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Sample records for additive mass renormalization

  1. Renormalization of the neutrino mass matrix

    NASA Astrophysics Data System (ADS)

    Chiu, S. H.; Kuo, T. K.

    2016-09-01

    In terms of a rephasing invariant parametrization, the set of renormalization group equations (RGE) for Dirac neutrino parameters can be cast in a compact and simple form. These equations exhibit manifest symmetry under flavor permutations. We obtain both exact and approximate RGE invariants, in addition to some approximate solutions and examples of numerical solutions.

  2. Mass renormalization in cavity QED

    SciTech Connect

    Matloob, Reza

    2011-01-15

    We show that the presence of a background medium and a boundary surface or surfaces in cavity QED produces no change in the energy shift of a free charged particle due to its coupling to the fluctuating electromagnetic field of the vacuum. This clarifies that the electromagnetic and the observed mass of the charged particle are not affected by the modification of the field of the vacuum. The calculations are nonrelativistic and restricted to the dipole approximation but are otherwise based on the general requirements of causality.

  3. Infrared Renormalization-Group Flow for Heavy-Quark Masses

    SciTech Connect

    Hoang, Andre H.; Jain, Ambar; Stewart, Iain W.; Scimemi, Ignazio

    2008-10-10

    A short-distance heavy-quark mass depends on two parameters: the renormalization scale {mu} and a scale R controlling the absorption of infrared fluctuations. The radius for perturbative corrections that build up the mass beyond its pointlike definition in the pole scheme is {approx}1/R. Treating R as a variable gives a renormalization-group equation. R evolution improves the stability of conversion between short-distance mass schemes, allowing us to avoid large logs and the renormalon. R evolution can also be used to study IR renormalons without using bubble chains, yielding a convergent sum rule for the coefficient of the O({lambda}{sub QCD}) renormalon ambiguity of the pole mass.

  4. Renormalization of a two-loop neutrino mass model

    SciTech Connect

    Babu, K. S.; Julio, J.

    2014-01-01

    We analyze the renormalization group structure of a radiative neutrino mass model consisting of a singly charged and a doubly charged scalar fields. Small Majorana neutrino masses are generated by the exchange of these scalars via two-loop diagrams. We derive boundedness conditions for the Higgs potential and show how they can be satisfied to energies up to the Planck scale. Combining boundedness and perturbativity constraints with neutrino oscillation phenomenology, new limits on the masses and couplings of the charged scalars are derived. These in turn lead to lower limits on the branching ratios for certain lepton flavor violating (LFV) processes such as μ→eγ, μ→3e and μ – e conversion in nuclei. Improved LFV measurements could test the model, especially in the case of inverted neutrino mass hierarchy where these are more prominent.

  5. Renormalization of a two-loop neutrino mass model

    NASA Astrophysics Data System (ADS)

    Babu, K. S.; Julio, J.

    2014-06-01

    We analyze the renormalization group structure of a radiative neutrino mass model consisting of a singly charged and a doubly charged scalar fields. Small Majorana neutrino masses are generated by the exchange of these scalars via two-loop diagrams. We derive boundedness conditions for the Higgs potential and show how they can be satisfied to energies up to the Planck scale. Combining boundedness and perturbativity constraints with neutrino oscillation phenomenology, new limits on the masses and couplings of the charged scalars are derived. These in turn lead to lower limits on the branching ratios for certain lepton flavor violating (LFV) processes such as μ→eγ, μ→3e and μ - e conversion in nuclei. Improved LFV measurements could test the model, especially in the case of inverted neutrino mass hierarchy where these are more prominent.

  6. Fermion Mass Renormalization Using Time-dependent Relativistic Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Kutnink, Timothy; Santrach, Amelia; Hocket, Sarah; Barcus, Scott; Petridis, Athanasios

    2015-10-01

    The time-dependent electromagnetically self-coupled Dirac equation is solved numerically by means of the staggered-leap-frog algorithm with refcecting boundary conditions. The stability region of the method versus the interaction strength and the spatial-grid size over time-step ratio is established. The expectation values of several dynamic operators are then evaluated as functions of time. These include the fermion and electromagnetic energies and the fermion dynamic mass, as the self-interacting spinors are no longer mass-eigenfunctions. There is a characteristic, non-exponential, oscillatory dependence leading to asymptotic constants of these expectation values. In the case of the fermion mass this amounts to renormalization. The dependence of the expectation values on the spatial-grid size is evaluated in detail. Statistical regularization is proposed to remove the grid-size dependence.

  7. Complex-mass shell renormalization of the higher-derivative electrodynamics

    NASA Astrophysics Data System (ADS)

    Turcati, Rodrigo; Neves, Mario Junior

    2016-08-01

    We consider a higher-derivative extension of QED modified by the addition of a gauge-invariant dimension-6 kinetic operator in the U(1) gauge sector. The Feynman diagrams at one-loop level are then computed. The modification in the spin-1 sector leads the electron self-energy and vertex corrections diagrams finite in the ultraviolet regime. Indeed, no regularization prescription is used to calculate these diagrams because the modified propagator always occurs coupled to conserved currents. Moreover, besides the usual massless pole in the spin-1 sector, there is the emergence of a massive one, which becomes complex when computing the radiative corrections at one-loop order. This imaginary part defines the finite decay width of the massive mode. To check consistency, we also derive the decay length using the electron-positron elastic scattering and show that both results are equivalent. Because the presence of this unstable mode, the standard renormalization procedures cannot be used and is necessary adopt an appropriate framework to perform the perturbative renormalization. For this purpose, we apply the complex-mass shell scheme (CMS) to renormalize the aforementioned model. As an application of the formalism developed, we estimate a quantum bound on the massive parameter using the measurement of the electron anomalous magnetic moment and compute the Uehling potential. At the end, the renormalization group is analyzed.

  8. Renormalization and additional degrees of freedom within the chiral effective theory for spin-1 resonances

    SciTech Connect

    Kampf, Karol; Novotny, Jiri; Trnka, Jaroslav

    2010-06-01

    We study in detail various aspects of the renormalization of the spin-1 resonance propagator in the effective field theory framework. First, we briefly review the formalisms for the description of spin-1 resonances in the path integral formulation with the stress on the issue of propagating degrees of freedom. Then we calculate the one-loop 1{sup --} meson self-energy within the resonance chiral theory in the chiral limit using different methods for the description of spin-1 particles, namely, the Proca field, antisymmetric tensor field, and the first-order formalisms. We discuss in detail technical aspects of the renormalization procedure which are inherent to the power-counting nonrenormalizable theory and give a formal prescription for the organization of both the counterterms and one-particle irreducible graphs. We also construct the corresponding propagators and investigate their properties. We show that the additional poles corresponding to the additional one-particle states are generated by loop corrections, some of which are negative norm ghosts or tachyons. We count the number of such additional poles and briefly discuss their physical meaning.

  9. Renormalization of quark propagators from twisted-mass lattice QCD at N{sub f}=2

    SciTech Connect

    Blossier, B.; Boucaud, Ph.; Pene, O.; Petrov, K.; Brinet, M.; Liu, Z.; Morenas, V.

    2011-04-01

    We present results concerning the nonperturbative evaluation of the renormalization constant for the quark field, Z{sub q}, from lattice simulations with twisted-mass quarks and three values of the lattice spacing. We use the regularization-invariant momentum-subtraction (RI'-MOM) scheme. Z{sub q} has very large lattice spacing artefacts; it is considered here as a test bed to elaborate accurate methods which will be used for other renormalization constants. We recall and develop the nonperturbative correction methods and propose tools to test the quality of the correction. These tests are also applied to the perturbative correction method. We check that the lattice-spacing artefacts indeed scale as a{sup 2}p{sup 2}. We then study the running of Z{sub q} with particular attention to the nonperturbative effects, presumably dominated by the dimension-two gluon condensate in Landau gauge. We show indeed that this effect is present, and not small. We check its scaling in physical units, confirming that it is a continuum effect. It gives a {approx}4% contribution at 2 GeV. Different variants are used in order to test the reliability of our result and estimate the systematic uncertainties. Finally, combining all our results and using the known Wilson coefficient of , we find g{sup 2}({mu}{sup 2}){sub {mu}}{sup 2}{sub CM}=2.01(11)({sub -0.73}{sup +0.61})GeV{sup 2} at {mu}=10 GeV, the local operator A{sup 2} being renormalized in the MS scheme. This last result is in fair agreement within uncertainties with the value independently extracted from the strong coupling constant. We convert the nonperturbative part of Z{sub q} from the regularization-invariant momentum-subtraction (RI'-MOM) scheme to MS. Our result for the quark field renormalization constant in the MS scheme is Z{sub q} {sup MS} {sup pert}((2 GeV){sup 2},g{sub bare}{sup 2})=0.750(3)(7)-0.313(20)(g{sub bare}{sup 2}-1.5) for the perturbative contribution and Z{sub q

  10. Renormalization scheme dependence with renormalization group summation

    NASA Astrophysics Data System (ADS)

    McKeon, D. G. C.

    2015-08-01

    We consider all perturbative radiative corrections to the total e+e- annihilation cross section Re+e- showing how the renormalization group (RG) equation associated with the radiatively induced mass scale μ can be used to sum the logarithmic contributions in two ways. First of all, one can sum leading-log, next-to-leading-log, etc., contributions to Re+e- using in turn the one-loop, two-loop, etc., contributions to the RG function β . A second summation shows how all logarithmic corrections to Re+e- can be expressed entirely in terms of the log-independent contributions when one employs the full β -function. Next, using Stevenson's characterization of any choice of renormalization scheme by the use of the contributions to the β -function arising beyond two-loop order, we examine the RG scheme dependence in Re+e- when using the second way of summing logarithms. The renormalization scheme invariants that arise are then related to the renormalization scheme invariants found by Stevenson. We next consider two choices of the renormalization scheme, one which can be used to express Re+e- solely in terms of two powers of a running coupling, and the second which can be used to express Re+e- as an infinite series in the two-loop running coupling (i.e., a Lambert W -function). In both cases, Re+e- is expressed solely in terms of renormalization scheme invariant parameters that are to be computed by a perturbative evaluation of Re+e-. We then establish how in general the coupling constant arising in one renormalization scheme can be expressed as a power series of the coupling arising in any other scheme. We then establish how, by using a different renormalization mass scale at each order of perturbation theory, all renormalization scheme dependence can be absorbed into these mass scales when one uses the second way of summing logarithmic corrections to Re+e-. We then employ the approach to renormalization scheme dependency that we have applied to Re+e- to a RG summed

  11. Optically induced effective mass renormalization: the case of graphite image potential states

    NASA Astrophysics Data System (ADS)

    Montagnese, M.; Pagliara, S.; Galimberti, G.; Dal Conte, S.; Ferrini, G.; van Loosdrecht, P. H. M.; Parmigiani, F.

    2016-10-01

    Many-body interactions with the underlying bulk electrons determine the properties of confined electronic states at the surface of a metal. Using momentum resolved nonlinear photoelectron spectroscopy we show that one can tailor these many-body interactions in graphite, leading to a strong renormalization of the dispersion and linewidth of the image potential state. These observations are interpreted in terms of a basic self-energy model, and may be considered as exemplary for optically induced many-body interactions.

  12. Optically induced effective mass renormalization: the case of graphite image potential states

    PubMed Central

    Montagnese, M.; Pagliara, S.; Galimberti, G.; Dal Conte, S.; Ferrini, G.; van Loosdrecht, P. H. M.; Parmigiani, F.

    2016-01-01

    Many-body interactions with the underlying bulk electrons determine the properties of confined electronic states at the surface of a metal. Using momentum resolved nonlinear photoelectron spectroscopy we show that one can tailor these many-body interactions in graphite, leading to a strong renormalization of the dispersion and linewidth of the image potential state. These observations are interpreted in terms of a basic self-energy model, and may be considered as exemplary for optically induced many-body interactions. PMID:27739489

  13. Renormalization in general theories with intergeneration mixing

    NASA Astrophysics Data System (ADS)

    Kniehl, Bernd A.; Sirlin, Alberto

    2012-02-01

    We derive general and explicit expressions for the unrenormalized and renormalized dressed propagators of fermions in parity-nonconserving theories with intergeneration mixing. The mass eigenvalues, the corresponding mass counterterms, and the effect of intergeneration mixing on their determination are discussed. Invoking the Aoki-Hioki-Kawabe-Konuma-Muta renormalization conditions and employing a number of very useful relations from matrix algebra, we show explicitly that the renormalized dressed propagators satisfy important physical properties.

  14. Renormalization group in internal space

    SciTech Connect

    Polonyi, J.; Sailer, K.

    2005-01-15

    Renormalization group in the internal space consists of the gradual change of the coupling constants. Functional evolution equations corresponding to the change of the mass or the coupling constant are presented in the framework of a scalar model. The evolution in the mass which yields the functional generalization of the Callan-Symanzik equation for the one-particle irreducible effective action is given in its renormalized, cutoff-independent form. The evolution of the coupling constant generates an evolution equation for the two-particle irreducible effective action.

  15. RENORM predictions of diffraction at LHC confirmed

    SciTech Connect

    Goulianos, Konstantin

    2015-04-10

    The RENORM model predictions of diffractive, total, and total-inelastic cross sections at the LHC are confirmed by recent measurements. The predictions of several other available models are discussed, highlighting their differences from RENORM, mainly arising from the way rapidity gap formation, low- and high-mass diffraction, unitarization, and hadronization are implemented.

  16. Renormalized action improvements

    SciTech Connect

    Zachos, C.

    1984-01-01

    Finite lattice spacing artifacts are suppressed on the renormalized actions. The renormalized action trajectories of SU(N) lattice gauge theories are considered from the standpoint of the Migdal-Kadanoff approximation. The minor renormalized trajectories which involve representations invariant under the center are discussed and quantified. 17 references.

  17. Renormalization flows in complex networks.

    PubMed

    Radicchi, Filippo; Barrat, Alain; Fortunato, Santo; Ramasco, José J

    2009-02-01

    Complex networks have acquired a great popularity in recent years, since the graph representation of many natural, social, and technological systems is often very helpful to characterize and model their phenomenology. Additionally, the mathematical tools of statistical physics have proven to be particularly suitable for studying and understanding complex networks. Nevertheless, an important obstacle to this theoretical approach is still represented by the difficulties to draw parallelisms between network science and more traditional aspects of statistical physics. In this paper, we explore the relation between complex networks and a well known topic of statistical physics: renormalization. A general method to analyze renormalization flows of complex networks is introduced. The method can be applied to study any suitable renormalization transformation. Finite-size scaling can be performed on computer-generated networks in order to classify them in universality classes. We also present applications of the method on real networks.

  18. Simple Approach to Renormalize the Cabibbo-Kobayashi-Maskawa Matrix

    SciTech Connect

    Kniehl, Bernd A.; Sirlin, Alberto

    2006-12-01

    We present an on-shell scheme to renormalize the Cabibbo-Kobayashi-Maskawa (CKM) matrix. It is based on a novel procedure to separate the external-leg mixing corrections into gauge-independent self-mass and gauge-dependent wave function renormalization contributions, and to implement the on-shell renormalization of the former with nondiagonal mass counterterm matrices. Diagonalization of the complete mass matrix leads to an explicit CKM counterterm matrix, which automatically satisfies all the following important properties: it is gauge independent, preserves unitarity, and leads to renormalized amplitudes that are nonsingular in the limit in which any two fermions become mass degenerate.

  19. Renormalized entanglement entropy

    NASA Astrophysics Data System (ADS)

    Taylor, Marika; Woodhead, William

    2016-08-01

    We develop a renormalization method for holographic entanglement entropy based on area renormalization of entangling surfaces. The renormalized entanglement en-tropy is derived for entangling surfaces in asymptotically locally anti-de Sitter spacetimes in general dimensions and for entangling surfaces in four dimensional holographic renor-malization group flows. The renormalized entanglement entropy for disk regions in AdS 4 spacetimes agrees precisely with the holographically renormalized action for AdS 4 with spherical slicing and hence with the F quantity, in accordance with the Casini-Huerta-Myers map. We present a generic class of holographic RG flows associated with deforma-tions by operators of dimension 3 /2 < Δ < 5 /2 for which the F quantity increases along the RG flow, hence violating the strong version of the F theorem. We conclude by explaining how the renormalized entanglement entropy can be derived directly from the renormalized partition function using the replica trick i.e. our renormalization method for the entangle-ment entropy is inherited directly from that of the partition function. We show explicitly how the entanglement entropy counterterms can be derived from the standard holographic renormalization counterterms for asymptotically locally anti-de Sitter spacetimes.

  20. All-order renormalization of the propagator matrix for fermionic systems with flavor mixing.

    PubMed

    Kniehl, Bernd A

    2014-02-21

    We consider a mixed system of Dirac fermions in a general parity-nonconserving theory and renormalize the propagator matrix to all orders in the pole scheme, in which the squares of the renormalized masses are identified with the complex pole positions and the wave-function renormalization (WFR) matrices are adjusted in compliance with the Lehmann-Symanzik-Zimmermann reduction formalism. We present closed analytic all-order expressions and their expansions through two loops for the renormalization constants in terms of the scalar, pseudoscalar, vector, and pseudovector parts of the unrenormalized self-energy matrix, which is computable from the one-particle-irreducible Feynman diagrams of the flavor transitions. We identify residual degrees of freedom in the WFR matrices and propose an additional renormalization condition to exhaust them. We then explain how our results may be generalized to the case of unstable fermions, in which we encounter the phenomenon of WFR bifurcation. In the special case of a solitary unstable fermion, the all-order-renormalized propagator is presented in a particularly compact form. PMID:24579589

  1. Renormalization for insulating states of matter

    NASA Astrophysics Data System (ADS)

    Hong, Seungmin

    In this thesis, we study three cases of insulating states of matter in terms of the renormalization procedure where the conventional renormalization group scheme is not simply applicable. The first subject is the spectral weight structure of hole-doped Mott insulators. As the mixing between two separate Hubbard bands is dynamically generated, additional charge degrees of freedom is required to give a proper description to the relevant low-energy physics. On this account, we first discuss how the low-energy Hubbard band should be partitioned to account for the extra degrees of freedom. Following the exact integration procedure of the upper Hubbard band, we explicitly demonstrate that the conserved charge cannot be exhausted by counting quasiparticles. In addition, we argue that it is the existence of dynamically generated charge degrees of freedom that gives rise to the coexistence of poles and zeroes in the single-particle Green function. In comparison to the Fermi arc structure, which is intrinsic to cuperate phenomenology, we suggest that the suppression of the spectral weight at the back side of the arc is a consequence of composite excitations, arising from dynamical mixing. The second topic we study is the nature of the transition between two insulating states of matter in a weakly disordered bosonic system. In particular, we investigate the instabilities of the Mott-insulating phase within a renormalization group analysis of the replica field theory obtained by a strong-coupling expansion around the atomic limit. To this end, we identify a new order parameter and associated correlation length scale that are capable of capturing the transition from a state with zero compressibility, the Mott insulator, to another insulating state with finite compressibility, the Bose glass. The order parameter is the relative variance of the disorder-induced mass distribution. From its distinctive behavior on each phase, we find that the divergence of the relative variance in

  2. Novel formulations of CKM matrix renormalization

    SciTech Connect

    Kniehl, Bernd A.; Sirlin, Alberto

    2009-12-17

    We review two recently proposed on-shell schemes for the renormalization of the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix in the Standard Model. One first constructs gauge-independent mass counterterm matrices for the up- and down-type quarks complying with the hermiticity of the complete mass matrices. Diagonalization of the latter then leads to explicit expressions for the CKM counterterm matrix, which are gauge independent, preserve unitarity, and lead to renormalized amplitudes that are non-singular in the limit in which any two quarks become mass degenerate. One of the schemes also automatically satisfies flavor democracy.

  3. Lattice simulations with Nf=2 +1 improved Wilson fermions at a fixed strange quark mass

    NASA Astrophysics Data System (ADS)

    Bali, Gunnar S.; Scholz, Enno E.; Simeth, Jakob; Söldner, Wolfgang; RQCD Collaboration

    2016-10-01

    The explicit breaking of chiral symmetry of the Wilson fermion action results in additive quark mass renormalization. Moreover, flavor singlet and nonsinglet scalar currents acquire different renormalization constants with respect to continuum regularization schemes. This complicates keeping the renormalized strange quark mass fixed when varying the light quark mass in simulations with Nf=2 +1 sea quark flavors. Here we present and validate our strategy within the CLS (coordinated lattice simulations) effort to achieve this in simulations with nonperturbatively order-a improved Wilson fermions. We also determine various combinations of renormalization constants and improvement coefficients.

  4. Relating theories via renormalization

    NASA Astrophysics Data System (ADS)

    Kadanoff, Leo P.

    2013-02-01

    The renormalization method is specifically aimed at connecting theories describing physical processes at different length scales and thereby connecting different theories in the physical sciences. The renormalization method used today is the outgrowth of 150 years of scientific study of thermal physics and phase transitions. Different phases of matter show qualitatively different behaviors separated by abrupt phase transitions. These qualitative differences seem to be present in experimentally observed condensed-matter systems. However, the "extended singularity theorem" in statistical mechanics shows that sharp changes can only occur in infinitely large systems. Abrupt changes from one phase to another are signaled by fluctuations that show correlation over infinitely long distances, and are measured by correlation functions that show algebraic decay as well as various kinds of singularities and infinities in thermodynamic derivatives and in measured system parameters. Renormalization methods were first developed in field theory to get around difficulties caused by apparent divergences at both small and large scales. However, no renormalization gives a fully satisfactory formulation of field theory. The renormalization (semi-)group theory of phase transitions was put together by Kenneth G. Wilson in 1971 based upon ideas of scaling and universality developed earlier in the context of phase transitions and of couplings dependent upon spatial scale coming from field theory. Correlations among regions with fluctuations in their order underlie renormalization ideas. Wilson's theory is the first approach to phase transitions to agree with the extended singularity theorem. Some of the history of the study of these correlations and singularities is recounted, along with the history of renormalization and related concepts of scaling and universality. Applications, particularly to condensed-matter physics and particle physics, are summarized. This note is partially a

  5. Multi-scale renormalization

    NASA Astrophysics Data System (ADS)

    Ford, C.; Wiesendanger, C.

    1997-02-01

    The standard MS renormalization prescription is inadequate for dealing with multi-scale problems. To illustrate this we consider the computation of the effective potential in the Higgs-Yukawa model. It is argued that it is natural to employ a two-scale renormalization group. We give a modified version of a two-scale scheme introduced by Einhorn and Jones. In such schemes the beta functions necessarily contain potentially large logarithms of the RG scale ratios. For credible perturbation theory one must implement a large logarithms resummation on the beta functions themselves. We show how the integrability condition for the two RG equations allows one to perform this resummation.

  6. Renormalization of Extended QCD2

    NASA Astrophysics Data System (ADS)

    Fukaya, Hidenori; Yamamura, Ryo

    2015-10-01

    Extended QCD (XQCD), proposed by Kaplan [D. B. Kaplan, arXiv:1306.5818], is an interesting reformulation of QCD with additional bosonic auxiliary fields. While its partition function is kept exactly the same as that of original QCD, XQCD naturally contains properties of low-energy hadronic models. We analyze the renormalization group flow of 2D (X)QCD, which is solvable in the limit of a large number of colors N_c, to understand what kind of roles the auxiliary degrees of freedom play and how the hadronic picture emerges in the low-energy region.

  7. Contractor renormalization group and the Haldane conjecture

    SciTech Connect

    Weinstein, Marvin

    2001-05-01

    The contractor renormalization group formalism (CORE) is a real-space renormalization group method which is the Hamiltonian analogue of the Wilson exact renormalization group equations. In an earlier paper [Phys. Rev. D 61, 034505 (2000)] I showed that the CORE method could be used to map a theory of free quarks and quarks interacting with gluons into a generalized frustrated Heisenberg antiferromagnet (HAF) and proposed using CORE methods to study these theories. Since generalizations of HAF's exhibit all sorts of subtle behavior which, from a continuum point of view, are related to topological properties of the theory, it is important to know that CORE can be used to extract this physics. In this paper I show that despite the folklore which asserts that all real-space renormalization group schemes are necessarily inaccurate, simple CORE computations can give highly accurate results even if one only keeps a small number of states per block and a few terms in the cluster expansion. In addition I argue that even very simple CORE computations give a much better qualitative understanding of the physics than naive renormalization group methods. In particular I show that the simplest CORE computation yields a first-principles understanding of how the famous Haldane conjecture works for the case of the spin-1/2 and spin-1 HAF.

  8. Renormalizing Entanglement Distillation.

    PubMed

    Waeldchen, Stephan; Gertis, Janina; Campbell, Earl T; Eisert, Jens

    2016-01-15

    Entanglement distillation refers to the task of transforming a collection of weakly entangled pairs into fewer highly entangled ones. It is a core ingredient in quantum repeater protocols, which are needed to transmit entanglement over arbitrary distances in order to realize quantum key distribution schemes. Usually, it is assumed that the initial entangled pairs are identically and independently distributed and are uncorrelated with each other, an assumption that might not be reasonable at all in any entanglement generation process involving memory channels. Here, we introduce a framework that captures entanglement distillation in the presence of natural correlations arising from memory channels. Conceptually, we bring together ideas from condensed-matter physics-ideas from renormalization and matrix-product states and operators-with those of local entanglement manipulation, Markov chain mixing, and quantum error correction. We identify meaningful parameter regions for which we prove convergence to maximally entangled states, arising as the fixed points of a matrix-product operator renormalization flow.

  9. Renormalizing Entanglement Distillation

    NASA Astrophysics Data System (ADS)

    Waeldchen, Stephan; Gertis, Janina; Campbell, Earl T.; Eisert, Jens

    2016-01-01

    Entanglement distillation refers to the task of transforming a collection of weakly entangled pairs into fewer highly entangled ones. It is a core ingredient in quantum repeater protocols, which are needed to transmit entanglement over arbitrary distances in order to realize quantum key distribution schemes. Usually, it is assumed that the initial entangled pairs are identically and independently distributed and are uncorrelated with each other, an assumption that might not be reasonable at all in any entanglement generation process involving memory channels. Here, we introduce a framework that captures entanglement distillation in the presence of natural correlations arising from memory channels. Conceptually, we bring together ideas from condensed-matter physics—ideas from renormalization and matrix-product states and operators—with those of local entanglement manipulation, Markov chain mixing, and quantum error correction. We identify meaningful parameter regions for which we prove convergence to maximally entangled states, arising as the fixed points of a matrix-product operator renormalization flow.

  10. Renormalization shielding effect on the Wannier-ridge mode for double-electron continua in partially ionized dense hydrogen plasmas

    NASA Astrophysics Data System (ADS)

    Lee, Myoung-Jae; Jung, Young-Dae

    2016-01-01

    The influence of renormalization shielding on the Wannier threshold law for the double-electron escapes by the electron-impact ionization is investigated in partially ionized dense plasmas. The renormalized electron charge and Wannier exponent are obtained by considering the equation of motion in the Wannier-ridge including the renormalization shielding effect. It is found that the renormalization shielding effect reduces the magnitude of effective electron charge, especially, within the Bohr radius in partially ionized dense plasmas. The maximum position of the renormalized electron charge approaches to the center of the target atom with an increase of the renormalization parameter. In addition, the Wannier exponent increases with an increase of the renormalization parameter. The variations of the renormalized electron charge and Wannier exponent due to the renormalization shielding effect are also discussed.

  11. Nonperturbative renormalization of QED in light-cone quantization

    SciTech Connect

    Hiller, J.R.; Brodsky, S.J.

    1996-08-01

    As a precursor to work on QCD, we study the dressed electron in QED non-perturbatively. The calculational scheme uses an invariant mass cutoff, discretized light cone quantization, a Tamm-Dancoff truncation of the Fock space, and a small photon mass. Nonperturbative renormalization of the coupling and electron mass is developed.

  12. Renormalization on noncommutative torus

    NASA Astrophysics Data System (ADS)

    D'Ascanio, D.; Pisani, P.; Vassilevich, D. V.

    2016-04-01

    We study a self-interacting scalar \\varphi ^4 theory on the d-dimensional noncommutative torus. We determine, for the particular cases d=2 and d=4, the counterterms required by one-loop renormalization. We discuss higher loops in two dimensions and two-loop contributions to the self-energy in four dimensions. Our analysis points toward the absence of any problems related to the ultraviolet/infrared mixing and thus to renormalizability of the theory. However, we find another potentially troubling phenomenon which is a wild behavior of the two-point amplitude as a function of the noncommutativity matrix θ.

  13. Renormalization group functional equations

    SciTech Connect

    Curtright, Thomas L.; Zachos, Cosmas K.

    2011-03-15

    Functional conjugation methods are used to analyze the global structure of various renormalization group trajectories and to gain insight into the interplay between continuous and discrete rescaling. With minimal assumptions, the methods produce continuous flows from step-scaling {sigma} functions and lead to exact functional relations for the local flow {beta} functions, whose solutions may have novel, exotic features, including multiple branches. As a result, fixed points of {sigma} are sometimes not true fixed points under continuous changes in scale and zeroes of {beta} do not necessarily signal fixed points of the flow but instead may only indicate turning points of the trajectories.

  14. Quantum gravity and renormalization

    NASA Astrophysics Data System (ADS)

    Anselmi, Damiano

    2015-01-01

    The properties of quantum gravity are reviewed from the point of view of renormalization. Various attempts to overcome the problem of non-renormalizability are presented, and the reasons why most of them fail for quantum gravity are discussed. Interesting possibilities come from relaxing the locality assumption, which also can inspire the investigation of a largely unexplored sector of quantum field theory. Another possibility is to work with infinitely many independent couplings, and search for physical quantities that only depend on a finite subset of them. In this spirit, it is useful to organize the classical action of quantum gravity, determined by renormalization, in a convenient way. Taking advantage of perturbative local field redefinitions, we write the action as the sum of the Hilbert term, the cosmological term, a peculiar scalar that is important only in higher dimensions, plus invariants constructed with at least three Weyl tensors. We show that the FRLW configurations, and many other locally conformally flat metrics, are exact solutions of the field equations in arbitrary dimensions d>3. If the metric is expanded around such configurations the quadratic part of the action is free of higher-time derivatives. Other well-known metrics, such as those of black holes, are instead affected in nontrivial ways by the classical corrections of quantum origin.

  15. Nonperturbative renormalization of scalar quantum electrodynamics in d=3

    SciTech Connect

    Dimock, J.

    2015-10-15

    For scalar quantum electrodynamics on a three-dimensional toroidal lattice with a fine lattice spacing, we consider the renormalization problem of choosing counter terms depending on the lattice spacing, so that the theory stays finite as the spacing goes to zero. We employ a renormalization group method which analyzes the flow of the mass and the vacuum energy as a problem in discrete dynamical systems. The main result is that counter terms can be chosen so that at the end of the iteration these quantities take preassigned values. No use is made of perturbation theory. The renormalization group transformations are defined with bounded fields, an approximation which can be justified in Balaban’s approach to the renormalization group.

  16. Mixed Meson Mass for Domain-Wall Valence and Staggered Sea Fermions

    SciTech Connect

    Konstantinos Orginos; Andre Walker-Loud

    2007-05-01

    Mixed action lattice calculations allow for an additive lattice spacing dependent mass renormalization of mesons composed of one sea and one valence quark, regardless of the type of fermion discretization methods used in the valence and sea sectors. The value of the mass renormalization depends upon the lattice actions used. This mixed meson mass shift is the most important lattice artifact to determine for mixed action calculations: because it modifies the pion mass, it plays a central role in the low energy dynamics of all hadronic correlation functions. We determine the leading order and next to leading order additive mass renormalization of valence-sea mesons for a mixed lattice action with domain-wall valence fermions and staggered sea fermions. We find that on the asqtad improved coarse MILC lattices, the leading order additive mass renormalization for the mixed mesons is Δ(am)^2 LO = 0.0409(11) which corresponds to a^2 Δ_Mix = (319 MeV)^2± (53 MeV)^2 for a = 0.125 fm. We also find significant next to leading order contributions which reduce the mass renormalization by a significant amount, such that for 0 < am_π ≤ 0.22 the mixed meson mass renormalization is well approximated by Δ(am)^2 = 0.0340 (23) or a^2δ_Mix = (290 MeV)^2 ± (76 MeV)^2. The full next-to-leading order analysis is presented in the text.

  17. Gutzwiller renormalization group

    NASA Astrophysics Data System (ADS)

    Lanatà, Nicola; Yao, Yong-Xin; Deng, Xiaoyu; Wang, Cai-Zhuang; Ho, Kai-Ming; Kotliar, Gabriel

    2016-01-01

    We develop a variational scheme called the "Gutzwiller renormalization group" (GRG), which enables us to calculate the ground state of Anderson impurity models (AIM) with arbitrary numerical precision. Our method exploits the low-entanglement property of the ground state of local Hamiltonians in combination with the framework of the Gutzwiller wave function and indicates that the ground state of the AIM has a very simple structure, which can be represented very accurately in terms of a surprisingly small number of variational parameters. We perform benchmark calculations of the single-band AIM that validate our theory and suggest that the GRG might enable us to study complex systems beyond the reach of the other methods presently available and pave the way to interesting generalizations, e.g., to nonequilibrium transport in nanostructures.

  18. Gutzwiller renormalization group

    DOE PAGES

    Lanatà, Nicola; Yao, Yong -Xin; Deng, Xiaoyu; Wang, Cai -Zhuang; Ho, Kai -Ming; Kotliar, Gabriel

    2016-01-06

    We develop a variational scheme called the “Gutzwiller renormalization group” (GRG), which enables us to calculate the ground state of Anderson impurity models (AIM) with arbitrary numerical precision. Our method exploits the low-entanglement property of the ground state of local Hamiltonians in combination with the framework of the Gutzwiller wave function and indicates that the ground state of the AIM has a very simple structure, which can be represented very accurately in terms of a surprisingly small number of variational parameters. Furthermore, we perform benchmark calculations of the single-band AIM that validate our theory and suggest that the GRG mightmore » enable us to study complex systems beyond the reach of the other methods presently available and pave the way to interesting generalizations, e.g., to nonequilibrium transport in nanostructures.« less

  19. Renormalized Lie perturbation theory

    SciTech Connect

    Rosengaus, E.; Dewar, R.L.

    1981-07-01

    A Lie operator method for constructing action-angle transformations continuously connected to the identity is developed for area preserving mappings. By a simple change of variable from action to angular frequency a perturbation expansion is obtained in which the small denominators have been renormalized. The method is shown to lead to the same series as the Lagrangian perturbation method of Greene and Percival, which converges on KAM surfaces. The method is not superconvergent, but yields simple recursion relations which allow automatic algebraic manipulation techniques to be used to develop the series to high order. It is argued that the operator method can be justified by analytically continuing from the complex angular frequency plane onto the real line. The resulting picture is one where preserved primary KAM surfaces are continuously connected to one another.

  20. Tensor Network Renormalization.

    PubMed

    Evenbly, G; Vidal, G

    2015-10-30

    We introduce a coarse-graining transformation for tensor networks that can be applied to study both the partition function of a classical statistical system and the Euclidean path integral of a quantum many-body system. The scheme is based upon the insertion of optimized unitary and isometric tensors (disentanglers and isometries) into the tensor network and has, as its key feature, the ability to remove short-range entanglement or correlations at each coarse-graining step. Removal of short-range entanglement results in scale invariance being explicitly recovered at criticality. In this way we obtain a proper renormalization group flow (in the space of tensors), one that in particular (i) is computationally sustainable, even for critical systems, and (ii) has the correct structure of fixed points, both at criticality and away from it. We demonstrate the proposed approach in the context of the 2D classical Ising model.

  1. Renormalization Group Tutorial

    NASA Technical Reports Server (NTRS)

    Bell, Thomas L.

    2004-01-01

    Complex physical systems sometimes have statistical behavior characterized by power- law dependence on the parameters of the system and spatial variability with no particular characteristic scale as the parameters approach critical values. The renormalization group (RG) approach was developed in the fields of statistical mechanics and quantum field theory to derive quantitative predictions of such behavior in cases where conventional methods of analysis fail. Techniques based on these ideas have since been extended to treat problems in many different fields, and in particular, the behavior of turbulent fluids. This lecture will describe a relatively simple but nontrivial example of the RG approach applied to the diffusion of photons out of a stellar medium when the photons have wavelengths near that of an emission line of atoms in the medium.

  2. Tensor Network Renormalization Yields the Multiscale Entanglement Renormalization Ansatz.

    PubMed

    Evenbly, G; Vidal, G

    2015-11-13

    We show how to build a multiscale entanglement renormalization ansatz (MERA) representation of the ground state of a many-body Hamiltonian H by applying the recently proposed tensor network renormalization [G. Evenbly and G. Vidal, Phys. Rev. Lett. 115, 180405 (2015)] to the Euclidean time evolution operator e(-βH) for infinite β. This approach bypasses the costly energy minimization of previous MERA algorithms and, when applied to finite inverse temperature β, produces a MERA representation of a thermal Gibbs state. Our construction endows tensor network renormalization with a renormalization group flow in the space of wave functions and Hamiltonians (and not merely in the more abstract space of tensors) and extends the MERA formalism to classical statistical systems.

  3. Tensor Network Renormalization Yields the Multiscale Entanglement Renormalization Ansatz

    NASA Astrophysics Data System (ADS)

    Evenbly, G.; Vidal, G.

    2015-11-01

    We show how to build a multiscale entanglement renormalization ansatz (MERA) representation of the ground state of a many-body Hamiltonian H by applying the recently proposed tensor network renormalization [G. Evenbly and G. Vidal, Phys. Rev. Lett. 115, 180405 (2015)] to the Euclidean time evolution operator e-β H for infinite β . This approach bypasses the costly energy minimization of previous MERA algorithms and, when applied to finite inverse temperature β , produces a MERA representation of a thermal Gibbs state. Our construction endows tensor network renormalization with a renormalization group flow in the space of wave functions and Hamiltonians (and not merely in the more abstract space of tensors) and extends the MERA formalism to classical statistical systems.

  4. The Additional-Mass Effect of Plates as Determined by Experiments

    NASA Technical Reports Server (NTRS)

    Gracey, William

    1941-01-01

    The apparent increase in the inertia properties of a body moving in a fluid medium has been called the additional-mass effect. This report presents a resume of test procedures and results of experimental determinations of the additional-mass effect of flat plates. In addition to data obtained from various foreign sources and from a NACA investigation in 1933, the results of tests recently conducted by the National Advisory Committee for Aeronautics are included.

  5. Holographic renormalization and the electroweak precision parameters

    SciTech Connect

    Round, Mark

    2010-09-01

    We study the effects of holographic renormalization on an AdS/QCD inspired description of dynamical electroweak symmetry breaking. Our model is a 5D slice of AdS{sub 5} geometry containing a bulk scalar and SU(2)xSU(2) gauge fields. The scalar field obtains a vacuum expectation value (VEV) which represents a condensate that triggers electroweak symmetry breaking. Fermion fields are constrained to live on the UV brane and do not propagate in the bulk. The two-point functions are holographically renormalized through the addition of boundary counterterms. Measurable quantities are then expressed in terms of well-defined physical parameters, free from any spurious dependence on the UV cutoff. A complete study of the precision parameters is carried out and bounds on physical quantities derived. The large-N scaling of results is discussed.

