photocurrent are gauge invariant. We also discuss the requirement of the photoemission signal to be positive and the relationship of this constraint to gauge invariance. Here, we end by discussing some technical details related to the perturbative derivation of the photoemission spectra, which involve processes where the pump pulse photoemits electrons due to nonequilibrium effects.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Diffeomorphism invariance and quantum mechanical paradoxes

Paradoxes in gravitational physics, such as grandfather paradoxes with closed timelike curves or the AMPS paradox, are often constructed in a weak gravity regime but upon further examination engender strong gravitational responses such as unstable Cauchy horizons or firewalls. In contrast, some proposed paradoxes in nonrelativistic quantum mechanics ignore gravity completely. Such nonrelativistic proposed paradoxes are often not gauge invariant — they use local operators which should be forbidden by diffeomorphism-invariant quantum gravity. Ignoring this complication is reasonable if there is a consistent weak gravity regime where the paradox can be formulated with gauge invariant observables up to some order in Newton’s constant. Here, we show that this approach remains inconsistent due to a lack of analyticity of the necessary solutions. As a consequence, there is no consistent weak gravity, diffeomorphism invariant embedding of such paradoxes—just as in other gravitational paradoxes they generate a strong gravitational response and are in principle sensitive to quantum gravity.

quantum gravity↗
DOE OSTI2016

Observation of the spectrally invariant properties of clouds in cloudy-to-clear transition zones during the MAGIC field campaign

We use the spectrally invariant method to study the variability of cloud optical thickness τ and droplet effective radius reff in transition zones (between the cloudy and clear sky columns) observed from Solar Spectral Flux Radiometer (SSFR) and Shortwave Array Spectroradiometer-Zenith (SASZe) during the Marine ARM GPCI Investigation of Clouds (MAGIC) field campaign. The measurements from the SSFR and the SASZe are different, however inter-instrument differences of self-normalized measurements (divided by their own spectra at a fixed time) are small. The spectrally invariant method approximates the spectra in the cloud transition zone as a linear combination of definitely clear and cloudy spectra, where the coefficients, slope and intercept, character-ize the spectrally invariant properties of the transition zone. Simulation results from the SBDART (Santa Barbara DISORT Atmospheric Radiative Transfer) model demonstrate that (1) the slope of the visible band is positively correlated with the cloud optical thickness τ while the intercept of the near-infrared band has high negative cor-relation with the cloud drop effective radius reff even without the exact knowledge of τ; (2) the above relations hold for all Solar Zenith Angle (SZA) and for cloud-contaminated skies. In observations using redundant measure-ments from SSFR and SASZe, we find that during cloudy-to-clear transitions, (a) the slopes of the visible band de-crease, and (b) the intercepts of the near-infrared band remain almost constant near cloud edges. The findings in simulations and observations suggest that, while the optical thickness decreases during the cloudy-to-clear transition, the cloud drop effective radius does not change when cloud edges are approached. These results sup-port the hypothesis that inhomogeneous mixing dominates near cloud edges in the studied cases.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2014

GL(3,C) invariance of type B 3-fold supersymmetric systems

Type B 3-fold supersymmetry is a necessary and sufficient condition for a quantum Hamiltonian to admit three linearly independent local solutions in closed form. We show that any such a system is invariant under GL(3,C) homogeneous linear transformations. In particular, we prove explicitly that the parameter space is transformed as an adjoint representation of it and that every coefficient of the characteristic polynomial appeared in 3-fold superalgebra is algebraic invariants. In the type A case, it includes as a subgroup the GL(2,C) projective transformation studied in the literature. We argue that any N-fold supersymmetric system has a GL(N,C) invariance for an arbitrary integral N.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

Translationally invariant conservation laws of local Lindblad equations

We study the conditions under which one can conserve local translationally invariant operators by local translationally invariant Lindblad equations in one-dimensional rings of spin-1/2 particles. We prove that for any 1-local operator (e.g., particle density) there exist Lindblad dissipators that conserve that operator, while on the other hand we prove that among 2-local operators (e.g., energy density) only trivial ones of the Ising type can be conserved, while all the other cannot be conserved, neither locally nor globally, by any 2- or 3-local translationally invariant Lindblad equation. Our statements hold for rings of any finite length larger than some minimal length determined by the locality of Lindblad equation. These results show in particular that conservation of energy density in interacting systems is fundamentally more difficult than conservation of 1-local quantities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Galilei invariant technique for quantum system description

Problems with quantum systems models, violating Galilei invariance are examined. The method for arbitrary non-relativistic quantum system Galilei invariant wave function construction, applying a modified basis where center-of-mass excitations have been removed before Hamiltonian matrix diagonalization, is developed. For identical fermion system, the Galilei invariant wave function can be obtained while applying conventional antisymmetrization methods of wave functions, dependent on single particle spatial variables.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Numeric invariants from multidimensional persistence

