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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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At least 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

Oscillators: Old and new perspectives

We consider some of the well known oscillators in literature which are known to exhibit interesting effects of nonlinearity. We review the Lindstedt-Poincare technique for dealing with with the nonlinear effects and then go on to introduce the relevance of the renormalization group for the oscillator following the pioneering work of Chen et al. It is pointed out that the traditional Lindstedt-Poincare and the renormalization group techniques have operational connections. We use this to find an unexpected mode softening in the double pendulum. This mode softening prompted us to look for chaos in the double pendulum at low energies-energies that are just sufficient to allow the outer pendulum to rotate (the double pendulum is known to be chaotic at high energies-energies that are greater than that needed to make both pendulums to rotate). The emergence of the chaos is strongly dependent on initial conditions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2011

Quantum entanglement and quantum phase transition in the XY model with staggered Dzyaloshinskii-Moriya interaction

We study the quantum entanglement and quantum phase transition (QPT) of the anisotropic spin-1/2 XY model with staggered Dzyaloshinskii-Moriya (DM) interaction by means of the quantum renormalization group method. The scaling of coupling constants and the critical points of the system are obtained. It is found that when the number of renormalization group iterations tends to infinity, the system exhibit a QPT between the spin-fluid and Neel phases which correspond with two saturated values of the concurrence for a given value of the strength of DM interaction. The DM interaction can enhance the entanglement and influence the QPT of the system. To gain further insight, the first derivative of the entanglement exhibit a nonanalytic behavior at the critical point and it directly associates with the divergence of the correlation length. This shows that the correlation length exponent is closely related to the critical exponent, i.e., the scaling behaviors of the system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Constraining inflationary dark matter in the luminogenesis model

Using renormalization-group flow and cosmological constraints on inflation models, we exploit a unique connection between cosmological inflation and the dynamical mass of dark matter particles in the luminogenesis model, a unification model with the gauge group SU(3){sub C}×SU(6)×U(1){sub Y}, which breaks to the Standard Model with an extra gauge group for dark matter when the inflaton rolls into the true vacuum. In this model, inflaton decay gives rise to dark matter, which in turn decays to luminous matter in the right proportion that agrees with cosmological data. Some attractive features of this model include self-interacting dark matter, which may resolve the problems of dwarf galaxy structures and dark matter cusps at the centers of galaxies.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Nonperturbative running of the tensor operator for N f = 3 QCD from the chirally rotated Schrödinger functional

We study the renormalization group (RG) running of the nonsinglet tensor operator, for N f = 3 QCD with Wilson fermions in a mixed action setup, with standard Schrödinger functional (SF) boundary conditions for sea quarks and chirally rotated Schrödinger functional ( χ SF ) boundary conditions for valence quarks. Based on a recursive finite-size scaling technique we compute nonperturbatively the tensor step-scaling function for an energy range between a hadronic scale and an electroweak scale, above which perturbation theory may be safely applied. Our result is expressed as the RG-running factor T RGI / [ T ( μ had ) ] R , where the numerator is the scale independent (renormalization group invariant—RGI) tensor operator and the denominator is its renormalized counterpart at a hadronic scale μ had = 233 ( 8 ) MeV in a given scheme. We determine the step-scaling function in four distinct renormalization schemes. We also compute the renormalization parameters of these schemes at μ had which, combined with the RG-running factor, gives the scheme-independent quantity Z T RGI ( g 0 2 ) in four schemes and for a range of bare gauge couplings in which large volume hadronic matrix element simulations are performed by the CLS consortium in N f = 2 + 1 QCD. All four results are compatible and also agree with a recent determination based on a unitary setup for Wilson quarks with Schrödinger functional boundary conditions [arXiv:2309.04314]. This provides a strong universality test. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2022

Many-body localization transition with correlated disorder

We address the critical properties of the many-body localization (MBL) phase transition in one-dimensional systems subject to spatially correlated disorder. Rather than starting from a microscopic model, we analyze the transition within a strong-randomness renormalization group (RG) framework. We argue that anticorrelations in the disorder are generally irrelevant at the MBL transition. Furthermore, assuming the MBL transition is described by the recently developed renormalization-group scheme, we argue that even positively correlated disorder leaves the critical theory unchanged, although it modifies certain properties of the many-body localized phase.