  6. Cluster functional renormalization group

    NASA Astrophysics Data System (ADS)

    Reuther, Johannes; Thomale, Ronny

    2014-01-01

    Functional renormalization group (FRG) has become a diverse and powerful tool to derive effective low-energy scattering vertices of interacting many-body systems. Starting from a free expansion point of the action, the flow of the RG parameter Λ allows us to trace the evolution of the effective one- and two-particle vertices towards low energies by taking into account the vertex corrections between all parquet channels in an unbiased fashion. In this work, we generalize the expansion point at which the diagrammatic resummation procedure is initiated from a free UV limit to a cluster product state. We formulate a cluster FRG scheme where the noninteracting building blocks (i.e., decoupled spin clusters) are treated exactly, and the intercluster couplings are addressed via RG. As a benchmark study, we apply our cluster FRG scheme to the spin-1/2 bilayer Heisenberg model (BHM) on a square lattice where the neighboring sites in the two layers form the individual two-site clusters. Comparing with existing numerical evidence for the BHM, we obtain reasonable findings for the spin susceptibility, the spin-triplet excitation energy, and quasiparticle weight even in coupling regimes close to antiferromagnetic order. The concept of cluster FRG promises applications to a large class of interacting electron systems.

  7. The analytic renormalization group

    NASA Astrophysics Data System (ADS)

    Ferrari, Frank

    2016-08-01

    Finite temperature Euclidean two-point functions in quantum mechanics or quantum field theory are characterized by a discrete set of Fourier coefficients Gk, k ∈ Z, associated with the Matsubara frequencies νk = 2 πk / β. We show that analyticity implies that the coefficients Gk must satisfy an infinite number of model-independent linear equations that we write down explicitly. In particular, we construct "Analytic Renormalization Group" linear maps Aμ which, for any choice of cut-off μ, allow to express the low energy Fourier coefficients for |νk | < μ (with the possible exception of the zero mode G0), together with the real-time correlators and spectral functions, in terms of the high energy Fourier coefficients for |νk | ≥ μ. Operating a simple numerical algorithm, we show that the exact universal linear constraints on Gk can be used to systematically improve any random approximate data set obtained, for example, from Monte-Carlo simulations. Our results are illustrated on several explicit examples.

  8. Additives

    NASA Technical Reports Server (NTRS)

    Smalheer, C. V.

    1973-01-01

    The chemistry of lubricant additives is discussed to show what the additives are chemically and what functions they perform in the lubrication of various kinds of equipment. Current theories regarding the mode of action of lubricant additives are presented. The additive groups discussed include the following: (1) detergents and dispersants, (2) corrosion inhibitors, (3) antioxidants, (4) viscosity index improvers, (5) pour point depressants, and (6) antifouling agents.

  9. A shape dynamical approach to holographic renormalization

    NASA Astrophysics Data System (ADS)

    Gomes, Henrique; Gryb, Sean; Koslowski, Tim; Mercati, Flavio; Smolin, Lee

    2015-01-01

    We provide a bottom-up argument to derive some known results from holographic renormalization using the classical bulk-bulk equivalence of General Relativity and Shape Dynamics, a theory with spatial conformal (Weyl) invariance. The purpose of this paper is twofold: (1) to advertise the simple classical mechanism, trading off gauge symmetries, that underlies the bulk-bulk equivalence of General Relativity and Shape Dynamics to readers interested in dualities of the type of AdS/conformal field theory (CFT); and (2) to highlight that this mechanism can be used to explain certain results of holographic renormalization, providing an alternative to the AdS/CFT conjecture for these cases. To make contact with the usual semiclassical AdS/CFT correspondence, we provide, in addition, a heuristic argument that makes it plausible that the classical equivalence between General Relativity and Shape Dynamics turns into a duality between radial evolution in gravity and the renormalization group flow of a CFT. We believe that Shape Dynamics provides a new perspective on gravity by giving conformal structure a primary role within the theory. It is hoped that this work provides the first steps toward understanding what this new perspective may be able to teach us about holographic dualities.

  10. Renormalization plasma shielding effects on scattering entanglement fidelity in dense plasmas

    SciTech Connect

    Lee, Gyeong Won; Shim, Jaewon; Jung, Young-Dae

    2014-10-15

    The influence of renormalization plasma screening on the entanglement fidelity for the elastic electron-atom scattering is investigated in partially ionized dense hydrogen plasmas. The partial wave analysis and effective interaction potential are employed to obtain the scattering entanglement fidelity in dense hydrogen plasmas as functions of the collision energy, the Debye length, and the renormalization parameter. It is found that the renormalization plasma shielding enhances the scattering entanglement fidelity. Hence, we show that the transmission of the quantum information can be increased about 10% due to the renormalization shielding effect in dense hydrogen plasmas. It is also found that the renormalization shielding effect on the entanglement fidelity for the electron-atom collision increases with an increase of the collision energy. In addition, the renormalization shielding function increases with increasing collision energy and saturates to the unity with an increase of the Debye length.

  11. Influence of renormalization shielding on the electron-impact ionization process in dense partially ionized plasmas

    SciTech Connect

    Song, Mi-Young; Yoon, Jung-Sik; Jung, Young-Dae

    2015-04-15

    The renormalization shielding effects on the electron-impact ionization of hydrogen atom are investigated in dense partially ionized plasmas. The effective projectile-target interaction Hamiltonian and the semiclassical trajectory method are employed to obtain the transition amplitude as well as the ionization probability as functions of the impact parameter, the collision energy, and the renormalization parameter. It is found that the renormalization shielding effect suppresses the transition amplitude for the electron-impact ionization process in dense partially ionized plasmas. It is also found that the renormalization effect suppresses the differential ionization cross section in the peak impact parameter region. In addition, it is found that the influence of renormalization shielding on the ionization cross section decreases with an increase of the relative collision energy. The variations of the renormalization shielding effects on the electron-impact ionization cross section are also discussed.

  12. Renormalization group invariants and sum rules in the deflected mirage mediation supersymmetry breaking

    NASA Astrophysics Data System (ADS)

    Huitu, Katri; Pandita, P. N.; Tiitola, Paavo

    2015-10-01

    We examine the deflected mirage mediation supersymmetry breaking (DMMSB) scenario, which combines three supersymmetry breaking scenarios, namely anomaly mediation, gravity mediation and gauge mediation using the one-loop renormalization group invariants (RGIs). We examine the effects on the RGIs at the threshold where the gauge messengers emerge, and derive the supersymmetry breaking parameters in terms of the RGIs. We further discuss whether the supersymmetry breaking mediation mechanism can be determined using a limited set of invariants, and derive sum rules valid for DMMSB below the gauge messenger scale. In addition we examine the implications of the measured Higgs mass for the DMMSB spectrum.

  13. Renormalization in Coulomb gauge QCD

    SciTech Connect

    Andrasi, A.; Taylor, John C.

    2011-04-15

    Research Highlights: > The Hamiltonian in the Coulomb gauge of QCD contains a non-linear Christ-Lee term. > We investigate the UV divergences from higher order graphs. > We find that they cannot be absorbed by renormalization of the Christ-Lee term. - Abstract: In the Coulomb gauge of QCD, the Hamiltonian contains a non-linear Christ-Lee term, which may alternatively be derived from a careful treatment of ambiguous Feynman integrals at 2-loop order. We investigate how and if UV divergences from higher order graphs can be consistently absorbed by renormalization of the Christ-Lee term. We find that they cannot.

  14. Dimensional renormalization: Ladders and rainbows

    SciTech Connect

    Delbourgo, R.; Kalloniatis, A.C.; Thompson, G.

    1996-10-01

    Renormalization factors are most easily extracted by going to the massless limit of the quantum field theory and retaining only a single momentum scale. We derive the factors and renormalized Green{close_quote}s functions to {ital all} orders in perturbation theory for rainbow graphs and vertex (or scattering) diagrams at zero momentum transfer, in the context of dimensional regularization, and we prove that the correct anomalous dimensions for those processes emerge in the limit {ital D}{r_arrow}4. {copyright} {ital 1996 The American Physical Society.}

  15. Electron hamiltonian renormalized by optical phonons in a two-orbital model of mixed valence

    NASA Astrophysics Data System (ADS)

    Spał, J.; Chao, K. A.

    1985-02-01

    We use a poor man's scaling argument along the line developed by Hewson in order to obtain an effective electronic model of mixed valence, with its interaction parameters renormalized by virtual optical phonon excitations. The atomic (f) electrons acquire a finite bandwidth, in addition to the renormalization of the hybridization.

  16. More on the renormalization group limit cycle in QCD

    SciTech Connect

    Evgeny Epelbaum; Hans-Werner Hammer; Ulf-G. Meissner; Andreas Nogga

    2006-02-26

    We present a detailed study of the recently conjectured infrared renormalization group limit cycle in QCD using chiral effective field theory. We show that small increases in the up and down quark masses, corresponding to a pion mass around 200 MeV, can move QCD to the critical renormalization group trajectory for an infrared limit cycle in the three-nucleon system. At the critical values of the quark masses, the binding energies of the deuteron and its spin-singlet partner are tuned to zero and the triton has infinitely many excited states with an accumulation point at the three-nucleon threshold. At next-to-leading order in the chiral counting, we find three parameter sets where this effect occurs. For one of them, we study the structure of the three-nucleon system using both chiral and contact effective field theories in detail. Furthermore, we calculate the influence of the limit cycle on scattering observables.

  17. Model Scramjet Inlet Unstart Induced by Mass Addition and Heat Release

    NASA Astrophysics Data System (ADS)

    Im, Seong-Kyun; Baccarella, Damiano; McGann, Brendan; Liu, Qili; Wermer, Lydiy; Do, Hyungrok

    2015-11-01

    The inlet unstart phenomena in a model scramjet are investigated at an arc-heated hypersonic wind tunnel. The unstart induced by nitrogen or ethylene jets at low or high enthalpy Mach 4.5 freestream flow conditions are compared. The jet injection pressurizes the downstream flow by mass addition and flow blockage. In case of the ethylene jet injection, heat release from combustion increases the backpressure further. Time-resolved schlieren imaging is performed at the jet and the lip of the model inlet to visualize the flow features during unstart. High frequency pressure measurements are used to provide information on pressure fluctuation at the scramjet wall. In both of the mass and heat release driven unstart cases, it is observed that there are similar flow transient and quasi-steady behaviors of unstart shockwave system during the unstart processes. Combustion driven unstart induces severe oscillatory flow motions of the jet and the unstart shock at the lip of the scramjet inlet after the completion of the unstart process, while the unstarted flow induced by solely mass addition remains relatively steady. The discrepancies between the processes of mass and heat release driven unstart are explained by flow choking mechanism.

  18. Algebraic Lattices in QFT Renormalization

    NASA Astrophysics Data System (ADS)

    Borinsky, Michael

    2016-07-01

    The structure of overlapping subdivergences, which appear in the perturbative expansions of quantum field theory, is analyzed using algebraic lattice theory. It is shown that for specific QFTs the sets of subdivergences of Feynman diagrams form algebraic lattices. This class of QFTs includes the standard model. In kinematic renormalization schemes, in which tadpole diagrams vanish, these lattices are semimodular. This implies that the Hopf algebra of Feynman diagrams is graded by the coradical degree or equivalently that every maximal forest has the same length in the scope of BPHZ renormalization. As an application of this framework, a formula for the counter terms in zero-dimensional QFT is given together with some examples of the enumeration of primitive or skeleton diagrams.

  19. Tensor networks and the numerical renormalization group

    NASA Astrophysics Data System (ADS)

    Weichselbaum, Andreas

    2012-12-01

    The full-density-matrix numerical renormalization group has evolved as a systematic and transparent setting for the calculation of thermodynamical quantities at arbitrary temperatures within the numerical renormalization group (NRG) framework. It directly evaluates the relevant Lehmann representations based on the complete basis sets introduced by Anders and Schiller [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.95.196801 95, 196801 (2005)]. In addition, specific attention is given to the possible feedback from low-energy physics to high energies by the explicit and careful construction of the full thermal density matrix, naturally generated over a distribution of energy shells. Specific examples are given in terms of spectral functions (fdmNRG), time-dependent NRG (tdmNRG), Fermi-golden-rule calculations (fgrNRG) as well as the calculation of plain thermodynamic expectation values. Furthermore, based on the very fact that, by its iterative nature, the NRG eigenstates are naturally described in terms of matrix product states, the language of tensor networks has proven enormously convenient in the description of the underlying algorithmic procedures. This paper therefore also provides a detailed introduction and discussion of the prototypical NRG calculations in terms of their corresponding tensor networks.

  20. Efficient implementation of the time renormalization group

    NASA Astrophysics Data System (ADS)

    Vollmer, Adrian; Amendola, Luca; Catena, Riccardo

    2016-02-01

    The time renormalization group (TRG) is an effective method for accurate calculations of the matter power spectrum at the scale of the first baryonic acoustic oscillations. By using a particular variable transformation in the TRG formalism, we can reduce the 2D integral in the source term of the equations of motion for the power spectrum into a series of 1D integrals. The shape of the integrand allows us to precompute only 13 antiderivatives numerically, which can then be reused when evaluating the outer integral. While this introduces a few challenges to keep numerical noise under control, we find that the computation time for nonlinear corrections to the matter power spectrum decreases by a factor of 50. This opens up the possibility to use TRG for mass production as in Markov chain Monte Carlo methods. A fortran code demonstrating this new algorithm is publicly available.

  1. Revisiting on-shell renormalization conditions in theories with flavor mixing

    NASA Astrophysics Data System (ADS)

    Grimus, W.; Löschner, M.

    2016-08-01

    In this review, we present a derivation of the on-shell renormalization conditions for scalar and fermionic fields in theories with and without parity conservation. We also discuss the specifics of Majorana fermions. Our approach only assumes a canonical form for the renormalized propagators and exploits the fact that the inverse propagators are nonsingular in 𝜀 = p2 - m n2, where p is the external four-momentum and mn is a pole mass. In this way, we obtain full agreement with commonly used on-shell conditions. We also discuss how they are implemented in renormalization.

  2. Hybrid Residual Flexibility/Mass-Additive Method for Structural Dynamic Testing

    NASA Technical Reports Server (NTRS)

    Tinker, M. L.

    2003-01-01

    A large fixture was designed and constructed for modal vibration testing of International Space Station elements. This fixed-base test fixture, which weighs thousands of pounds and is anchored to a massive concrete floor, initially utilized spherical bearings and pendulum mechanisms to simulate Shuttle orbiter boundary constraints for launch of the hardware. Many difficulties were encountered during a checkout test of the common module prototype structure, mainly due to undesirable friction and excessive clearances in the test-article-to-fixture interface bearings. Measured mode shapes and frequencies were not representative of orbiter-constrained modes due to the friction and clearance effects in the bearings. As a result, a major redesign effort for the interface mechanisms was undertaken. The total cost of the fixture design, construction and checkout, and redesign was over $2 million. Because of the problems experienced with fixed-base testing, alternative free-suspension methods were studied, including the residual flexibility and mass-additive approaches. Free-suspension structural dynamics test methods utilize soft elastic bungee cords and overhead frame suspension systems that are less complex and much less expensive than fixed-base systems. The cost of free-suspension fixturing is on the order of tens of thousands of dollars as opposed to millions, for large fixed-base fixturing. In addition, free-suspension test configurations are portable, allowing modal tests to be done at sites without modal test facilities. For example, a mass-additive modal test of the ASTRO-1 Shuttle payload was done at the Kennedy Space Center launch site. In this Technical Memorandum, the mass-additive and residual flexibility test methods are described in detail. A discussion of a hybrid approach that combines the best characteristics of each method follows and is the focus of the study.

  3. Quark lepton complementarity and renormalization group effects

    SciTech Connect

    Schmidt, Michael A.; Smirnov, Alexei Yu.

    2006-12-01

    We consider a scenario for the quark-lepton complementarity relations between mixing angles in which the bimaximal mixing follows from the neutrino mass matrix. According to this scenario in the lowest order the angle {theta}{sub 12} is {approx}1{sigma} (1.5 degree sign -2 degree sign ) above the best fit point coinciding practically with the tribimaximal mixing prediction. Realization of this scenario in the context of the seesaw type-I mechanism with leptonic Dirac mass matrices approximately equal to the quark mass matrices is studied. We calculate the renormalization group corrections to {theta}{sub 12} as well as to {theta}{sub 13} in the standard model (SM) and minimal supersymmetric standard model (MSSM). We find that in a large part of the parameter space corrections {delta}{theta}{sub 12} are small or negligible. In the MSSM version of the scenario, the correction {delta}{theta}{sub 12} is in general positive. Small negative corrections appear in the case of an inverted mass hierarchy and opposite CP parities of {nu}{sub 1} and {nu}{sub 2} when leading contributions to {theta}{sub 12} running are strongly suppressed. The corrections are negative in the SM version in a large part of the parameter space for values of the relative CP phase of {nu}{sub 1} and {nu}{sub 2}: {phi}>{pi}/2.

  4. Systematic renormalization of the effective theory of Large Scale Structure

    NASA Astrophysics Data System (ADS)

    Akbar Abolhasani, Ali; Mirbabayi, Mehrdad; Pajer, Enrico

    2016-05-01

    A perturbative description of Large Scale Structure is a cornerstone of our understanding of the observed distribution of matter in the universe. Renormalization is an essential and defining step to make this description physical and predictive. Here we introduce a systematic renormalization procedure, which neatly associates counterterms to the UV-sensitive diagrams order by order, as it is commonly done in quantum field theory. As a concrete example, we renormalize the one-loop power spectrum and bispectrum of both density and velocity. In addition, we present a series of results that are valid to all orders in perturbation theory. First, we show that while systematic renormalization requires temporally non-local counterterms, in practice one can use an equivalent basis made of local operators. We give an explicit prescription to generate all counterterms allowed by the symmetries. Second, we present a formal proof of the well-known general argument that the contribution of short distance perturbations to large scale density contrast δ and momentum density π(k) scale as k2 and k, respectively. Third, we demonstrate that the common practice of introducing counterterms only in the Euler equation when one is interested in correlators of δ is indeed valid to all orders.

  5. Ambient ionisation mass spectrometry for the characterisation of polymers and polymer additives: a review.

    PubMed

    Paine, Martin R L; Barker, Philip J; Blanksby, Stephen J

    2014-01-15

    The purpose of this review is to showcase the present capabilities of ambient sampling and ionisation technologies for the analysis of polymers and polymer additives by mass spectrometry (MS) while simultaneously highlighting their advantages and limitations in a critical fashion. To qualify as an ambient ionisation technique, the method must be able to probe the surface of solid or liquid samples while operating in an open environment, allowing a variety of sample sizes, shapes, and substrate materials to be analysed. The main sections of this review will be guided by the underlying principle governing the desorption/extraction step of the analysis; liquid extraction, laser ablation, or thermal desorption, and the major component investigated, either the polymer itself or exogenous compounds (additives and contaminants) present within or on the polymer substrate. The review will conclude by summarising some of the challenges these technologies still face and possible directions that would further enhance the utility of ambient ionisation mass spectrometry as a tool for polymer analysis.

  6. Analysis of additives in dairy products by liquid chromatography coupled to quadrupole-orbitrap mass spectrometry.

    PubMed

    Jia, Wei; Ling, Yun; Lin, Yuanhui; Chang, James; Chu, Xiaogang

    2014-04-01

    A new method combining QuEChERS with ultrahigh-performance liquid chromatography and electrospray ionization quadrupole Orbitrap high-resolution mass spectrometry (UHPLC/ESI Q-Orbitrap) was developed for the highly accurate and sensitive screening of 43 antioxidants, preservatives and synthetic sweeteners in dairy products. Response surface methodology was employed to optimize a quick, easy, cheap, effective, rugged, and safe (QuEChERS) sample preparation method for the determination of 42 different analytes in dairy products for the first time. After optimization, the maximum predicted recovery was 99.33% rate for aspartame under the optimized conditions of 10 mL acetionitrile, 1.52 g sodium acetate, 410 mg PSA and 404 mgC18. For the matrices studied, the recovery rates of the other 42 compounds ranged from 89.4% to 108.2%, with coefficient of variation <6.4%. UHPLC/ESI Q-Orbitrap Mass full scan mode acquired full MS data was used to identify and quantify additives, and data-dependent scan mode obtained fragment ion spectra for confirmation. The mass accuracy typically obtained is routinely better than 1.5ppm, and only need to calibrate once a week. The 43 compounds behave dynamic in the range 0.001-1000 μg kg(-1) concentration, with correlation coefficient >0.999. The limits of detection for the analytes are in the range 0.0001-3.6 μg kg(-1). This method has been successfully applied on screening of antioxidants, preservatives and synthetic sweeteners in commercial dairy product samples, and it is very useful for fast screening of different food additives.

  7. Renormalization of dimension 6 gluon operators

    NASA Astrophysics Data System (ADS)

    Kim, HyungJoo; Lee, Su Houng

    2015-09-01

    We identify the independent dimension 6 twist 4 gluon operators and calculate their renormalization in the pure gauge theory. By constructing the renormalization group invariant combinations, we find the scale invariant condensates that can be estimated in nonperturbative calculations and used in QCD sum rules for heavy quark systems in medium.

  8. Kenneth Wilson — Renormalization and QCD

    NASA Astrophysics Data System (ADS)

    Wegner, Franz J.

    2014-07-01

    Kenneth Wilson had an enormous impact on field theory, in particular on the renormalization group and critical phenomena, and on QCD. I had the great pleasure to work in three fields to which he contributed essentially: Critical phenomena, gauge-invariance in duality and QCD, and flow equations and similarity renormalization.

  9. Determination of plastic additives in packaging by liquid chromatography coupled to high resolution mass spectrometry.

    PubMed

    Moreta, Cristina; Tena, María-Teresa

    2015-10-01

    A simple and sensitive analytical method for the determination of several plastic additives in multilayer packaging based on solid-liquid extraction (SLE) and ultra-high performance liquid chromatography (UHPLC) coupled to variable wavelength (VWD) and time of flight mass spectrometry (TOF-MS) detectors is presented. The proposed method allows the simultaneous determination of fourteen additives belonging to different families such as antioxidants, slip agents and light stabilizers, as well as two oxidation products in only 9min. The developed method was validated in terms of linearity, matrix effect error, detection and quantification limits, repeatability and intermediate precision. The instrumental method showed satisfactory repeatability and intermediate precision at concentrations closed to LOQ with RSDs less than 7 and 20%, respectively, and LODs until 5000 times more sensitive than other GC-FID and HPLC-VWD methods previously reported. Also, focused ultrasound solid-liquid extraction (FUSLE) was optimized and evaluated to extract plastic additives from packaging. Extraction results obtained by FUSLE and SLE were compared to those obtained by pressurized liquid extraction (PLE). All extraction methods showed excellent extraction efficiency for slip agents, however quantitative recovery of all analytes was achieved only by SLE with just 5ml of hexane for 10h. Finally, the selected method was applied to the analysis of packaging samples where erucamide, Irgafos 168, oxidized Irgafos 168, Irganox 1076 and Irganox 1010 were detected and quantified. PMID:26319625

  10. Determination of plastic additives in packaging by liquid chromatography coupled to high resolution mass spectrometry.

    PubMed

    Moreta, Cristina; Tena, María-Teresa

    2015-10-01

    A simple and sensitive analytical method for the determination of several plastic additives in multilayer packaging based on solid-liquid extraction (SLE) and ultra-high performance liquid chromatography (UHPLC) coupled to variable wavelength (VWD) and time of flight mass spectrometry (TOF-MS) detectors is presented. The proposed method allows the simultaneous determination of fourteen additives belonging to different families such as antioxidants, slip agents and light stabilizers, as well as two oxidation products in only 9min. The developed method was validated in terms of linearity, matrix effect error, detection and quantification limits, repeatability and intermediate precision. The instrumental method showed satisfactory repeatability and intermediate precision at concentrations closed to LOQ with RSDs less than 7 and 20%, respectively, and LODs until 5000 times more sensitive than other GC-FID and HPLC-VWD methods previously reported. Also, focused ultrasound solid-liquid extraction (FUSLE) was optimized and evaluated to extract plastic additives from packaging. Extraction results obtained by FUSLE and SLE were compared to those obtained by pressurized liquid extraction (PLE). All extraction methods showed excellent extraction efficiency for slip agents, however quantitative recovery of all analytes was achieved only by SLE with just 5ml of hexane for 10h. Finally, the selected method was applied to the analysis of packaging samples where erucamide, Irgafos 168, oxidized Irgafos 168, Irganox 1076 and Irganox 1010 were detected and quantified.

  11. Renormalization effects on the MSSM from a calculable model of a strongly coupled hidden sector

    SciTech Connect

    Arai, Masato; Okada, Nobuchika

    2011-10-01

    We investigate possible renormalization effects on the low-energy mass spectrum of the minimal supersymmetric standard model (MSSM), using a calculable model of strongly coupled hidden sector. We model the hidden sector by N=2 supersymmetric quantum chromodynamics with gauge group SU(2)xU(1) and N{sub f}=2 matter hypermultiplets, perturbed by a Fayet-Iliopoulos term which breaks the supersymmetry down to N=0 on a metastable vacuum. In the hidden sector the Kaehler potential is renormalized. Upon identifying a hidden sector modulus with the renormalization scale, and extrapolating to the strongly coupled regime using the Seiberg-Witten solution, the contribution from the hidden sector to the MSSM renormalization group flows is computed. For concreteness, we consider a model in which the renormalization effects are communicated to the MSSM sector via gauge mediation. In contrast to the perturbative toy examples of hidden sector renormalization studied in the literature, we find that our strongly coupled model exhibits rather intricate effects on the MSSM soft scalar mass spectrum, depending on how the hidden sector fields are coupled to the messenger fields. This model provides a concrete example in which the low-energy spectrum of MSSM particles that are expected to be accessible in collider experiments is obtained using strongly coupled hidden sector dynamics.

  12. Renormalization Group and Phase Transitions in Spin, Gauge, and QCD Like Theories

    SciTech Connect

    Liu, Yuzhi

    2013-08-01

    In this thesis, we study several different renormalization group (RG) methods, including the conventional Wilson renormalization group, Monte Carlo renormalization group (MCRG), exact renormalization group (ERG, or sometimes called functional RG), and tensor renormalization group (TRG).

  13. Non-perturbative Renormalization with Staggered Fermions

    NASA Astrophysics Data System (ADS)

    Lytle, Andrew

    Lattice studies of Standard Model phenomenology frequently require knowledge of matching factors, or "Z-factors," that convert lattice operators defined at the lattice scale to operators in a continuum scheme at a scale mu. We make the first non-perturbative determinations of Z-factors for improved, fully dynamical staggered fermions. We compute the mass renormalization factor Zm for the Asqtad action, which is the action used by the MILC collaboration[1]. We find the strange quark mass to be mMSs (2 GeV) = 103(3) MeV; significantly larger than the result obtained using the perturbative Z-factor[2]. We compute all 256 bilinear Z-factors for the HYP-smeared action, which provides a laboratory for comparison to the results of one-loop perturbation theory[3]. Our results indicate broad agreement for ratios of Z-factors, at the few percent level, while the Z-factors themselves differ at around the ten percent level. The bilinear calculations are a stepping stone towards computation of the four-Fermi Z-factors relevant for an ongoing precision calculation of BK[4, 5, 6, 7], the knowledge of which is used to constrain the CKM matrix. Uncertainty in the required matching factors constitutes the dominant source of error.

  14. Multilogarithmic velocity renormalization in graphene

    NASA Astrophysics Data System (ADS)

    Sharma, Anand; Kopietz, Peter

    2016-06-01

    We reexamine the effect of long-range Coulomb interactions on the quasiparticle velocity in graphene. Using a nonperturbative functional renormalization group approach with partial bosonization in the forward scattering channel and momentum transfer cutoff scheme, we calculate the quasiparticle velocity, v (k ) , and the quasiparticle residue, Z , with frequency-dependent polarization. One of our most striking results is that v (k ) ∝ln[Ck(α ) /k ] where the momentum- and interaction-dependent cutoff scale Ck(α ) vanishes logarithmically for k →0 . Here k is measured with respect to one of the charge neutrality (Dirac) points and α =2.2 is the strength of dimensionless bare interaction. Moreover, we also demonstrate that the so-obtained multilogarithmic singularity is reconcilable with the perturbative expansion of v (k ) in powers of the bare interaction.

  15. Renormalization Group (RG) in Turbulence: Historical and Comparative Perspective

    NASA Technical Reports Server (NTRS)

    Zhou, Ye; McComb, W. David; Vahala, George

    1997-01-01

    The term renormalization and renormalization group are explained by reference to various physical systems. The extension of renormalization group to turbulence is then discussed; first as a comprehensive review and second concentrating on the technical details of a few selected approaches. We conclude with a discussion of the relevance and application of renormalization group to turbulence modelling.

  16. Two-dimensional N=(2,2) Wess-Zumino model in the functional renormalization group approach

    SciTech Connect

    Synatschke-Czerwonka, Franziska; Fischbacher, Thomas; Bergner, Georg

    2010-10-15

    We study the supersymmetric N=(2,2) Wess-Zumino model in two dimensions with the functional renormalization group. At leading order in the supercovariant derivative expansion we recover the nonrenormalization theorem which states that the superpotential has no running couplings. Beyond leading order the renormalization of the bare mass is caused by a momentum-dependent wave function renormalization. To deal with the partial differential equations we have developed a numerical toolbox called FlowPy. For weak couplings the quantum corrections to the bare mass found in lattice simulations are reproduced with high accuracy. But in the regime with intermediate couplings higher-order operators that are not constrained by the nonrenormalization theorem yield the dominating contribution to the renormalized mass.

  17. Improved Monte Carlo Renormalization Group Method

    DOE R&D Accomplishments Database

    Gupta, R.; Wilson, K. G.; Umrigar, C.

    1985-01-01

    An extensive program to analyze critical systems using an Improved Monte Carlo Renormalization Group Method (IMCRG) being undertaken at LANL and Cornell is described. Here we first briefly review the method and then list some of the topics being investigated.

  18. Topological invariants and renormalization of Lorenz maps

    NASA Astrophysics Data System (ADS)

    Silva, Luis; Sousa Ramos, J.

    2002-02-01

    We prove that the invariants of the topological semiconjugation of Lorenz maps with β-transformations remains constant on the renormalization archipelagoes and analyze how the dynamics on the archipelagoes depends on its structure.

  19. The Synergism Between Heat and Mass Transfer Additive and Advanced Surfaces in Aqueous LiBr Horizontal Tube Absorbers

    SciTech Connect

    Miller, W.A.

    1999-03-24

    Experiments were conducted in a laboratory to investigate the absorption of water vapor into a falling-film of aqueous lithium bromide (LiBr). A mini-absorber test stand was used to test smooth tubes and a variety of advanced tube surfaces placed horizontally in a single-row bundle. The bundle had six copper tubes; each tube had an outside diameter of 15.9-mm and a length of 0.32-m. A unique feature of the stand is its ability to operate continuously and support testing of LiBr brine at mass fractions {ge} 0.62. The test stand can also support testing to study the effect of the failing film mass flow rate, the coolant mass flow rate, the coolant temperature, the absorber pressure and the tube spacing. Manufacturers of absorption chillers add small quantities of a heat and mass transfer additive to improve the performance of the absorbers. The additive causes surface stirring which enhances the transport of absorbate into the bulk of the film. Absorption may also be enhanced with advanced tube surfaces that mechanically induce secondary flows in the falling film without increasing the thickness of the film. Several tube geometry's were identified and tested with the intent of mixing the film and renewing the interface with fresh solution from the tube wall. Testing was completed on a smooth tube and several different externally enhanced tube surfaces. Experiments were conducted over the operating conditions of 6.5 mm Hg absorber pressure, coolant temperatures ranging from 20 to 35 C and LiBr mass fractions ranging from 0.60 through 0.62. Initially the effect of tube spacing was investigated for the smooth tube surface, tested with no heat and mass transfer additive. Test results showed the absorber load and the mass absorbed increased as the tube spacing increased because of the improved wetting of the tube bundle. However, tube spacing was not a critical factor if heat and mass transfer additive was active in the mini-absorber. The additive dramatically affected

  20. Renormalization in Periodically Driven Quantum Dots.

    PubMed

    Eissing, A K; Meden, V; Kennes, D M

    2016-01-15

    We report on strong renormalization encountered in periodically driven interacting quantum dots in the nonadiabatic regime. Correlations between lead and dot electrons enhance or suppress the amplitude of driving depending on the sign of the interaction. Employing a newly developed flexible renormalization-group-based approach for periodic driving to an interacting resonant level we show analytically that the magnitude of this effect follows a power law. Our setup can act as a non-Markovian, single-parameter quantum pump. PMID:26824557

  1. From dynamical systems to renormalization

    SciTech Connect

    Menous, Frédéric

    2013-09-15

    In this paper we study logarithmic derivatives associated to derivations on completed graded Lie algebra, as well as the existence of inverses. These logarithmic derivatives, when invertible, generalize the exp-log correspondence between a Lie algebra and its Lie group. Such correspondences occur naturally in the study of dynamical systems when dealing with the linearization of vector fields and the non linearizability of a resonant vector fields corresponds to the non invertibility of a logarithmic derivative and to the existence of normal forms. These concepts, stemming from the theory of dynamical systems, can be rephrased in the abstract setting of Lie algebra and the same difficulties as in perturbative quantum field theory (pQFT) arise here. Surprisingly, one can adopt the same ideas as in pQFT with fruitful results such as new constructions of normal forms with the help of the Birkhoff decomposition. The analogy goes even further (locality of counter terms, choice of a renormalization scheme) and shall lead to more interactions between dynamical systems and quantum field theory.

  2. From dynamical systems to renormalization

    NASA Astrophysics Data System (ADS)

    Menous, Frédéric

    2013-09-01

    In this paper we study logarithmic derivatives associated to derivations on completed graded Lie algebra, as well as the existence of inverses. These logarithmic derivatives, when invertible, generalize the exp-log correspondence between a Lie algebra and its Lie group. Such correspondences occur naturally in the study of dynamical systems when dealing with the linearization of vector fields and the non linearizability of a resonant vector fields corresponds to the non invertibility of a logarithmic derivative and to the existence of normal forms. These concepts, stemming from the theory of dynamical systems, can be rephrased in the abstract setting of Lie algebra and the same difficulties as in perturbative quantum field theory (pQFT) arise here. Surprisingly, one can adopt the same ideas as in pQFT with fruitful results such as new constructions of normal forms with the help of the Birkhoff decomposition. The analogy goes even further (locality of counter terms, choice of a renormalization scheme) and shall lead to more interactions between dynamical systems and quantum field theory.

  3. Euclidean Epstein-Glaser renormalization

    NASA Astrophysics Data System (ADS)

    Keller, Kai J.

    2009-10-01

    In the framework of perturbative algebraic quantum field theory recently developed by Brunetti, Dütsch, and Fredenhagen (http://arxiv.org/abs/0901.2038) I give a general construction of so-called Euclidean time-ordered products, i.e., algebraic versions of the Schwinger functions, for scalar quantum field theories on spaces of Euclidean signature. This is done by generalizing the recursive construction of time-ordered products by Epstein and Glaser, originally formulated for quantum field theories on Minkowski space [Epstein and Glaser, Ann. Inst. Henri Poincare 19, 211 (1973)]. An essential input of Epstein-Glaser renormalization is the causal structure of Minkowski space. The absence of this causal structure in the Euclidean framework makes it necessary to modify the original construction of Epstein and Glaser at two points. First, the whole construction has to be performed with an only partially defined product on (interaction) functionals. This is due to the fact that the fundamental solutions of the Helmholtz operator (-Δ+m2) of Euclidean quantum field theory have a unique singularity structure, i.e., they are unique up to a smooth part. Second, one needs to (re)introduce a (rather natural) "Euclidean causality" condition for the recursion of Epstein and Glaser to be applicable.

  4. Euclidean Epstein-Glaser renormalization

    SciTech Connect

    Keller, Kai J.

    2009-10-15

    In the framework of perturbative algebraic quantum field theory recently developed by Brunetti, Duetsch, and Fredenhagen (http://arxiv.org/abs/0901.2038) I give a general construction of so-called Euclidean time-ordered products, i.e., algebraic versions of the Schwinger functions, for scalar quantum field theories on spaces of Euclidean signature. This is done by generalizing the recursive construction of time-ordered products by Epstein and Glaser, originally formulated for quantum field theories on Minkowski space [Epstein and Glaser, Ann. Inst. Henri Poincare 19, 211 (1973)]. An essential input of Epstein-Glaser renormalization is the causal structure of Minkowski space. The absence of this causal structure in the Euclidean framework makes it necessary to modify the original construction of Epstein and Glaser at two points. First, the whole construction has to be performed with an only partially defined product on (interaction) functionals. This is due to the fact that the fundamental solutions of the Helmholtz operator (-{delta}+m{sup 2}) of Euclidean quantum field theory have a unique singularity structure, i.e., they are unique up to a smooth part. Second, one needs to (re)introduce a (rather natural) 'Euclidean causality' condition for the recursion of Epstein and Glaser to be applicable.

  5. Supersymmetry-breaking parameters from renormalization group invariants at the LHC

    SciTech Connect

    Carena, Marcela; Draper, Patrick; Shah, Nausheen R.; Wagner, Carlos E. M.

    2011-02-01

    We study renormalization group invariant (RGI) quantities in the minimal supersymmetric standard model and show that they are a powerful and simple instrument for testing high-scale models of supersymmetry (SUSY) breaking. For illustration, we analyze the frameworks of minimal and general gauge-mediated (MGM and GGM) SUSY breaking, with additional arbitrary soft Higgs mass parameters at the messenger scale. We show that if a gaugino and two first generation sfermion soft masses are determined at the LHC, the RGIs lead to MGM sum rules that yield accurate predictions for the other gaugino and first generation soft masses. RGIs can also be used to reconstruct the fundamental MGM parameters (including the messenger scale), calculate the hypercharge D-term, and find relationships among the third generation and Higgs soft masses. We then study the extent to which measurements of the full first generation spectrum at the LHC may distinguish different SUSY-breaking scenarios. In the case of the MGM model, although most deviations violate the sum rules by more than estimated experimental errors, we find a one-parameter family of GGM models that satisfy the constraints and produce the same first generation spectrum. The GGM-MGM degeneracy is lifted by differences in the third generation masses and the messenger scales.

  6. Fourier Monte Carlo renormalization-group approach to crystalline membranes.

    PubMed

    Tröster, A

    2015-02-01

    The computation of the critical exponent η characterizing the universal elastic behavior of crystalline membranes in the flat phase continues to represent challenges to theorists as well as computer simulators that manifest themselves in a considerable spread of numerical results for η published in the literature. We present additional insight into this problem that results from combining Wilson's momentum shell renormalization-group method with the power of modern computer simulations based on the Fourier Monte Carlo algorithm. After discussing the ideas and difficulties underlying this combined scheme, we present a calculation of the renormalization-group flow of the effective two-dimensional Young modulus for momentum shells of different thickness. Extrapolation to infinite shell thickness allows us to produce results in reasonable agreement with those obtained by functional renormalization group or by Fourier Monte Carlo simulations in combination with finite-size scaling. Moreover, our method allows us to obtain a decent estimate for the value of the Wegner exponent ω that determines the leading correction to scaling, which in turn allows us to refine our numerical estimate for η previously obtained from precise finite-size scaling data.

  7. Density matrix renormalization group approach to the massive Schwinger model

    NASA Astrophysics Data System (ADS)

    Byrnes, T. M.; Sriganesh, P.; Bursill, R. J.; Hamer, C. J.

    2002-07-01

    The massive Schwinger model is studied using a density matrix renormalization group approach to the staggered lattice Hamiltonian version of the model. Lattice sizes up to 256 sites are calculated, and the estimates in the continuum limit are almost two orders of magnitude more accurate than previous calculations. Coleman's picture of ``half-asymptotic'' particles at a background field θ=π is confirmed. The predicted phase transition at finite fermion mass (m/g) is accurately located and demonstrated to belong in the 2D Ising universality class.

  8. Conformation space renormalization of polymers. I. Single chain equilibrium properties using Wilson-type renormalization

    NASA Astrophysics Data System (ADS)

    Oono, Y.; Freed, Karl F.