Topological data analysis is the study of data using techniques from algebraic topology. Often, one begins with a finite set of points representing data and a “filter” function which assigns a real number to each datum. Using both the data and the filter function, one can construct a filtered complex for further analysis. For example, applying the homology functor to the filtered complex produces an algebraic object known as a “one-dimensional persistence module”, which can often be interpreted as a finite set of intervals representing various geometric features in the data. If one runs the above process incorporating multiple filter functions simultaneously, one instead obtains a multidimensional persistence module. Unfortunately, these are much more difficult to interpret. In this article, we analyze the space of multidimensional persistence modules from the perspective of algebraic geometry. First we build a moduli space of a certain subclass of easily analyzed multidimensional persistence modules, which we construct specifically to capture much of the information which can be gained by using multidimensional persistence instead of one-dimensional persistence. Fruthermore, we argue that the global sections of this space provide interesting numeric invariants when evaluated against our subclass of multidimensional persistence modules. Finally, we extend these global sections to the space of all multidimensional persistence modules and discuss how the resulting numeric invariants might be used to study data. This paper extends the results of Adcock et al. (Homol Homotopy Appl 18(1), 381–402, 2016) by constructing numeric invariants from the computation of a multidimensional persistence module as given by Carlsson et al. (J Comput Geom 1(1), 72–100, 2010).

58 GEOSCIENCES↗
DOE OSTI2015

Some cosmological consequences of Weyl invariance

We examine some Weyl invariant cosmological models in the framework of generalized dilaton gravity, in which the action is made of a set of N conformally coupled scalar fields. It will be shown that when the FRW ansatz for the spacetime metric is assumed, the Ward identity for conformal invariance guarantees that the gravitational equations hold whenever the scalar fields EM do so. It follows that any scale factor can solve the theory provided a non-trivial profile for a dilaton field. In particular, accelerated expansion is a natural solution to the full set of equations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

Effect of VSR invariant Chern-Simons Lagrangian on photon polarization

We propose a generalization of the Chern-Simons (CS) Lagrangian which is invariant under the SIM(2) transformations but not under the full Lorentz group. The generalized lagrangian is also invariant under a SIM(2) gauge transformation. We study the effect of such a term on radiation propagating over cosmological distances. We find that the dominant effect of this term is to produce circular polarization as radiation propagates through space. We use the circular polarization data from distant radio sources in order to impose a limit on this term.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

Disformal invariance of cosmological perturbations in a generalized class of Horndeski theories

It is known that Horndeski theories can be transformed to a sub-class of Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories under the disformal transformation of the metric g{sub μν}→Ω{sup 2}(ϕ)g{sub μν}+Γ(ϕ,X)∇{sub μ}ϕ∇{sub ν}ϕ, where Ω is a function of a scalar field ϕ and Γ is another function depending on both ϕ and X=g{sup μν}∇{sub μ}ϕ∇{sub ν}ϕ. We show that, with the choice of unitary gauge, both curvature and tensor perturbations on the flat isotropic cosmological background are generally invariant under the disformal transformation. By means of the effective field theories encompassing Horndeski and GLPV theories, we obtain the second-order actions of scalar/tensor perturbations and present the relations for physical quantities between the two frames. The invariance of the inflationary power spectra under the disformal transformation is explicitly proved up to next-to-leading order in slow-roll. In particular, we identify the existence of the Einstein frame in which the tensor power spectrum is of the same form as that in General Relativity and derive the condition under which the spectrum of gravitational waves in GLPV theories is red-tilted.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Extension of the Concept of Invariance and Statistically Weakly Invariant Sets of Controllable Systems

We continue the study of statistically invariant and statistically weakly invariant sets with respect to controllable systems and differential inclusions launched by Prof. E. L. Tonkov. We examine properties of such statistical characteristics as the lower freq{sub *}(𝜑) and upper freq{sup *}(𝜑) relative frequencies of hitting a solution 𝜑(t) of a differential inclusion in a prescribed set. We obtain estimates and conditions of coincidence of these characteristics for functions whose difference tends to zero at infinity. We also present conditions of statistically weak invariance of a given set of a relatively controllable system.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Groups of homeomorphisms of the line. Criteria for the existence of invariant and projectively invariant measures in terms of the commutator subgroup

Existence criteria for invariant and projectively invariant measures are obtained for a group G of homeomorphisms of the line. These criteria are formulated in terms of the commutator subgroup [G,G]. For the special (but very important) case of groups of homeomorphisms of the line containing a freely acting element we obtain a criterion for the existence of a projectively invariant measure in the form of the absence of a special subgroup with two generators in which one of the generating elements is a freely acting element. Bibliography: 20 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Bi-invariant functions on the group of transformations leaving a measure quasi-invariant