1-dimensional systems↗
DOE OSTI2014

En route to Background Independence: Broken split-symmetry, and how to restore it with bi-metric average actions

The most momentous requirement a quantum theory of gravity must satisfy is Background Independence, necessitating in particular an ab initio derivation of the arena all non-gravitational physics takes place in, namely spacetime. Using the background field technique, this requirement translates into the condition of an unbroken split-symmetry connecting the (quantized) metric fluctuations to the (classical) background metric. If the regularization scheme used violates split-symmetry during the quantization process it is mandatory to restore it in the end at the level of observable physics. In this paper we present a detailed investigation of split-symmetry breaking and restoration within the Effective Average Action (EAA) approach to Quantum Einstein Gravity (QEG) with a special emphasis on the Asymptotic Safety conjecture. In particular we demonstrate for the first time in a non-trivial setting that the two key requirements of Background Independence and Asymptotic Safety can be satisfied simultaneously. Carefully disentangling fluctuation and background fields, we employ a ‘bi-metric’ ansatz for the EAA and project the flow generated by its functional renormalization group equation on a truncated theory space spanned by two separate Einstein–Hilbert actions for the dynamical and the background metric, respectively. A new powerful method is used to derive the corresponding renormalization group (RG) equations for the Newton- and cosmological constant, both in the dynamical and the background sector. We classify and analyze their solutions in detail, determine their fixed point structure, and identify an attractor mechanism which turns out instrumental in the split-symmetry restoration. We show that there exists a subset of RG trajectories which are both asymptotically safe and split-symmetry restoring: In the ultraviolet they emanate from a non-Gaussian fixed point, and in the infrared they loose all symmetry violating contributions inflicted on them by the non-invariant functional RG equation. As an application, we compute the scale dependent spectral dimension which governs the fractal properties of the effective QEG spacetimes at the bi-metric level. Earlier tests of the Asymptotic Safety conjecture almost exclusively employed ‘single-metric truncations’ which are blind towards the difference between quantum and background fields. We explore in detail under which conditions they can be reliable, and we discuss how the single-metric based picture of Asymptotic Safety needs to be revised in the light of the new results. We shall conclude that the next generation of truncations for quantitatively precise predictions (of critical exponents, for instance) is bound to be of the bi-metric type. - Highlights: • The Asymptotic Safety scenario in quantum gravity is explored. • A bi-metric generalization of the Einstein–Hilbert truncation is investigated. • We find that Background Independence can coexist with Asymptotic Safety. • RG trajectories restoring (background-quantum) split-symmetry are constructed. • The degree of validity of single-metric truncations is critically assessed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2010

Non-perturbative renormalization of quark mass in N-f=2+1 QCD with the Schrodinger functional scheme

We present an evaluation of the quark mass renormalization factor for N{sub f} = 2 + 1 QCD. The Schroedinger functional scheme is employed as the intermediate scheme to carry out non-perturbative running from the low energy region, where renormalization of bare mass is performed on the lattice, to deep in the high energy perturbative region, where the conversion to the renormalization group invariant mass or the {ovr MS} scheme is safely carried out. For numerical simulations we adopted the Iwasaki gauge action and nonperturbatively improved Wilson fermion action with the clover term. Seven renormalization scales are used to cover from low to high energy regions and three lattice spacings to take the continuum limit at each scale. The regularization independent step scaling function of the quark mass for the N{sub f} = 2 + 1 QCD is obtained in the continuum limit. Renormalization factors for the pseudo scalar density and the axial vector current are also evaluated for the same action and the bare couplings as two recent large scale N{sub f} = 2 + 1 simulations; previous work of the CP-PACS/JLQCD collaboration, which covered the up-down quark mass range heavier than m{sub {pi}} {approx} 500 MeV and that of PACS-CS collaboration for much lighter quark masses down to m{sub {pi}} = 155MeV. The quark mass renormalization factor is used to renormalize bare PCAC masses in these simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1992

Analysis of an RNG based turbulence model for separated flows

It is shown in this paper that the original version of the renormalization group K-epsilon model substantially underpredicts the reattachment point in the backstep problem - a deficiency that is traced to the modeling of the production of dissipation term. However, with recent improvements in the renormalization group K-epsilon model proposed by Yakhot et al. (1986) improved results for the backstep problem are obtained. These results are not that sensitive to the details of the near wall treatment.