    1981-07-01

    A conformation space renormalization group is developed to describe polymer excluded volume in single polymer chains. The theory proceeds in ordinary space in terms of position variables and the contour variable along the chain, and it considers polymers of fixed chain length. The theory is motivated along two lines. The first presents the renormalization group transformation as the means for extracting the macroscopic long wavelength quantities from the theory. An alternative viewpoint shows how the renormalization group transformation follows as a natural consequence of an attempt to correctly treat the presence of a cut-off length scale. It is demonstrated that the current configuration space renormalization method has a one-to-one correspondence with the Wilson-Fisher field theory formulation, so our method is valid to all orders in ɛ = 4-d where d is the spatial dimensionality. This stands in contrast to previous attempts at a configuration space renormalization approach which are limited to first order in ɛ because they arbitrarily assign monomers to renormalized ''blobs.'' In the current theory the real space chain conformations dictate the coarse graining transformation. The calculations are presented to lowest order in ɛ to enable the development of techniques necessary for the treatment of dynamics in Part II. The theory is presented both in terms of the simple delta function interaction as well as using realistic-type interaction potentials. This illustrates the renormalization of the interactions, the emergence of renormalized many-body interactions, and the complexity of the theta point.

  9. Application of Tapping-Mode Scanning Probe Electrospray Ionization to Mass Spectrometry Imaging of Additives in Polymer Films

    PubMed Central

    Shimazu, Ryo; Yamoto, Yoshinari; Kosaka, Tomoya; Kawasaki, Hideya; Arakawa, Ryuichi

    2014-01-01

    We report the application of tapping-mode scanning probe electrospray ionization (t-SPESI) to mass spectrometry imaging of industrial materials. The t-SPESI parameters including tapping solvent composition, solvent flow rate, number of tapping at each spot, and step-size were optimized using a quadrupole mass spectrometer to improve mass spectrometry (MS) imaging of thin-layer chromatography (TLC) and additives in polymer films. Spatial resolution of approximately 100 μm was achieved by t-SPESI imaging mass spectrometry using a fused-silica capillary (50 μm i.d., 150 μm o.d.) with the flow rate set at 0.2 μL/min. This allowed us to obtain discriminable MS imaging profiles of three dyes separated by TLC and the additive stripe pattern of a PMMA model film depleted by UV irradiation. PMID:26819894

  10. Determining the structure of supersymmetry breaking with renormalization group invariants

    SciTech Connect

    Carena, Marcela; Draper, Patrick; Shah, Nausheen R.; Wagner, Carlos E. M.

    2010-10-01

    If collider experiments demonstrate that the minimal supersymmetric standard model (MSSM) is a good description of nature at the weak scale, the experimental priority will be the precise determination of superpartner masses. These masses are governed by the weak scale values of the soft supersymmetry-breaking (SUSY-breaking) parameters, which are in turn highly dependent on the SUSY-breaking scheme present at high scales. It is therefore of great interest to find patterns in the soft parameters that can distinguish different high-scale SUSY-breaking structures, identify the scale at which the breaking is communicated to the visible sector, and determine the soft breaking parameters at that scale. In this work, we demonstrate that 1-loop renormalization group invariant quantities present in the MSSM may be used to answer each of these questions. We apply our method first to generic flavor-blind models of SUSY breaking, and then we examine in detail the subset of these models described by general gauge mediation and the constrained MSSM with nonuniversal Higgs masses. As renormalization group invariance generally does not hold beyond leading-log order, we investigate the magnitude and direction of the 2-loop corrections. We find that with superpartners at the TeV scale, these 2-loop effects are either negligible, or they are of the order of optimistic experimental uncertainties and have definite signs, which allows them to be easily accounted for in the overall uncertainty.

  11. Renormalization from Classical to Quantum Physics

    NASA Astrophysics Data System (ADS)

    Kar, Arnab

    The concept of renormalization was first introduced by Dirac to investigate the infinite self energy of an electron classically. This radical theory was probably the first time when an infinity occurring in a physical system was systematically investigated. This thesis presents a new perspective of renormalization by introducing methods from metric geometry to control divergences. We start by extending Dirac's work and analyzing how the radiation reaction due to the precision of the electron's magnetic moment affects its motion. This is followed by modeling scalar field theory on lattices of various kinds. Scale invariance, which plays a major role in the very few renormalizable theories in nature, is inbuilt in our formalism. We also use Wilson's ideas of effective theory and finite element methods to study continuum systems. Renormalization group transformations form the central theme in this picture. By incorporating finite element methods, an idea borrowed from mechanical engineering, we study scalar fields on triangular lattices in a hierarchal manner. In our case, the cotangent formula turns out to be a fixed point of the renormalization group transformations. We end our thesis by introducing a new metric for space-time which emerges from the scalar field itself. The standard techniques used in the theory of renormalization so far attempt to redefine coupling constants of the theory to remove divergences at short distance scales. In our formalism, we deduce the distance scale itself. In our notion of distance, built from correlation functions of the fields, the divergences disappear.

  12. Mass Spectrometry contamination from Tinuvin 770, a common additive in laboratory plastics

    Technology Transfer Automated Retrieval System (TEKTRAN)

    The superior sensitivity of current mass spectrometers makes them prone to contamination issues which can have deleterious effects on sample analysis. Here, Bis(2,2,6,6-tetramethyl-4-piperidyl) sebacate (marketed under the name Tinuvin 770) is identified as a major contaminant in applications utiliz...

  13. Mass analysis addition to the Differential Ion Flux Probe (DIFP) study

    NASA Technical Reports Server (NTRS)

    Wright, K. H., Jr.; Jolley, Richard

    1994-01-01

    The objective of this study is to develop a technique to measure the characteristics of space plasmas under highly disturbed conditions; e.g., non-Maxwellian plasmas with strong drifting populations and plasmas contaminated by spacecraft outgassing. The approach, conducted in conjunction with current MSFC activities, is to extend the capabilities of the Differential Ion Flux Probe (DIFP) to include a high throughput mass measurement that does not require either high voltage or contamination sensitive devices such as channeltron electron multipliers or microchannel plates. This will significantly reduce the complexity and expense of instrument fabrication, testing, and integration of flight hardware compared to classical mass analyzers. The feasibility of the enhanced DIFP has been verified by using breadboard test models in a controlled plasma environment. The ability to manipulate particles through the instrument regardless of incident angle, energy, or ionic component has been amply demonstrated. The energy analysis mode is differential and leads directly to a time-of-flight mass measurement. With the new design, the DIFP will separate multiple ion streams and analyze each stream independently for ion flux intensity, velocity (including direction of motion), mass, and temperature (or energy distribution). In particular, such an instrument will be invaluable on follow-on electrodynamic TSS missions and, possibly, for environmental monitoring on the space station.

  14. Gauge mediation scenario with hidden sector renormalization in MSSM

    SciTech Connect

    Arai, Masato; Okada, Nobuchika

    2010-02-01

    We study the hidden sector effects on the mass renormalization of a simplest gauge-mediated supersymmetry breaking scenario. We point out that possible hidden sector contributions render the soft scalar masses smaller, resulting in drastically different sparticle mass spectrum at low energy. In particular, in the 5+5 minimal gauge-mediated supersymmetry breaking with high messenger scale (that is favored by the gravitino cold dark matter scenario), we show that a stau can be the next lightest superparticle for moderate values of hidden sector self-coupling. This provides a very simple theoretical model of long-lived charged next lightest superparticles, which imply distinctive signals in ongoing and upcoming collider experiments.

  15. Boundary quantum critical phenomena with entanglement renormalization

    SciTech Connect

    Evenbly, G.; Pfeifer, R. N. C.; Tagliacozzo, L.; McCulloch, I. P.; Vidal, G.; Pico, V.; Iblisdir, S.

    2010-10-15

    We propose the use of entanglement renormalization techniques to study boundary critical phenomena on a lattice system. The multiscale entanglement renormalization ansatz (MERA), in its scale invariant version, offers a very compact approximation to quantum critical ground states. Here we show that, by adding a boundary to the MERA, an accurate approximation to the ground state of a semi-infinite critical chain with an open boundary is obtained, from which one can extract boundary scaling operators and their scaling dimensions. As in Wilson's renormalization-group formulation of the Kondo problem, our construction produces, as a side result, an effective chain displaying explicit separation of energy scales. We present benchmark results for the quantum Ising and quantum XX models with free and fixed boundary conditions.

  16. Nontargeted Screening Method for Illegal Additives Based on Ultrahigh-Performance Liquid Chromatography-High-Resolution Mass Spectrometry.

    PubMed

    Fu, Yanqing; Zhou, Zhihui; Kong, Hongwei; Lu, Xin; Zhao, Xinjie; Chen, Yihui; Chen, Jia; Wu, Zeming; Xu, Zhiliang; Zhao, Chunxia; Xu, Guowang

    2016-09-01

    Identification of illegal additives in complex matrixes is important in the food safety field. In this study a nontargeted screening strategy was developed to find illegal additives based on ultrahigh-performance liquid chromatography-high-resolution mass spectrometry (UHPLC-HRMS). First, an analytical method for possible illegal additives in complex matrixes was established including fast sample pretreatment, accurate UHPLC separation, and HRMS detection. Second, efficient data processing and differential analysis workflow were suggested and applied to find potential risk compounds. Third, structure elucidation of risk compounds was performed by (1) searching online databases [Metlin and the Human Metabolome Database (HMDB)] and an in-house database which was established at the above-defined conditions of UHPLC-HRMS analysis and contains information on retention time, mass spectra (MS), and tandem mass spectra (MS/MS) of 475 illegal additives, (2) analyzing fragment ions, and (3) referring to fragmentation rules. Fish was taken as an example to show the usefulness of the nontargeted screening strategy, and six additives were found in suspected fish samples. Quantitative analysis was further carried out to determine the contents of these compounds. The satisfactory application of this strategy in fish samples means that it can also be used in the screening of illegal additives in other kinds of food samples.

  17. Nontargeted Screening Method for Illegal Additives Based on Ultrahigh-Performance Liquid Chromatography-High-Resolution Mass Spectrometry.

    PubMed

    Fu, Yanqing; Zhou, Zhihui; Kong, Hongwei; Lu, Xin; Zhao, Xinjie; Chen, Yihui; Chen, Jia; Wu, Zeming; Xu, Zhiliang; Zhao, Chunxia; Xu, Guowang

    2016-09-01

    Identification of illegal additives in complex matrixes is important in the food safety field. In this study a nontargeted screening strategy was developed to find illegal additives based on ultrahigh-performance liquid chromatography-high-resolution mass spectrometry (UHPLC-HRMS). First, an analytical method for possible illegal additives in complex matrixes was established including fast sample pretreatment, accurate UHPLC separation, and HRMS detection. Second, efficient data processing and differential analysis workflow were suggested and applied to find potential risk compounds. Third, structure elucidation of risk compounds was performed by (1) searching online databases [Metlin and the Human Metabolome Database (HMDB)] and an in-house database which was established at the above-defined conditions of UHPLC-HRMS analysis and contains information on retention time, mass spectra (MS), and tandem mass spectra (MS/MS) of 475 illegal additives, (2) analyzing fragment ions, and (3) referring to fragmentation rules. Fish was taken as an example to show the usefulness of the nontargeted screening strategy, and six additives were found in suspected fish samples. Quantitative analysis was further carried out to determine the contents of these compounds. The satisfactory application of this strategy in fish samples means that it can also be used in the screening of illegal additives in other kinds of food samples. PMID:27480407

  18. Self-Consistency Requirements of the Renormalization Group for Setting the Renormalization Scale

    SciTech Connect

    Brodsky, Stanley J.; Wu, Xing-Gang

    2012-08-07

    In conventional treatments, predictions from fixed-order perturbative QCD calculations cannot be fixed with certainty due to ambiguities in the choice of the renormalization scale as well as the renormalization scheme. In this paper we present a general discussion of the constraints of the renormalization group (RG) invariance on the choice of the renormalization scale. We adopt the RG based equations, which incorporate the scheme parameters, for a general exposition of RG invariance, since they simultaneously express the invariance of physical observables under both the variation of the renormalization scale and the renormalization scheme parameters. We then discuss the self-consistency requirements of the RG, such as reflexivity, symmetry, and transitivity, which must be satisfied by the scale-setting method. The Principle of Minimal Sensitivity (PMS) requires the slope of the approximant of an observable to vanish at the renormalization point. This criterion provides a scheme-independent estimation, but it violates the symmetry and transitivity properties of the RG and does not reproduce the Gell-Mann-Low scale for QED observables. The Principle of Maximum Conformality (PMC) satisfies all of the deductions of the RG invariance - reflectivity, symmetry, and transitivity. Using the PMC, all non-conformal {βRi}-terms (R stands for an arbitrary renormalization scheme) in the perturbative expansion series are summed into the running coupling, and one obtains a unique, scale-fixed, scheme-independent prediction at any finite order. The PMC scales and the resulting finite-order PMC predictions are both to high accuracy independent of the choice of initial renormalization scale, consistent with RG invariance.

  19. The large-N{sub c} renormalization group

    SciTech Connect

    Dorey, N.; Mattis, M.P.

    1995-05-01

    In this talk, we review how effective theories of mesons and baryons become exactly soluble in the large-N{sub c}, limit. We start with a generic hadron Lagrangian constrained only by certain well-known large-N{sub c}, selection rules. The bare vertices of the theory are dressed by an infinite class of UV divergent Feynman diagrams at leading order in 1/N{sub c}. We show how all these leading-order dia, grams can be summed exactly using semiclassical techniques. The saddle-point field configuration is reminiscent of the chiral bag: hedgehog pions outside a sphere of radius {Lambda}{sup {minus}1} ({Lambda} being the UV cutoff of the effective theory) matched onto nucleon degrees of freedom for r {le} {Lambda}{sup {minus}1}. The effect of this pion cloud is to renormalize the bare nucleon mass, nucleon-{Delta} hyperfine mass splitting, and Yukawa couplings of the theory. The corresponding large-N{sub c}, renormalization group equations for these parameters are presented, and solved explicitly in a series of simple models. We explain under what conditions the Skyrmion emerges as a UV fixed-point of the RG flow as {Lambda} {yields} {infinity}.

  20. Renormalization Group Trajectories Between Two Fixed Points

    NASA Astrophysics Data System (ADS)

    Abdesselam, Abdelmalek

    2010-03-01

    We report on our recent rigorous construction of complete renormalization group trajectories between two fixed points for the three-dimensional phi-four model with modified propagator considered by Brydges, Mitter and Scoppola (BMS). These are discrete critical trajectories which connect the ultraviolet Gaussian fixed point to the nontrivial BMS infrared fixed point which is an analogue of the Wilson-Fisher fixed point. The renormalization group map is defined rigorously and nonperturbatively, without using the hierarchical approximation. The trajectories are constructed by a fixed point argument in a suitable Banach space of sequences, where one perturbs a nonlinear one-dimensional iteration.

  1. Tensor hypercontraction. II. Least-squares renormalization

    NASA Astrophysics Data System (ADS)

    Parrish, Robert M.; Hohenstein, Edward G.; Martínez, Todd J.; Sherrill, C. David

    2012-12-01

    The least-squares tensor hypercontraction (LS-THC) representation for the electron repulsion integral (ERI) tensor is presented. Recently, we developed the generic tensor hypercontraction (THC) ansatz, which represents the fourth-order ERI tensor as a product of five second-order tensors [E. G. Hohenstein, R. M. Parrish, and T. J. Martínez, J. Chem. Phys. 137, 044103 (2012)], 10.1063/1.4732310. Our initial algorithm for the generation of the THC factors involved a two-sided invocation of overlap-metric density fitting, followed by a PARAFAC decomposition, and is denoted PARAFAC tensor hypercontraction (PF-THC). LS-THC supersedes PF-THC by producing the THC factors through a least-squares renormalization of a spatial quadrature over the otherwise singular 1/r12 operator. Remarkably, an analytical and simple formula for the LS-THC factors exists. Using this formula, the factors may be generated with O(N^5) effort if exact integrals are decomposed, or O(N^4) effort if the decomposition is applied to density-fitted integrals, using any choice of density fitting metric. The accuracy of LS-THC is explored for a range of systems using both conventional and density-fitted integrals in the context of MP2. The grid fitting error is found to be negligible even for extremely sparse spatial quadrature grids. For the case of density-fitted integrals, the additional error incurred by the grid fitting step is generally markedly smaller than the underlying Coulomb-metric density fitting error. The present results, coupled with our previously published factorizations of MP2 and MP3, provide an efficient, robust O(N^4) approach to both methods. Moreover, LS-THC is generally applicable to many other methods in quantum chemistry.

  2. Tensor hypercontraction. II. Least-squares renormalization.

    PubMed

    Parrish, Robert M; Hohenstein, Edward G; Martínez, Todd J; Sherrill, C David

    2012-12-14

    The least-squares tensor hypercontraction (LS-THC) representation for the electron repulsion integral (ERI) tensor is presented. Recently, we developed the generic tensor hypercontraction (THC) ansatz, which represents the fourth-order ERI tensor as a product of five second-order tensors [E. G. Hohenstein, R. M. Parrish, and T. J. Martínez, J. Chem. Phys. 137, 044103 (2012)]. Our initial algorithm for the generation of the THC factors involved a two-sided invocation of overlap-metric density fitting, followed by a PARAFAC decomposition, and is denoted PARAFAC tensor hypercontraction (PF-THC). LS-THC supersedes PF-THC by producing the THC factors through a least-squares renormalization of a spatial quadrature over the otherwise singular 1∕r(12) operator. Remarkably, an analytical and simple formula for the LS-THC factors exists. Using this formula, the factors may be generated with O(N(5)) effort if exact integrals are decomposed, or O(N(4)) effort if the decomposition is applied to density-fitted integrals, using any choice of density fitting metric. The accuracy of LS-THC is explored for a range of systems using both conventional and density-fitted integrals in the context of MP2. The grid fitting error is found to be negligible even for extremely sparse spatial quadrature grids. For the case of density-fitted integrals, the additional error incurred by the grid fitting step is generally markedly smaller than the underlying Coulomb-metric density fitting error. The present results, coupled with our previously published factorizations of MP2 and MP3, provide an efficient, robust O(N(4)) approach to both methods. Moreover, LS-THC is generally applicable to many other methods in quantum chemistry. PMID:23248986

  3. Finite volume renormalization scheme for fermionic operators

    SciTech Connect

    Monahan, Christopher; Orginos, Kostas

    2013-11-01

    We propose a new finite volume renormalization scheme. Our scheme is based on the Gradient Flow applied to both fermion and gauge fields and, much like the Schr\\"odinger functional method, allows for a nonperturbative determination of the scale dependence of operators using a step-scaling approach. We give some preliminary results for the pseudo-scalar density in the quenched approximation.

  4. Lectures on renormalization and asymptotic safety

    SciTech Connect

    Nagy, Sandor

    2014-11-15

    A short introduction is given on the functional renormalization group method, putting emphasis on its nonperturbative aspects. The method enables to find nontrivial fixed points in quantum field theoretic models which make them free from divergences and leads to the concept of asymptotic safety. It can be considered as a generalization of the asymptotic freedom which plays a key role in the perturbative renormalization. We summarize and give a short discussion of some important models, which are asymptotically safe such as the Gross–Neveu model, the nonlinear σ model, the sine–Gordon model, and we consider the model of quantum Einstein gravity which seems to show asymptotic safety, too. We also give a detailed analysis of infrared behavior of such scalar models where a spontaneous symmetry breaking takes place. The deep infrared behavior of the broken phase cannot be treated within the framework of perturbative calculations. We demonstrate that there exists an infrared fixed point in the broken phase which creates a new scaling regime there, however its structure is hidden by the singularity of the renormalization group equations. The theory spaces of these models show several similar properties, namely the models have the same phase and fixed point structure. The quantum Einstein gravity also exhibits similarities when considering the global aspects of its theory space since the appearing two phases there show analogies with the symmetric and the broken phases of the scalar models. These results be nicely uncovered by the functional renormalization group method.

  5. Numerical simulation for the influence of laser-induced plasmas addition on air mass capture of hypersonic inlet

    NASA Astrophysics Data System (ADS)

    Zhao, Wei; Dou, Zhiguo; Li, Qian

    2012-03-01

    The theory of laser-induced plasmas addition to hypersonic airflow off a vehicle to increase air mass capture and improve the performance of hypersonic inlets at Mach numbers below the design value is explored. For hypersonic vehicles, when flying at mach numbers lower than the design one, we can increase the mass capture ratio of inlet through laser-induced plasmas injection to the hypersonic flow upstream of cowl lip to form a virtual cowl. Based on the theory, the model of interaction between laser-induced plasmas and hypersonic flow was established. The influence on the effect of increasing mass capture ratio was studied at different positions of laser-induced plasmas region for the external compression hypersonic inlet at Mach 5 while the design value is 6, the power of plasmas was in the range of 1-8mJ. The main results are as follows: 1. the best location of the plasma addition region is near the intersection of the nose shock of the vehicle with the continuation of the cowl line, and slightly below that line. In that case, the shock generated by the heating is close to the shock that is a reflection of the vehicle nose shock off the imaginary solid surface-extension of the cowl. 2. Plasma addition does increase mass capture, and the effect becomes stronger as more energy is added, the peak value appeared when the power of plasma was about 4mJ, when the plasma energy continues to get stronger, the mass capture will decline slowly.

  6. The quantitative surface analysis of an antioxidant additive in a lubricant oil matrix by desorption electrospray ionization mass spectrometry

    PubMed Central

    Da Costa, Caitlyn; Reynolds, James C; Whitmarsh, Samuel; Lynch, Tom; Creaser, Colin S

    2013-01-01

    RATIONALE Chemical additives are incorporated into commercial lubricant oils to modify the physical and chemical properties of the lubricant. The quantitative analysis of additives in oil-based lubricants deposited on a surface without extraction of the sample from the surface presents a challenge. The potential of desorption electrospray ionization mass spectrometry (DESI-MS) for the quantitative surface analysis of an oil additive in a complex oil lubricant matrix without sample extraction has been evaluated. METHODS The quantitative surface analysis of the antioxidant additive octyl (4-hydroxy-3,5-di-tert-butylphenyl)propionate in an oil lubricant matrix was carried out by DESI-MS in the presence of 2-(pentyloxy)ethyl 3-(3,5-di-tert-butyl-4-hydroxyphenyl)propionate as an internal standard. A quadrupole/time-of-flight mass spectrometer fitted with an in-house modified ion source enabling non-proximal DESI-MS was used for the analyses. RESULTS An eight-point calibration curve ranging from 1 to 80 µg/spot of octyl (4-hydroxy-3,5-di-tert-butylphenyl)propionate in an oil lubricant matrix and in the presence of the internal standard was used to determine the quantitative response of the DESI-MS method. The sensitivity and repeatability of the technique were assessed by conducting replicate analyses at each concentration. The limit of detection was determined to be 11 ng/mm2 additive on spot with relative standard deviations in the range 3–14%. CONCLUSIONS The application of DESI-MS to the direct, quantitative surface analysis of a commercial lubricant additive in a native oil lubricant matrix is demonstrated. © 2013 The Authors. Rapid Communications in Mass Spectrometry published by John Wiley & Sons, Ltd. PMID:24097398

  7. Source Distribution Method for Unsteady One-Dimensional Flows With Small Mass, Momentum, and Heat Addition and Small Area Variation

    NASA Technical Reports Server (NTRS)

    Mirels, Harold

    1959-01-01

    A source distribution method is presented for obtaining flow perturbations due to small unsteady area variations, mass, momentum, and heat additions in a basic uniform (or piecewise uniform) one-dimensional flow. First, the perturbations due to an elemental area variation, mass, momentum, and heat addition are found. The general solution is then represented by a spatial and temporal distribution of these elemental (source) solutions. Emphasis is placed on discussing the physical nature of the flow phenomena. The method is illustrated by several examples. These include the determination of perturbations in basic flows consisting of (1) a shock propagating through a nonuniform tube, (2) a constant-velocity piston driving a shock, (3) ideal shock-tube flows, and (4) deflagrations initiated at a closed end. The method is particularly applicable for finding the perturbations due to relatively thin wall boundary layers.

  8. Renormalization of transport equations in Fokker-Planck models

    NASA Astrophysics Data System (ADS)

    Grabert, Hermann; Weidlich, Wolfgang

    1980-06-01

    This paper is concerned with the derivation of nonlinear fluctuation-renormalized transport equations of a fluctuating thermodynamic system, on the assumption that the macroscopic variables defining a state undergo a Fokker-Planck process. It is shown that the renormalization effect may consist of two parts: a renormalization of the thermodynamic forces and a renormalization of the transport coefficients. Closed analytical expressions for the renormalized quantities in terms of the bare quantities appearing in the Fokker-Planck equation are derived. A scheme for the approximate evaluation of these expressions is given.

  9. Energy positivity, non-renormalization, and holomorphy in Lorentz-violating supersymmetric theories

    NASA Astrophysics Data System (ADS)

    Clark, Adam B.

    2014-01-01

    This paper shows that the positive-energy and non-renormalization theorems of traditional supersymmetry survive the addition of Lorentz violating interactions. The Lorentz-violating coupling constants in theories using the construction of Berger and Kostelecky must obey certain constraints in order to preserve the positive energy theorem. Seiberg's holomorphic arguments are used to prove that the superpotential remains non-renormalized (perturbatively) in the presence of Lorentz-violating interactions of the Berger-Kostelecky type. We briefly comment on Lorentz-violating theories of the type constructed by Nibbelink and Pospelov to note that holomorphy arguments offer elegant proofs of many non-renormalization results, some known by other arguments, some new.

  10. Aluminium content of some processed foods, raw materials and food additives in China by inductively coupled plasma-mass spectrometry.

    PubMed

    Deng, Gui-Fang; Li, Ke; Ma, Jing; Liu, Fen; Dai, Jing-Jing; Li, Hua-Bin

    2011-01-01

    The level of aluminium in 178 processed food samples from Shenzhen city in China was evaluated using inductively coupled plasma-mass spectrometry. Some processed foods contained a concentration of up to 1226 mg/kg, which is about 12 times the Chinese food standard. To establish the main source in these foods, Al levels in the raw materials were determined. However, aluminium concentrations in raw materials were low (0.10-451.5 mg/kg). Therefore, aluminium levels in food additives used in these foods was determined and it was found that some food additives contained a high concentration of aluminium (0.005-57.4 g/kg). The results suggested that, in the interest of public health, food additives containing high concentrations of aluminium should be replaced by those containing less. This study has provided new information on aluminium levels in Chinese processed foods, raw materials and a selection of food additives.

  11. Elliptical galaxies kinematics within general relativity with renormalization group effects

    SciTech Connect

    Rodrigues, Davi C.

    2012-09-01

    The renormalization group framework can be applied to Quantum Field Theory on curved space-time, but there is no proof whether the beta-function of the gravitational coupling indeed goes to zero in the far infrared or not. In a recent paper [1] we have shown that the amount of dark matter inside spiral galaxies may be negligible if a small running of the General Relativity coupling G is present (δG/G{sub 0}∼<10{sup −7} across a galaxy). Here we extend the proposed model to elliptical galaxies and present a detailed analysis on the modeling of NGC 4494 (an ordinary elliptical) and NGC 4374 (a giant elliptical). In order to compare our results to a well known alternative model to the standard dark matter picture, we also evaluate NGC 4374 with MOND. In this galaxy MOND leads to a significative discrepancy with the observed velocity dispersion curve and has a significative tendency towards tangential anisotropy. On the other hand, the approach based on the renormalization group and general relativity (RGGR) could be applied with good results to these elliptical galaxies and is compatible with lower mass-to-light ratios (of about the Kroupa IMF type)

  12. Exposure to mass media and interpersonal counseling has additive effects on exclusive breastfeeding and its psychosocial determinants among Vietnamese mothers.

    PubMed

    Nguyen, Phuong H; Kim, Sunny S; Nguyen, Tuan T; Hajeebhoy, Nemat; Tran, Lan M; Alayon, Silvia; Ruel, Marie T; Rawat, Rahul; Frongillo, Edward A; Menon, Purnima

    2016-10-01

    The pathways through which behavior change interventions impact breastfeeding practices have not been well studied. This study aimed to examine: (1) the effects of exposure to mass media and interpersonal counseling on exclusive breastfeeding (EBF) and hypothesized psychosocial determinants (i.e. knowledge, intention, beliefs, social norms, and self-efficacy); and (2) the pathways through which exposure to mass media and interpersonal counseling are associated with EBF. We used survey data from mothers with children < 2 year (n = 2045) from the 2013 process evaluation of Alive & Thrive's program in Viet Nam. Multiple linear regression analyses and structural equation modeling were used to estimate effects. Exposure to mass media only, interpersonal counseling only, both or neither was 51%, 5%, 19% and 25%, respectively. Exposure to both mass media and interpersonal counseling had additive effects on EBF as well as on related psychosocial factors, compared with no exposure. For example, EBF prevalence was 26.1 percentage points (pp) higher in the group that received interpersonal counseling only, 3.9 pp higher in the mass media group and 31.8 pp higher in the group that received both interventions. As hypothesized, more than 90% of the total effect of the two interventions on EBF was explained by the psychosocial factors measured. Our findings suggest that combining different behavior change interventions leads to greater changes in psychosocial factors, which in turn positively affects breastfeeding behaviors.

  13. Exposure to mass media and interpersonal counseling has additive effects on exclusive breastfeeding and its psychosocial determinants among Vietnamese mothers.

    PubMed

    Nguyen, Phuong H; Kim, Sunny S; Nguyen, Tuan T; Hajeebhoy, Nemat; Tran, Lan M; Alayon, Silvia; Ruel, Marie T; Rawat, Rahul; Frongillo, Edward A; Menon, Purnima

    2016-10-01

    The pathways through which behavior change interventions impact breastfeeding practices have not been well studied. This study aimed to examine: (1) the effects of exposure to mass media and interpersonal counseling on exclusive breastfeeding (EBF) and hypothesized psychosocial determinants (i.e. knowledge, intention, beliefs, social norms, and self-efficacy); and (2) the pathways through which exposure to mass media and interpersonal counseling are associated with EBF. We used survey data from mothers with children < 2 year (n = 2045) from the 2013 process evaluation of Alive & Thrive's program in Viet Nam. Multiple linear regression analyses and structural equation modeling were used to estimate effects. Exposure to mass media only, interpersonal counseling only, both or neither was 51%, 5%, 19% and 25%, respectively. Exposure to both mass media and interpersonal counseling had additive effects on EBF as well as on related psychosocial factors, compared with no exposure. For example, EBF prevalence was 26.1 percentage points (pp) higher in the group that received interpersonal counseling only, 3.9 pp higher in the mass media group and 31.8 pp higher in the group that received both interventions. As hypothesized, more than 90% of the total effect of the two interventions on EBF was explained by the psychosocial factors measured. Our findings suggest that combining different behavior change interventions leads to greater changes in psychosocial factors, which in turn positively affects breastfeeding behaviors. PMID:27334544

  14. Focal masses in a non-cirrhotic liver: The additional benefit of CEUS over baseline imaging.

    PubMed

    Chiorean, L; Cantisani, V; Jenssen, C; Sidhu, P S; Baum, U; Dietrich, C F

    2015-09-01

    Incidentally detected focal liver lesions are commonly encountered in clinical practice presenting a challenge in the daily department work flow. Guidelines for the management of incidental focal liver lesions have been published but comments, illustrations and recommendations regarding practical issues are crucial. The unique features of contrast-enhanced ultrasound in non-invasive assessment of focal liver lesion enhancement throughout the vascular phases in real-time has allowed an impressive improvement in the diagnostic accuracy of ultrasound. We highlight the additional benefit of contrast-enhanced ultrasound over conventional B-mode ultrasound imaging in detection, characterization, differential and final diagnosis of focal liver lesions, as well as for liver metastases screening. The current roles of cross-sectional imaging are explained in detail, with indications and limitations for each procedure. The advantages of CEUS, such as non-ionizing radiation exposure, cost benefits, non-iodinate contrast agents, and repeatability are also described ultimately improving patient management.

  15. Effect of inorganic salts and glucose additives on dose-response, melting point and mass density of genipin gel dosimeters.

    PubMed

    Al-jarrah, A M; Abdul Rahman, Azhar; Shahrim, Iskandar; Razak, Nik Noor Ashikin Nik Ab; Ababneh, Baker; Tousi, Ehsan Taghizadeh

    2016-01-01

    Genipin gel dosimeters are hydrogels infused with a radiation-sensitive material which yield dosimetric information in three dimensions (3D). The effect of inorganic salts and glucose on the visible absorption dose-response, melting points and mass density of genipin gel dosimeters has been experimentally evaluated using 6-MV LINAC photons. As a result, the addition of glucose with optimum concentration of 10% (w/w) was found to improve the thermal stability of the genipin gel and increase its melting point (Tm) by 6 °C accompanied by a slight decrease of dose-response. Furthermore, glucose helps to adjust the gel mass density to obtain the desired tissue-equivalent properties. A drop of Tm was observed when salts were used as additives. As the salt concentration increased, gel Tm decreased. The mass density and melting point of the genipin gel could be adjusted using different amounts of glucose that improved the genipin gel suitability for 3D dose measurements without introducing additional toxicity to the final gel.

  16. Un-renormalized classical electromagnetism

    SciTech Connect

    Ibison, Michael . E-mail: ibison@earthtech.org

    2006-02-15

    This paper follows in the tradition of direct-action versions of electromagnetism having the aim of avoiding a balance of infinities wherein a mechanical mass offsets an infinite electromagnetic mass so as to arrive at a finite observed value. However, the direct-action approach ultimately failed in that respect because its initial exclusion of self-action was later found to be untenable in the relativistic domain. Pursing the same end, this paper examines instead a version of electromagnetism wherein mechanical action is excluded and self-action is retained. It is shown that the resulting theory is effectively interacting due to the presence of infinite forces. A vehicle for the investigation is a pair of classical point charges in a positronium-like arrangement for which the orbits are found to be self-sustaining and naturally quantized.

  17. Nonlocal Polyakov-Nambu-Jona-Lasinio model with wave function renormalization at finite temperature and chemical potential

    SciTech Connect

    Contrera, G. A.; Orsaria, M.; Scoccola, N. N.

    2010-09-01

    We study the phase diagram of strongly interacting matter in the framework of a nonlocal SU(2) chiral quark model which includes wave function renormalization and coupling to the Polyakov loop. Both nonlocal interactions based on the frequently used exponential form factor, and on fits to the quark mass and renormalization functions obtained in lattice calculations are considered. Special attention is paid to the determination of the critical points, both in the chiral limit and at finite quark mass. In particular, we study the position of the critical end point as well as the value of the associated critical exponents for different model parametrizations.

  18. Simple on-shell renormalization framework for the Cabibbo-Kobayashi-Maskawa matrix

    SciTech Connect

    Kniehl, Bernd A.; Sirlin, Alberto

    2006-12-01

    We present an explicit on-shell framework to renormalize the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix at the one-loop level. It is based on a novel procedure to separate the external-leg mixing corrections into gauge-independent self-mass (sm) and gauge-dependent wave-function renormalization contributions, and to adjust nondiagonal mass counterterm matrices to cancel all the divergent sm contributions, and also their finite parts subject to constraints imposed by the Hermiticity of the mass matrices. It is also shown that the proof of gauge independence and finiteness of the remaining one-loop corrections to W{yields}q{sub i}+q{sub j} reduces to that in the unmixed, single-generation case. Diagonalization of the complete mass matrices leads then to an explicit expression for the CKM counterterm matrix, which is gauge independent, preserves unitarity, and leads to renormalized amplitudes that are nonsingular in the limit in which any two fermions become mass degenerate.

  19. Poissonian renormalizations, exponentials, and power laws

    NASA Astrophysics Data System (ADS)

    Eliazar, Iddo

    2013-05-01

    This paper presents a comprehensive “renormalization study” of Poisson processes governed by exponential and power-law intensities. These Poisson processes are of fundamental importance, as they constitute the very bedrock of the universal extreme-value laws of Gumbel, Fréchet, and Weibull. Applying the method of Poissonian renormalization we analyze the emergence of these Poisson processes, unveil their intrinsic dynamical structures, determine their domains of attraction, and characterize their structural phase transitions. These structural phase transitions are shown to be governed by uniform and harmonic intensities, to have universal domains of attraction, to uniquely display intrinsic invariance, and to be intimately connected to “white noise” and to “1/f noise.” Thus, we establish a Poissonian explanation to the omnipresence of white and 1/f noises.

  20. Poissonian renormalizations, exponentials, and power laws.

    PubMed

    Eliazar, Iddo

    2013-05-01

    This paper presents a comprehensive "renormalization study" of Poisson processes governed by exponential and power-law intensities. These Poisson processes are of fundamental importance, as they constitute the very bedrock of the universal extreme-value laws of Gumbel, Fréchet, and Weibull. Applying the method of Poissonian renormalization we analyze the emergence of these Poisson processes, unveil their intrinsic dynamical structures, determine their domains of attraction, and characterize their structural phase transitions. These structural phase transitions are shown to be governed by uniform and harmonic intensities, to have universal domains of attraction, to uniquely display intrinsic invariance, and to be intimately connected to "white noise" and to "1/f noise." Thus, we establish a Poissonian explanation to the omnipresence of white and 1/f noises.

  1. Renormalized Resonance Quartets in Dispersive Wave Turbulence

    SciTech Connect

    Lee, Wonjung; Kovacic, Gregor; Cai, David

    2009-07-10

    Using the (1+1)D Majda-McLaughlin-Tabak model as an example, we present an extension of the wave turbulence (WT) theory to systems with strong nonlinearities. We demonstrate that nonlinear wave interactions renormalize the dynamics, leading to (i) a possible destruction of scaling structures in the bare wave systems and a drastic deformation of the resonant manifold even at weak nonlinearities, and (ii) creation of nonlinear resonance quartets in wave systems for which there would be no resonances as predicted by the linear dispersion relation. Finally, we derive an effective WT kinetic equation and show that our prediction of the renormalized Rayleigh-Jeans distribution is in excellent agreement with the simulation of the full wave system in equilibrium.

  2. Black Hole Entropy and the Renormalization Group

    NASA Astrophysics Data System (ADS)

    Satz, Alejandro; Jacobson, Ted

    2015-01-01

    Four decades after its first postulation by Bekenstein, black hole entropy remains mysterious. It has long been suggested that the entanglement entropy of quantum fields on the black hole gravitational background should represent at least an important contribution to the total Bekenstein-Hawking entropy, and that the divergences in the entanglement entropy should be absorbed in the renormalization of the gravitational couplings. In this talk, we describe how an improved understanding of black hole entropy is obtained by combining these notions with the renormalization group. By introducing an RG flow scale, we investigate whether the total entropy of the black hole can be partitioned in a "gravitational" part related to the flowing gravitational action, and a "quantum" part related to the unintegrated degrees of freedom. We describe the realization of this idea for free fields, and the complications and qualifications arising for interacting fields.

  3. Renormalization of the jet-quenching parameter

    NASA Astrophysics Data System (ADS)

    Blaizot, Jean-Paul; Mehtar-Tani, Yacine

    2014-09-01

    We study the radiative processes that affect the propagation of a high energy gluon in a dense medium, such as a quark-gluon plasma. In particular, we investigate the role of the large double logarithmic corrections, ∼αsln2 L /τ0, that were recently identified in the study of p⊥-broadening by Liou, Mueller and Wu. We show that these large corrections can be reabsorbed in a renormalization of the jet quenching parameter controlling both momentum broadening and energy loss. We argue that the probabilistic description of these phenomena remains valid, in spite of the large non-locality in time of the radiative corrections. The renormalized jet-quenching parameter is enhanced compared to its standard perturbative estimate. As a particular consequence, the radiative energy loss scales with medium size L as L 2 + γ, with γ = 2√{αsNc / π }, as compared to the standard scaling in L2.