Let Gms be the group of transformations of a Lebesgue space leaving the measure quasi-invariant. Let Ams be a subgroup of it consisting of transformations preserving the measure. We describe canonical forms of double cosets of Gms by the subgroup Ams and show that all continuous Ams-bi-invariant functions on Gms are functionals of the distribution of a Radon-Nikodym derivative. Bibliography: 14 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Galilean invariant resummation schemes of cosmological perturbations

Many of the methods proposed so far to go beyond Standard Perturbation Theory break invariance under time-dependent boosts (denoted here as extended Galilean Invariance, or GI). This gives rise to spurious large scale effects which spoil the small scale predictions of these approximation schemes. By using consistency relations we derive fully non-perturbative constraints that GI imposes on correlation functions. We then introduce a method to quantify the amount of GI breaking of a given scheme, and to correct it by properly tailored counterterms. Finally, we formulate resummation schemes which are manifestly GI, discuss their general features, and implement them in the so called Time-Flow, or TRG, equations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Invariant-mass and fractional-energy dependence of inclusive production of dihadrons in e + e - annihilation at s = 10.58 GeV

The inclusive cross sections for dihadrons of charged pions and kaons ( e + e - → h h X ) in electron-positron annihilation are observed and reported on. They are obtained as a function of the total fractional energy and invariant mass for any di-hadron combination in the same hemisphere as defined by the thrust event-shape variable and its axis. Since same-hemisphere dihadrons can be assumed to originate predominantly from the same initial parton, di-hadron fragmentation functions are probed. Moreove, these di-hadron fragmentation functions are needed as an unpolarized baseline in order to quantitatively understand related spin-dependent measurements in other processes and to apply them to the extraction of quark transversity distribution functions in the nucleon. The di-hadron cross sections are obtained from a 655 fb - 1 data sample collected at or near the Υ ( 4 S ) resonance with the Belle detector at the KEKB asymmetric-energy e + e - collider.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

A permutationally invariant full-dimensional ab initio potential energy surface for the abstraction and exchange channels of the H + CH{sub 4} system

We report a permutationally invariant global potential energy surface (PES) for the H + CH{sub 4} system based on ∼63 000 data points calculated at a high ab initio level (UCCSD(T)-F12a/AVTZ) using the recently proposed permutation invariant polynomial-neural network method. The small fitting error (5.1 meV) indicates a faithful representation of the ab initio points over a large configuration space. The rate coefficients calculated on the PES using tunneling corrected transition-state theory and quasi-classical trajectory are found to agree well with the available experimental and previous quantum dynamical results. The calculated total reaction probabilities (J{sub tot} = 0) including the abstraction and exchange channels using the new potential by a reduced dimensional quantum dynamic method are essentially the same as those on the Xu-Chen-Zhang PES [Chin. J. Chem. Phys. 27, 373 (2014)].

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Pair Invariant Mass to Isolate Background in the Search for the Chiral Magnetic Effect in Au+Au Collisions at √sNN = 200 GeV

Quark interactions with topological gluon configurations can induce local chirality imbalance and parity violation in quantum chromodynamics, which can lead to the chiral magnetic effect (CME)-an electric charge separation along the strong magnetic field in relativistic heavy-ion collisions. The CME-sensitive azimuthal correlator observable (Delta gamma) is contaminated by background arising, in part, from resonance decays coupled with elliptic anisotropy (v(2)). We report here differential measurements of the correlator as a function of the pair invariant mass (m(inv)) in 20-50% centrality Au + Au collisions at root s(NN) = 200 GeV by the STAR experiment at the BNL Relativistic Heavy Ion Collider. Strong resonance background contributions to Delta gamma. are observed. At large m(inv) where this background is significantly reduced, the Delta gamma. value is found to be significantly smaller. An event-shape-engineering technique is deployed to determine the v(2) background shape as a function of m(inv). We extract a v(2)-independent and m(inv)-averaged signal Delta gamma(sig) = (0.03 +/- 0.06 +/- 0.08) x 10(-4), or (2 +/- 4 +/- 5)% of the inclusive Delta gamma (m(inv) > 0.4 GeV/c(2)) = (1.58 +/- 0.02 +/- 0.02) x 10(-4), within pion p(T) = 0.2-0.8 GeV/c and averaged over pseudorapidity ranges of -1 < eta < -0.05 and 0.05 < eta < 1. This represents an upper limit of 0.23 x 10(-4), or 15% of the inclusive result, at 95% confidence level for the m(inv)-integrated CME contribution.

Adam, J.↗