Speziale, C. G.↗
NASA NTRS1987

Infrared properties of an anisotropically stirred fluid

A renormalization group is developed for the Navier-Stokes equations driven by an anisotropically correlated random stirring force. The stirring force generates homogeneous turbulence with a preferred direction. The force correlation is the sum of a small anisotropic perturbation and an isotropic correlation chosen, so that the fixed point of renormalization group has a k exp -5/3 energy spectrum. Fixed points for the anisotropic correlation are found near this isotropic fixed point. Two types of anisotropy are analyzed. when the additional stirring is in the plane perpendicular to the preferred direction, the renormalized viscosity is increased. When it is aligned with the preferred direction, the viscosity is decreased. A possible connection with the inverse energy cascade of two-dimensional turbulence is discussed.

Rubinstein, Robert↗
DOE OSTI2022

QCD analysis of Δ S = 0 hadronic parity violation

We present a QCD analysis of the effective weak Hamiltonian at hadronic energy scales for strangeness-nonchanging (ΔS = 0) hadronic processes. Performing a leading-order renormalization group analysis in QCD from the W to the O(2 GeV) energy scale, we derive the pertinent effective Hamiltonian for hadronic parity violation, including the effects of both neutral and charged weak currents. We compute the complete renormalization group evolution of all isosectors and the evolution through heavy-flavor thresholds for the first time. We show that the additional four-quark operators that enter below the W mass scale from QCD operator mixing effects form a closed set, and they result in a 12 x 12 anomalous dimension matrix. Computing the resulting effective Hamiltonian and comparing to earlier results, we affirm the importance of operator mixing effects and find, as an example, that the parity-violating pion-nucleon coupling constant, using the factorization Ansatz and an assessment of the pertinent quark charge of the nucleon in lattice QCD at the 2 GeV scale, is in better agreement with recent experiments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2011

The mass spectra, hierarchy and cosmology of B-L MSSM heterotic compactifications

The matter spectrum of the MSSM, including three right-handed neutrino supermultiplets and one pair of Higgs-Higgs conjugate superfields, can be obtained by compactifying the E₈ x E₈ heterotic string and M-theory on Calabi-Yau manifolds with specific SU(4) vector bundles. These theories have the standard model gauge group augmented by an additional gauged U(1) B-L . Their minimal content requires that the B-L gauge symmetry be spontaneously broken by a vacuum expectation value of at least one right-handed neutrino. In previous papers, we presented the results of a quasi-analytic renormalization group analysis showing that B-L gauge symmetry is indeed radiatively broken with an appropriate B-L/electroweak hierarchy. In this paper, we extend these results by 1) enlarging the initial parameter space and 2) explicitly calculating all renormalization group equations numerically. The regions of the initial parameter space leading to realistic vacua are presented and the B-L/electroweak hierarchy computed over these regimes. At representative points, the mass spectrum for all particles and Higgs fields is calculated and shown to be consistent with present experimental bounds. Some fundamental phenomenological signatures of a non-zero right-handed neutrino expectation value are discussed, particularly the cosmology and proton lifetime arising from induced lepton and baryon number violating interactions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2011

The Principle of Maximum Conformality

A key problem in making precise perturbative QCD predictions is the uncertainty in determining the renormalization scale of the running coupling {alpha}{sub s}({mu}{sup 2}). It is common practice to guess a physical scale {mu} = Q which is of order of a typical momentum transfer Q in the process, and then vary the scale over a range Q/2 and 2Q. This procedure is clearly problematic since the resulting fixed-order pQCD prediction will depend on the renormalization scheme, and it can even predict negative QCD cross sections at next-to-leading-order. Other heuristic methods to set the renormalization scale, such as the 'principle of minimal sensitivity', give unphysical results for jet physics, sum physics into the running coupling not associated with renormalization, and violate the transitivity property of the renormalization group. Such scale-setting methods also give incorrect results when applied to Abelian QED. Note that the factorization scale in QCD is introduced to match nonperturbative and perturbative aspects of the parton distributions in hadrons; it is present even in conformal theory and thus is a completely separate issue from renormalization scale setting. The PMC provides a consistent method for determining the renormalization scale in pQCD. The PMC scale-fixed prediction is independent of the choice of renormalization scheme, a key requirement of renormalization group invariance. The results avoid renormalon resummation and agree with QED scale-setting in the Abelian limit. The PMC global scale can be derived efficiently at NLO from basic properties of the PQCD cross section. The elimination of the renormalization scheme ambiguity using the PMC will not only increases the precision of QCD tests, but it will also increase the sensitivity of colliders to new physics beyond the Standard Model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Green’s functions on a renormalized lattice: An improved method for the integer quantum Hall transition