  4. Study on Antiwear and Repairing Performances about Mass of Nano-copper Lubricating Additives to 45 Steel

    NASA Astrophysics Data System (ADS)

    Wang, X. L.; Yin, Y. L.; Zhang, G. N.; Wang, W. Y.; Zhao, K. K.

    Nano-copper usually serve for lubricating additives in tribology field. The antiwear and reducing friction performances both basic lubrication oil and basic lubrication oil with nano-copper in different mass were tested by friction wear test machine. The morphologies and the main elements of worn surfaces were analyzed by SEM. The results indicated that nano-copper could improve tribology performances of basic lubrication oil. Comparing with base lubrication oil, the mass is 0.15% of nano-copper, the friction coefficient and the worn trace width can be reduced 34% and 32% respectively. Nano-copper can form self-repairing film in lubrication oil which availably separates the friction materials in friction process. Therefore, nano-copper has wonderful antiwear, reducing friction and self-repairing performances. And the function mechanism of Cu nanoparticles is studied in the paper.

  5. Holographic renormalization group and cosmology in theories with quasilocalized gravity

    NASA Astrophysics Data System (ADS)

    Csáki, Csaba; Erlich, Joshua; Hollowood, Timothy J.; Terning, John

    2001-03-01

    We study the long distance behavior of brane theories with quasilocalized gravity. The five-dimensional (5D) effective theory at large scales follows from a holographic renormalization group flow. As intuitively expected, the graviton is effectively four dimensional at intermediate scales and becomes five dimensional at large scales. However, in the holographic effective theory the essentially 4D radion dominates at long distances and gives rise to scalar antigravity. The holographic description shows that at large distances the Gregory-Rubakov-Sibiryakov (GRS) model is equivalent to the model recently proposed by Dvali, Gabadadze, and Porrati (DGP), where a tensionless brane is embedded into 5D Minkowski space, with an additional induced 4D Einstein-Hilbert term on the brane. In the holographic description the radion of the GRS model is automatically localized on the tensionless brane, and provides the ghostlike field necessary to cancel the extra graviton polarization of the DGP model. Thus, there is a holographic duality between these theories. This analysis provides physical insight into how the GRS model works at intermediate scales; in particular it sheds light on the size of the width of the graviton resonance, and also demonstrates how the holographic renormalization group can be used as a practical tool for calculations.

  6. Entanglement renormalization and two dimensional string theory

    NASA Astrophysics Data System (ADS)

    Molina-Vilaplana, J.

    2016-04-01

    The entanglement renormalization flow of a (1 + 1) free boson is formulated as a path integral over some auxiliary scalar fields. The resulting effective theory for these fields amounts to the dilaton term of non-critical string theory in two spacetime dimensions. A connection between the scalar fields in the two theories is provided, allowing to acquire novel insights into how a theory of gravity emerges from the entanglement structure of another one without gravity.

  7. Cosmology is not a renormalization group flow.

    PubMed

    Woodard, R P

    2008-08-22

    A critical examination is made of two simple implementations of the idea that cosmology can be viewed as a renormalization group (RG) flow. Both implementations are shown to fail when applied to a massless, minimally coupled scalar with a quartic self-interaction on a locally de Sitter background. Cosmological evolution in this model is not driven by any RG screening of couplings but rather by inflationary particle production gradually filling an initially empty universe with a sea of long wavelength scalars.

  8. Renormalization in Chern-Simons Gauge Theories and Vector Meson Theory 2+1 Space

    NASA Astrophysics Data System (ADS)

    Ramaswamy, Suresh

    1991-02-01

    The study of radiative corrections to the topological mass of the photon in Chern-Simons gauge theories and the current coupled vector meson model in 2 + 1 space comprise the major concerns of this thesis. Some general aspects of 2 + 1 dimensional field theories, including CS gauge theories, are reviewed. The photon topological mass is renormalized through the addition of the parity odd part of the current correlation function evaluated at zero external momentum (|Pi(0)). Nontrivial contributions arise from a spinor current. It is argued that the Coleman-Hill theorem, which postulates that the one loop fermion graph constitutes the only correction, is overly restrictive. It is shown by explicit calculation that charged vector mesons also contribute. The topological mass corrections from spin zero, spin one-half and (the finite contribution of) spin one fields are combined into a unified expression, suggestive of generalization to higher spins. The current coupled vector meson model is considered next, utilizing a general formulation. Sum rules are derived for the spectral functions characterizing the propagator. One of the sum rules is found to allow the wave function renormalization constant (Z) to exceed unity. A rescaling of the fields, however, is found to resolve the problem. Such behaviour is shown perturbatively for a coupling to a spinor current, and in a soluble model. The former results also reveal parity violation induced through radiative corrections. A bound state is found to exist near the two fermion threshold, for arbitrarily weak coupling. Chapter V considers Aharonov-Bohm scattering of spinning particles. Known results for spin zero and spin one-half scattering are reviewed. In the case of scattering of spin one particles, the wave equation is found to be too singular for spin effects to survive. In the Galilean limit of the problem, the unboundedness disappears and results parallel those for spin one-half. Cross sections for some pure state

  9. Holographic entanglement renormalization of topological insulators

    NASA Astrophysics Data System (ADS)

    Wen, Xueda; Cho, Gil Young; Lopes, Pedro L. S.; Gu, Yingfei; Qi, Xiao-Liang; Ryu, Shinsei

    2016-08-01

    We study the real-space entanglement renormalization group flows of topological band insulators in (2+1) dimensions by using the continuum multiscale entanglement renormalization ansatz (cMERA). Given the ground state of a Chern insulator, we construct and study its cMERA by paying attention, in particular, to how the bulk holographic geometry and the Berry curvature depend on the topological properties of the ground state. It is found that each state defined at different energy scale of cMERA carries a nonzero Berry flux, which is emanated from the UV layer of cMERA, and flows towards the IR. Hence, a topologically nontrivial UV state flows under the renormalization group to an IR state, which is also topologically nontrivial. On the other hand, we found that there is an obstruction to construct the exact ground state of a topological insulator with a topologically trivial IR state. That is, if we try to construct a cMERA for the ground state of a Chern insulator by taking a topologically trivial IR state, the resulting cMERA does not faithfully reproduce the exact ground state at all length scales.

  10. The renormalization group via statistical inference

    NASA Astrophysics Data System (ADS)

    Bény, Cédric; Osborne, Tobias J.

    2015-08-01

    In physics, one attempts to infer the rules governing a system given only the results of imperfect measurements. Hence, microscopic theories may be effectively indistinguishable experimentally. We develop an operationally motivated procedure to identify the corresponding equivalence classes of states, and argue that the renormalization group (RG) arises from the inherent ambiguities associated with the classes: one encounters flow parameters as, e.g., a regulator, a scale, or a measure of precision, which specify representatives in a given equivalence class. This provides a unifying framework and reveals the role played by information in renormalization. We validate this idea by showing that it justifies the use of low-momenta n-point functions as statistically relevant observables around a Gaussian hypothesis. These results enable the calculation of distinguishability in quantum field theory. Our methods also provide a way to extend renormalization techniques to effective models which are not based on the usual quantum-field formalism, and elucidates the relationships between various type of RG.

  11. Renormalized strong-coupling quenched QED in four dimensions

    SciTech Connect

    Hawes, F.T.; Sizer, T.; Williams, A.G. |

    1997-03-01

    We study renormalized quenched strong-coupling QED in four dimensions in an arbitrary covariant gauge. Above the critical coupling leading to dynamical chiral symmetry breaking, we show that there is no finite chiral limit. This behavior is found to be independent of the detailed choice of photon-fermion proper vertex in the Dyson-Schwinger equation formalism, provided that the vertex is consistent with the Ward-Takahashi identity and multiplicative renormalizability. We show that the finite solutions previously reported lie in an unphysical regime of the theory with multiple solutions and ultraviolet oscillations in the mass functions. This study is consistent with the assertion that in four dimensions strong coupling QED does not have a continuum limit in the conventional sense. {copyright} {ital 1997} {ital The American Physical Society}

  12. Gauge-independent renormalization of the 2-Higgs-doublet model

    NASA Astrophysics Data System (ADS)

    Krause, Marcel; Lorenz, Robin; Mühlleitner, Margarete; Santos, Rui; Ziesche, Hanna

    2016-09-01

    The 2-Higgs-Doublet Model (2HDM) belongs to the simplest extensions of the Standard Model (SM) Higgs sector that are in accordance with theoretical and experimental constraints. In order to be able to properly investigate the experimental Higgs data and, in the long term to distinguish between possible models beyond the SM, precise predictions for the Higgs boson observables have to be made available on the theory side. This requires the inclusion of the higher order corrections. In this work, we investigate in detail the renormalization of the 2HDM, a pre-requisite for the computation of higher order corrections. We pay particular attention to the renormalization of the mixing angles α and β, which diagonalize the Higgs mass matrices and which enter all Higgs observables. The implications of various renormalization schemes in next-to-leading order corrections to the sample processes H ± → W ± h/H and H → ZZ are investigated. Based on our findings, we will present a renormalization scheme that is at the same time process independent, gauge independent and numerically stable.

  13. Chiral dynamics in a magnetic field from the functional renormalization group

    NASA Astrophysics Data System (ADS)

    Kamikado, Kazuhiko; Kanazawa, Takuya

    2014-03-01

    We investigate the quark-meson model in a magnetic field using the functional renormalization group equation beyond the local-potential approximation. Our truncation of the effective action involves anisotropic wave function renormalization for mesons, which allows us to investigate how the magnetic field distorts the propagation of neutral mesons. Solving the flow equation numerically, we find that the transverse velocity of mesons decreases with the magnetic field at all temperatures, which is most prominent at zero temperature. The meson screening masses and the pion decay constants are also computed. The constituent quark mass is found to increase with magnetic field at all temperatures, resulting in the crossover temperature that increases monotonically with the magnetic field. This tendency is consistent with most model calculations but not with the lattice simulation performed at the physical point. Our work suggests that the strong anisotropy of meson propagation may not be the fundamental origin of the inverse magnetic catalysis.

  14. Investigating the effect of additional gases in an atmospheric-pressure helium plasma jet using ambient mass spectrometry

    NASA Astrophysics Data System (ADS)

    Oh, Jun-Seok; Furuta, Hiroshi; Hatta, Akimitsu; Bradley, James W.

    2015-01-01

    Using ambient mass spectrometry, positive and negative ions created in an atmospheric-pressure plasma jet have been detected for a variation of different traces gases (Ar, N2, and O2) added to the flow, downstream of the main helium discharge plasma. We find that such additions can change the chemistry in the outflow plasma plume. For instance, small amounts of O2 increases the formation of positive ion clusters, e.g., water clusters H+(H2O)n (with n up to 5) through hydration reactions, but decreases the intensity of heavy negative ions detected. With the addition of Ar and N2 we see a marked decrease in the intensity of negative ions in the plume but with increased Ar+ and nitrous oxide ions (e.g., N2O+) for the two cases respectively. From broadband optical emission measurements of the glowing plasma we see that the relative emission intensity of OH radical were changed with addition of the four different gases but the emission spectra were not changed. A calculation of rotational temperature of OH radicals, indicates that the gas temperatures is about 290 K for the four different gas mixture cases.

  15. Nonperturbative renormalization and the electron{close_quote}s anomalous moment in large-{alpha} QED

    SciTech Connect

    Hiller, J.R.; Brodsky, S.J.

    1999-01-01

    We study the physical electron in quantum electrodynamics expanded on the light-cone Fock space in order to address two problems: (1) the physics of the electron{close_quote}s anomalous magnetic moment a{sub e} in nonperturbative QED and (2) the practical problems of ultraviolet regularization and renormalization in truncated nonperturbative light-cone Hamiltonian theory. We present results for a{sub e} computed in a light-cone gauge Fock space truncated to include one bare electron and at most two photons, i.e., up to two photons in flight. The calculational scheme uses an invariant mass cutoff, discretized light-cone quantization (DLCQ), a Tamm-Dancoff truncation of the Fock space, and a photon mass regulator. We introduce new weighting methods which greatly improve convergence to the continuum within DLCQ. Nonperturbative renormalization of the coupling and electron mass are carried out, and a limit on the magnitude of the effective physical coupling strength is computed. A large renormalized coupling strength {alpha}{sub R}=0.1 is then used to make the nonperturbative effects in the electron anomalous moment from the one-electron, two-photon Fock state sector numerically detectable. {copyright} {ital 1998} {ital The American Physical Society}

  16. Renormalization Group for Critical Phenomena in Complex Networks

    PubMed Central

    Boettcher, S.; Brunson, C. T.

    2011-01-01

    We discuss the behavior of statistical models on a novel class of complex “Hanoi” networks. Such modeling is often the cornerstone for the understanding of many dynamical processes in complex networks. Hanoi networks are special because they integrate small-world hierarchies common to many social and economical structures with the inevitable geometry of the real world these structures exist in. In addition, their design allows exact results to be obtained with the venerable renormalization group (RG). Our treatment will provide a detailed, pedagogical introduction to RG. In particular, we will study the Ising model with RG, for which the fixed points are determined and the RG flow is analyzed. We show that the small-world bonds result in non-universal behavior. It is shown that a diversity of different behaviors can be observed with seemingly small changes in the structure of hierarchical networks generally, and we provide a general theory to describe our findings. PMID:22194725

  17. Renormalization group flows and continual Lie algebras

    NASA Astrophysics Data System (ADS)

    Bakas, Ioannis

    2003-08-01

    We study the renormalization group flows of two-dimensional metrics in sigma models using the one-loop beta functions, and demonstrate that they provide a continual analogue of the Toda field equations in conformally flat coordinates. In this algebraic setting, the logarithm of the world-sheet length scale, t, is interpreted as Dynkin parameter on the root system of a novel continual Lie algebra, denoted by Script G(d/dt;1), with anti-symmetric Cartan kernel K(t,t') = delta'(t-t'); as such, it coincides with the Cartan matrix of the superalgebra sl(N|N+1) in the large-N limit. The resulting Toda field equation is a non-linear generalization of the heat equation, which is integrable in target space and shares the same dissipative properties in time, t. We provide the general solution of the renormalization group flows in terms of free fields, via Bäcklund transformations, and present some simple examples that illustrate the validity of their formal power series expansion in terms of algebraic data. We study in detail the sausage model that arises as geometric deformation of the O(3) sigma model, and give a new interpretation to its ultra-violet limit by gluing together two copies of Witten's two-dimensional black hole in the asymptotic region. We also provide some new solutions that describe the renormalization group flow of negatively curved spaces in different patches, which look like a cane in the infra-red region. Finally, we revisit the transition of a flat cone C/Zn to the plane, as another special solution, and note that tachyon condensation in closed string theory exhibits a hidden relation to the infinite dimensional algebra Script G(d/dt;1) in the regime of gravity. Its exponential growth holds the key for the construction of conserved currents and their systematic interpretation in string theory, but they still remain unknown.

  18. Renormalization of the periodic scalar field theory by Polchinski's renormalization group method

    NASA Astrophysics Data System (ADS)

    Nándori, I.; Sailer, K.; Jentschura, U. D.; Soff, G.

    2002-04-01

    The renormalization group (RG) flow for the two-dimensional sine-Gordon model is determined by means of Polchinski's RG equation at next-to-leading order in the derivative expansion. In this paper, we have two different goals, (i) to consider the renormalization scheme-dependence of Polchinski's method by matching Polchinski's equation with the Wegner-Houghton equation and with the real space RG equations for the two-dimensional dilute Coulomb-gas, (ii) to go beyond the local potential approximation in the gradient expansion in order to clarify the supposed role of the field-dependent wave-function renormalization. The well-known Coleman fixed point of the sine-Gordon model is recovered after linearization, whereas the flow exhibits strong dependence on the choice of the renormalization scheme when non-linear terms are kept. The RG flow is compared to those obtained in the Wegner-Houghton approach and in the dilute gas approximation for the two-dimensional Coulomb-gas.

  19. Nonuniversal quantities from dual renormalization group transformations.

    PubMed

    Meurice, Y; Niermann, S

    1999-09-01

    Using a simplified version of the renormalization group (RG) transformation of Dyson's hierarchical model, we show that one can calculate all the nonuniversal quantities entering into the scaling laws by combining an expansion about the high-temperature fixed point with a dual expansion about the critical point. The magnetic susceptibility is expressed in terms of two dual quantities transforming covariantly under an RG transformation and has a smooth behavior in the high-temperature limit. Using the analogy with Hamiltonian mechanics, the simplified example discussed here is similar to the anharmonic oscillator, while more realistic examples can be thought of as coupled oscillators, allowing resonance phenomena. PMID:11970062

  20. Renormalization schemes: Where do we stand

    SciTech Connect

    Ward, B.F.L.

    1989-07-01

    We consider the status of the current approaches to the application of the renormalization program to the standard SU/sub 2L/ /times/ U/sub 1/ theory from the standpoint of the interplay of the scheme chosen for such an application and the attendant high-precision tests of the respective loop effects. We thus review the available schemes and discuss their theoretical relationships. We also show how such schemes stand in numerical relation to one another in the context of high-precision Z/sup 0/ physics, as an illustration. 15 refs., 2 figs., 2 tabs.

  1. Extraction, clean-up and gas chromatography-mass spectrometry characterization of zilpaterol as feed additive in fattening cattle.

    PubMed

    Bocca, B; Di Mattia, M; Cartoni, C; Fiori, M; Felli, M; Neri, B; Brambilla, G

    2003-01-01

    Zilpaterol is an adrenergic drug currently licensed in Mexico and South Africa as a feed additive for cattle close to consignment. In this study an analytical method to detect zilpaterol in commercial feeds was set up. The influence of extraction solvent and matrix was evaluated. The drug as a trimethylsilyl derivative was characterized by GC-MS, on a quadrupole detector, in the electron impact mode. Acidic extraction, solid-phase extraction C(18) non-endcapped clean-up and mass characterization on ions m/z 308, 291, 405, 390 provided zilpaterol recoveries >75.3% and repeatability <3.3% in feeds spiked in the range 30.0-120.0 ng/g. The limits of detection and quantification were 7.5 and 25.0 ng/g, respectively. Such limits are well below the dose of 5.0-20.0 microgram/g proposed as effective.

  2. [Simultaneous determination of 16 organic acids in feed additives by on-line enrichment and ion chromatography-mass spectrometry].

    PubMed

    Xiong, Zhiyu; Dong, Ying; Zhou, Hongbin; Yu, Yang; Li, Jing; Sun, Li

    2014-02-01

    A novel analytical method for simultaneous determination of sixteen organic acids by on-line enrichment and ion chromatography-mass spectrometry (IC-MS) was developed. Online enrichment and separation of the organic acids were performed by ion chromatography on a homemade enrichment column and a homemade separation column. The qualitative and quantitative analyses of the organic acids were performed by mass spectrometry in selected ion monitoring (SIM) mode on the basis of atmospheric pressure chemical ionization (APCI) source in negative mode. The sample of 200 microL was injected for the analysis, and the on-line enrichment time was 3 min. The sodium hydroxide solution was used as a gradient elution system. The two columns made it possible to have a low limit of detection due to the good enrichment and separation capability. The sixteen organic acids were separated completely within 30 min. All curves showed good linearity within the test concentration ranges. The limits of detection (LODs) were between 0.01 and 0.22 mg/L, and the average recoveries were between 70.6% and 110.8%. The relative standard deviations (RSDs) were less than 6.3%. The results indicate that this method is simple, rapid, sensitive and accurate for the determination of the organic acids in feed additives.

  3. To overcome the appearance of the efflorescences by magnesium carbonate addition in a mass for manufacture of bricks of construction

    NASA Astrophysics Data System (ADS)

    Chemani, H.

    2011-01-01

    Following the tendency of some European countries the briquetiers develop further the aesthetic aspect of their products and, the supply of colors and, aspects of surface will be further extended. The recovery of the sustainability of facades in bricks apparent, the quality of raw materials, and their determination remain a major problem. The presence of soluble salts in the field is fairly harmful for the product terracotta because they are the cause of apparitions of efflorescences. To defeat this type of default our study is on an addition of MgCO3 a mixture of two kinds of clay. The doses MgCO3 were between (0,25-0,5-0,75-1-1,5%) of the dry mass to treat. With rates of clay yellow and, gray which are respectively (40-60%). In comparison with a previous study where the addition was BaCO3. Finished products obtained with 1% MgCO3 exhibited a better aesthetic aspect, of the qualities insulating, and a mechanical resistance significantly higher than the bricks ceramics ordinary marketed at the present time.

  4. Renormalization group analysis in nonrelativistic QCD for colored scalars

    SciTech Connect

    Hoang, Andre H.; Ruiz-Femenia, Pedro

    2006-01-01

    The velocity nonrelativistic QCD Lagrangian for colored heavy scalar fields in the fundamental representation of QCD and the renormalization group analysis of the corresponding operators are presented. The results are an important ingredient for renormalization group improved computations of scalar-antiscalar bound state energies and production rates at next-to-next-to-leading-logarithmic (NNLL) order.

  5. Deep, Low-mass Ratio Overcontact Binary Systems. XII. CK Bootis with Possible Cyclic Magnetic Activity and Additional Companion

    NASA Astrophysics Data System (ADS)

    Yang, Y.-G.; Qian, S.-B.; Soonthornthum, B.

    2012-05-01

    We present precision CCD photometry, a period study, and a two-color simultaneous Wilson code solution of the short-period contact binary CK Bootis. The asymmetric light curves were modeled by a dark spot on the primary component. The result identifies that CK Boo is an A-type W UMa binary with a high fillout of f = 71.7(± 4.4)%. From the O - C curve, it is found that the orbital period changes in a complicated mode, i.e., a long-term increase with two sinusoidal variations. One cyclic oscillation with a period of 10.67(± 0.20) yr may result from magnetic activity cycles, which are identified by the variability of Max. I - Max. II. Another sinusoidal variation (i.e., A = 0.0131 days(± 0.0009 days) and P 3 = 24.16(± 0.64) yr) may be attributed to the light-time effect due to a third body. This kind of additional companion can extract angular momentum from the central binary system. The orbital period secularly increases at a rate of dP/dt = +9.79 (±0.80) × 10-8 days yr-1, which may be interpreted by conservative mass transfer from the secondary to the primary. This kind of deep, low-mass ratio overcontact binaries may evolve into a rapid-rotating single star, only if the contact configuration do not break down at J spin > (1/3)J orb.

  6. Heavy quark masses

    NASA Technical Reports Server (NTRS)

    Testa, Massimo

    1990-01-01

    In the large quark mass limit, an argument which identifies the mass of the heavy-light pseudoscalar or scalar bound state with the renormalized mass of the heavy quark is given. The following equation is discussed: m(sub Q) = m(sub B), where m(sub Q) and m(sub B) are respectively the mass of the heavy quark and the mass of the pseudoscalar bound state.

  7. On the renormalization of the electroweak chiral Lagrangian with a Higgs

    NASA Astrophysics Data System (ADS)

    Gavela, M. B.; Kanshin, K.; Machado, P. A. N.; Saa, S.

    2015-03-01

    We consider the scalar sector of the effective non-linear electroweak Lagrangian with a light "Higgs" particle. For a leading order Lagrangian, the complete one-loop off-shell renormalization procedure is performed, including the effects of a finite Higgs mass. This determines the complete set of independent chiral invariant scalar counterterms required for consistency; these include bosonic operators often disregarded. A novel general parametrization of the Goldstone boson matrix is proposed, which reduces to the various usual ones for specific values of its parameter. Furthermore, new counterterms involving the Higgs field which are apparently chiral non-invariant are identified in the perturbative analysis. A redefinition of the Goldstone boson fields which absorbs all chiral non-invariant counterterms is then explicitly determined. The physical results translate into renormalization group equations which may be useful when comparing future Higgs data at different energies.

  8. Implementation of an Environmental Focus in an Undergraduate Chemistry Curriculum by the Addition of Gas Chromatography-Mass Spectrometry

    NASA Astrophysics Data System (ADS)

    Atterholt, Cynthia; Butcher, David J.; Bacon, J. Roger; Kwochka, William R.; Woosley, Royce

    2000-12-01

    The Department Chemistry and Physics at Western Carolina University has added an environmental focus to its curriculum, and gas chromatography-mass spectrometry (GC-MS) was identified as an essential tool in environmental analysis. GC-MS is used in undergraduate chemistry courses in: (i) the identification of synthesized compounds and natural products, (ii) monitoring compounds and their degradation in the environment, and (iii) analytical method development. In Organic Chemistry, the GC-MS is used to characterize natural products and the products of an environmentally benign chemical synthesis. In Environmental Chemistry, the GC-MS is used to identify compounds of environmental interest, such as pesticides in soil samples, polycyclic aromatic hydrocarbons in water, and hydrocarbons in gasoline samples. In Instrumental Analysis I, students characterize numerous compounds in cigarette smoke using GC-MS. In Instrumental Analysis II, students are presented with an analytical chemistry problem for which they research protocols, collect samples, and perform the analyses. The GC-MS has been used to identify volatile compounds in a number of complex mixtures. Also, research in chemistry is a significant part of our curriculum, and numerous undergraduate students have used the GC-MS in their research. The addition of GC-MS has enhanced many of our undergraduate laboratory courses and student-led research projects.

  9. Abortion after deliberate Arthrotec® addition to food. Mass spectrometric detection of diclofenac, misoprostol acid, and their urinary metabolites.

    PubMed

    Watzer, Bernhard; Lusthof, Klaas J; Schweer, Horst

    2015-07-01

    Arthrotec(®) (AT) is a combination of diclofenac, a nonsteroidal anti-inflammatory drug (NSAID), and misoprostol (MP), a synthetic analogue of prostaglandin E1 (PGE1). MP is a lipophilic methyl ester prodrug. It is readily metabolized to the biologically active misoprostol acid (MPA). During the last few years, medical studies exhibited MP to be an excellent abortive. In this paper, we describe a rare criminal case of MP abortion, initiated by the expectant father. After the abortion, samples of vomit and urine were collected. Systemic exposure to MP is difficult to prove, because both MP and the active metabolite MPA are hardly excreted in urine. Therefore, in addition to routine toxicological analysis, we used slightly modified, well-established liquid and gas chromatographic/tandem mass spectrometric (LC/MS/MS and GC/MS/MS) methods, for the direct and the indirect detection of MPA and its metabolites. In this case, we were able to demonstrate the presence of the major MP metabolites 2,3-dinor-MPA and 2,3,4,5-tetranor-MPA in the urine of the victim. We also detected paracetamol, 3-methoxyparacetamol and diclofenac-glucuronide in the urine. In the vomit of the victim, we detected diclofenac and MPA. These results, combined with the criminal investigations, showed that the accused had mixed MP into the food of his pregnant girlfriend. Finally, these investigations contributed to a confession of the accused.

  10. The Density Matrix Renormalization Group for Strongly Correlated Electron Systems: A Generic Implementation

    SciTech Connect

    Alvarez, Gonzalo

    2009-01-01

    The purpose of this paper is (1) to present a generic and fully functional implementation of the density-matrix renormalization group (DMRG) algorithm, and (2) to describe how to write additional strongly-correlated electron models and geometries by using templated classes. Besides considering general models and geometries, the code implements Hamiltonian symmetries in a generic way and parallelization over symmetry-related matrix blocks.

  11. The Magnus expansion and the in-medium similarity renormalization group

    SciTech Connect

    Morris, T. D.; Bogner, S. K.

    2014-10-15

    We present a variant of the in-medium similarity renormalization group(IMSRG) based on the Magnus expansion. In this new variant, the unitary transformation of the IMSRG is constructed explicitly, which allows for the transformation of observables quickly and easily. Additionally, the stiffness of equations encountered by the traditional solution of the IMSRG can be alleviated greatly. We present results and comparisons for the 3d electron gas.

  12. RGIsearch: A C++ program for the determination of renormalization group invariants

    NASA Astrophysics Data System (ADS)

    Verheyen, Rob

    2016-05-01

    RGIsearch is a C++ program that searches for invariants of a user-defined set of renormalization group equations. Based on the general shape of the β-functions of quantum field theories, RGIsearch searches for several types of invariants that require different methods. Additionally, it supports the computation of invariants up to two-loop level. A manual for the program is given, including the settings and set-up of the program, as well as a test case.

  13. The Renormalization Group in Nuclear Physics

    NASA Astrophysics Data System (ADS)

    Furnstahl, R. J.

    2012-07-01

    Modern techniques of the renormalization group (RG) combined with effective field theory (EFT) methods are revolutionizing nuclear many-body physics. In these lectures we will explore the motivation for RG in low-energy nuclear systems and its implementation in systems ranging from the deuteron to neutron stars, both formally and in practice. Flow equation approaches applied to Hamiltonians both in free space and in the medium will be emphasized. This is a conceptually simple technique to transform interactions to more perturbative and universal forms. An unavoidable complication for nuclear systems from both the EFT and flow equation perspective is the need to treat many-body forces and operators, so we will consider these aspects in some detail. We'll finish with a survey of current developments and open problems in nuclear RG.

  14. Charge renormalization in nominally apolar colloidal dispersions

    NASA Astrophysics Data System (ADS)

    Evans, Daniel J.; Hollingsworth, Andrew D.; Grier, David G.

    2016-04-01

    We present high-resolution measurements of the pair interactions between dielectric spheres dispersed in a fluid medium with a low dielectric constant. Despite the absence of charge control agents or added organic salts, these measurements reveal strong and long-ranged repulsions consistent with substantial charges on the particles whose interactions are screened by trace concentrations of mobile ions in solution. The dependence of the estimated charge on the particles' radii is consistent with charge renormalization theory and, thus, offers insights into the charging mechanism in this interesting class of model systems. The measurement technique, based on optical-tweezer manipulation and artifact-free particle tracking, makes use of optimal statistical methods to reduce measurement errors to the femtonewton frontier while covering an extremely wide range of interaction energies.

  15. Anomalies, equivalence and renormalization of cosmological frames

    NASA Astrophysics Data System (ADS)

    Herrero-Valea, Mario

    2016-05-01

    We study the question of whether two frames of a given physical theory are equivalent or not in the presence of quantum corrections. By using field theory arguments, we claim that equivalence is broken in the presence of anomalous symmetries in one of the frames. This is particularized to the case of the relation between the Einstein and Jordan frames in scalar-tensor theories used to describe early Universe dynamics. Although in this case a regularization that cancels the anomaly exists, the renormalized theory always develops a nonvanishing contribution to the S matrix that is present only in the Jordan frame, promoting the different frames to different physical theories that must be UV completed in a different way.

  16. Semihard processes with BLM renormalization scale setting

    SciTech Connect

    Caporale, Francesco; Murdaca, Beatrice; Papa, Alessandro

    2015-04-10

    We apply the BLM scale setting procedure directly to amplitudes (cross sections) of several semihard processes. It is shown that, due to the presence of β{sub 0}-terms in the NLA results for the impact factors, the obtained optimal renormalization scale is not universal, but depends both on the energy and on the process in question. We illustrate this general conclusion considering the following semihard processes: (i) inclusive production of two forward high-p{sub T} jets separated by large interval in rapidity (Mueller-Navelet jets); (ii) high-energy behavior of the total cross section for highly virtual photons; (iii) forward amplitude of the production of two light vector mesons in the collision of two virtual photons.

  17. Holographic trace anomaly and local renormalization group

    NASA Astrophysics Data System (ADS)

    Rajagopal, Srivatsan; Stergiou, Andreas; Zhu, Yechao

    2015-11-01

    The Hamilton-Jacobi method in holography has produced important results both at a renormalization group (RG) fixed point and away from it. In this paper we use the Hamilton-Jacobi method to compute the holographic trace anomaly for four- and six-dimensional boundary conformal field theories (CFTs), assuming higher-derivative gravity and interactions of scalar fields in the bulk. The scalar field contributions to the anomaly appear in CFTs with exactly marginal operators. Moving away from the fixed point, we show that the Hamilton-Jacobi formalism provides a deep connection between the holographic and the local RG. We derive the local RG equation holographically, and verify explicitly that it satisfies Weyl consistency conditions stemming from the commutativity of Weyl scalings. We also consider massive scalar fields in the bulk corresponding to boundary relevant operators, and comment on their effects to the local RG equation.

  18. Mass

    SciTech Connect

    Quigg, Chris

    2007-12-05

    In the classical physics we inherited from Isaac Newton, mass does not arise, it simply is. The mass of a classical object is the sum of the masses of its parts. Albert Einstein showed that the mass of a body is a measure of its energy content, inviting us to consider the origins of mass. The protons we accelerate at Fermilab are prime examples of Einsteinian matter: nearly all of their mass arises from stored energy. Missing mass led to the discovery of the noble gases, and a new form of missing mass leads us to the notion of dark matter. Starting with a brief guided tour of the meanings of mass, the colloquium will explore the multiple origins of mass. We will see how far we have come toward understanding mass, and survey the issues that guide our research today.

  19. Sleep and Synaptic Renormalization: A Computational Study

    PubMed Central

    Olcese, Umberto; Esser, Steve K.

    2010-01-01

    Recent evidence indicates that net synaptic strength in cortical and other networks increases during wakefulness and returns to a baseline level during sleep. These homeostatic changes in synaptic strength are accompanied by corresponding changes in sleep slow wave activity (SWA) and in neuronal firing rates and synchrony. Other evidence indicates that sleep is associated with an initial reactivation of learned firing patterns that decreases over time. Finally, sleep can enhance performance of learned tasks, aid memory consolidation, and desaturate the ability to learn. Using a large-scale model of the corticothalamic system equipped with a spike-timing dependent learning rule, in agreement with experimental results, we demonstrate a net increase in synaptic strength in the waking mode associated with an increase in neuronal firing rates and synchrony. In the sleep mode, net synaptic strength decreases accompanied by a decline in SWA. We show that the interplay of activity and plasticity changes implements a control loop yielding an exponential, self-limiting renormalization of synaptic strength. Moreover, when the model “learns” a sequence of activation during waking, the learned sequence is preferentially reactivated during sleep, and reactivation declines over time. Finally, sleep-dependent synaptic renormalization leads to increased signal-to-noise ratios, increased resistance to interference, and desaturation of learning capabilities. Although the specific mechanisms implemented in the model cannot capture the variety and complexity of biological substrates, and will need modifications in line with future evidence, the present simulations provide a unified, parsimonious account for diverse experimental findings coming from molecular, electrophysiological, and behavioral approaches. PMID:20926617

  20. Renormalization scheme dependence in a QCD cross section

    NASA Astrophysics Data System (ADS)

    Chishtie, Farrukh; McKeon, D. G. C.; Sherry, T. N.

    2016-09-01

    The zero to four loop contribution to the cross section Re+e- for e+e-→ hadrons, when combined with the renormalization group equation, allows for summation of all leading-log, next-to-leading-log, …, next-to-next-to-next-to-leading-log perturbative contributions. It is shown how all logarithmic contributions to Re+e- can be summed and that Re+e- can be expressed in terms of the log-independent contributions, and once this is done, the running coupling a is evaluated at a point independent of the renormalization scale μ . All explicit dependence of Re+e- on μ cancels against its implicit dependence on μ through the running coupling a so that the ambiguity associated with the value of μ is shown to disappear. The renormalization scheme dependency of the "summed" cross section Re+e- is examined in three distinct renormalization schemes. In the first two schemes, Re+e- is expressible in terms of renormalization scheme-independent parameters τi and is explicitly and implicitly independent of the renormalization scale μ . Two of the forms are then compared graphically both with each other and with the purely perturbative results and the renormalization group-summed next-to-next-to-next-to-leading-log results.

  1. Importance of proper renormalization scale-setting for QCD testing at colliders

    NASA Astrophysics Data System (ADS)

    Wu, Xing-Gang; Wang, Sheng-Quan; Brodsky, Stanley J.

    2016-02-01

    A primary problem affecting perturbative quantum chromodynamic (pQCD) analyses is the lack of a method for setting the QCD running-coupling renormalization scale such that maximally precise fixed-order predictions for physical observables are obtained. The Principle of Maximum Conformality (PMC) eliminates the ambiguities associated with the conventional renormalization scale-setting procedure, yielding predictions that are independent of the choice of renormalization scheme. The QCD coupling scales and the effective number of quark flavors are set order-by-order in the pQCD series. The PMC has a solid theoretical foundation, satisfying the standard renormalization group invariance condition and all of the self-consistency conditions derived from the renormalization group. The PMC scales at each order are obtained by shifting the arguments of the strong force coupling constant α s to eliminate all non-conformal { β i } terms in the pQCD series. The { β i } terms are determined from renormalization group equations without ambiguity. The correct behavior of the running coupling at each order and at each phase-space point can then be obtained. The PMC reduces in the N C → 0 Abelian limit to the Gell-Mann-Low method. In this brief report, we summarize the results of our recent application of the PMC to a number of collider processes, emphasizing the generality and applicability of this approach. A discussion of hadronic Z decays shows that, by applying the PMC, one can achieve accurate predictions for the total and separate decay widths at each order without scale ambiguities. We also show that, if one employs the PMC to determine the top-quark pair forward-backward asymmetry at the next-to-next-to-leading order level, one obtains a comprehensive, self-consistent pQCD explanation for the Tevatron measurements of the asymmetry. This accounts for the "increasing-decreasing" behavior observed by the D0 collaboration for increasing t overline t invariant mass. At

  2. Importance of proper renormalization scale-setting for QCD testing at colliders

    SciTech Connect

    Wu, Xing -Gang; Wang, Sheng -Quan; Brodsky, Stanley J.

    2015-12-22

    A primary problem affecting perturbative quantum chromodynamic (pQCD) analyses is the lack of a method for setting the QCD running-coupling renormalization scale such that maximally precise fixed-order predictions for physical observables are obtained. The Principle of Maximum Conformality (PMC) eliminates the ambiguities associated with the conventional renormalization scale-setting procedure, yielding predictions that are independent of the choice of renormalization scheme. The QCD coupling scales and the effective number of quark flavors are set order-by-order in the pQCD series. The PMC has a solid theoretical foundation, satisfying the standard renormalization group invariance condition and all of the self-consistency conditions derived from the renormalization group. The PMC scales at each order are obtained by shifting the arguments of the strong force coupling constant αs to eliminate all non-conformal {βi} terms in the pQCD series. The {βi} terms are determined from renormalization group equations without ambiguity. The correct behavior of the running coupling at each order and at each phase-space point can then be obtained. The PMC reduces in the NC → 0 Abelian limit to the Gell-Mann-Low method. In this brief report, we summarize the results of our recent application of the PMC to a number of collider processes, emphasizing the generality and applicability of this approach. A discussion of hadronic Z decays shows that, by applying the PMC, one can achieve accurate predictions for the total and separate decay widths at each order without scale ambiguities. We also show that, if one employs the PMC to determine the top-quark pair forward-backward asymmetry at the next-to-next-to-leading order level, one obtains a comprehensive, self-consistent pQCD explanation for the Tevatron measurements of the asymmetry. This accounts for the “increasing-decreasing” behavior observed by the D0 collaboration for increasing tt¯ invariant mass. At lower

  3. Importance of proper renormalization scale-setting for QCD testing at colliders

    DOE PAGES

    Wu, Xing -Gang; Wang, Sheng -Quan; Brodsky, Stanley J.

    2015-12-22

    A primary problem affecting perturbative quantum chromodynamic (pQCD) analyses is the lack of a method for setting the QCD running-coupling renormalization scale such that maximally precise fixed-order predictions for physical observables are obtained. The Principle of Maximum Conformality (PMC) eliminates the ambiguities associated with the conventional renormalization scale-setting procedure, yielding predictions that are independent of the choice of renormalization scheme. The QCD coupling scales and the effective number of quark flavors are set order-by-order in the pQCD series. The PMC has a solid theoretical foundation, satisfying the standard renormalization group invariance condition and all of the self-consistency conditions derived frommore » the renormalization group. The PMC scales at each order are obtained by shifting the arguments of the strong force coupling constant αs to eliminate all non-conformal {βi} terms in the pQCD series. The {βi} terms are determined from renormalization group equations without ambiguity. The correct behavior of the running coupling at each order and at each phase-space point can then be obtained. The PMC reduces in the NC → 0 Abelian limit to the Gell-Mann-Low method. In this brief report, we summarize the results of our recent application of the PMC to a number of collider processes, emphasizing the generality and applicability of this approach. A discussion of hadronic Z decays shows that, by applying the PMC, one can achieve accurate predictions for the total and separate decay widths at each order without scale ambiguities. We also show that, if one employs the PMC to determine the top-quark pair forward-backward asymmetry at the next-to-next-to-leading order level, one obtains a comprehensive, self-consistent pQCD explanation for the Tevatron measurements of the asymmetry. This accounts for the “increasing-decreasing” behavior observed by the D0 collaboration for increasing tt¯ invariant mass. At lower

  4. Physics implications of the diphoton excess from the perspective of renormalization group flow

    DOE PAGES

    Gu, Jiayin; Liu, Zhen

    2016-04-06

    A very plausible explanation for the recently observed diphoton excess at the 13 TeV LHC is a (pseudo)scalar with mass around 750 GeV, which couples to a gluon pair and to a photon pair through loops involving vector-like quarks (VLQs). To accommodate the observed rate, the required Yukawa couplings tend to be large. A large Yukawa coupling would rapidly run up with the scale and quickly reach the perturbativity bound, indicating that new physics, possibly with a strong dynamics origin, is near by. The case becomes stronger especially if the ATLAS observation of a large width persists. In this papermore » we study the implication on the scale of new physics from the 750 GeV diphoton excess using the method of renormalization group running with careful treatment of different contributions and perturbativity criterion. Our results suggest that the scale of new physics is generically not much larger than the TeV scale, in particular if the width of the hinted (pseudo)scalar is large. Introducing multiple copies of VLQs, lowing the VLQ masses and enlarging VLQ electric charges help reduce the required Yukawa couplings and can push the cutoff scale to higher values. Nevertheless, if the width of the 750 GeV resonance turns out to be larger than about 1 GeV, it is very hard to increase the cutoff scale beyond a few TeVs. This is a strong hint that new particles in addition to the 750 GeV resonance and the vector-like quarks should be around the TeV scale.« less

  5. Physics implications of the diphoton excess from the perspective of renormalization group flow

    NASA Astrophysics Data System (ADS)

    Gu, Jiayin; Liu, Zhen

    2016-04-01

    A very plausible explanation for the recently observed diphoton excess at the 13 TeV LHC is a (pseudo)scalar with mass around 750 GeV, which couples to a gluon pair and to a photon pair through loops involving vectorlike quarks (VLQs). To accommodate the observed rate, the required Yukawa couplings tend to be large. A large Yukawa coupling would rapidly run up with the scale and quickly reach the perturbativity bound, indicating that new physics, possibly with a strong dynamics origin, is nearby. The case becomes stronger especially if the ATLAS observation of a large width persists. In this paper we study the implication on the scale of new physics from the 750 GeV diphoton excess using the method of renormalization group running with careful treatment of different contributions and perturbativity criterion. Our results suggest that the scale of new physics is generically not much larger than the TeV scale, in particular if the width of the hinted (pseudo)scalar is large. Introducing multiple copies of VLQs, lowering the VLQ masses, and enlarging VLQ electric charges help reduce the required Yukawa couplings and can push the cutoff scale to higher values. Nevertheless, if the width of the 750 GeV resonance turns out to be larger than about 1 GeV, it is very hard to increase the cutoff scale beyond a few TeVs. This is a strong hint that new particles in addition to the 750 GeV resonance and the vectorlike quarks should be around the TeV scale.

  6. Renormalization group invariance and optimal QCD renormalization scale-setting: a key issues review.

    PubMed

    Wu, Xing-Gang; Ma, Yang; Wang, Sheng-Quan; Fu, Hai-Bing; Ma, Hong-Hao; Brodsky, Stanley J; Mojaza, Matin

    2015-12-01

    A valid prediction for a physical observable from quantum field theory should be independent of the choice of renormalization scheme--this is the primary requirement of renormalization group invariance (RGI). Satisfying scheme invariance is a challenging problem for perturbative QCD (pQCD), since a truncated perturbation series does not automatically satisfy the requirements of the renormalization group. In a previous review, we provided a general introduction to the various scale setting approaches suggested in the literature. As a step forward, in the present review, we present a discussion in depth of two well-established scale-setting methods based on RGI. One is the 'principle of maximum conformality' (PMC) in which the terms associated with the β-function are absorbed into the scale of the running coupling at each perturbative order; its predictions are scheme and scale independent at every finite order. The other approach is the 'principle of minimum sensitivity' (PMS), which is based on local RGI; the PMS approach determines the optimal renormalization scale by requiring the slope of the approximant of an observable to vanish. In this paper, we present a detailed comparison of the PMC and PMS procedures by analyzing two physical observables R(e+e-) and [Formula: see text] up to four-loop order in pQCD. At the four-loop level, the PMC and PMS predictions for both observables agree within small errors with those of conventional scale setting assuming a physically-motivated scale, and each prediction shows small scale dependences. However, the convergence of the pQCD series at high orders, behaves quite differently: the PMC displays the best pQCD convergence since it eliminates divergent renormalon terms; in contrast, the convergence of the PMS prediction is questionable, often even worse than the conventional prediction based on an arbitrary guess for the renormalization scale. PMC predictions also have the property that any residual dependence on the choice

  7. Renormalization group invariance and optimal QCD renormalization scale-setting: a key issues review

    NASA Astrophysics Data System (ADS)

    Wu, Xing-Gang; Ma, Yang; Wang, Sheng-Quan; Fu, Hai-Bing; Ma, Hong-Hao; Brodsky, Stanley J.; Mojaza, Matin

    2015-12-01

    A valid prediction for a physical observable from quantum field theory should be independent of the choice of renormalization scheme—this is the primary requirement of renormalization group invariance (RGI). Satisfying scheme invariance is a challenging problem for perturbative QCD (pQCD), since a truncated perturbation series does not automatically satisfy the requirements of the renormalization group. In a previous review, we provided a general introduction to the various scale setting approaches suggested in the literature. As a step forward, in the present review, we present a discussion in depth of two well-established scale-setting methods based on RGI. One is the ‘principle of maximum conformality’ (PMC) in which the terms associated with the β-function are absorbed into the scale of the running coupling at each perturbative order; its predictions are scheme and scale independent at every finite order. The other approach is the ‘principle of minimum sensitivity’ (PMS), which is based on local RGI; the PMS approach determines the optimal renormalization scale by requiring the slope of the approximant of an observable to vanish. In this paper, we present a detailed comparison of the PMC and PMS procedures by analyzing two physical observables R e+e- and Γ(H\\to b\\bar{b}) up to four-loop order in pQCD. At the four-loop level, the PMC and PMS predictions for both observables agree within small errors with those of conventional scale setting assuming a physically-motivated scale, and each prediction shows small scale dependences. However, the convergence of the pQCD series at high orders, behaves quite differently: the PMC displays the best pQCD convergence since it eliminates divergent renormalon terms; in contrast, the convergence of the PMS prediction is questionable, often even worse than the conventional prediction based on an arbitrary guess for the renormalization scale. PMC predictions also have the property that any residual dependence on

  8. Renormalization group invariance and optimal QCD renormalization scale-setting: a key issues review.

    PubMed

    Wu, Xing-Gang; Ma, Yang; Wang, Sheng-Quan; Fu, Hai-Bing; Ma, Hong-Hao; Brodsky, Stanley J; Mojaza, Matin

    2015-12-01

    A valid prediction for a physical observable from quantum field theory should be independent of the choice of renormalization scheme--this is the primary requirement of renormalization group invariance (RGI). Satisfying scheme invariance is a challenging problem for perturbative QCD (pQCD), since a truncated perturbation series does not automatically satisfy the requirements of the renormalization group. In a previous review, we provided a general introduction to the various scale setting approaches suggested in the literature. As a step forward, in the present review, we present a discussion in depth of two well-established scale-setting methods based on RGI. One is the 'principle of maximum conformality' (PMC) in which the terms associated with the β-function are absorbed into the scale of the running coupling at each perturbative order; its predictions are scheme and scale independent at every finite order. The other approach is the 'principle of minimum sensitivity' (PMS), which is based on local RGI; the PMS approach determines the optimal renormalization scale by requiring the slope of the approximant of an observable to vanish. In this paper, we present a detailed comparison of the PMC and PMS procedures by analyzing two physical observables R(e+e-) and [Formula: see text] up to four-loop order in pQCD. At the four-loop level, the PMC and PMS predictions for both observables agree within small errors with those of conventional scale setting assuming a physically-motivated scale, and each prediction shows small scale dependences. However, the convergence of the pQCD series at high orders, behaves quite differently: the PMC displays the best pQCD convergence since it eliminates divergent renormalon terms; in contrast, the convergence of the PMS prediction is questionable, often even worse than the conventional prediction based on an arbitrary guess for the renormalization scale. PMC predictions also have the property that any residual dependence on the choice

  9. Renormalization group improved Higgs inflation with a running kinetic term

    NASA Astrophysics Data System (ADS)

    Takahashi, Fuminobu; Takahashi, Ryo

    2016-09-01

    We study a Higgs inflation model with a running kinetic term, taking account of the renormalization group evolution of relevant coupling constants. Specifically we study two types of the running kinetic Higgs inflation, where the inflaton potential is given by the quadratic or linear term potential in a frame where the Higgs field is canonically normalized. We solve the renormalization group equations at two-loop level and calculate the scalar spectral index and the tensor-to-scalar ratio. We find that, even if the renormalization group effects are included, the quadratic inflation is ruled out by the CMB observations, while the linear one is still allowed.

  10. Nucleon-nucleon scattering within a multiple subtractive renormalization approach

    SciTech Connect

    Timoteo, V. S.; Frederico, T.; Delfino, A.; Tomio, Lauro

    2011-06-15

    We present a methodology to renormalize the nucleon-nucleon interaction in momentum space, using a recursive multiple subtraction approach that prescinds from a cutoff regularization, to construct the kernel of the scattering equation. The subtracted scattering equation is solved with the next-leading-order and next-to-next-leading-order interactions. The results are presented for all partial waves up to j=2, fitted to low-energy experimental data. In this renormalization group invariant approach, the subtraction energy emerges as a renormalization scale and the momentum associated with it comes to be about the QCD scale ({Lambda}{sub QCD}), irrespectively to the partial wave.

  11. Degeneracy relations in QCD and the equivalence of two systematic all-orders methods for setting the renormalization scale

    SciTech Connect

    Bi, Huan -Yu; Wu, Xing -Gang; Ma, Yang; Ma, Hong -Hao; Brodsky, Stanley J.; Mojaza, Matin

    2015-06-26

    The Principle of Maximum Conformality (PMC) eliminates QCD renormalization scale-setting uncertainties using fundamental renormalization group methods. The resulting scale-fixed pQCD predictions are independent of the choice of renormalization scheme and show rapid convergence. The coefficients of the scale-fixed couplings are identical to the corresponding conformal series with zero β-function. Two all-orders methods for systematically implementing the PMC-scale setting procedure for existing high order calculations are discussed in this article. One implementation is based on the PMC-BLM correspondence (PMC-I); the other, more recent, method (PMC-II) uses the Rδ-scheme, a systematic generalization of the minimal subtraction renormalization scheme. Both approaches satisfy all of the principles of the renormalization group and lead to scale-fixed and scheme-independent predictions at each finite order. In this work, we show that PMC-I and PMC-II scale-setting methods are in practice equivalent to each other. We illustrate this equivalence for the four-loop calculations of the annihilation ratio Re+e and the Higgs partial width I'(H→bb¯). Both methods lead to the same resummed (‘conformal’) series up to all orders. The small scale differences between the two approaches are reduced as additional renormalization group {βi}-terms in the pQCD expansion are taken into account. In addition, we show that special degeneracy relations, which underly the equivalence of the two PMC approaches and the resulting conformal features of the pQCD series, are in fact general properties of non-Abelian gauge theory.

  12. Breaking generalized covariance, classical renormalization, and boundary conditions from superpotentials

    NASA Astrophysics Data System (ADS)

    Livshits, Gideon I.

    2014-02-01

    Superpotentials offer a direct means of calculating conserved charges associated with the asymptotic symmetries of space-time. Yet superpotentials have been plagued with inconsistencies, resulting in nonphysical or incongruent values for the mass, angular momentum, and energy loss due to radiation. The approach of Regge and Teitelboim, aimed at a clear Hamiltonian formulation with a boundary, and its extension to the Lagrangian formulation by Julia and Silva have resolved these issues, and have resulted in a consistent, well-defined and unique variational equation for the superpotential, thereby placing it on a firm footing. A hallmark solution of this equation is the KBL superpotential obtained from the first-order Lovelock Lagrangian. Nevertheless, here we show that these formulations are still insufficient for Lovelock Lagrangians of higher orders. We present a paradox, whereby the choice of fields affects the superpotential for equivalent on-shell dynamics. We offer two solutions to this paradox: either the original Lagrangian must be effectively renormalized, or that boundary conditions must be imposed, so that space-time be asymptotically maximally symmetric. Non-metricity is central to this paradox, and we show how quadratic non-metricity in the bulk of space-time contributes to the conserved charges on the boundary, where it vanishes identically. This is a realization of the gravitational Higgs mechanism, proposed by Percacci, where the non-metricity is the analogue of the Goldstone boson.

  13. Reductive renormalization of the phase-field crystal equation.

    PubMed

    Oono, Y; Shiwa, Y

    2012-12-01

    It has been known for some time that singular perturbation and reductive perturbation can be unified from the renormalization-group theoretical point of view: Reductive extraction of space-time global behavior is the essence of singular perturbation methods. Reductive renormalization was proposed to make this unification practically accessible; actually, this reductive perturbation is far simpler than most reduction methods, such as the rather standard scaling expansion. However, a rather cryptic exposition of the method seems to have been the cause of some trouble. Here, an explicit demonstration of the consistency of the reductive renormalization-group procedure is given for partial differentiation equations (of a certain type, including time-evolution semigroup type equations). Then, the procedure is applied to the reduction of a phase-field crystal equation to illustrate the streamlined reduction method. We conjecture that if the original system is structurally stable, the reductive renormalization-group result and that of the original equation are diffeomorphic.

  14. Renormalization-scheme-invariant perturbation theory: Miracle or mirage

    SciTech Connect

    Chyla, J.

    1985-05-15

    A recently proposed solution to the renormalization-scheme ambiguity in perturbation theory is critically analyzed and shown to possess another kind of ambiguity closely related to the one it is supposed to cure.

  15. The renormalized Jellium model of colloidal suspensions with multivalent counterions

    NASA Astrophysics Data System (ADS)

    Colla, Thiago E.; Levin, Yan

    2010-12-01

    An extension of the renormalized Jellium model which allows to study colloidal suspensions containing trivalent counterions is proposed. The theory is based on a modified Poisson-Boltzmann equation which incorporates the effects of counterion correlations near the colloidal surfaces using a new boundary condition. The renormalized charges, the counterion density profiles, and osmotic pressures can be easily calculated using the modified renormalized Jellium model. The results are compared with the ones obtained using the traditional Wigner-Seitz (WS) cell approximation also with a new boundary condition. We find that while the thermodynamic functions obtained within the renormalized Jellium model are in a good agreement with their WS counterpart, the effective charges predicted by the two theories can be significantly different.

  16. Renormalization of the Brazilian chiral nucleon-nucleon potential

    SciTech Connect

    Da Rocha, Carlos A.; Timoteo, Varese S.

    2013-03-25

    In this work we present a renormalization of the Brazilian nucleon-nucleon (NN) potential using a subtractive method. We show that the exchange of correlated two pion is important for isovector channels, mainly in tensor and central potentials.

  17. Renormalization and power counting of chiral nuclear forces

    SciTech Connect

    Long, Bingwei

    2013-08-01

    I discuss the progress we have made on modifying Weinberg's prescription for chiral nuclear forces, using renormalization group invariance as the guideline. Some of the published results are presented.

  18. Renormalization of the Brazilian chiral nucleon-nucleon potential

    NASA Astrophysics Data System (ADS)

    Da Rocha, Carlos A.; Timóteo, Varese S.

    2013-03-01

    In this work we present a renormalization of the Brazilian nucleon-nucleon (NN) potential using a subtractive method. We show that the exchange of correlated two pion is important for isovector channels, mainly in tensor and central potentials.

  19. Real-space renormalization in statistical mechanics

    NASA Astrophysics Data System (ADS)

    Efrati, Efi; Wang, Zhe; Kolan, Amy; Kadanoff, Leo P.

    2014-04-01

    This review compares the conceptualization and practice of early real-space renormalization group methods with the conceptualization of more recent real-space transformations based on tensor networks. For specificity, it focuses upon two basic methods: the "potential-moving" approach most used in the period 1975-1980 and the "rewiring method" as it has been developed in the last five years. The newer method, part of a development called the tensor renormalization group, was originally based on principles of quantum entanglement. It is specialized for computing approximations for tensor products constituting, for example, the free energy or the ground state energy of a large system. It can attack a wide variety of problems, including quantum problems, which would otherwise be intractable. The older method is formulated in terms of spin variables and permits a straightforward construction and analysis of fixed points in rather transparent terms. However, in the form described here it is unsystematic, offers no path for improvement, and of unknown reliability. The new method is formulated in terms of index variables which may be considered as linear combinations of the statistical variables. Free energies emerge naturally, but fixed points are more subtle. Further, physical interpretations of the index variables are often elusive due to a gauge symmetry which allows only selected combinations of tensor entries to have physical significance. In applications, both methods employ analyses with varying degrees of complexity. The complexity is parametrized by an integer called χ (or D in the recent literature). Both methods are examined in action by using them to compute fixed points related to Ising models for small values of the complexity parameter. They behave quite differently. The old method gives a reasonably good picture of the fixed point, as measured, for example, by the accuracy of the measured critical indices. This happens at low values of χ, but there is no

  20. Screening of heterogeneous surfaces: charge renormalization of Janus particles.

    PubMed

    Boon, N; Carvajal Gallardo, E; Zheng, S; Eggen, E; Dijkstra, M; van Roij, R

    2010-03-17

    Nonlinear ionic screening theory for heterogeneously charged spheres is developed in terms of a mode decomposition of the surface charge. A far-field analysis of the resulting electrostatic potential leads to a natural generalization of charge renormalization from purely monopolar to dipolar, quadrupolar, etc, including 'mode couplings'. Our novel scheme is generally applicable to large classes of surface heterogeneities, and is explicitly applied here to Janus spheres with differently charged upper and lower hemispheres, revealing strong renormalization effects for all multipoles.

  1. Degeneracy relations in QCD and the equivalence of two systematic all-orders methods for setting the renormalization scale

    NASA Astrophysics Data System (ADS)

    Bi, Huan-Yu; Wu, Xing-Gang; Ma, Yang; Ma, Hong-Hao; Brodsky, Stanley J.; Mojaza, Matin

    2015-09-01

    The Principle of Maximum Conformality (PMC) eliminates QCD renormalization scale-setting uncertainties using fundamental renormalization group methods. The resulting scale-fixed pQCD predictions are independent of the choice of renormalization scheme and show rapid convergence. The coefficients of the scale-fixed couplings are identical to the corresponding conformal series with zero β-function. Two all-orders methods for systematically implementing the PMC-scale setting procedure for existing high order calculations are discussed in this article. One implementation is based on the PMC-BLM correspondence (PMC-I); the other, more recent, method (PMC-II) uses the Rδ-scheme, a systematic generalization of the minimal subtraction renormalization scheme. Both approaches satisfy all of the principles of the renormalization group and lead to scale-fixed and scheme-independent predictions at each finite order. In this work, we show that PMC-I and PMC-II scale-setting methods are in practice equivalent to each other. We illustrate this equivalence for the four-loop calculations of the annihilation ratio Re+e- and the Higgs partial width Γ (H → b b bar). Both methods lead to the same resummed ('conformal') series up to all orders. The small scale differences between the two approaches are reduced as additional renormalization group {βi }-terms in the pQCD expansion are taken into account. We also show that special degeneracy relations, which underly the equivalence of the two PMC approaches and the resulting conformal features of the pQCD series, are in fact general properties of non-Abelian gauge theory.

  2. Aspects of renormalization in finite-density field theory

    NASA Astrophysics Data System (ADS)

    Fitzpatrick, A. Liam; Torroba, Gonzalo; Wang, Huajia

    2015-05-01

    We study the renormalization of the Fermi surface coupled to a massless boson near three spatial dimensions. For this, we set up a Wilsonian RG with independent decimation procedures for bosons and fermions, where the four-fermion interaction "Landau parameters" run already at tree level. Our explicit one-loop analysis resolves previously found obstacles in the renormalization of finite-density field theory, including logarithmic divergences in nonlocal interactions and the appearance of multilogarithms. The key aspects of the RG are the above tree-level running, and a UV-IR mixing between virtual bosons and fermions at the quantum level, which is responsible for the renormalization of the Fermi velocity. We apply this approach to the renormalization of 2 kF singularities, and to Fermi surface instabilities in a companion paper, showing how multilogarithms are properly renormalized. We end with some comments on the renormalization of finite-density field theory with the inclusion of Landau damping of the boson.

  3. Nonperturbative Renormalization Group Approach to Polymerized Membranes

    NASA Astrophysics Data System (ADS)

    Essafi, Karim; Kownacki, Jean-Philippe; Mouhanna, Dominique

    2014-03-01

    Membranes or membrane-like materials play an important role in many fields ranging from biology to physics. These systems form a very rich domain in statistical physics. The interplay between geometry and thermal fluctuations lead to exciting phases such flat, tubular and disordered flat phases. Roughly speaking, membranes can be divided into two group: fluid membranes in which the molecules are free to diffuse and thus no shear modulus. On the other hand, in polymerized membranes the connectivity is fixed which leads to elastic forces. This difference between fluid and polymerized membranes leads to a difference in their critical behaviour. For instance, fluid membranes are always crumpled, whereas polymerized membranes exhibit a phase transition between a crumpled phase and a flat phase. In this talk, I will focus only on polymerized phantom, i.e. non-self-avoiding, membranes. The critical behaviour of both isotropic and anisotropic polymerized membranes are studied using a nonperturbative renormalization group approach (NPRG). This allows for the investigation of the phase transitions and the low temperature flat phase in any internal dimension D and embedding d. Interestingly, graphene behaves just as a polymerized membrane in its flat phase.

  4. Polarizable Embedding Density Matrix Renormalization Group.

    PubMed

    Hedegård, Erik D; Reiher, Markus

    2016-09-13

    The polarizable embedding (PE) approach is a flexible embedding model where a preselected region out of a larger system is described quantum mechanically, while the interaction with the surrounding environment is modeled through an effective operator. This effective operator represents the environment by atom-centered multipoles and polarizabilities derived from quantum mechanical calculations on (fragments of) the environment. Thereby, the polarization of the environment is explicitly accounted for. Here, we present the coupling of the PE approach with the density matrix renormalization group (DMRG). This PE-DMRG method is particularly suitable for embedded subsystems that feature a dense manifold of frontier orbitals which requires large active spaces. Recovering such static electron-correlation effects in multiconfigurational electronic structure problems, while accounting for both electrostatics and polarization of a surrounding environment, allows us to describe strongly correlated electronic structures in complex molecular environments. We investigate various embedding potentials for the well-studied first excited state of water with active spaces that correspond to a full configuration-interaction treatment. Moreover, we study the environment effect on the first excited state of a retinylidene Schiff base within a channelrhodopsin protein. For this system, we also investigate the effect of dynamical correlation included through short-range density functional theory. PMID:27537835

  5. Nonlinear dynamics in combinatorial games: Renormalizing Chomp

    NASA Astrophysics Data System (ADS)

    Friedman, Eric J.; Landsberg, Adam Scott

    2007-06-01

    We develop a new approach to combinatorial games that reveals connections between such games and some of the central ideas of nonlinear dynamics: scaling behaviors, complex dynamics and chaos, universality, and aggregation processes. We take as our model system the combinatorial game Chomp, which is one of the simplest in a class of "unsolved" combinatorial games that includes Chess, Checkers, and Go. We discover that the game possesses an underlying geometric structure that "grows" (reminiscent of crystal growth), and show how this growth can be analyzed using a renormalization procedure adapted from physics. In effect, this methodology allows one to transform a combinatorial game like Chomp into a type of dynamical system. Not only does this provide powerful insights into the game of Chomp (yielding a complete probabilistic description of optimal play in Chomp and an answer to a longstanding question about the nature of the winning opening move), but more generally, it offers a mathematical framework for exploring this unexpected relationship between combinatorial games and modern dynamical systems theory.

  6. Nonlocal scaling operators with entanglement renormalization

    SciTech Connect

    Evenbly, G.; Corboz, P.; Vidal, G.

    2010-10-01

    The multiscale entanglement renormalization ansatz (MERA) can be used, in its scale invariant version, to describe the ground state of a lattice system at a quantum-critical point. From the scale invariant MERA one can determine the local scaling operators of the model. Here we show that, in the presence of a global symmetry G, it is also possible to determine a class of nonlocal scaling operators. Each operator consists, for a given group element g is an element of G, of a semi-infinite string {Gamma}{sub g} with a local operator {phi} attached to its open end. In the case of the quantum Ising model, G=Z{sub 2}, they correspond to the disorder operator {mu}, the fermionic operators {psi} and {psi}, and all their descendants. Together with the local scaling operators identity I, spin {sigma}, and energy {epsilon}, the fermionic and disorder scaling operators {psi}, {psi}, and {mu} are the complete list of primary fields of the Ising CFT. Therefore the scale invariant MERA allows us to characterize all the conformal towers of this CFT.

  7. Electronic instabilities of the extended Hubbard model on the honeycomb lattice from functional renormalization

    NASA Astrophysics Data System (ADS)

    Volpez, Yanick; Scherer, Daniel D.; Scherer, Michael M.

    2016-10-01

    Interacting fermions on the half-filled honeycomb lattice with short-range repulsions have been suggested to host a variety of interesting many-body ground states, e.g., a topological Mott insulator. A number of recent studies of the spinless case in terms of exact diagonalization, the infinite density matrix renormalization group, and the functional renormalization group, however, indicate a suppression of the topological Mott insulating phase in the whole range of interaction parameters. Here, we complement the previous studies by investigating the quantum many-body instabilities of the physically relevant case of spin-1/2 fermions with onsite, nearest-neighbor, and second-nearest-neighbor repulsion. To this end, we employ the multipatch functional renormalization group for correlated fermions with refined momentum resolution observing the emergence of an antiferromagnetic spin-density wave and a charge-density wave for dominating onsite and nearest-neighbor repulsions, respectively. For dominating second-nearest neighbor interaction our results favor an ordering tendency towards a charge-modulated ground state over the topological Mott insulating state. The latter evades a stabilization as the leading instability by the additional onsite interaction.

  8. Biorthonormal transfer-matrix renormalization-group method for non-Hermitian matrices.

    PubMed

    Huang, Yu-Kun

    2011-03-01

    A biorthonormal transfer-matrix renormalization-group (BTMRG) method for non-Hermitian matrices is presented. This BTMRG produces a dual set of biorthonormal bases to construct the renormalized transfer matrix with only half the dimensions of the matrix of a conventional transfer-matrix renormalization group (TMRG). We show that under generic conditions, such biorthonormal bases always exist. Based on a special E·S·E scheme (where S and E represent the system and environment blocks, respectively, and the two dots in between represent two additional physical sites), the BTMRG method can achieve zero truncation of any reduced state in describing both current left and right Perron states so as to reach a high degree of efficiency and accuracy. We believe that the BTMRG constitutes a more powerful and robust tool than conventional TMRG for non-Hermitian matrices and that it would allow us to better understand the collective behaviors and emerging phenomena of strongly correlated many-body systems. We also show that this scheme is particularly adapted to the calculation of the two-site correlation function of a one-dimensional quantum or two-dimensional classical lattice model.

  9. Renormalization-group-invariant partial sum of Feynman diagrams and its application to phase transitions

    NASA Astrophysics Data System (ADS)

    Hong, Seok-In

    1995-08-01

    The phase transition of the three-dimensional (3D) φ4 theory is considered in terms of the two-dimensional (2D) effective φ4 theory for sufficiently high temperatures. Instead of the effective potential, we use the renormalization-group-(RG-) invariant mass parameter Γ(2)(p=0) directly. For practical use, we find that superdaisy diagrams are a RG-invariant subset of Feynman diagrams for Γ(2)(p=0). The parameters of the effective theory are related to the original ones by certain matching conditions. The resulting critical temperature is the same as that obtained by Einhorn and Jones.

  10. Renormalization group evolution of the universal theories EFT

    DOE PAGES

    Wells, James D.; Zhang, Zhengkang

    2016-06-21

    The conventional oblique parameters analyses of precision electroweak data can be consistently cast in the modern framework of the Standard Model effective field theory (SMEFT) when restrictions are imposed on the SMEFT parameter space so that it describes universal theories. However, the usefulness of such analyses is challenged by the fact that universal theories at the scale of new physics, where they are matched onto the SMEFT, can flow to nonuniversal theories with renormalization group (RG) evolution down to the electroweak scale, where precision observables are measured. The departure from universal theories at the electroweak scale is not arbitrary, butmore » dictated by the universal parameters at the matching scale. But to define oblique parameters, and more generally universal parameters at the electroweak scale that directly map onto observables, additional prescriptions are needed for the treatment of RG-induced nonuniversal effects. Finally, we perform a RG analysis of the SMEFT description of universal theories, and discuss the impact of RG on simplified, universal-theories-motivated approaches to fitting precision electroweak and Higgs data.« less

  11. Renormalized second post-Newtonian spin contributions to the accumulated orbital phase for LISA sources

    SciTech Connect

    Gergely, Laszlo Arpad; Mikoczi, Balazs

    2009-03-15

    We give here a new third post-Newtonian (3PN) spin-spin contribution (in the PN parameter {epsilon}) to the accumulated orbital phase of a compact binary, arising from the spin-orbit precessional motion of the spins. In the equal mass case, this contribution vanishes, but Laser Interferometer Space Antenna (LISA) sources of merging supermassive binary black holes have typically a mass ratio of 1:10. For such nonequal masses, this 3PN correction is periodic in time, with a period approximately {epsilon}{sup -1} times larger than the period of gravitational waves. We derive a renormalized and simpler expression of the spin-spin coefficient at 2PN, as an average over the time scale of this period of the combined 2PN and 3PN contribution. We also find that for LISA sources the quadrupole-monopole contribution to the phase dominates over the spin-spin contribution, while the self-spin contribution is negligible even for the dominant spin. Finally, we define a renormalized total spin coefficient {sigma} to be employed in the search for gravitational waves emitted by LISA sources.

  12. Determination of 30 synthetic food additives in soft drinks by HPLC/electrospray ionization-tandem mass spectrometry.

    PubMed

    Gao, Hui; Yang, Minli; Wang, Minglin; Zhao, Yansheng; Cao, Ya; Chu, Xiaogang

    2013-01-01

    A method combining SPE with HPLC/electrospray ionization-MS/MS was developed for simultaneous determination of 30 synthetic food additives, including synthetic colorants, preservatives, and sweeteners in soft drinks. All targets were efficiently separated using the optimized chromatographic and MS conditions and parameters in a single run within 18 min. The LOD of the analytes ranged from 0.01 to 20 microg/kg, and the method was validated with recoveries in the 80.8 to 106.4% range. This multisynthetic additive method was found to be accurate and reliable and will be useful to ensure the safety of food products, such as the labeling and proper use of synthetic food additives in soft drinks.

  13. Determination of arsenic, chromium, lead, manganese, and mercury in certifiable color additives by inductively coupled plasma/mass spectrometry.

    PubMed

    Hepp, Nancy Morris

    2015-01-01

    Specifications in the Code of Federal Regulations limit the levels of As, Pb, and Hg in most certifiable color additives, and some have additional specification limits for Cr and Mn. A new ICP/MS method was developed and validated for the quantitative determination of these elements in various certifiable color additives. One dissolution and two microwave-assisted digestion sample preparation procedures were optimized to address initial low Hg and enhanced As recoveries. Results using the three sample preparation procedures were generally equivalent for all of the elements determined. LOQ values were 0.3 mg/kg for As, 0.7 mg/kg for Cr, 0.4 mg/kg for Pb, 0.7 mg/kg for Mn, and 0.1 mg/kg for Hg.

  14. Renormalization group running of neutrino parameters.

    PubMed

    Ohlsson, Tommy; Zhou, Shun

    2014-01-01

    Neutrinos are the most elusive particles in our Universe. They have masses at least one million times smaller than the electron mass, carry no electric charge and very weakly interact with other particles, meaning that they are rarely captured in terrestrial detectors. Tremendous efforts in the past two decades have revealed that neutrinos can transform from one type to another as a consequence of neutrino oscillations--a quantum mechanical effect over macroscopic distances--yet the origin of neutrino masses remains puzzling. The physical evolution of neutrino parameters with respect to energy scale may help elucidate the mechanism for their mass generation. PMID:25322932

  15. Renormalization group running of neutrino parameters.

    PubMed

    Ohlsson, Tommy; Zhou, Shun

    2014-01-01

    Neutrinos are the most elusive particles in our Universe. They have masses at least one million times smaller than the electron mass, carry no electric charge and very weakly interact with other particles, meaning that they are rarely captured in terrestrial detectors. Tremendous efforts in the past two decades have revealed that neutrinos can transform from one type to another as a consequence of neutrino oscillations--a quantum mechanical effect over macroscopic distances--yet the origin of neutrino masses remains puzzling. The physical evolution of neutrino parameters with respect to energy scale may help elucidate the mechanism for their mass generation.

  16. Renormalization of massless Feynman amplitudes in configuration space

    NASA Astrophysics Data System (ADS)

    Nikolov, Nikolay M.; Stora, Raymond; Todorov, Ivan

    2014-05-01

    A systematic study of recursive renormalization of Feynman amplitudes is carried out both in Euclidean and in Minkowski configuration spaces. For a massless quantum field theory (QFT), we use the technique of extending associate homogeneous distributions to complete the renormalization recursion. A homogeneous (Poincaré covariant) amplitude is said to be convergent if it admits a (unique covariant) extension as a homogeneous distribution. For any amplitude without subdivergences — i.e. for a Feynman distribution that is homogeneous off the full (small) diagonal — we define a renormalization invariant residue. Its vanishing is a necessary and sufficient condition for the convergence of such an amplitude. It extends to arbitrary — not necessarily primitively divergent — Feynman amplitudes. This notion of convergence is finer than the usual power counting criterion and includes cancellation of divergences.

  17. Renormalization group and the superconducting susceptibility of a Fermi liquid

    SciTech Connect

    Parameswaran, S. A.; Sondhi, S. L.; Shankar, R.

    2010-11-15

    A free Fermi gas has, famously, a superconducting susceptibility that diverges logarithmically at zero temperature. In this paper we ask whether this is still true for a Fermi liquid and find that the answer is that it does not. From the perspective of the renormalization group for interacting fermions, the question arises because a repulsive interaction in the Cooper channel is a marginally irrelevant operator at the Fermi liquid fixed point and thus is also expected to infect various physical quantities with logarithms. Somewhat surprisingly, at least from the renormalization group viewpoint, the result for the superconducting susceptibility is that two logarithms are not better than one. In the course of this investigation we derive a Callan-Symanzik equation for the repulsive Fermi liquid using the momentum-shell renormalization group, and use it to compute the long-wavelength behavior of the superconducting correlation function in the emergent low-energy theory. We expect this technique to be of broader interest.

  18. Monodisperse Clusters in Charged Attractive Colloids: Linear Renormalization of Repulsion.

    PubMed

    Růžička, Štěpán; Allen, Michael P

    2015-08-11

    Experiments done on polydisperse particles of cadmium selenide have recently shown that the particles form spherical isolated clusters with low polydispersity of cluster size. The computer simulation model of Xia et al. ( Nat. Nanotechnol. 2011 , 6 , 580 ) explaining this behavior used a short-range van der Waals attraction combined with a variable long-range screened electrostatic repulsion, depending linearly on the volume of the clusters. In this work, we term this dependence "linear renormalization" of the repulsive term, and we use advanced Monte Carlo simulations to investigate the kinetically slowed down phase separation in a similar but simpler model. We show that amorphous drops do not dissolve and crystallinity evolves very slowly under linear renormalization, and we confirm that low polydispersity of cluster size can also be achieved using this model. The results indicate that the linear renormalization generally leads to monodisperse clusters.

  19. The ab-initio density matrix renormalization group in practice

    SciTech Connect

    Olivares-Amaya, Roberto; Hu, Weifeng; Sharma, Sandeep; Yang, Jun; Chan, Garnet Kin-Lic; Nakatani, Naoki

    2015-01-21

    The ab-initio density matrix renormalization group (DMRG) is a tool that can be applied to a wide variety of interesting problems in quantum chemistry. Here, we examine the density matrix renormalization group from the vantage point of the quantum chemistry user. What kinds of problems is the DMRG well-suited to? What are the largest systems that can be treated at practical cost? What sort of accuracies can be obtained, and how do we reason about the computational difficulty in different molecules? By examining a diverse benchmark set of molecules: π-electron systems, benchmark main-group and transition metal dimers, and the Mn-oxo-salen and Fe-porphine organometallic compounds, we provide some answers to these questions, and show how the density matrix renormalization group is used in practice.

  20. The ab-initio density matrix renormalization group in practice

    NASA Astrophysics Data System (ADS)

    Olivares-Amaya, Roberto; Hu, Weifeng; Nakatani, Naoki; Sharma, Sandeep; Yang, Jun; Chan, Garnet Kin-Lic

    2015-01-01

    The ab-initio density matrix renormalization group (DMRG) is a tool that can be applied to a wide variety of interesting problems in quantum chemistry. Here, we examine the density matrix renormalization group from the vantage point of the quantum chemistry user. What kinds of problems is the DMRG well-suited to? What are the largest systems that can be treated at practical cost? What sort of accuracies can be obtained, and how do we reason about the computational difficulty in different molecules? By examining a diverse benchmark set of molecules: π-electron systems, benchmark main-group and transition metal dimers, and the Mn-oxo-salen and Fe-porphine organometallic compounds, we provide some answers to these questions, and show how the density matrix renormalization group is used in practice.

  1. Renormalizations and Wandering Jordan Curves of Rational Maps

    NASA Astrophysics Data System (ADS)

    Cui, Guizhen; Peng, Wenjuan; Tan, Lei

    2016-05-01

    We realize a dynamical decomposition for a post-critically finite rational map which admits a combinatorial decomposition. We split the Riemann sphere into two completely invariant subsets. One is a subset of the Julia set consisting of uncountably many Jordan curve components. Most of them are wandering. The other consists of components that are pullbacks of finitely many renormalizations, together with possibly uncountably many points. The quotient action on the decomposed pieces is encoded by a dendrite dynamical system. We also introduce a surgery procedure to produce post-critically finite rational maps with wandering Jordan curves and prescribed renormalizations.

  2. Renormalized dissipation in the nonconservatively forced Burgers equation

    SciTech Connect

    Krommes, J.A.

    2000-01-19

    A previous calculation of the renormalized dissipation in the nonconservatively forced one-dimensional Burgers equation, which encountered a catastrophic long-wavelength divergence approximately [k min]-3, is reconsidered. In the absence of velocity shear, analysis of the eddy-damped quasi-normal Markovian closure predicts only a benign logarithmic dependence on kmin. The original divergence is traced to an inconsistent resonance-broadening type of diffusive approximation, which fails in the present problem. Ballistic scaling of renormalized pulses is retained, but such scaling does not, by itself, imply a paradigm of self-organized criticality. An improved scaling formula for a model with velocity shear is also given.