Highlights: • Speed up of numerical calculations by exact renormalization group steps. • Practical approach to handle delicate scaling analysis. • Absence of evidence to prefer marginal corrections over power-law corrections. We introduce a performance-optimized method to simulate localization problems on bipartite tight-binding lattices. It combines an exact renormalization group step to reduce the sparseness of the original problem with the recursive Green’s function method. We apply this framework to investigate the critical behavior of the integer quantum Hall transition of a tight-binding Hamiltonian defined on a simple square lattice. In addition, we employ an improved scaling analysis that includes two irrelevant exponents to characterize the shift of the critical energy as well as the corrections to the dimensionless Lyapunov exponent. We compare our findings with the results of a conventional implementation of the recursive Green’s function method, and we put them into broader perspective in view of recent development in this field.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Canonical Drude Weight for Non-integrable Quantum Spin Chains

The Drude weight is a central quantity for the transport properties of quantum spin chains. The canonical definition of Drude weight is directly related to Kubo formula of conductivity. However, the difficulty in the evaluation of such expression has led to several alternative formulations, accessible to different methods. In particular, the Euclidean, or imaginary-time, Drude weight can be studied via rigorous renormalization group. As a result, in the past years several universality results have been proven for such quantity at zero temperature; remarkably, the proofs work for both integrable and non-integrable quantum spin chains. Here we establish the equivalence of Euclidean and canonical Drude weights at zero temperature. Our proof is based on rigorous renormalization group methods, Ward identities, and complex analytic ideas.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Higher derivative terms, toroidal compactification, and Weyl anomalies in six-dimensional (2, 0) theories

We systematically analyze the effective action on the moduli space of (2,0) superconformal field theories in six dimensions, as well as their toroidal compactification to maximally supersymmetric Yang-Mills theories in five and four dimensions. We present a streamlined approach to non-renormalization theorems that constrain this effective action. The first several orders in its derivative expansion are determined by a one-loop calculation in five-dimensional Yang-Mills theory. This fixes the leading higher-derivative operators that describe the renormalization group flow into theories residing at singular points on the moduli space of the compactified (2,0) theories. This understanding allows us to compute the a-type Weyl anomaly for all (2,0) superconformal theories. We show that it decreases along every renormalization group flow that preserves (2,0) supersymmetry, thereby establishing the a-theorem for this class of theories. Along the way, we encounter various field-theoretic arguments for the ADE classification of (2,0) theories.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2016

A multiscale asymptotic analysis of time evolution equations on the complex plane

Using an appropriate norm on the space of entire functions, we extend to the complex plane the renormalization group method as developed by Bricmont et al. The method is based upon a multiscale approach that allows for a detailed description of the long time asymptotics of solutions to initial value problems. The time evolution equation considered here arises in the study of iterations of the block spin renormalization group transformation for the hierarchical N-vector model. We show that, for initial conditions belonging to a certain Fréchet space of entire functions of exponential type, the asymptotics is universal in the sense that it is dictated by the fixed point of a certain operator acting on the space of initial conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

The geometric β-function in curved space-time under operator regularization

In this paper, I compare the generators of the renormalization group flow, or the geometric β-functions, for dimensional regularization and operator regularization. I then extend the analysis to show that the geometric β-function for a scalar field theory on a closed compact Riemannian manifold is defined on the entire manifold. I then extend the analysis to find the generator of the renormalization group flow to conformally coupled scalar-field theories on the same manifolds. The geometric β-function in this case is not defined.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Block2 : A comprehensive open source framework to develop and apply state-of-the-art DMRG algorithms in electronic structure and beyond

block2 is an open source framework to implement and perform density matrix renormalization group and matrix product state algorithms. Out-of-the-box it supports the eigenstate, time-dependent, response, and finite-temperature algorithms. In addition, it carries special optimizations for ab initio electronic structure Hamiltonians and implements many quantum chemistry extensions to the density matrix renormalization group, such as dynamical correlation theories. The code is designed with an emphasis on flexibility, extensibility, and efficiency and to support integration with external numerical packages. Here, we explain the design principles and currently supported features and present numerical examples in a range of applications.

Chemistry↗