  3. Screening of heterogeneous surfaces: charge renormalization of Janus particles.

    PubMed

    Boon, N; Carvajal Gallardo, E; Zheng, S; Eggen, E; Dijkstra, M; van Roij, R

    2010-03-17

    Nonlinear ionic screening theory for heterogeneously charged spheres is developed in terms of a mode decomposition of the surface charge. A far-field analysis of the resulting electrostatic potential leads to a natural generalization of charge renormalization from purely monopolar to dipolar, quadrupolar, etc, including 'mode couplings'. Our novel scheme is generally applicable to large classes of surface heterogeneities, and is explicitly applied here to Janus spheres with differently charged upper and lower hemispheres, revealing strong renormalization effects for all multipoles. PMID:21389438

  4. Renormalized time scale for anticipating and lagging synchronization.

    PubMed

    Hayashi, Yoshikatsu; Nasuto, Slawomir J; Eberle, Henry

    2016-05-01

    Anticipating synchronization has been recently proposed as a mechanism of interaction in dynamical systems which are able to bring about predictions of future states of a driver system. We suggest that an interesting insight into anticipating synchronization can be obtained by the renormalization of the time scale in the driven system. Our approach directly links the feedback delay of the driven system with the renormalized time scale of the driven system, identifying the main component in the anticipating synchronization paradigm and suggesting an alternative method to generate anticipating and lagging synchronization. PMID:27300902

  5. λφ 4 q-Renormalization program

    NASA Astrophysics Data System (ADS)

    Rodriguez-Romo, Suemi

    1994-03-01

    A regularization scheme for quantum field theories given in a q-mutator algebra for the internal momentum space in a loop integration is constructed. We show Feynman integrals that are finite for q≠ 1but diverse as q → 1. Using this regularization scheme, we propose a renormalization program in q-mutator space ( q-renormalization program) for the λf 4 theory as an example, up to some one-loop diagrams. This work paves the way to obtaining physically measurable quantities from quantum field theories over spaces that neither commute nor anticommute.

  6. [lambda][phi][sup 4] q-renormalization program

    SciTech Connect

    Rodriguez-Romo, S. )

    1994-03-01

    A regularization scheme for quantum field theories given in q-mutator algebra for the internal momentum space in a loop integration is constructed. The author shows Feynman integrals that are finite for q [ne] 1 but diverse as q [yields] 1. Using this regularization scheme, the author proposes a renormalization program in q-mutator space (q-renormalization program) for the [lambda][phi][sup 4] theory as an example, up to some one-loop diagrams. This work paves the way to obtaining physically measureable quantities from quantum field theories over spaces that neither commute nor anticommute.

  7. Dimension-5 C P -odd operators: QCD mixing and renormalization

    NASA Astrophysics Data System (ADS)

    Bhattacharya, Tanmoy; Cirigliano, Vincenzo; Gupta, Rajan; Mereghetti, Emanuele; Yoon, Boram

    2015-12-01

    We study the off-shell mixing and renormalization of flavor-diagonal dimension-five T - and P -odd operators involving quarks, gluons, and photons, including quark electric dipole and chromoelectric dipole operators. We present the renormalization matrix to one loop in the MS ¯ scheme. We also provide a definition of the quark chromoelectric dipole operator in a regularization-independent momentum-subtraction scheme suitable for nonperturbative lattice calculations and present the matching coefficients with the MS ¯ scheme to one loop in perturbation theory, using both the naïve dimensional regularization and 't Hooft-Veltman prescriptions for γ5.

  8. Two loop divergences studied with one loop constrained differential renormalization

    SciTech Connect

    Seijas, Cesar . E-mail: cesar@fpaxp1.usc.es

    2007-08-15

    In the context of differential renormalization, using constrained differential renormalization rules at one-loop, we show how to obtain concrete results in two-loop calculations without making use of Ward identities. In order to do that, we obtain a list of integrals with overlapping divergences compatible with CDR that can be applied to various two-loop background field calculations. As an example, we obtain the two-loop coefficient of the beta function of QED, SuperQED and Yang-Mills theory.

  9. Peripheral NN scattering from subtractive renormalization of chiral interactions

    SciTech Connect

    Batista, E. F.; Szpigel, S.; Timóteo, V. S.

    2014-11-11

    We apply five subtractions in the Lippman-Schwinger (LS) equation in order to perform a non-perturbative renormalization of chiral N3LO nucleon-nucleon interactions. Here we compute the phase shifts for the uncoupled peripheral waves at renormalization scales between 0.1 fm{sup −1} and 1 fm{sup −1}. In this range, the results are scale invariant and provide an overall good agreement with the Nijmegen partial wave analysis up to at least E{sub lab} = 150 MeV, with a cutoff at Λ = 30 fm{sup −1}.

  10. Background field functional renormalization group for absorbing state phase transitions.

    PubMed

    Buchhold, Michael; Diehl, Sebastian

    2016-07-01

    We present a functional renormalization group approach for the active to inactive phase transition in directed percolation-type systems, in which the transition is approached from the active, finite density phase. By expanding the effective potential for the density field around its minimum, we obtain a background field action functional, which serves as a starting point for the functional renormalization group approach. Due to the presence of the background field, the corresponding nonperturbative flow equations yield remarkably good estimates for the critical exponents of the directed percolation universality class, even in low dimensions. PMID:27575107

  11. Background field functional renormalization group for absorbing state phase transitions

    NASA Astrophysics Data System (ADS)

    Buchhold, Michael; Diehl, Sebastian

    2016-07-01

    We present a functional renormalization group approach for the active to inactive phase transition in directed percolation-type systems, in which the transition is approached from the active, finite density phase. By expanding the effective potential for the density field around its minimum, we obtain a background field action functional, which serves as a starting point for the functional renormalization group approach. Due to the presence of the background field, the corresponding nonperturbative flow equations yield remarkably good estimates for the critical exponents of the directed percolation universality class, even in low dimensions.

  12. From infinite to two dimensions through the functional renormalization group.

    PubMed

    Taranto, C; Andergassen, S; Bauer, J; Held, K; Katanin, A; Metzner, W; Rohringer, G; Toschi, A

    2014-05-16

    We present a novel scheme for an unbiased, nonperturbative treatment of strongly correlated fermions. The proposed approach combines two of the most successful many-body methods, the dynamical mean field theory and the functional renormalization group. Physically, this allows for a systematic inclusion of nonlocal correlations via the functional renormalization group flow equations, after the local correlations are taken into account nonperturbatively by the dynamical mean field theory. To demonstrate the feasibility of the approach, we present numerical results for the two-dimensional Hubbard model at half filling. PMID:24877952

  13. Mixed O/W emulsions stabilized by solid particles: a model system for controlled mass transfer triggered by surfactant addition.

    PubMed

    Drelich, Audrey; Grossiord, Jean-Louis; Gomez, François; Clausse, Danièle; Pezron, Isabelle

    2012-11-15

    This article deals with a model mixed oil-in-water (O/W) emulsion system developed to study the effect of surfactants on mass transfer between dispersed oil droplets of different composition. In this purpose, our goal was to formulate O/W emulsions without any surface active agents as stabilizer, which was achieved by replacing surfactants by a mixture of hydrophilic/hydrophobic silica particles. Then, to study the specific role of surfactants in the oil transfer process, different types and concentrations of surfactants were added to the mixed emulsion after its preparation. In such a way, the same original emulsion can be used for all experiments and the influence of various surface active molecules on the oil transfer mechanism can be directly studied. The model mixed emulsion used consists of a mixture of hexadecane-in-water and tetradecane-in-water emulsions. The transfer between tetradecane and hexadecane droplets was monitored by using differential scanning calorimetry, which allows the detection of freezing and melting signals characteristic of the composition of the dispersed oil droplets. The results obtained showed that it is possible to trigger the transfer of tetradecane towards hexadecane droplets by adding surfactants at concentrations above their critical micellar concentration, measured in presence of solid particles, through micellar transport mechanism. PMID:22909967

  14. Theory of droplet. Part 1: Renormalized laws of droplet vaporization in non-dilute sprays

    NASA Technical Reports Server (NTRS)

    Chiu, H. H.

    1989-01-01

    The vaporization of a droplet, interacting with its neighbors in a non-dilute spray environment is examined as well as a vaporization scaling law established on the basis of a recently developed theory of renormalized droplet. The interacting droplet consists of a centrally located droplet and its vapor bubble which is surrounded by a cloud of droplets. The distribution of the droplets and the size of the cloud are characterized by a pair-distribution function. The vaporization of a droplet is retarded by the collective thermal quenching, the vapor concentration accumulated in the outer sphere, and by the limited percolative passages for mass, momentum and energy fluxes. The retardation is scaled by the local collective interaction parameters (group combustion number of renormalized droplet, droplet spacing, renormalization number and local ambient conditions). The numerical results of a selected case study reveal that the vaporization correction factor falls from unity monotonically as the group combustion number increases, and saturation is likely to occur when the group combustion number reaches 35 to 40 with interdroplet spacing of 7.5 diameters and an environment temperature of 500 K. The scaling law suggests that dense sprays can be classified into: (1) a diffusively dense cloud characterized by uniform thermal quenching in the cloud; (2) a stratified dense cloud characterized by a radial stratification in temperature by the differential thermal quenching of the cloud; or (3) a sharply dense cloud marked by fine structure in the quasi-droplet cloud and the corresponding variation in the correction factor due to the variation in the topological structure of the cloud characterized by a pair-distribution function of quasi-droplets.

  15. Changes in the nanoparticle aggregation rate due to the additional effect of electrostatic and magnetic forces on mass transport coefficients.

    PubMed

    Rosická, Dana; Sembera, Jan

    2013-01-01

    : The need may arise to be able to simulate the migration of groundwater nanoparticles through the ground. Transportation velocities of nanoparticles are different from that of water and depend on many processes that occur during migration. Unstable nanoparticles, such as zero-valent iron nanoparticles, are especially slowed down by aggregation between them. The aggregation occurs when attracting forces outweigh repulsive forces between the particles. In the case of iron nanoparticles that are used for remediation, magnetic forces between particles contribute to attractive forces and nanoparticles aggregate rapidly. This paper describes the addition of attractive magnetic forces and repulsive electrostatic forces between particles (by 'particle', we mean both single nanoparticles and created aggregates) into a basic model of aggregation which is commonly used. This model is created on the basis of the flow of particles in the proximity of observed particles that gives the rate of aggregation of the observed particle. By using a limit distance that has been described in our previous work, the flow of particles around one particle is observed in larger spacing between the particles. Attractive magnetic forces between particles draw the particles into closer proximity and result in aggregation. This model fits more closely with rapid aggregation which occurs between magnetic nanoparticles.

  16. Communication: Four-component density matrix renormalization group

    SciTech Connect

    Knecht, Stefan Reiher, Markus; Legeza, Örs

    2014-01-28

    We present the first implementation of the relativistic quantum chemical two- and four-component density matrix renormalization group algorithm that includes a variational description of scalar-relativistic effects and spin–orbit coupling. Numerical results based on the four-component Dirac–Coulomb Hamiltonian are presented for the standard reference molecule for correlated relativistic benchmarks: thallium hydride.

  17. Renormalization Group Flows, Cycles, and c-Theorem Folklore

    NASA Astrophysics Data System (ADS)

    Curtright, Thomas L.; Jin, Xiang; Zachos, Cosmas K.

    2012-03-01

    Monotonic renormalization group flows of the “c” and “a” functions are often cited as reasons why cyclic or chaotic coupling trajectories cannot occur. It is argued here, based on simple examples, that this is not necessarily true. Simultaneous monotonic and cyclic flows can be compatible if the flow function is multivalued in the couplings.

  18. Renormalization group flows, cycles, and c-theorem folklore.

    PubMed

    Curtright, Thomas L; Jin, Xiang; Zachos, Cosmas K

    2012-03-30

    Monotonic renormalization group flows of the "c" and "a" functions are often cited as reasons why cyclic or chaotic coupling trajectories cannot occur. It is argued here, based on simple examples, that this is not necessarily true. Simultaneous monotonic and cyclic flows can be compatible if the flow function is multivalued in the couplings.

  19. Renormalization of NN Interaction with Relativistic Chiral Two Pion Exchange

    SciTech Connect

    Higa, R; Valderrama, M Pavon; Arriola, E Ruiz

    2007-06-14

    The renormalization of the NN interaction with the Chiral Two Pion Exchange Potential computed using relativistic baryon chiral perturbation theory is considered. The short distance singularity reduces the number of counter-terms to about a half as those in the heavy-baryon expansion. Phase shifts and deuteron properties are evaluated and a general overall agreement is observed.

  20. Renormalization of interactions of ultracold atoms in simulated Rashba gauge fields

    SciTech Connect

    Ozawa, Tomoki; Baym, Gordon

    2011-10-15

    Interactions of ultracold atoms with Rashba spin-orbit coupling, currently being studied with simulated (artificial) gauge fields, have nontrivial ultraviolet and infrared behavior. Examining the ultrastructure of the Bethe-Salpeter equation, we show that the linear ultraviolet divergence in the bare interaction can be renormalized as usual in terms of low-energy scattering lengths, and that for both bosons and fermions ultraviolet logarithmic divergences are absent. Calculating the leading order effective interaction with full dependence on the spin-orbit coupling strength and the center-of-mass momentum of the colliding pair, we elucidate the relation between mean-field interactions and physical three-dimensional scattering lengths. As a consequence of infrared logarithmic divergences in the two-particle propagator, the effective interaction vanishes as the center-of-mass momentum approaches zero.

  1. Renormalization group equation study of the scalar sector of the minimal B-L extension of the standard model

    SciTech Connect

    Basso, Lorenzo; Moretti, Stefano; Pruna, Giovanni Marco

    2010-09-01

    We present the complete set of renormalization group equations at one loop for the nonexotic minimal U(1) extension of the standard model (SM). It includes all models that are anomaly-free with the SM fermion content augmented by one right-handed neutrino per generation. We then pursue the numerical study of the pure B-L model, deriving the triviality and vacuum stability bounds on an enlarged scalar sector comprising one additional Higgs singlet field with respect to the SM.

  2. Holographic renormalization of asymptotically flat gravity

    NASA Astrophysics Data System (ADS)

    Park, Miok; Mann, Robert B.

    2012-12-01

    We compute the boundary stress tensor associated with Mann-Marolf counterterm in asymptotically flat and static spacetime for a cylindrical boundary surface as r → ∞, andfindthattheformoftheboundarystresstensoristhesameasthehyperbolic boundary case in 4 dimensions, but has additional terms in more than 4 dimensions. We find that these additional terms are impotent and do not contribute to conserved charges. We also check the conservation of the boundary stress tensor D a T ab = 0, and apply our result to the ( n + 3)-dimensional static black hole solution. As a result, we show that the stress boundary tensor with the Mann-Marolf counterterm works well for standard boundary surfaces.

  3. The renormalization scale problem and novel perspectives for QCD

    NASA Astrophysics Data System (ADS)

    Brodsky, Stanley J.

    2015-11-01

    I discuss a number of novel tests of QCD, measurements which can illuminate fundamental features of hadron physics. These include the origin of the “ridge” in proton-proton collisions; the production of the Higgs at high xF; the role of digluon-initiated processes for quarkonium production; flavor-dependent anti-shadowing; the effect of nuclear shadowing on QCD sum rules; direct production of hadrons at high transverse momentum; and leading-twist lensing corrections; and the breakdown of perturbative QCD factorization. I also review the “Principle of Maximum Conformalit” (PMC) which systematically sets the renormalization scale order-by-order in pQCD, independent of the choice of renormalization scheme, thus eliminating an unnecessary theoretical uncertainty.

  4. On the renormalization of non-commutative field theories

    NASA Astrophysics Data System (ADS)

    Blaschke, Daniel N.; Garschall, Thomas; Gieres, François; Heindl, Franz; Schweda, Manfred; Wohlgenannt, Michael

    2013-01-01

    This paper addresses three topics concerning the quantization of non-commutative field theories (as defined in terms of the Moyal star product involving a constant tensor describing the non-commutativity of coordinates in Euclidean space). To start with, we discuss the Quantum Action Principle and provide evidence for its validity for non-commutative quantum field theories by showing that the equation of motion considered as insertion in the generating functional Z c [ j] of connected Green functions makes sense (at least at one-loop level). Second, we consider the generalization of the BPHZ renormalization scheme to non-commutative field theories and apply it to the case of a self-interacting real scalar field: Explicit computations are performed at one-loop order and the generalization to higher loops is commented upon. Finally, we discuss the renormalizability of various models for a self-interacting complex scalar field by using the approach of algebraic renormalization.

  5. Renormalization group analysis of graphene with a supercritical Coulomb impurity

    NASA Astrophysics Data System (ADS)

    Nishida, Yusuke

    2016-08-01

    We develop a field-theoretic approach to massless Dirac fermions in a supercritical Coulomb potential. By introducing an Aharonov-Bohm solenoid at the potential center, the critical Coulomb charge can be made arbitrarily small for one partial-wave sector, where a perturbative renormalization group analysis becomes possible. We show that a scattering amplitude for reflection of particle at the potential center exhibits the renormalization group limit cycle, i.e., log-periodic revolutions as a function of the scattering energy, revealing the emergence of discrete scale invariance. This outcome is further incorporated in computing the induced charge and current densities, which turn out to have power-law tails with coefficients log-periodic with respect to the distance from the potential center. Our findings are consistent with the previous prediction obtained by directly solving the Dirac equation and can in principle be realized by graphene experiments with charged impurities.

  6. Infrared Yang-Mills theory: A renormalization group perspective

    NASA Astrophysics Data System (ADS)

    Weber, Axel; Dall’Olio, Pietro; Astorga, Francisco

    2016-05-01

    We describe a technically very simple analytical approach to the deep infrared regime of Yang-Mills theory in the Landau gauge via Callan-Symanzik renormalization group equations in an epsilon expansion. This approach recovers all the solutions for the infrared gluon and ghost propagators previously found by solving the Dyson-Schwinger equations of the theory and singles out the solution with decoupling behavior, confirmed by lattice calculations, as the only one corresponding to an infrared attractive fixed point (for space-time dimensions above two). For the case of four dimensions, we describe the crossover of the system from the ultraviolet to the infrared fixed point and determine the complete momentum dependence of the propagators. The results for different renormalization schemes are compared to the lattice data.

  7. Renormalization and universality of blowup in hydrodynamic flows.

    PubMed

    Mailybaev, Alexei A

    2012-06-01

    We consider self-similar solutions describing intermittent bursts in shell models of turbulence and study their relationship with blowup phenomena in continuous hydrodynamic models. First, we show that these solutions are very close to self-similar solution for the Fourier transformed inviscid Burgers equation corresponding to shock formation from smooth initial data. Then, the result is generalized to hyperbolic conservation laws in one space dimension describing compressible flows. It is shown that the renormalized wave profile tends to a universal function, which is independent both of initial conditions and of a specific form of the conservation law. This phenomenon can be viewed as a new manifestation of the renormalization group theory. Finally, we discuss possibilities for application of the developed theory for detecting and describing a blowup in incompressible flows.

  8. E-cigarette Marketing and Older Smokers: Road to Renormalization

    PubMed Central

    Cataldo, Janine K.; Petersen, Anne Berit; Hunter, Mary; Wang, Julie; Sheon, Nicolas

    2015-01-01

    Objectives To describe older smokers’ perceptions of risks and use of e-cigarettes, and their responses to marketing and knowledge of, and opinions about, regulation of e-cigarettes. Methods Eight 90-minute focus groups with 8 to 9 participants met in urban and suburban California to discuss topics related to cigarettes and alternative tobacco products. Results Older adults are using e-cigarettes for cessation and as a way to circumvent no-smoking policies; they have false perceptions about the effectiveness and safety of e-cigarettes. They perceive e-cigarette marketing as a way to renormalize smoking. Conclusions To stem the current epidemic of nicotine addiction, the FDA must take immediate action because e-cigarette advertising promotes dual use and may contribute to the renormalization of smoking. PMID:25741681

  9. BOOK REVIEW: Renormalization Methods---A Guide For Beginners

    NASA Astrophysics Data System (ADS)

    Cardy, J.

    2004-05-01

    The stated goal of this book is to fill a perceived gap between undergraduate texts on critical phenomena and advanced texts on quantum field theory, in the general area of renormalization methods. It is debatable whether this gap really exists nowadays, as a number of books have appeared in which it is made clear that field-theoretic renormalization group methods are not the preserve of particle theory, and indeed are far more easily appreciated in the contexts of statistical and condensed matter physics. Nevertheless, this volume does have a fresh aspect to it, perhaps because of the author's background in fluid dynamics and turbulence theory, rather than through the more traditional migration from particle physics. The book begins at a very elementary level, in an effort to motivate the use of renormalization methods. This is a worthy effort, but it is likely that most of this section will be thought too elementary by readers wanting to get their teeth into the subject, while those for whom this section is apparently written are likely to find the later chapters rather challenging. The author's particular approach then leads him to emphasise the role of renormalized perturbation theory (rather than the renormalization group) in a number of problems, including non-linear systems and turbulence. Some of these ideas will be novel and perhaps even surprising to traditionally trained field theorists. Most of the rest of the book is on far more familiar territory: the momentum-space renormalization group, epsilon-expansion, and so on. This is standard stuff, and, like many other textbooks, it takes a considerable chunk of the book to explain all the formalism. As a result, there is only space to discuss the standard phi4 field theory as applied to the Ising model (even the N-vector model is not covered) so that no impression is conveyed of the power and extent of all the applications and generalizations of the techniques. It is regrettable that so much space is spent

  10. Dimension-5 CP -odd operators: QCD mixing and renormalization

    DOE PAGES

    Bhattacharya, Tanmoy; Cirigliano, Vincenzo; Gupta, Rajan; Mereghetti, Emanuele; Yoon, Boram

    2015-12-23

    Here, we study the off-shell mixing and renormalization of flavor-diagonal dimension-five T- and P-odd operators involving quarks, gluons, and photons, including quark electric dipole and chromoelectric dipole operators. Furthermore, we present the renormalization matrix to one loop in themore » $$\\bar{MS}$$ scheme. We also provide a definition of the quark chromoelectric dipole operator in a regularization-independent momentum-subtraction scheme suitable for nonperturbative lattice calculations and present the matching coefficients with the $$\\bar{MS}$$ scheme to one loop in perturbation theory, using both the naïve dimensional regularization and ’t Hooft–Veltman prescriptions for γ5.« less

  11. Large-cell Monte Carlo renormalization of irreversible growth processes

    NASA Technical Reports Server (NTRS)

    Nakanishi, H.; Family, F.

    1985-01-01

    Monte Carlo sampling is applied to a recently formulated direct-cell renormalization method for irreversible, disorderly growth processes. Large-cell Monte Carlo renormalization is carried out for various nonequilibrium problems based on the formulation dealing with relative probabilities. Specifically, the method is demonstrated by application to the 'true' self-avoiding walk and the Eden model of growing animals for d = 2, 3, and 4 and to the invasion percolation problem for d = 2 and 3. The results are asymptotically in agreement with expectations; however, unexpected complications arise, suggesting the possibility of crossovers, and in any case, demonstrating the danger of using small cells alone, because of the very slow convergence as the cell size b is extrapolated to infinity. The difficulty of applying the present method to the diffusion-limited-aggregation model, is commented on.

  12. Rapidity renormalized TMD soft and beam functions at two loops

    NASA Astrophysics Data System (ADS)

    Lübbert, Thomas; Oredsson, Joel; Stahlhofen, Maximilian

    2016-03-01

    We compute the transverse momentum dependent (TMD) soft function for the production of a color-neutral final state at the LHC within the rapidity renormalization group (RRG) framework to next-to-next-to-leading order (NNLO). We use this result to extract the universal renormalized TMD beam functions (aka TMDPDFs) in the same scheme and at the same order from known results in another scheme. We derive recurrence relations for the logarithmic structure of the soft and beam functions, which we use to cross check our calculation. We also explicitly confirm the non-Abelian exponentiation of the TMD soft function in the RRG framework at two loops. Our results provide the ingredients for resummed predictions of p ⊥-differential cross sections at NNLL' in the RRG formalism. The RRG provides a systematic framework to resum large (rapidity) logarithms through (R)RG evolution and assess the associated perturbative uncertainties.

  13. New applications of renormalization group methods in nuclear physics.

    PubMed

    Furnstahl, R J; Hebeler, K

    2013-12-01

    We review recent developments in the use of renormalization group (RG) methods in low-energy nuclear physics. These advances include enhanced RG technology, particularly for three-nucleon forces, which greatly extends the reach and accuracy of microscopic calculations. We discuss new results for the nucleonic equation of state with applications to astrophysical systems such as neutron stars, new calculations of the structure and reactions of finite nuclei, and new explorations of correlations in nuclear systems.

  14. Renormalization and Induced Gauge Action on a Noncommutative Space

    NASA Astrophysics Data System (ADS)

    Grosse, H.; Wohlgenannt, M.

    Field theories on deformed spaces suffer from the IR/UV mxing and renormalization is generically spoiled. In work with R.~Wulkenhaar, one of us realized a way to cure this desease by adding one more marginal operator. We review these ideas, show the application to φ^3 models and use heat kernel expansion methods for a scalar field theory coupled to an external gauge field on a θ-deformed space and derive noncommutative gauge actions.

  15. Renormalization-group calculation of excitation properties for impurity models

    NASA Astrophysics Data System (ADS)

    Yoshida, M.; Whitaker, M. A.; Oliveira, L. N.

    1990-05-01

    The renormalization-group method developed by Wilson to calculate thermodynamical properties of dilute magnetic alloys is generalized to allow the calculation of dynamical properties of many-body impurity Hamiltonians. As a simple illustration, the impurity spectral density for the resonant-level model (i.e., the U=0 Anderson model) is computed. As a second illustration, for the same model, the longitudinal relaxation rate for a nuclear spin coupled to the impurity is calculated as a function of temperature.

  16. Renormalized transport equations for the bistable potential model

    NASA Astrophysics Data System (ADS)

    Weidlich, Wolfgang; Grabert, Hermann

    1980-09-01

    Renormalized transport equations for general Fokker-Planck systems are derived and applied to the bistable potential model. The exact equation for the expectation value < x> t can be evaluated in both domains < D>∈ x ± and < x>∈ D 0 outside and between the potential minima, leading to drastic differences of the dynamics prevailing in D ± and D 0, respectively.

  17. Towards a complete renormalization group trajectory between two fixed points

    NASA Astrophysics Data System (ADS)

    Abdesselam, Abdelmalek

    2007-12-01

    We give a rigorous nonperturbative construction of a massless discrete trajectory for Wilson’s exact renormalization group. The model is a three dimensional Euclidean field theory with a modified free propagator. The trajectory realizes the mean field to critical crossover from the ultraviolet Gaussian fixed point to an analog recently constructed by Brydges, Mitter and Scoppola of the Wilson-Fisher nontrivial fixed point.

  18. Wilsonian renormalization group equation for nuclear current operators

    SciTech Connect

    Kvinikhidze, A. N.; Blankleider, B.

    2007-12-15

    We present the solution to the recently derived Wilsonian renormalization group (RG) equation for nuclear current operators. To eliminate the present ambiguity in the RG equation itself, we introduce a new condition specifying the cutoff independence of the five-point Green function corresponding to the two-body propagator with current operator insertion. The resulting effective current operator is then shown to obey a modified Ward-Takahashi identity that differs from the usual one, but that nevertheless leads to current conservation.

  19. Universal Dynamics and Renormalization in Many-Body-Localized Systems

    NASA Astrophysics Data System (ADS)

    Altman, Ehud; Vosk, Ronen

    2015-03-01

    We survey the recent progress made in understanding nonequilibrium dynamics in closed random systems. The emphasis is on the important role played by concepts from quantum information theory and on the application of systematic renormalization group methods to capture universal aspects of the dynamics. Finally, we outline some outstanding open questions, which include the description of the many-body-localization phase transition and the identification of physical systems that allow systematic experimental study of these phenomena.

  20. Subtractive Renormalization Group Invariance: Pionless EFT at NLO

    SciTech Connect

    Timoteo, Varese S.; Szpigel, Sergio; Duraes, Francisco O.

    2010-11-12

    We show some results concerning the renormalization group (RG) invariance of the nucleon-nucleon (NN) interaction in pionless effective field theory at next-to-leading order (NLO), using a non-relativistic Callan-Symanzik equation (NRCS) for the driving term of the Lippmann-Schwinger (LS) equation with three recursive subtractions. The phase-shifts obtained for the RG evolved potential are same as those for the original potential, apart from relative differences of order 10{sup -15}.

  1. A renormalization approach to the universality of scaling in phyllotaxis

    NASA Astrophysics Data System (ADS)

    Reick, Christian H.

    2015-04-01

    Phyllotaxis, i.e. the arrangement of plant organs like leaves, florets, scales, bracts etc. around a shoot, stem, or cone, is often highly regular. Across the plant kingdom phyllotaxis shows not only qualitatively, but also quantitatively identical features, like the occurrence of divergence angles close to noble irrationals. In a previous study (Reick, 2012) a mechanism has been identified that explains the selection of these particular divergence angles on the basis of self-similarity and scaling, numerically found in the bifurcation diagrams of simple dynamical models of phyllataxis. In the present paper, by constructing a renormalization theory, the universality of this scaling is proved for a whole class of models, prototypically represented by Thornley's model of phyllotaxis (Thornley, 1975). The renormalization is constructed from another self-similarity found numerically for the Fourier transform of the abstract potential governing the mutual inhibition of primordia. Surprisingly, the resulting renormalization transformation is already known from the treatment of the quasiperiodic transition to chaos but operates here on a different function space. It turns out that the fixed points of the renormalization transformation are characterized by divergences of the form Θ (κ) = 1 /τ (κ), where, written as continued fraction, τ (κ) = [ κ ; κ , κ , … ] , κ ∈N+. To show the universality of the scaling, it is demonstrated that the fixed points are unstable and that the associated scaling factors α (κ) = -(τ (κ)) 2 and β (κ) =τ (κ) are exactly those that were numerically found in (Reick, 2012) to rule the selfsimilarity of the bifurcation structure. Thereby, the present paper puts forward an explanation for the universal appearance of certain phyllotactic patterns that is independent of physiological detail of plant growth.

  2. Dynamical renormalization group resummation of finite temperature infrared divergences

    SciTech Connect

    Boyanovsky, D.; de Vega, H.J. ); Boyanovsky, D.; de Vega, H.J.; Simionato, M. et Denis Diderot , Tour 16, 1er. etage, 4, Place Jussieu, 75252 Paris, Cedex 05 ); Holman, R. ); Simionato, M. )

    1999-09-01

    We introduce the method of dynamical renormalization group to study relaxation and damping out of equilibrium directly in real time and apply it to the study of infrared divergences in scalar QED. This method allows a consistent resummation of infrared effects associated with the exchange of quasistatic transverse photons and leads to anomalous logarithmic relaxation of the form e[sup [minus][alpha] hthinsp;T hthinsp;t hthinsp;ln[t/t[sub 0

  3. Power counting and Wilsonian renormalization in nuclear effective field theory

    NASA Astrophysics Data System (ADS)

    Valderrama, Manuel Pavón

    2016-05-01

    Effective field theories are the most general tool for the description of low energy phenomena. They are universal and systematic: they can be formulated for any low energy systems we can think of and offer a clear guide on how to calculate predictions with reliable error estimates, a feature that is called power counting. These properties can be easily understood in Wilsonian renormalization, in which effective field theories are the low energy renormalization group evolution of a more fundamental — perhaps unknown or unsolvable — high energy theory. In nuclear physics they provide the possibility of a theoretically sound derivation of nuclear forces without having to solve quantum chromodynamics explicitly. However there is the problem of how to organize calculations within nuclear effective field theory: the traditional knowledge about power counting is perturbative but nuclear physics is not. Yet power counting can be derived in Wilsonian renormalization and there is already a fairly good understanding of how to apply these ideas to non-perturbative phenomena and in particular to nuclear physics. Here we review a few of these ideas, explain power counting in two-nucleon scattering and reactions with external probes and hint at how to extend the present analysis beyond the two-body problem.

  4. Real-space renormalized dynamical mean field theory

    NASA Astrophysics Data System (ADS)

    Kubota, Dai; Sakai, Shiro; Imada, Masatoshi

    2016-05-01

    We propose real-space renormalized dynamical mean field theory (rr-DMFT) to deal with large clusters in the framework of a cluster extension of the DMFT. In the rr-DMFT, large clusters are decomposed into multiple smaller clusters through a real-space renormalization. In this work, the renormalization effect is taken into account only at the lowest order with respect to the intercluster coupling, which nonetheless reproduces exactly both the noninteracting and atomic limits. Our method allows us large cluster-size calculations which are intractable with the conventional cluster extensions of the DMFT with impurity solvers, such as the continuous-time quantum Monte Carlo and exact diagonalization methods. We benchmark the rr-DMFT for the two-dimensional Hubbard model on a square lattice at and away from half filling, where the spatial correlations play important roles. Our results on the spin structure factor indicate that the growth of the antiferromagnetic spin correlation is taken into account beyond the decomposed cluster size. We also show that the self-energy obtained from the large-cluster solver is reproduced by our method better than the solution obtained directly for the smaller cluster. When applied to the Mott metal-insulator transition, the rr-DMFT is able to reproduce the reduced critical value for the Coulomb interaction comparable to the large cluster result.

  5. Renormalizing a viscous fluid model for large scale structure formation

    NASA Astrophysics Data System (ADS)

    Führer, Florian; Rigopoulos, Gerasimos

    2016-02-01

    Using the Stochastic Adhesion Model (SAM) as a simple toy model for cosmic structure formation, we study renormalization and the removal of the cutoff dependence from loop integrals in perturbative calculations. SAM shares the same symmetry with the full system of continuity+Euler equations and includes a viscosity term and a stochastic noise term, similar to the effective theories recently put forward to model CDM clustering. We show in this context that if the viscosity and noise terms are treated as perturbative corrections to the standard eulerian perturbation theory, they are necessarily non-local in time. To ensure Galilean Invariance higher order vertices related to the viscosity and the noise must then be added and we explicitly show at one-loop that these terms act as counter terms for vertex diagrams. The Ward Identities ensure that the non-local-in-time theory can be renormalized consistently. Another possibility is to include the viscosity in the linear propagator, resulting in exponential damping at high wavenumber. The resulting local-in-time theory is then renormalizable to one loop, requiring less free parameters for its renormalization.

  6. Adaptive random renormalization group classification of multiscale dispersive processes

    NASA Astrophysics Data System (ADS)

    Cushman, John; O'Malley, Dan

    2013-04-01

    Renormalization group operators provide a detailed classification tool for dispersive processes. We begin by reviewing a two-scale renormalization group classification scheme. Repeated application of one operator is associated with long time behavior of the process while repeated application of the other is associated with short time behavior. This approach is shown to be robust even in the presence of non-stationary increments and/or infinite second moments. Fixed points of the operators can be used for further sub classification of the processes when appropriate limits exist. As an example we look at advective dispersion in an ergodic velocity field. Let X(t) be a fixed point of the long-time renormalization group operator (RGO) RX(t)=X(rt)/r^p. Scaling laws for the probability density, mean first passage times, and finite-size Lyapunov exponents of such fixed points are reviewed in anticipation of more general results. A generalized RGO, Rp, where the exponent in R above is now a random variable is introduced. Scaling laws associated with these random RGOs (RRGOs) are demonstrated numerically and applied to a process modeling the transition from sub-dispersion to Fickian dispersion. The scaling laws for the RRGO are not simple power laws, but instead are a weighted average of power laws. The weighting in the scaling laws can be determined adaptively via Bayes' theorem.

  7. Nonperturbative renormalization for 2PI effective action techniques

    SciTech Connect

    Berges, J. . E-mail: j.berges@thphys.uni-heidelberg.de; Borsanyi, Sz. . E-mail: borsanyi@thphys.uni-heidelberg.de; Reinosa, U. . E-mail: julien.serreau@th.u-psud.fr

    2005-12-15

    Nonperturbative approximation schemes based on two-particle irreducible (2PI) effective actions provide an important means for our current understanding of (non-)equilibrium quantum field theory. A remarkable property is their renormalizability, since these approximations involve selective summations to infinite perturbative orders. In this paper, we show how to renormalize all n-point functions of the theory, which are given by derivatives of the 2PI-resummed effective action {gamma} [{phi}] for scalar fields {phi}. This provides a complete description in terms of the generating functional for renormalized proper vertices, which extends previous prescriptions in the literature on the renormalization for 2PI effective actions. The importance of the 2PI-resummed generating functional for proper vertices stems from the fact that the latter respect all symmetry properties of the theory and, in particular, Goldstone's theorem in the phase with spontaneous symmetry breaking. This is important in view of the application of these techniques to gauge theories, where Ward identities play a crucial role.

  8. The role of methanol addition to water samples in reducing analyte adsorption and matrix effects in liquid chromatography-tandem mass spectrometry.

    PubMed

    Li, Wei; Liu, Yucan; Duan, Jinming; Saint, Christopher P; Mulcahy, Dennis

    2015-04-10

    Liquid chromatography-tandem mass spectrometry (LC-MS/MS) analysis coupled simply with water filtering before injection has proven to be a simple, economic and time-saving method for analyzing trace-level organic pollutants in aqueous environments. However, the linearity, precision and detection limits of such methods for late-eluting analytes were found to be much poorer than for early-eluting ones due to adsorption of the analytes in the operating system, such as sample vial, flow path and sample loop, creating problems in quantitative analysis. Addition of methanol (MeOH) into water samples as a modifier was shown to be effective in alleviating or even eliminating the negative effect on signal intensity for the late-eluting analytes and at the same time being able to reduce certain matrix effects for real water samples. Based on the maximum detection signal intensity obtained on desorption of the analytes with MeOH addition, the ratio of the detection signal intensity without addition of MeOH to the maximum intensity can be used to evaluate the effectiveness of methanol addition. Accordingly, the values of <50%, 50-80%, 80-120% could be used to indicate strong, medium and no effects, respectively. Based on this concept, an external matrix-matched calibration method with the addition of MeOH has been successfully established for analyzing fifteen pesticides with diverse physico-chemical properties in surface and groundwater with good linearity (r(2): 0.9929-0.9996), precision (intra-day relative standard deviation (RSD): 1.4-10.7%, inter-day RSD: 1.5-9.4%), accuracy (76.9-126.7%) and low limits of detection (0.003-0.028μg/L).

  9. Significance of Additional Non-Mass Enhancement in Patients with Breast Cancer on Preoperative 3T Dynamic Contrast Enhanced MRI of the Breast

    PubMed Central

    Cho, Yun Hee; Cho, Kyu Ran; Park, Eun Kyung; Seo, Bo Kyoung; Woo, Ok Hee; Cho, Sung Bum; Bae, Jeoung Won

    2016-01-01

    Background In preoperative assessment of breast cancer, MRI has been shown to identify more additional breast lesions than are detectable using conventional imaging techniques. The characterization of additional lesions is more important than detection for optimal surgical treatment. Additional breast lesions can be included in focus, mass, and non-mass enhancement (NME) on MRI. According to the fifth edition of the breast imaging reporting and data system (BI-RADS®), which includes several changes in the NME descriptors, few studies to date have evaluated NME in preoperative assessment of breast cancer. Objectives We investigated the diagnostic accuracy of BI-RADS descriptors in predicting malignancy for additional NME lesions detected on preoperative 3T dynamic contrast enhanced MRI (DCE-MRI) in patients with newly diagnosed breast cancer. Patients and Methods Between January 2008 and December 2012, 88 patients were enrolled in our study, all with NME lesions other than the index cancer on preoperative 3T DCE-MRI and all with accompanying histopathologic examination. The MRI findings were analyzed according to the BI-RADS MRI lexicon. We evaluated the size, distribution, internal enhancement pattern, and location of NME lesions relative to the index cancer (i.e., same quadrant, different quadrant, or contralateral breast). Results On histopathologic analysis of the 88 NME lesions, 73 (83%) were malignant and 15 (17%) were benign. Lesion size did not differ significantly between malignant and benign lesions (P = 0.410). Malignancy was more frequent in linear (P = 0.005) and segmental (P = 0.011) distributions, and benignancy was more frequent in focal (P = 0.004) and regional (P < 0.001) NME lesions. The highest positive predictive value (PPV) for malignancy occurred in segmental (96.8%), linear (95.1%), clustered ring (100%), and clumped (92.0%) enhancement. Asymmetry demonstrated a high positive predictive value of 85.9%. The frequency of malignancy was higher

  10. Renormalization group study of the minimal Majoronic dark radiation and dark matter model

    NASA Astrophysics Data System (ADS)

    Chang, We-Fu; Ng, John N.

    2016-07-01

    We study the 1-loop renormalization group equation running in the simplest singlet Majoron model constructed by us earlier to accommodate the dark radiation and dark matter content in the universe. A comprehensive numerical study was performed to explore the whole model parameter space. A smaller effective number of neutrinos triangle Neff~ 0.05, or a Majoron decoupling temperature higher than the charm quark mass, is preferred. We found that a heavy scalar dark matter, ρ, of mass 1.5-4 TeV is required by the stability of the scalar potential and an operational type-I see-saw mechanism for neutrino masses. A neutral scalar, S, of mass in the 10-100 GeV range and its mixing with the standard model Higgs as large as 0.1 is also predicted. The dominant decay modes are S into bbar b and/or ωω. A sensitive search will come from rare Z decays via the chain Z → S+ fbar f, where f is a Standard Model fermion, followed by S into a pair of Majoron and/or b-quarks. The interesting consequences of dark matter bound state due to the sizable Sρ ρ-coupling are discussed as well. In particular, shower-like events with an apparent neutrino energy at Mρ could contribute to the observed effective neutrino flux in underground neutrino detectors such as IceCube.

  11. Unique determination of the effective potential in terms of renormalization group functions

    SciTech Connect

    Chishtie, F. A.; Hanif, T.; McKeon, D. G. C.; Steele, T. G.

    2008-03-15

    The perturbative effective potential V in the massless {lambda}{phi}{sup 4} model with a global O(N) symmetry is uniquely determined to all orders by the renormalization group functions alone when the Coleman-Weinberg renormalization condition (d{sup 4}V/d{phi}{sup 4})|{sub {phi}}{sub ={mu}}={lambda} is used, where {mu} represents the renormalization scale. Systematic methods are developed to express the n-loop effective potential in the Coleman-Weinberg scheme in terms of the known n-loop minimal-subtraction (MS) renormalization group functions. Moreover, it also proves possible to sum the leading- and subsequent-to-leading-logarithm contributions to V. An essential element of this analysis is a conversion of the renormalization group functions in the Coleman-Weinberg scheme to the renormalization group functions in the MS scheme. As an example, the explicit five-loop effective potential is obtained from the known five-loop MS renormalization group functions and we explicitly sum the leading-logarithm, next-to-leading-logarithm, and further subleading-logarithm contributions to V. Extensions of these results to massless scalar QED are also presented. Because massless scalar QED has two couplings, conversion of the renormalization group functions from the MS scheme to the Coleman-Weinberg scheme requires the use of multiscale renormalization group methods.

  12. Improved detection of sugar addition to maple syrup using malic acid as internal standard and in 13C isotope ratio mass spectrometry (IRMS).

    PubMed

    Tremblay, Patrice; Paquin, Réal

    2007-01-24

    Stable carbon isotope ratio mass spectrometry (delta13C IRMS) was used to detect maple syrup adulteration by exogenous sugar addition (beet and cane sugar). Malic acid present in maple syrup is proposed as an isotopic internal standard to improve actual adulteration detection levels. A lead precipitation method has been modified to isolate quantitatively malic acid from maple syrup using preparative reversed-phase liquid chromatography. The stable carbon isotopic ratio of malic acid isolated from this procedure shows an excellent accuracy and repeatability of 0.01 and 0.1 per thousand respectively, confirming that the modified lead precipitation method is an isotopic fractionation-free process. A new approach is proposed to detect adulteration based on the correlation existing between the delta13Cmalic acid and the delta13Csugars-delta13Cmalic acid (r = 0.704). This technique has been tested on a set of 56 authentic maple syrup samples. Additionally, authentic samples were spiked with exogeneous sugars. The mean theoretical detection level was statistically lowered using this technique in comparison with the usual two-standard deviation approach, especially when maple syrup is adulterated with beet sugar : 24 +/- 12% of adulteration detection versus 48 +/- 20% (t-test, p = 7.3 x 10-15). The method was also applied to published data for pineapple juices and honey with the same improvement. PMID:17227042

  13. Application of dispersive solid-phase extraction and ultra-fast liquid chromatography-tandem quadrupole mass spectrometry in food additive residue analysis of red wine.

    PubMed

    Chen, Xiao-Hong; Zhao, Yong-Gang; Shen, Hao-Yu; Jin, Mi-Cong

    2012-11-01

    A novel and effective dispersive solid-phase extraction (dSPE) procedure with rapid magnetic separation using ethylenediamine-functionalized magnetic polymer as an adsorbent was developed. The new procedure had excellent clean-up ability for the selective removal of the matrix in red wine. An accurate, simple, and rapid analytical method using ultra-fast liquid chromatography-tandem quadrupole mass spectrometry (UFLC-MS/MS) for the simultaneous determination of nine food additives (i.e., acesulfame, saccharin, sodium cyclamate, aspartame, benzoic acid, sorbic acid, stevioside, dehydroacetic acid, and neotame) in red wine was also used and validated. Recoveries ranging from 78.5% to 99.2% with relative standard deviations ranging from 0.46% to 6.3% were obtained using the new method. All target compounds showed good linearities in the tested range with correlation coefficients (r) higher than 0.9993. The limits of quantification for the nine food additives were between 0.10 μg/L and 50.0 μg/L. The proposed dSPE-UFLC-MS/MS method was successfully applied in the food-safety risk monitoring of real red wine in Zhejiang Province, China.

  14. [Simultaneous determination of eight additives in polymer food packaging materials by ultra-performance liquid chromatography-electrospray ionization tandem mass spectrometry].

    PubMed

    Zhang, Xulong; Liu, Yin; Gong, Zhiguo; Wang, Pengju; Wang, Jide; Feng, Shun

    2014-08-01

    An ultra-high performance liquid chromatography-tandem mass spectrometry (UPLC-MS/MS) method was proposed for the simultaneous determination of eight additives (Irgafos 168 (tri(2.4-di-tert-butylphenyl)phosphite), Irganox 1076 (octadecyl-β-(4-hydroxy-3, 5-di-tert-butylphenyl)propionate), Irganox 1010 (pentaerythritol tetrakys 3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate), BHA (butyl hydroxy anisole), TBHQ (tertiary butylhydroquinone), PG (propyl gallate), DG (dodecyl gallate), UV-326 (2-( 2'-hydroxyl-3'-tert-butyl-5'-methylphenyl)-5-chlorobenzotriazole) in food packaging materials. After extracted by chloromethane through ultrasonic extraction, the samples were analyzed by UPLC-MS/MS. The chromatographic conditions were optimized, and the best separation was obtained on a Waters BEH-C18 column (50 mm x 2. 1 mm, 1.7 μm) with gradient elution of 0. 05% acetic acid solu- tion and methanol. The analysis was performed by UPLC-MS/MS with electrospray ionization (ESI) source in switching between the positive and negative ion modes in one run for multiple reaction monitoring. The eight additives showed good linear relationships in the ranges with all the correlation coefficients (R2) more than 0. 993. The limits of detection (LODs, S/N= 3) and limits of quantitation (LOQs, S/N= 10) of this method were 0. 13-5.50 μg/L and 0.45-17.50 μg/L, respectively. The recoveries were in the range of 63. 9% - 127. 0% with all the RSDs < 15. 8% (n= 6). This method is simple, accurate and effective for the analysis of the eight additives in food packaging materials.

  15. Pattern of trends in stock markets as revealed by the renormalization method

    NASA Astrophysics Data System (ADS)

    Zhang, H. S.; Shen, X. Y.; Huang, J. P.

    2016-08-01

    Predicting the movement of prices is a challenging topic in financial markets. So far, many investigations have been performed to help understand the dynamics of stock prices. In this work, we utilize the renormalization method to analyze the scaling and pattern of stock price trends. According to the analysis of length and changing velocity of the price trends, we find that there exist asymmetric phenomena of the trends in American stock market. In addition, a stronger Herd behavior is also discovered in the Chinese stock market. Since the Chinese (American) stock market is a representative of emerging (mature) market, the study on comparing the markets between these two countries is of potential value, which can leave us a wiser about both the pattern of the markets and the underlying physical mechanisms.

  16. Dynamic structure factor of a Fibonacci lattice: A renormalization-group approach

    NASA Astrophysics Data System (ADS)

    Karmakar, S. N.; Chakrabarti, Arunava; Moitra, R. K.

    1992-08-01

    We present a real-space renormalization-group method for evaluating the exact dynamic structure factor S(q,ω) of a quasiperiodic Fibonacci chain. Contrary to earlier work that takes account only of the global aspects of the symmetry of the chain, our method additionally takes care of the local environmental aspects of the symmetry by separating the original lattice into a finite number of self-similar interpenetrating sublattices, followed by elimination of the coupling between them. Our method also yields correctly the positions of the Bragg peaks of the Fibonacci chain. Moreover, the present method allows the sites of the chain to be grouped into classes following a ``genealogical'' classification, the members of a given class being equivalent up to a certain length scale. Based on this classification, the proof of the existence of a key site, which has only been conjectured in our earlier work using numerical search, has been given.

  17. The metric on field space, functional renormalization, and metric-torsion quantum gravity

    NASA Astrophysics Data System (ADS)

    Reuter, Martin; Schollmeyer, Gregor M.

    2016-04-01

    Searching for new non-perturbatively renormalizable quantum gravity theories, functional renormalization group (RG) flows are studied on a theory space of action functionals depending on the metric and the torsion tensor, the latter parameterized by three irreducible component fields. A detailed comparison with Quantum Einstein-Cartan Gravity (QECG), Quantum Einstein Gravity (QEG), and "tetrad-only" gravity, all based on different theory spaces, is performed. It is demonstrated that, over a generic theory space, the construction of a functional RG equation (FRGE) for the effective average action requires the specification of a metric on the infinite-dimensional field manifold as an additional input. A modified FRGE is obtained if this metric is scale-dependent, as it happens in the metric-torsion system considered.

  18. Bose gases near resonance: Renormalized interactions in a condensate

    SciTech Connect

    Zhou, Fei Mashayekhi, Mohammad S.

    2013-01-15

    Bose gases at large scattering lengths or beyond the usual dilute limit for a long time have been one of the most challenging problems in many-body physics. In this article, we investigate the fundamental properties of a near-resonance Bose gas and illustrate that three-dimensional Bose gases become nearly fermionized near resonance when the chemical potential as a function of scattering lengths reaches a maximum and the atomic condensates lose metastability. The instability and accompanying maximum are shown to be a precursor of the sign change of g{sub 2}, the renormalized two-body interaction between condensed atoms. g{sub 2} changes from effectively repulsive to attractive when approaching resonance from the molecular side, even though the scattering length is still positive. This occurs when dimers, under the influence of condensates, emerge at zero energy in the atomic gases at a finite positive scattering length. We carry out our studies of Bose gases via applying a self-consistent renormalization group equation which is further subject to a boundary condition. We also comment on the relation between the approach here and the diagrammatic calculation in an early article [D. Borzov, M.S. Mashayekhi, S. Zhang, J.-L. Song, F. Zhou, Phys. Rev. A 85 (2012) 023620]. - Highlights: Black-Right-Pointing-Pointer A Bose gas becomes nearly fermionized when its chemical potential approaches a maximum near resonance. Black-Right-Pointing-Pointer At the maximum, an onset instability sets in at a positive scattering length. Black-Right-Pointing-Pointer Condensates strongly influence the renormalization flow of few-body running coupling constants. Black-Right-Pointing-Pointer The effective two-body interaction constant changes its sign at a positive scattering length.

  19. Renormalized dynamics of the Dean-Kawasaki model

    NASA Astrophysics Data System (ADS)

    Bidhoodi, Neeta; Das, Shankar P.

    2015-07-01

    We study the model of a supercooled liquid for which the equation of motion for the coarse-grained density ρ (x ,t ) is the nonlinear diffusion equation originally proposed by Dean and Kawasaki, respectively, for Brownian and Newtonian dynamics of fluid particles. Using a Martin-Siggia-Rose (MSR) field theory we study the renormalization of the dynamics in a self-consistent form in terms of the so-called self-energy matrix Σ . The appropriate model for the renormalized dynamics involves an extended set of field variables {ρ ,θ } , linked through a nonlinear constraint. The latter incorporates, in a nonperturbative manner, the effects of an infinite number of density nonlinearities in the dynamics. We show that the contributing element of Σ which renormalizes the bare diffusion constant D0 to DR is same as that proposed by Kawasaki and Miyazima [Z. Phys. B Condens. Matter 103, 423 (1997), 10.1007/s002570050396]. DR sharply decreases with increasing density. We consider the likelihood of a ergodic-nonergodic (ENE) transition in the model beyond a critical point. The transition is characterized by the long-time limit of the density correlation freezing at a nonzero value. From our analysis we identify an element of Σ which arises from the above-mentioned nonlinear constraint and is key to the viability of the ENE transition. If this self-energy would be zero, then the model supports a sharp ENE transition with DR=0 as predicted by Kawasaki and Miyazima. With the full model having nonzero value for this self-energy, the density autocorrelation function decays to zero in the long-time limit. Hence the ENE transition is not supported in the model.

  20. Error estimates and specification parameters for functional renormalization

    SciTech Connect

    Schnoerr, David; Boettcher, Igor; Pawlowski, Jan M.; Wetterich, Christof

    2013-07-15

    We present a strategy for estimating the error of truncated functional flow equations. While the basic functional renormalization group equation is exact, approximated solutions by means of truncations do not only depend on the choice of the retained information, but also on the precise definition of the truncation. Therefore, results depend on specification parameters that can be used to quantify the error of a given truncation. We demonstrate this for the BCS–BEC crossover in ultracold atoms. Within a simple truncation the precise definition of the frequency dependence of the truncated propagator affects the results, indicating a shortcoming of the choice of a frequency independent cutoff function.

  1. Renormalization Group Theory of Bolgiano Scaling in Boussinesq Turbulence

    NASA Technical Reports Server (NTRS)

    Rubinstein, Robert

    1994-01-01

    Bolgiano scaling in Boussinesq turbulence is analyzed using the Yakhot-Orszag renormalization group. For this purpose, an isotropic model is introduced. Scaling exponents are calculated by forcing the temperature equation so that the temperature variance flux is constant in the inertial range. Universal amplitudes associated with the scaling laws are computed by expanding about a logarithmic theory. Connections between this formalism and the direct interaction approximation are discussed. It is suggested that the Yakhot-Orszag theory yields a lowest order approximate solution of a regularized direct interaction approximation which can be corrected by a simple iterative procedure.

  2. Constraint on Defect and Boundary Renormalization Group Flows.

    PubMed

    Jensen, Kristan; O'Bannon, Andy

    2016-03-01

    A conformal field theory (CFT) in dimension d≥3 coupled to a planar, two-dimensional, conformal defect is characterized in part by a "central charge" b that multiplies the Euler density in the defect's Weyl anomaly. For defect renormalization group flows, under which the bulk remains critical, we use reflection positivity to show that b must decrease or remain constant from the ultraviolet to the infrared. Our result applies also to a CFT in d=3 flat space with a planar boundary. PMID:26991169

  3. Current-induced phonon renormalization in molecular junctions

    NASA Astrophysics Data System (ADS)

    Bai, Meilin; Cucinotta, Clotilde S.; Jiang, Zhuoling; Wang, Hao; Wang, Yongfeng; Rungger, Ivan; Sanvito, Stefano; Hou, Shimin

    2016-07-01

    We explain how the electrical current flow in a molecular junction can modify the vibrational spectrum of the molecule by renormalizing its normal modes of oscillations. This is demonstrated with first-principles self-consistent transport theory, where the current-induced forces are evaluated from the expectation value of the ionic momentum operator. We explore here the case of H2 sandwiched between two Au electrodes and show that the current produces stiffening of the transverse translational and rotational modes and softening of the stretching modes along the current direction. Such behavior is understood in terms of charge redistribution, potential drop, and elasticity changes as a function of the current.

  4. Lagrangian constraints and renormalization of 4D gravity

    NASA Astrophysics Data System (ADS)

    Park, I. Y.

    2015-04-01

    It has been proposed in [21] that 4D Einstein gravity becomes effectively reduced to 3D after solving the Lagrangian analogues of the Hamiltonian and momentum constraints of the Hamiltonian quantization. The analysis in [21] was carried out at the classical/operator level. We review the proposal and make a transition to the path integral account. We then set the stage for explicitly carrying out the two-loop renormalization procedure of the resulting 3D action. We also address a potentially subtle issue in the gravity context concerning whether renormalizability does not depend on the background around which the original action is expanded.

  5. Density matrix renormalization group numerical study of the kagome antiferromagnet.

    PubMed

    Jiang, H C; Weng, Z Y; Sheng, D N

    2008-09-12

    We numerically study the spin-1/2 antiferromagnetic Heisenberg model on the kagome lattice using the density-matrix renormalization group method. We find that the ground state is a magnetically disordered spin liquid, characterized by an exponential decay of spin-spin correlation function in real space and a magnetic structure factor showing system-size independent peaks at commensurate magnetic wave vectors. We obtain a spin triplet excitation gap DeltaE(S=1)=0.055+/-0.005 by extrapolation based on the large size results, and confirm the presence of gapless singlet excitations. The physical nature of such an exotic spin liquid is also discussed.

  6. Renormalization In Quantum Gauge Theory Using Zeta-Function Method

    SciTech Connect

    Chiritoiu, Viorel; Zet, Gheorghe

    2009-05-22

    It is possible to consider space-time symmetries (for example Poincare or de Sitter) as purely inner symmetries. A formulation of the de Sitter symmetry as purely inner symmetry defined on a fixed Minkowski space-time is presented. We define the generators of the de Sitter group and write the equations of structure using a constant deformation parameter {lambda}. Local gauge transformations and corresponding covariant derivative depending on gauge fields are obtained. The method of generalized zeta-function is used to realize the renormalization. An effective integral of action is obtained and a comparison with other results is given.

  7. Tensor renormalization group analysis of CP (N -1 ) model

    NASA Astrophysics Data System (ADS)

    Kawauchi, Hikaru; Takeda, Shinji

    2016-06-01

    We apply the higher-order tensor renormalization group to the lattice CP (N -1 ) model in two dimensions. A tensor network representation of the CP (N -1 ) model in the presence of the θ term is derived. We confirm that the numerical results of the CP(1) model without the θ term using this method are consistent with that of the O(3) model which is analyzed by the same method in the region β ≫1 and that obtained by the Monte Carlo simulation in a wider range of β . The numerical computation including the θ term is left for future challenges.

  8. Renormalized anisotropic exchange for representing heat assisted magnetic recording media

    SciTech Connect

    Jiao, Yipeng; Liu, Zengyuan; Victora, R. H.

    2015-05-07

    Anisotropic exchange has been incorporated in a description of magnetic recording media near the Curie temperature, as would be found during heat assisted magnetic recording. The new parameters were found using a cost function that minimized the difference between atomistic properties and those of renormalized spin blocks. Interestingly, the anisotropic exchange description at 1.5 nm discretization yields very similar switching and magnetization behavior to that found at 1.2 nm (and below) discretization for the previous isotropic exchange. This suggests that the increased accuracy of anisotropic exchange may also reduce the computational cost during simulation.

  9. Renormalization of high-energy Lorentz-violating QED

    SciTech Connect

    Anselmi, Damiano; Taiuti, Martina

    2010-04-15

    We study a QED extension that is unitary, CPT invariant, and super-renormalizable, but violates Lorentz symmetry at high energies, and contains higher-dimension operators (LVQED). Divergent diagrams are only one- and two-loop. We compute the one-loop renormalizations at high and low energies and analyze the relation between them. It emerges that the powerlike divergences of the low-energy theory are multiplied by arbitrary constants, inherited by the high-energy theory, and therefore can be set to zero at no cost, bypassing the hierarchy problem.

  10. Self-interaction in the Bopp-Podolsky electrodynamics: Can the observable mass of a charged particle depend on its acceleration?

    NASA Astrophysics Data System (ADS)

    Zayats, Alexei E.

    2014-03-01

    In this paper we obtain the expression for the self-force in the model with the Lagrangian containing additional terms, quadratic in Maxwell tensor derivatives (so-called Bopp-Podolsky electrodynamics). Features of this force are analyzed for various limiting cases. When a charged particle moves along straight line with a uniform acceleration, an explicit formula is found. In the framework of the considered model, an observable renormalized particle mass is shown to depend on its acceleration. This dependence allows, in principle, to extract experimentally a value of the particle bare mass.

  11. Shaping frequency response of a vibrating plate for passive and active control applications by simultaneous optimization of arrangement of additional masses and ribs. Part II: Optimization

    NASA Astrophysics Data System (ADS)

    Wrona, Stanislaw; Pawelczyk, Marek

    2016-03-01

    It was shown in Part I that an ability to shape frequency response of a vibrating plate according to precisely defined demands has a very high practical potential. It can be used to improve acoustic radiation of the plate for required frequencies or enhance acoustic isolation of noise barriers and device casings. It can be used for both passive and active control. The proposed method is based on mounting several additional ribs and masses (passive and/or active) to the plate surface at locations followed from an optimisation process. In Part I a relevant model of such structure, as a function of arrangement of the additional elements was derived and validated. The model allows calculating natural frequencies and mode-shapes of the whole structure. The aim of this companion paper, Part II, is to present the second stage of the method. This is an optimization process that results in arrangement of the elements guaranteeing desired plate frequency response, and enhancement of controllability and observability measures. For that purpose appropriate cost functions, and constraints followed from technological feasibility are defined. Then, a memetic algorithm is employed to obtain a numerical solution with parameters of the arrangement. The optimization results are initially presented for simple cases to validate the method. Then, more complex scenarios are analysed with very special demands concerning the frequency response to present the full potential of the method. Subsequently, a laboratory experiment is presented and discussed. Finally, other areas of applications of the proposed method are shown and conclusions for future research are drawn.

  12. Renormalization-group analysis of layered sine-Gordon type models

    NASA Astrophysics Data System (ADS)

    Nándori, I.; Nagy, S.; Sailer, K.; Jentschura, U. D.

    2005-10-01

    We analyze the phase structure and the renormalization group (RG) flow of the generalized sine-Gordon models with nonvanishing mass terms, using the Wegner-Houghton RG method in the local potential approximation. Particular emphasis is laid upon the layered sine-Gordon (LSG) model, which is the bosonized version of the multi-flavour Schwinger model and approaches the sum of two "normal", massless sine-Gordon (SG) models in the limit of a vanishing interlayer coupling J. Another model of interest is the massive sine-Gordon (MSG) model. The leading-order approximation to the UV (ultraviolet) RG flow predicts two phases for the LSG as well as for the MSG, just as it would be expected for the SG model, where the two phases are known to be separated by the Coleman fixed point. The presence of finite mass terms (for the LSG and the MSG) leads to corrections to the UV RG flow, which are naturally identified as the "mass corrections". The leading-order mass corrections are shown to have the following consequences: (i) for the MSG model, only one phase persists, and (ii) for the LSG model, the transition temperature is modified. Within the mass-corrected UV scaling laws, the limit of J→0 is thus nonuniform with respect to the phase structure of the model. The modified phase structure of general massive sine-Gordon models is connected with the breaking of symmetries in the internal space spanned by the field variables. For the LSG, the second-order subleading mass corrections suggest that there exists a cross-over regime before the IR scaling sets in, and the nonlinear terms show explicitly that higher-order Fourier modes appear in the periodic blocked potential.

  13. Solid-phase microextraction with gas chromatography and mass spectrometry determination of benzo(a)pyrene in microcrystalline waxes used as food additives.

    PubMed

    Conchione, Chiara; Purcaro, Giorgia; Conte, Lanfranco S; Moret, Sabrina

    2015-05-01

    Microcrystalline waxes are mixtures of solid, saturated hydrocarbons mainly branched and characterized by a carbon number over C60. They are used as food additives for the surface treatment of confectionery and some fruit varieties, in chewing gum base, protective coatings, defoaming agents, and surface finishing agents. Commission Regulation No 231/2012 established physical and chemical specifications for microcrystalline waxes to use in food, and posed a limit of 50 μg/kg for benzo(a)pyrene. Due to the low solubility of microcrystalline waxes in organic solvents and matrix interferences, analytical determination of benzo(a)pyrene represents a difficult task. The official method for indirect determination of total polycyclic aromatic hydrocarbons uses unspecific spectrophotometric detection and a quite laborious, time- and solvent-consuming extraction method. A liquid-liquid partition method followed by solid-phase microextraction was developed to isolate benzo(a)pyrene from the bulk of saturated hydrocarbons in microcrystalline waxes, with the aim to have a simple and effective method to verify compliance with the legal limit. The final determination was carried out by gas chromatography coupled to mass spectrometry. Good linearity was obtained, along with a recovery of about 80% from the liquid-liquid partitions. The repeatability of the entire method was <6% and accuracy was <3%.

  14. Superfluid phase transition with activated velocity fluctuations: Renormalization group approach.

    PubMed

    Dančo, Michal; Hnatič, Michal; Komarova, Marina V; Lučivjanský, Tomáš; Nalimov, Mikhail Yu

    2016-01-01

    A quantum field model that incorporates Bose-condensed systems near their phase transition into a superfluid phase and velocity fluctuations is proposed. The stochastic Navier-Stokes equation is used for a generation of the velocity fluctuations. As such this model generalizes model F of critical dynamics. The field-theoretic action is derived using the Martin-Siggia-Rose formalism and path integral approach. The regime of equilibrium fluctuations is analyzed within the perturbative renormalization group method. The double (ε,δ)-expansion scheme is employed, where ε is a deviation from space dimension 4 and δ describes scaling of velocity fluctuations. The renormalization procedure is performed to the leading order. The main corollary gained from the analysis of the thermal equilibrium regime suggests that one-loop calculations of the presented models are not sufficient to make a definite conclusion about the stability of fixed points. We also show that critical exponents are drastically changed as a result of the turbulent background and critical fluctuations are in fact destroyed by the developed turbulence fluctuations. The scaling exponent of effective viscosity is calculated and agrees with expected value 4/3.

  15. Superfluid phase transition with activated velocity fluctuations: Renormalization group approach

    NASA Astrophysics Data System (ADS)

    Dančo, Michal; Hnatič, Michal; Komarova, Marina V.; Lučivjanský, Tomáš; Nalimov, Mikhail Yu.

    2016-01-01

    A quantum field model that incorporates Bose-condensed systems near their phase transition into a superfluid phase and velocity fluctuations is proposed. The stochastic Navier-Stokes equation is used for a generation of the velocity fluctuations. As such this model generalizes model F of critical dynamics. The field-theoretic action is derived using the Martin-Siggia-Rose formalism and path integral approach. The regime of equilibrium fluctuations is analyzed within the perturbative renormalization group method. The double (ɛ ,δ ) -expansion scheme is employed, where ɛ is a deviation from space dimension 4 and δ describes scaling of velocity fluctuations. The renormalization procedure is performed to the leading order. The main corollary gained from the analysis of the thermal equilibrium regime suggests that one-loop calculations of the presented models are not sufficient to make a definite conclusion about the stability of fixed points. We also show that critical exponents are drastically changed as a result of the turbulent background and critical fluctuations are in fact destroyed by the developed turbulence fluctuations. The scaling exponent of effective viscosity is calculated and agrees with expected value 4 /3 .

  16. Signal inference with unknown response: Calibration-uncertainty renormalized estimator

    NASA Astrophysics Data System (ADS)

    Dorn, Sebastian; Enßlin, Torsten A.; Greiner, Maksim; Selig, Marco; Boehm, Vanessa

    2015-01-01

    The calibration of a measurement device is crucial for every scientific experiment, where a signal has to be inferred from data. We present CURE, the calibration-uncertainty renormalized estimator, to reconstruct a signal and simultaneously the instrument's calibration from the same data without knowing the exact calibration, but its covariance structure. The idea of the CURE method, developed in the framework of information field theory, is to start with an assumed calibration to successively include more and more portions of calibration uncertainty into the signal inference equations and to absorb the resulting corrections into renormalized signal (and calibration) solutions. Thereby, the signal inference and calibration problem turns into a problem of solving a single system of ordinary differential equations and can be identified with common resummation techniques used in field theories. We verify the CURE method by applying it to a simplistic toy example and compare it against existent self-calibration schemes, Wiener filter solutions, and Markov chain Monte Carlo sampling. We conclude that the method is able to keep up in accuracy with the best self-calibration methods and serves as a noniterative alternative to them.

  17. Superfluid phase transition with activated velocity fluctuations: Renormalization group approach.

    PubMed

    Dančo, Michal; Hnatič, Michal; Komarova, Marina V; Lučivjanský, Tomáš; Nalimov, Mikhail Yu

    2016-01-01

    A quantum field model that incorporates Bose-condensed systems near their phase transition into a superfluid phase and velocity fluctuations is proposed. The stochastic Navier-Stokes equation is used for a generation of the velocity fluctuations. As such this model generalizes model F of critical dynamics. The field-theoretic action is derived using the Martin-Siggia-Rose formalism and path integral approach. The regime of equilibrium fluctuations is analyzed within the perturbative renormalization group method. The double (ε,δ)-expansion scheme is employed, where ε is a deviation from space dimension 4 and δ describes scaling of velocity fluctuations. The renormalization procedure is performed to the leading order. The main corollary gained from the analysis of the thermal equilibrium regime suggests that one-loop calculations of the presented models are not sufficient to make a definite conclusion about the stability of fixed points. We also show that critical exponents are drastically changed as a result of the turbulent background and critical fluctuations are in fact destroyed by the developed turbulence fluctuations. The scaling exponent of effective viscosity is calculated and agrees with expected value 4/3. PMID:26871026

  18. Communication: Random phase approximation renormalized many-body perturbation theory

    SciTech Connect

    Bates, Jefferson E.; Furche, Filipp

    2013-11-07

    We derive a renormalized many-body perturbation theory (MBPT) starting from the random phase approximation (RPA). This RPA-renormalized perturbation theory extends the scope of single-reference MBPT methods to small-gap systems without significantly increasing the computational cost. The leading correction to RPA, termed the approximate exchange kernel (AXK), substantially improves upon RPA atomization energies and ionization potentials without affecting other properties such as barrier heights where RPA is already accurate. Thus, AXK is more balanced than second-order screened exchange [A. Grüneis et al., J. Chem. Phys. 131, 154115 (2009)], which tends to overcorrect RPA for systems with stronger static correlation. Similarly, AXK avoids the divergence of second-order Møller-Plesset (MP2) theory for small gap systems and delivers a much more consistent performance than MP2 across the periodic table at comparable cost. RPA+AXK thus is an accurate, non-empirical, and robust tool to assess and improve semi-local density functional theory for a wide range of systems previously inaccessible to first-principles electronic structure calculations.

  19. Signal inference with unknown response: calibration-uncertainty renormalized estimator.

    PubMed

    Dorn, Sebastian; Enßlin, Torsten A; Greiner, Maksim; Selig, Marco; Boehm, Vanessa

    2015-01-01

    The calibration of a measurement device is crucial for every scientific experiment, where a signal has to be inferred from data. We present CURE, the calibration-uncertainty renormalized estimator, to reconstruct a signal and simultaneously the instrument's calibration from the same data without knowing the exact calibration, but its covariance structure. The idea of the CURE method, developed in the framework of information field theory, is to start with an assumed calibration to successively include more and more portions of calibration uncertainty into the signal inference equations and to absorb the resulting corrections into renormalized signal (and calibration) solutions. Thereby, the signal inference and calibration problem turns into a problem of solving a single system of ordinary differential equations and can be identified with common resummation techniques used in field theories. We verify the CURE method by applying it to a simplistic toy example and compare it against existent self-calibration schemes, Wiener filter solutions, and Markov chain Monte Carlo sampling. We conclude that the method is able to keep up in accuracy with the best self-calibration methods and serves as a noniterative alternative to them.

  20. Renormalization group methods for the Reynolds stress transport equations

    NASA Technical Reports Server (NTRS)

    Rubinstein, R.

    1992-01-01

    The Yakhot-Orszag renormalization group is used to analyze the pressure gradient-velocity correlation and return to isotropy terms in the Reynolds stress transport equations. The perturbation series for the relevant correlations, evaluated to lowest order in the epsilon-expansion of the Yakhot-Orszag theory, are infinite series in tensor product powers of the mean velocity gradient and its transpose. Formal lowest order Pade approximations to the sums of these series produce a rapid pressure strain model of the form proposed by Launder, Reece, and Rodi, and a return to isotropy model of the form proposed by Rotta. In both cases, the model constants are computed theoretically. The predicted Reynolds stress ratios in simple shear flows are evaluated and compared with experimental data. The possibility is discussed of deriving higher order nonlinear models by approximating the sums more accurately. The Yakhot-Orszag renormalization group provides a systematic procedure for deriving turbulence models. Typical applications have included theoretical derivation of the universal constants of isotropic turbulence theory, such as the Kolmogorov constant, and derivation of two equation models, again with theoretically computed constants and low Reynolds number forms of the equations. Recent work has applied this formalism to Reynolds stress modeling, previously in the form of a nonlinear eddy viscosity representation of the Reynolds stresses, which can be used to model the simplest normal stress effects. The present work attempts to apply the Yakhot-Orszag formalism to Reynolds stress transport modeling.

  1. Measuring the aspect ratio renormalization of anisotropic-lattice gluons

    SciTech Connect

    Alford, M.; Drummond, I. T.; Horgan, R. R.; Shanahan, H.; Peardon, M.

    2001-04-01

    Using tadpole-improved actions we investigate the consistency between different methods of measuring the aspect ratio renormalization of anisotropic-lattice gluons for bare aspect ratios {chi}{sub 0}=4,6,10 and inverse lattice spacing in the range a{sub s}{sup -1}=660--840 MeV. The tadpole corrections to the action, which are established self-consistently, are defined for two cases, mean link tadpoles in the Landau gauge and gauge invariant mean plaquette tadpoles. Parameters in the latter case exhibited no dependence on the spatial lattice size L, while in the former, parameters showed only a weak dependence on L easily extrapolated to L={infinity}. The renormalized anisotropy {chi}{sub R} was measured using both the torelon dispersion relation and the sideways potential method. There is general agreement between these approaches, but there are discrepancies which are evidence for the presence of lattice artifact contributions. For the torelon these are estimated to be O({alpha}{sub S}a{sub s}{sup 2}/R{sup 2}), where R is the flux-tube radius. We also present some new data that suggest that rotational invariance is established more accurately for the mean-link action than the plaquette action.

  2. Running-mass inflation model and primordial black holes

    SciTech Connect

    Drees, Manuel; Erfani, Encieh E-mail: erfani@th.physik.uni-bonn.de

    2011-04-01

    We revisit the question whether the running-mass inflation model allows the formation of Primordial Black Holes (PBHs) that are sufficiently long-lived to serve as candidates for Dark Matter. We incorporate recent cosmological data, including the WMAP 7-year results. Moreover, we include ''the running of the running'' of the spectral index of the power spectrum, as well as the renormalization group ''running of the running'' of the inflaton mass term. Our analysis indicates that formation of sufficiently heavy, and hence long-lived, PBHs still remains possible in this scenario. As a by-product, we show that the additional term in the inflaton potential still does not allow significant negative running of the spectral index.

  3. An exact, finite, gauge-invariant, non-perturbative approach to QCD renormalization

    SciTech Connect

    Fried, H.M.; Tsang, P.H.; Gabellini, Y.; Grandou, T.; Sheu, Y.-M.

    2015-08-15

    A particular choice of renormalization, within the simplifications provided by the non-perturbative property of Effective Locality, leads to a completely finite, non-perturbative approach to renormalized QCD, in which all correlation functions can, in principle, be defined and calculated. In this Model of renormalization, only the Bundle chain-Graphs of the cluster expansion are non-zero. All Bundle graphs connecting to closed quark loops of whatever complexity, and attached to a single quark line, provided no ‘self-energy’ to that quark line, and hence no effective renormalization. However, the exchange of momentum between one quark line and another, involves only the cluster-expansion’s chain graphs, and yields a set of contributions which can be summed and provide a finite color-charge renormalization that can be incorporated into all other QCD processes. An application to High Energy elastic pp scattering is now underway.

  4. High-order terms in the renormalized perturbation theory for the Anderson impurity model

    NASA Astrophysics Data System (ADS)

    Pandis, Vassilis; Hewson, Alex C.

    2015-09-01

    We study the renormalized perturbation theory of the single-impurity Anderson model, particularly the high-order terms in the expansion of the self-energy in powers of the renormalized coupling U ˜. Though the presence of counterterms in the renormalized theory may appear to complicate the diagrammatics, we show how these can be seamlessly accommodated by carrying out the calculation order-by-order in terms of skeleton diagrams. We describe how the diagrams pertinent to the renormalized self-energy and four vertex can be automatically generated, translated into integrals, and numerically integrated. To maximize the efficiency of our approach we introduce a generalized k -particle/hole propagator, which is used to analytically simplify the resultant integrals and reduce the dimensionality of the integration. We present results for the self-energy and spectral density to fifth order in U ˜, for various values of the model asymmetry, and compare them to a numerical renormalization group calculation.

  5. Remarks on the Renormalization Properties of Lorentz- and CPT-Violating Quantum Electrodynamics

    NASA Astrophysics Data System (ADS)

    Santos, Tiago R. S.; Sobreiro, Rodrigo F.

    2016-08-01

    In this work, we employ algebraic renormalization technique to show the renormalizability to all orders in perturbation theory of the Lorentz- and CPT-violating QED. Essentially, we control the breaking terms by using a suitable set of external sources. Thus, with the symmetries restored, a perturbative treatment can be consistently employed. After showing the renormalizability, the external sources attain certain physical values, which allow the recovering of the starting physical action. The main result is that the original QED action presents the three usual independent renormalization parameters. The Lorentz-violating sector can be renormalized by 19 independent parameters. Moreover, vacuum divergences appear with extra independent renormalization. Remarkably, the bosonic odd sector (Chern-Simons-like term) does not renormalize and is not radiatively generated. One-loop computations are also presented and compared with the existing literature.

  6. Tensor network algorithm by coarse-graining tensor renormalization on finite periodic lattices

    NASA Astrophysics Data System (ADS)

    Zhao, Hui-Hai; Xie, Zhi-Yuan; Xiang, Tao; Imada, Masatoshi

    2016-03-01

    We develop coarse-graining tensor renormalization group algorithms to compute physical properties of two-dimensional lattice models on finite periodic lattices. Two different coarse-graining strategies, one based on the tensor renormalization group and the other based on the higher-order tensor renormalization group, are introduced. In order to optimize the tensor network model globally, a sweeping scheme is proposed to account for the renormalization effect from the environment tensors under the framework of second renormalization group. We demonstrate the algorithms by the classical Ising model on the square lattice and the Kitaev model on the honeycomb lattice, and show that the finite-size algorithms achieve substantially more accurate results than the corresponding infinite-size ones.

  7. Band-Renormalization Effects and Predominant Antiferromagnetic Order in Two-Dimensional Hubbard Model

    NASA Astrophysics Data System (ADS)

    Sato, Ryo; Yokoyama, Hisatoshi

    2016-07-01

    Band renormalization effects (BRE) are comprehensively studied for a mixed state of dx2 - y2-wave superconducting (d-SC) and antiferromagnetic (AF) orders, in addition to simple d-SC, AF, and normal (paramagnetic) states, by applying a variational Monte Carlo method to a two-dimensional Hubbard (t-t'-U) model. In a weakly correlated regime (U/t ≲ 6), BRE are negligible on all the states studied. As previously shown, the effective band of d-SC is greatly renormalized but the modifications of physical quantities, including energy improvement, are negligible. In contrast, BRE on the AF state considerably affects various features of the system. Because the energy is markedly improved for t'/t < 0, the AF state occupies almost the whole underdoped regime in phase diagrams. A doped metallic AF state undergoes a kind of Lifshitz transition at t' = t'{L} ˜ - 0.05t as t'/t varies, irrespective of the values of U/t and δ (doping rate). Pocket Fermi surfaces arise around (π ,0) [(π /2,π /2)] for t' > t'{L} [t' < t'{L}], which corresponds to the electron-hole asymmetry observed in angle-resolved photoemission spectroscopy (ARPES) spectra. The coexistent state of the two orders is possible basically for t' > t'{L}, because the existence of Fermi surfaces near (π ,0) is a requisite for the electron scattering of {q} = (π ,π ). Actually, the coexistent state appears mainly for t'{L}/t < t'/t ≲ 0.2 in the mixed state. Nevertheless, the AF and coexisting states become unstable toward phase separation for - 0.05 ≲ t'/t ≲ 0.2 but become stable at other values of t'/t owing to the energy reduction by the diagonal hopping of doped holes. We show that this instability does not directly correlate with the strength of d-SC.

  8. Random interface growth in a random environment: Renormalization group analysis of a simple model

    NASA Astrophysics Data System (ADS)

    Antonov, N. V.; Kakin, P. I.

    2015-10-01

    We study the effects of turbulent mixing on the random growth of an interface in the problem of the deposition of a substance on a substrate. The growth is modeled by the well-known Kardar-Parisi-Zhang model. The turbulent advecting velocity field is modeled by the Kraichnan rapid-change ensemble: Gaussian statistics with the correlation function < vv> ∝ δ( t - tς ) k - d-ξ, where k is the wave number and ξ is a free parameter, 0 < ξ < 2. We study the effects of the fluid compressibility. Using the field theory renormalization group, we show that depending on the relation between the exponent ξ and the spatial dimension d, the system manifests different types of large-scale, long-time asymptotic behavior associated with four possible fixed points of the renormalization group equations. In addition to the known regimes (ordinary diffusion, the ordinary growth process, and a passively advected scalar field), we establish the existence of a new nonequilibrium universality class. We calculate the fixed-point coordinates and their stability regions and critical dimensions to the first order of the double expansion in ξ and ɛ = 2 - d (one-loop approximation). It turns out that for an incompressible fluid, the most realistic values ξ = 4/3 or ξ = 2 and d = 1 or d = 2 correspond to the case of a passive scalar field, where the nonlinearity of the Kardar-Parisi-Zhang model is irrelevant and the interface growth is completely determined by the turbulent transfer. If the compressibility becomes sufficiently strong, then a crossover occurs in the critical behavior, and these values of d and ξ are in the stability region of the new regime, where the advection and nonlinearity are both important. But the coordinates of the fixed point for this regime are in the unphysical region, and its physical interpretation hence remains an open problem.

  9. Implementation of the locally renormalized CCSD(T) approaches for arbitrary reference function.

    PubMed

    Kowalski, Karol

    2005-07-01

    Several new variants of the locally-renormalized coupled-cluster (CC) approaches that account for the effect of triples (LR-CCSD(T)) have been formulated and implemented for arbitrary reference states using the TENSOR CONTRACTION ENGINE functionality, enabling the automatic generation of an efficient parallel code. Deeply rooted in the recently derived numerator-denominator-connected (NDC) expansion for the ground-state energy [K. Kowalski and P. Piecuch, J. Chem. Phys. 122, 074107 (2005)], LR-CCSD(T) approximations use, in analogy to the completely renormalized CCSD(T) (CR-CCSD(T)) approach, the three-body moments in constructing the noniterative corrections to the energies obtained in CC calculations with singles and doubles (CCSD). In contrast to the CR-CCSD(T) method, the LR-CCSD(T) approaches discussed in this paper employ local denominators, which assure the additive separability of the energies in the noninteracting system limit when the localized occupied spin-orbitals are employed in the CCSD and LR-CCSD(T) calculations. As clearly demonstrated on several challenging examples, including breaking the bonds of the F2, N2, and CN molecules, the LR-CCSD(T) approaches are capable of providing a highly accurate description of the entire potential-energy surface (PES), while maintaining the characteristic N(7) scaling of the ubiquitous CCSD(T) approach. Moreover, as illustrated numerically for the ozone molecule, the LR-CCSD(T) approaches yield highly competitive values for a number of equilibrium properties including bond lengths, angles, and harmonic frequencies. PMID:16035828

  10. Background field method and the cohomology of renormalization

    NASA Astrophysics Data System (ADS)

    Anselmi, Damiano

    2016-03-01

    Using the background field method and the Batalin-Vilkovisky formalism, we prove a key theorem on the cohomology of perturbatively local functionals of arbitrary ghost numbers in renormalizable and nonrenormalizable quantum field theories whose gauge symmetries are general covariance, local Lorentz symmetry, non-Abelian Yang-Mills symmetries and Abelian gauge symmetries. Interpolating between the background field approach and the usual, nonbackground approach by means of a canonical transformation, we take advantage of the properties of both approaches and prove that a closed functional is the sum of an exact functional plus a functional that depends only on the physical fields and possibly the ghosts. The assumptions of the theorem are the mathematical versions of general properties that characterize the counterterms and the local contributions to the potential anomalies. This makes the outcome a theorem on the cohomology of renormalization, rather than the whole local cohomology. The result supersedes numerous involved arguments that are available in the literature.

  11. Space and time renormalization in phase transition dynamics

    DOE PAGES

    Francuz, Anna; Dziarmaga, Jacek; Gardas, Bartłomiej; Zurek, Wojciech H.

    2016-02-18

    Here, when a system is driven across a quantum critical point at a constant rate, its evolution must become nonadiabatic as the relaxation time τ diverges at the critical point. According to the Kibble-Zurek mechanism (KZM), the emerging post-transition excited state is characterized by a finite correlation length ξˆ set at the time tˆ=τˆ when the critical slowing down makes it impossible for the system to relax to the equilibrium defined by changing parameters. This observation naturally suggests a dynamical scaling similar to renormalization familiar from the equilibrium critical phenomena. We provide evidence for such KZM-inspired spatiotemporal scaling by investigatingmore » an exact solution of the transverse field quantum Ising chain in the thermodynamic limit.« less

  12. Tensor renormalization group approach to classical dimer models

    NASA Astrophysics Data System (ADS)

    Roychowdhury, Krishanu; Huang, Ching-Yu

    2015-05-01

    We analyze classical dimer models on a square and a triangular lattice using a tensor network representation of the dimers. The correlation functions are numerically calculated using the recently developed "tensor renormalization group" (TRG) technique. The partition function for the dimer problem can be calculated exactly by the Pfaffian method, which is used here as a platform for comparing the numerical results. The TRG approach turns out to be a powerful tool for describing gapped systems with exponentially decaying correlations very efficiently due to its fast convergence. This is the case for the dimer model on the triangular lattice. However, the convergence becomes very slow and unstable in the case of the square lattice where the model has algebraically decaying correlations. We highlight these aspects with numerical simulations and critically appraise the robustness of the TRG approach by contrasting the results for small and large system sizes against the exact calculations. Furthermore, we benchmark our TRG results with the classical Monte Carlo method.

  13. Autonomous renormalization of Φ4 in finite geometry

    NASA Astrophysics Data System (ADS)

    Ritschel, U.

    1993-12-01

    The autonomous renormalization of the O (N)-symmetric scalar theory is based on an infinite re-scaling of constant fields, whereas finite-momentum modes remain finite. The natural framework for a detailed analysis of this method is a system of finite size, where all non-constant modes can be integrated out perturbatively and the constant mode is treated by a saddle-point approximation in the thermodynamic limit. Our calculation provides a better understanding of the properties of the effective action and corroborates earlier findings concerning a heavy Higgs particle at about 2 TeV [M. Consoli, Phys. Lett. B 305 (1993) 93; R. Iban~ez-Meier and P.M. Stevenson, Phys. Lett. B 297 (1992) 144; R. Iban~ez-Meier, I. Stancu and P.M. Stevenson, Gaussian Effective Potential for U(1) Higgs Model, Rice University preprint DOE/ER/05096-51].

  14. Advanced density matrix renormalization group method for nuclear structure calculations

    NASA Astrophysics Data System (ADS)

    Legeza, Ã.-.; Veis, L.; Poves, A.; Dukelsky, J.

    2015-11-01

    We present an efficient implementation of the Density Matrix Renormalization Group (DMRG) algorithm that includes an optimal ordering of the proton and neutron orbitals and an efficient expansion of the active space utilizing various concepts of quantum information theory. We first show how this new DMRG methodology could solve a previous 400 keV discrepancy in the ground state energy of 56Ni. We then report the first DMRG results in the p f +g 9 /2 shell model space for the ground 0+ and first 2+ states of 64Ge which are benchmarked with reference data obtained from a Monte Carlo shell model. The corresponding correlation structure among the proton and neutron orbitals is determined in terms of two-orbital mutual information. Based on such correlation graphs we propose several further algorithmic improvement possibilities that can be utilized in a new generation of tensor network based algorithms.

  15. Renormalization group analysis of the Reynolds stress transport equation

    NASA Technical Reports Server (NTRS)

    Rubinstein, R.; Barton, J. M.

    1992-01-01

    The pressure velocity correlation and return to isotropy term in the Reynolds stress transport equation are analyzed using the Yakhot-Orszag renormalization group. The perturbation series for the relevant correlations, evaluated to lowest order in the epsilon-expansion of the Yakhot-Orszag theory, are infinite series in tensor product powers of the mean velocity gradient and its transpose. Formal lowest order Pade approximations to the sums of these series produce a fast pressure strain model of the form proposed by Launder, Reece, and Rodi, and a return to isotropy model of the form proposed by Rotta. In both cases, the model constant are computed theoretically. The predicted Reynolds stress ratios in simple shear flows are evaluated and compared with experimental data. The possibility is discussed of driving higher order nonlinear models by approximating the sums more accurately.

  16. Quasiparticle scattering interference in the renormalized Hubbard model

    NASA Astrophysics Data System (ADS)

    Wang, Shu-Hua; Zhao, Huai-Song; Yuan, Feng

    2015-02-01

    In this paper, we study the quasiparticle scattering interference phenomenon in the presence of a single impurity within the renormalized Hubbard model. By calculating the energy and momentum dependence of the Fourier-transformed local density of states in the full Brillouin zone, we can qualitatively describe the main features of the quasiparticle scattering interference phenomenon in cuprate superconductors using a single point-like impurity. In particular, we show that with increasing energy, the position of the peak along the nodal ([0, 0] → [ π, π]) direction moves steadily to a large momentum region, while the position of the peak along the antinodal ([0, 0] → [ π, 0]) direction moves toward the center of the Brillouin zone.

  17. Anomalous contagion and renormalization in networks with nodal mobility

    NASA Astrophysics Data System (ADS)

    Manrique, Pedro D.; Qi, Hong; Zheng, Minzhang; Xu, Chen; Hui, Pak Ming; Johnson, Neil F.

    2016-07-01

    A common occurrence in everyday human activity is where people join, leave and possibly rejoin clusters of other individuals —whether this be online (e.g. social media communities) or in real space (e.g. popular meeting places such as cafes). In the steady state, the resulting interaction network would appear static over time if the identities of the nodes are ignored. Here we show that even in this static steady-state limit, a non-zero nodal mobility leads to a diverse set of outbreak profiles that is dramatically different from known forms, and yet matches well with recent real-world social outbreaks. We show how this complication of nodal mobility can be renormalized away for a particular class of networks.

  18. Renormalized Newtonian cosmic evolution with primordial non-Gaussianity

    SciTech Connect

    Izumi, Keisuke; Soda, Jiro

    2007-10-15

    We study Newtonian cosmological perturbation theory from a field theoretical point of view. We derive a path integral representation for the cosmological evolution of stochastic fluctuations. Our main result is the closed form of the generating functional valid for any initial statistics. Moreover, we extend the renormalization group method proposed by Mataresse and Pietroni to the case of primordial non-Gaussian density and velocity fluctuations. As an application, we calculate the nonlinear propagator and examine how the non-Gaussianity affects the memory of cosmic fields to their initial conditions. It turns out that the non-Gaussianity affects the nonlinear propagator. In the case of positive skewness, the onset of the nonlinearity is advanced with a given comoving wave number. On the other hand, the negative skewness gives the opposite result.

  19. Random Renormalization Group Operators Applied to Stochastic Dynamics

    NASA Astrophysics Data System (ADS)

    O'Malley, Daniel; Cushman, John H.

    2012-11-01

    Let X( t) be a fixed point the renormalization group operator (RGO), R p, r X( t)= X( rt)/ r p . Scaling laws for the probability density, mean first passage times, finite-size Lyapunov exponents of such fixed points are reviewed in anticipation of more general results. A generalized RGO, {R}_{P,n} where P is a random variable, is introduced. Scaling laws associated with these random RGOs (RRGOs) are demonstrated numerically and applied to subdiffusion in bacterial cytoplasm and a process modeling the transition from subdiffusion to classical diffusion. The scaling laws for the RRGO are not simple power laws, but are a weighted average of power laws. The weighting used in the scaling laws can be determined adaptively via Bayes' theorem.

  20. Local Scale Transformations on the Lattice with Tensor Network Renormalization.

    PubMed

    Evenbly, G; Vidal, G

    2016-01-29

    Consider the partition function of a classical system in two spatial dimensions, or the Euclidean path integral of a quantum system in two space-time dimensions, both on a lattice. We show that the tensor network renormalization algorithm [G. Evenbly and G. Vidal Phys. Rev. Lett. 115, 180405 (2015)] can be used to implement local scale transformations on these objects, namely, a lattice version of conformal maps. Specifically, we explain how to implement the lattice equivalent of the logarithmic conformal map that transforms the Euclidean plane into a cylinder. As an application, and with the 2D critical Ising model as a concrete example, we use this map to build a lattice version of the scaling operators of the underlying conformal field theory, from which one can extract their scaling dimensions and operator product expansion coefficients.

  1. Local Scale Transformations on the Lattice with Tensor Network Renormalization

    NASA Astrophysics Data System (ADS)

    Evenbly, G.; Vidal, G.

    2016-01-01

    Consider the partition function of a classical system in two spatial dimensions, or the Euclidean path integral of a quantum system in two space-time dimensions, both on a lattice. We show that the tensor network renormalization algorithm [G. Evenbly and G. Vidal Phys. Rev. Lett. 115, 180405 (2015)] can be used to implement local scale transformations on these objects, namely, a lattice version of conformal maps. Specifically, we explain how to implement the lattice equivalent of the logarithmic conformal map that transforms the Euclidean plane into a cylinder. As an application, and with the 2D critical Ising model as a concrete example, we use this map to build a lattice version of the scaling operators of the underlying conformal field theory, from which one can extract their scaling dimensions and operator product expansion coefficients.

  2. Percolation, renormalization, and quantum computing with nondeterministic gates.

    PubMed

    Kieling, K; Rudolph, T; Eisert, J

    2007-09-28

    We apply a notion of static renormalization to the preparation of entangled states for quantum computing, exploiting ideas from percolation theory. Such a strategy yields a novel way to cope with the randomness of nondeterministic quantum gates. This is most relevant in the context of optical architectures, where probabilistic gates are common, and cold atoms in optical lattices, where hole defects occur. We demonstrate how to efficiently construct cluster states without the need for rerouting, thereby avoiding a massive amount of conditional dynamics; we furthermore show that except for a single layer of gates during the preparation, all subsequent operations can be shifted to the final adapted single-qubit measurements. Remarkably, cluster state preparation is achieved using essentially the same scaling in resources as if deterministic gates were available.

  3. Interactions of renormalized waves in thermalized Fermi-Pasta-Ulam chains.

    PubMed

    Gershgorin, Boris; Lvov, Yuri V; Cai, David

    2007-04-01

    The dispersive interacting waves in Fermi-Pasta-Ulam (FPU) chains of particles in thermal equilibrium are studied from both statistical and wave resonance perspectives. It is shown that, even in a strongly nonlinear regime, the chain in thermal equilibrium can be effectively described by a system of weakly interacting renormalized nonlinear waves that possess (i) the Rayleigh-Jeans distribution and (ii) zero correlations between waves, just as noninteracting free waves would. This renormalization is achieved through a set of canonical transformations. The renormalized linear dispersion of these renormalized waves is obtained and shown to be in excellent agreement with numerical experiments. Moreover, a dynamical interpretation of the renormalization of the dispersion relation is provided via a self-consistency, mean-field argument. It turns out that this renormalization arises mainly from the trivial resonant wave interactions, i.e., interactions with no momentum exchange. Furthermore, using a multiple time-scale, statistical averaging method, we show that the interactions of near-resonant waves give rise to the broadening of the resonance peaks in the frequency spectrum of renormalized modes. The theoretical prediction for the resonance width for the thermalized beta -FPU chain is found to be in very good agreement with its numerically measured value.

  4. Random sequential renormalization and agglomerative percolation in networks: Application to Erdös-Rényi and scale-free graphs

    NASA Astrophysics Data System (ADS)

    Bizhani, Golnoosh; Grassberger, Peter; Paczuski, Maya

    2011-12-01

    We study the statistical behavior under random sequential renormalization (RSR) of several network models including Erdös-Rényi (ER) graphs, scale-free networks, and an annealed model related to ER graphs. In RSR the network is locally coarse grained by choosing at each renormalization step a node at random and joining it to all its neighbors. Compared to previous (quasi-)parallel renormalization methods [Song , Nature (London)NATUAS0028-083610.1038/nature03248 433, 392 (2005)], RSR allows a more fine-grained analysis of the renormalization group (RG) flow and unravels new features that were not discussed in the previous analyses. In particular, we find that all networks exhibit a second-order transition in their RG flow. This phase transition is associated with the emergence of a giant hub and can be viewed as a new variant of percolation, called agglomerative percolation. We claim that this transition exists also in previous graph renormalization schemes and explains some of the scaling behavior seen there. For critical trees it happens as N/N0→0 in the limit of large systems (where N0 is the initial size of the graph and N its size at a given RSR step). In contrast, it happens at finite N/N0 in sparse ER graphs and in the annealed model, while it happens for N/N0→1 on scale-free networks. Critical exponents seem to depend on the type of the graph but not on the average degree and obey usual scaling relations for percolation phenomena. For the annealed model they agree with the exponents obtained from a mean-field theory. At late times, the networks exhibit a starlike structure in agreement with the results of Radicchi [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.101.148701 101, 148701 (2008)]. While degree distributions are of main interest when regarding the scheme as network renormalization, mass distributions (which are more relevant when considering “supernodes” as clusters) are much easier to study using the fast Newman-Ziff algorithm for

  5. Communication: Active space decomposition with multiple sites: Density matrix renormalization group algorithm

    SciTech Connect

    Parker, Shane M.; Shiozaki, Toru

    2014-12-07

    We extend the active space decomposition method, recently developed by us, to more than two active sites using the density matrix renormalization group algorithm. The fragment wave functions are described by complete or restricted active-space wave functions. Numerical results are shown on a benzene pentamer and a perylene diimide trimer. It is found that the truncation errors in our method decrease almost exponentially with respect to the number of renormalization states M, allowing for numerically exact calculations (to a few μE{sub h} or less) with M = 128 in both cases. This rapid convergence is because the renormalization steps are used only for the interfragment electron correlation.

  6. Renormalization group functions for two-dimensional phase transitions: To the problem of singular contributions

    SciTech Connect

    Pogorelov, A. A.; Suslov, I. M.

    2007-08-15

    According to the available publications, the field theoretical renormalization group approach in the two-dimensional case gives the critical exponents that differ from the known exact values. This property is associated with the existence of nonanalytic contributions in the renormalization group functions. The situation is analyzed in this work using a new algorithm for summing divergent series that makes it possible to determine the dependence of the results for the critical exponents on the expansion coefficients for the renormalization group functions. It has been shown that the exact values of all the exponents can be obtained with a reasonable form of the coefficient functions. These functions have small nonmonotonic sections or inflections, which are poorly reproduced in natural interpolations. It is not necessary to assume the existence of singular contributions in the renormalization group functions.

  7. Comment on the charge-renormalization effects of quartic scalar self-interactions

    SciTech Connect

    Jones, D.R.T.

    1980-12-15

    The charge-renormalization effects of quartic scalar interactions are calculated in a general gauge theory at the three-loop level using the Gegenbauer series expansion technique. The result agrees with a previous calculation by Curtright.

  8. Averaging and renormalization for the Korteveg–deVries–Burgers equation

    PubMed Central

    Chorin, Alexandre J.

    2003-01-01

    We consider traveling wave solutions of the Korteveg–deVries–Burgers equation and set up an analogy between the spatial averaging of these traveling waves and real-space renormalization for Hamiltonian systems. The result is an effective equation that reproduces means of the unaveraged, highly oscillatory, solution. The averaging enhances the apparent diffusion, creating an “eddy” (or renormalized) diffusion coefficient; the relation between the eddy diffusion coefficient and the original diffusion coefficient is found numerically to be one of incomplete similarity, setting up an instance of Barenblatt's renormalization group. The results suggest a relation between self-similar solutions of differential equations on one hand and renormalization groups and optimal prediction algorithms on the other. An analogy with hydrodynamics is pointed out. PMID:12913126

  9. Nonperturbative renormalization group study of the stochastic Navier-Stokes equation.

    PubMed

    Mejía-Monasterio, Carlos; Muratore-Ginanneschi, Paolo

    2012-07-01

    We study the renormalization group flow of the average action of the stochastic Navier-Stokes equation with power-law forcing. Using Galilean invariance, we introduce a nonperturbative approximation adapted to the zero-frequency sector of the theory in the parametric range of the Hölder exponent 4-2ε of the forcing where real-space local interactions are relevant. In any spatial dimension d, we observe the convergence of the resulting renormalization group flow to a unique fixed point which yields a kinetic energy spectrum scaling in agreement with canonical dimension analysis. Kolmogorov's -5/3 law is, thus, recovered for ε = 2 as also predicted by perturbative renormalization. At variance with the perturbative prediction, the -5/3 law emerges in the presence of a saturation in the ε dependence of the scaling dimension of the eddy diffusivity at ε = 3/2 when, according to perturbative renormalization, the velocity field becomes infrared relevant. PMID:23005533

  10. Noncompact lattice QED with two charges: Phase diagram and renormalization group flow

    SciTech Connect

    Ali Khan, A.

    1996-06-01

    The phase diagram of noncompact lattice QED in four dimensions with staggered fermions of charges 1 and {minus}1/2 is investigated. The renormalized charges are determined and found to be in agreement with perturbation theory. This is an indication that there is no continuum limit with nonvanishing renormalized gauge coupling, and that the theory has a validity bound for every finite value of the renormalized coupling. The renormalization group flow of the charges is investigated and an estimate for the validity bound as a function of the cutoff is obtained. Generalizing this estimate to all fermions in the standard model, it is found that a cutoff at the Planck scale implies that {alpha}{sub {ital R}} has to be less than 1/80. Because of spontaneous chiral symmetry breaking, strongly bound fermion-antifermion composite states are generated. Their spectrum is discussed. {copyright} {ital 1996 The American Physical Society.}

  11. Theory of fully developed hydrodynamic turbulent flow: Applications of renormalization-group methods

    NASA Astrophysics Data System (ADS)

    Yuan, Jian-Yang; Ronis, David

    1992-04-01

    A model for randomly stirred or homogeneous turbulent fluids is analyzed using renormalization-group methods on a path-integral representation of the Navier-Stokes equations containing a spatially and temporally colored noise source. For moderate Reynolds numbers and certain values of the dynamic exponent governing the noise correlation, an additional scaling regime is found at wave vectors k beyond those where the Kolmogorov 5/3 law holds. In this case, the energy spectrum decays as k-1-z, where 1additional scaling region disappears, and the Kolmogorov constant and Prandtl number become universal in the limit of infinite Reynolds number. In three spatial dimensions, the latter two equal 3/2( 5) / 3 )1/3 and √0.8 , respectively. The recent homodyne scattering experiments of Tong and co-workers [Phys. Rev. Lett. 65, 2780 (1990)] are analyzed, and the connection of the new scaling region with intermittency is discussed.

  12. Renormalization of the Higgs sector in the triplet model

    NASA Astrophysics Data System (ADS)

    Aoki, Mayumi; Kanemura, Shinya; Kikuchi, Mariko; Yagyu, Kei

    2012-08-01

    We study radiative corrections to the mass spectrum and the triple Higgs boson coupling in the model with an additional Y = 1 triplet field. In this model, the vacuum expectation value for the triplet field is strongly constrained from the electroweak precision data, under which characteristic mass spectrum appear at the tree level; i.e., mH++2 - mH+2 ≃ mH+2 - mA2 and mA2 ≃ mH2, where the CP-even (H), the CP-odd (A) and the doubly-charged (H±±) as well as the singly-charged (H±) Higgs bosons are the triplet-like. We evaluate how the tree-level formulae are modified at the one-loop level. The hhh coupling for the standard model-like Higgs boson (h) is also calculated at the one-loop level. One-loop corrections to these quantities can be large enough for identification of the model by future precision data at the LHC or the International Linear Collider.

  13. Material and Doping Dependence of the Nodal and Antinodal Dispersion Renormalizations in Single- and Multilayer Cuprates

    DOE PAGES

    Johnston, S.; Lee, W. S.; Chen, Y.; Nowadnick, E. A.; Moritz, B.; Shen, Z. -X.; Devereaux, T. P.

    2010-01-01

    We presenmore » t a review of bosonic renormalization effects on electronic carriers observed from angle-resolved photoemission spectra in the cuprates. Specifically, we discuss the viewpoint that these renormalizations represent coupling of the electrons to the lattice and review how materials dependence, such as the number of Cu O 2 layers, and doping dependence can be understood straightforwardly in terms of several aspects of electron-phonon coupling in layered correlated materials.« less

  14. Persistence-length renormalization of polymers in a crowded environment of hard disks.

    PubMed

    Schöbl, S; Sturm, S; Janke, W; Kroy, K

    2014-12-01

    The most conspicuous property of a semiflexible polymer is its persistence length, defined as the decay length of tangent correlations along its contour. Using an efficient stochastic growth algorithm to sample polymers embedded in a quenched hard-disk fluid, we find apparent wormlike chain statistics with a renormalized persistence length. We identify a universal form of the disorder renormalization that suggests itself as a quantitative measure of molecular crowding. PMID:25526167

  15. Renormalization of high-energy Lorentz-violating four-fermion models

    SciTech Connect

    Anselmi, Damiano; Ciuffoli, Emilio

    2010-04-15

    We study the one-loop renormalization of high-energy Lorentz-violating four-fermion models. We derive general formulas and then consider a number of specific models. We study the conditions for asymptotic freedom and give a practical method to determine the asymptotic-freedom domain. We also point out that in some models the renormalization-group flow contains rational Zimmermann trajectories that might hide new symmetries.

  16. Splitting mass spectra and muon g - 2 in Higgs-anomaly mediation

    NASA Astrophysics Data System (ADS)

    Yin, Wen; Yokozaki, Norimi

    2016-11-01

    We propose a scenario where only the Higgs multiplets have direct couplings to a supersymmetry (SUSY) breaking sector. The standard model matter multiplets as well as the gauge multiples are sequestered from the SUSY breaking sector; therefore, their masses arise via anomaly mediation at the high energy scale with a gravitino mass of ∼ 100TeV. Due to renormalization group running effects from the Higgs soft masses, the masses of the third generation sfermions become O (10)TeV at the low energy scale, while the first and second generation sfermion masses are O (0.1- 1)TeV, avoiding the tachyonic slepton problem and flavor changing neutral current problem. With the splitting mass spectrum, the muon g - 2 anomaly is explained consistently with the observed Higgs boson mass of 125 GeV. Moreover, the third generation Yukawa couplings are expected to be unified in some regions. New contributions to the Higgs boson mass: if there is an additional contribution to the Higgs boson mass, the SUSY particles are not necessarily heavy. In this case, the anomaly of the muon g - 2 is explained by the contributions from the fairly light SUSY particles. For instance, SUSY models with vector-like matter multiplets [14-17], the large trilinear coupling of the stop [18,19], or an extra gauge interaction [20] can accommodate both the observed Higgs boson mass and muon g - 2 anomaly.

  17. Quantum Structure of Field Theory and Standard Model Based on Infinity-Free Loop Regularization/renormalization

    NASA Astrophysics Data System (ADS)

    Wu, Yue-Liang

    2014-02-01

    To understand better the quantum structure of field theory and standard model in particle physics, it is necessary to investigate carefully the divergence structure in quantum field theories (QFTs) and work out a consistent framework to avoid infinities. The divergence has got us into trouble since developing quantum electrodynamics in 1930s. Its treatment via the renormalization scheme is satisfied not by all physicists, like Dirac and Feynman who have made serious criticisms. The renormalization group analysis reveals that QFTs can in general be defined fundamentally with the meaningful energy scale that has some physical significance, which motivates us to develop a new symmetry-preserving and infinity-free regularization scheme called loop regularization (LORE). A simple regularization prescription in LORE is realized based on a manifest postulation that a loop divergence with a power counting dimension larger than or equal to the space-time dimension must vanish. The LORE method is achieved without modifying original theory and leads the divergent Feynman loop integrals well-defined to maintain the divergence structure and meanwhile preserve basic symmetries of original theory. The crucial point in LORE is the presence of two intrinsic energy scales which play the roles of ultraviolet cutoff Mc and infrared cutoff μs to avoid infinities. As Mc can be made finite when taking appropriately both the primary regulator mass and number to be infinity to recover the original integrals, the two energy scales Mc and μs in LORE become physically meaningful as the characteristic energy scale and sliding energy scale, respectively. The key concept in LORE is the introduction of irreducible loop integrals (ILIs) on which the regularization prescription acts, which leads to a set of gauge invariance consistency conditions between the regularized tensor-type and scalar-type ILIs. An interesting observation in LORE is that the evaluation of ILIs with ultraviolet

  18. Quantum Structure of Field Theory and Standard Model Based on Infinity-Free Loop Regularization/renormalization

    NASA Astrophysics Data System (ADS)

    Wu, Yue-Liang

    2014-04-01

    To understand better the quantum structure of field theory and standard model in particle physics, it is necessary to investigate carefully the divergence structure in quantum field theories (QFTs) and work out a consistent framework to avoid infinities. The divergence has got us into trouble since developing quantum electrodynamics in 1930s. Its treatment via the renormalization scheme is satisfied not by all physicists, like Dirac and Feynman who have made serious criticisms. The renormalization group analysis reveals that QFTs can in general be defined fundamentally with the meaningful energy scale that has some physical significance, which motivates us to develop a new symmetry-preserving and infinity-free regularization scheme called loop regularization (LORE). A simple regularization prescription in LORE is realized based on a manifest postulation that a loop divergence with a power counting dimension larger than or equal to the space-time dimension must vanish. The LORE method is achieved without modifying original theory and leads the divergent Feynman loop integrals well-defined to maintain the divergence structure and meanwhile preserve basic symmetries of original theory. The crucial point in LORE is the presence of two intrinsic energy scales which play the roles of ultraviolet cutoff Mc and infrared cutoff μs to avoid infinities. As Mc can be made finite when taking appropriately both the primary regulator mass and number to be infinity to recover the original integrals, the two energy scales Mc and μs in LORE become physically meaningful as the characteristic energy scale and sliding energy scale, respectively. The key concept in LORE is the introduction of irreducible loop integrals (ILIs) on which the regularization prescription acts, which leads to a set of gauge invariance consistency conditions between the regularized tensor-type and scalar-type ILIs. An interesting observation in LORE is that the evaluation of ILIs with ultraviolet

  19. Renormalization group analysis of a fermionic hot-spot model

    NASA Astrophysics Data System (ADS)

    Whitsitt, Seth; Sachdev, Subir

    2014-09-01

    We present a renormalization group (RG) analysis of a fermionic "hot-spot" model of interacting electrons on the square lattice. We truncate the Fermi-surface excitations to linearly dispersing quasiparticles in the vicinity of eight hot spots on the Fermi surface, with each hot spot separated from another by the wave vector (π,π). This is motivated by the importance of these Fermi-surface locations to the onset of antiferromagnetic order; however, we allow for all possible quartic interactions between the fermions, and also for all possible ordering instabilities. We compute the RG equations for our model, which depend on whether or not the hot spots are perfectly nested, and relate our results to earlier models. We also compute the RG flow of the relevant order parameters for both Hubbard and J,V interactions, and present our results for the dominant instabilities in the nested and non-nested cases. In particular, we find that non-nested hot spots with J,V interactions have competing singlet dx2-y2 superconducting and d-form factor incommensurate density wave instabilities. We also investigate the enhancement of incommensurate density waves near experimentally observed wave vectors, and find dominant d-form factor enhancement for a range of couplings.

  20. Renormalization group optimized perturbation theory at finite temperatures

    NASA Astrophysics Data System (ADS)

    Kneur, Jean-Loïc; Pinto, Marcus B.

    2015-12-01

    A recently developed variant of the so-called optimized perturbation theory (OPT), making it perturbatively consistent with renormalization group (RG) properties, RGOPT, was shown to drastically improve its convergence for zero temperature theories. Here the RGOPT adapted to finite temperature is illustrated with a detailed evaluation of the two-loop pressure for the thermal scalar λ ϕ4 field theory. We show that already at the simple one-loop level this quantity is exactly scale-invariant by construction and turns out to qualitatively reproduce, with a rather simple procedure, results from more sophisticated resummation methods at two-loop order, such as the two-particle irreducible approach typically. This lowest order also reproduces the exact large-N results of the O (N ) model. Although very close in spirit, our RGOPT method and corresponding results differ drastically from similar variational approaches, such as the screened perturbation theory or its QCD-version, the (resummed) hard thermal loop perturbation theory. The latter approaches exhibit a sensibly degrading scale dependence at higher orders, which we identify as a consequence of missing RG invariance. In contrast RGOPT gives a considerably reduced scale dependence at two-loop level, even for relatively large coupling values √{λ /24 }˜O (1 ), making results much more stable as compared with standard perturbation theory, with expected similar properties for thermal QCD.

  1. Improved renormalization group theory for critical asymmetry of fluids

    NASA Astrophysics Data System (ADS)

    Wang, Long; Zhao, Wei; Wu, Liang; Li, Liyan; Cai, Jun

    2013-09-01

    We develop an improved renormalization group (RG) approach incorporating the critical vapor-liquid equilibrium asymmetry. In order to treat the critical asymmetry of vapor-liquid equilibrium, the integral measure is introduced in the Landau-Ginzbug partition function to achieve a crossover between the local order parameter in Ising model and the density of fluid systems. In the implementation of the improved RG approach, we relate the integral measure with the inhomogeneous density distribution of a fluid system and combine the developed method with SAFT-VR (statistical associating fluid theory of variable range) equation of state. The method is applied to various fluid systems including square-well fluid, square-well dimer fluid and real fluids such as methane (CH4), ethane (C2H6), trifluorotrichloroethane (C2F3Cl3), and sulfur hexafluoride (SF6). The descriptions of vapor-liquid equilibria provided by the developed method are in excellent agreement with simulation and experimental data. Furthermore, the improved method predicts accurate and qualitatively correct behavior of coexistence diameter near the critical point and produces the non-classical 3D Ising criticality.

  2. Magnetic moments induce strong phonon renormalization in FeSi

    PubMed Central

    Krannich, S.; Sidis, Y.; Lamago, D.; Heid, R.; Mignot, J.-M.; Löhneysen, H. v.; Ivanov, A.; Steffens, P.; Keller, T.; Wang, L.; Goering, E.; Weber, F.

    2015-01-01

    The interactions of electronic, spin and lattice degrees of freedom in solids result in complex phase diagrams, new emergent phenomena and technical applications. While electron–phonon coupling is well understood, and interactions between spin and electronic excitations are intensely investigated, only little is known about the dynamic interactions between spin and lattice excitations. Noncentrosymmetric FeSi is known to undergo with increasing temperature a crossover from insulating to metallic behaviour with concomitant magnetic fluctuations, and exhibits strongly temperature-dependent phonon energies. Here we show by detailed inelastic neutron-scattering measurements and ab initio calculations that the phonon renormalization in FeSi is linked to its unconventional magnetic properties. Electronic states mediating conventional electron–phonon coupling are only activated in the presence of strong magnetic fluctuations. Furthermore, phonons entailing strongly varying Fe–Fe distances are damped via dynamic coupling to the temperature-induced magnetic moments, highlighting FeSi as a material with direct spin–phonon coupling and multiple interaction paths. PMID:26611619

  3. Non-perturbative Renormalization in Truncated Yukawa Model

    NASA Astrophysics Data System (ADS)

    Karmanov, V. A.

    2016-06-01

    An approach to non-perturbative calculations in the light-front quantum field theory and its new developments are briefly reviewed. We start with the decomposition of the state vector in Fock components. After truncation of this decomposition (main approximation in this approach), the eigenvalue equation for the light-front Hamiltonian generates, in Minkowski space, a finite system of integral equations for the Fock components. Solving this system numerically and performing the non-perturbative renormalization, we find the state vector of fermion in the quenched scalar Yukawa model, up to the four-body truncation (one fermion + three bosons), for rather large values of the coupling constant. With the state vector, found in this way, the fermion electromagnetic form factors are calculated. Comparing results obtained in the four-body truncation with those found in the previous, three-body truncation, we discover very good convergence relative to truncation, that indicates that we are close to the exact non-perturbative solution in this field-theoretical model. The approach can be extended to more realistic field theories and, after further development, it could constitute an alternative to the lattice calculations.

  4. Renormalization group calculations with k∥ dependent couplings in a ladder

    NASA Astrophysics Data System (ADS)

    Abramovici, G.

    2006-05-01

    We investigate the phase diagram of a ladder system (two chains, with a Hubbard interaction U and an interband coupling t⊥). It is already known [M. Fabrizio, Phys. Rev. B 48 (1993) 15838] that backward interband scattering (gb) plays a particular role in this system. Moreover, some authors (for instance [ H.J. Schulz, Phys. Rev. B 53 (1996) R2959]) have early pointed out that, because of this coupling gb, parallel momentum (k∥) dependence could not be neglected. So we have introduced an original method to include k∥ dependence of couplings, in a RG calculation using the one particle irreducible (OPI) scheme. We calculate different susceptibilities, which are classified according to their symmetries. Our results depend on whether we include k∥ dependence or not. When we include this dependence, we observe a region with large antiferromagnetic fluctuations, in the vicinity of small t⊥, followed by a superconducting region with a simultaneous divergence of the spin density waves channel. The region with only spin density wave fluctuations disappears, when k∥ dependence is neglected. Altogether, our results prove that k∥ is an influential variable in the renormalization group flow, for a ladder.

  5. Renormalized phonons in nonlinear lattices: A variational approach

    NASA Astrophysics Data System (ADS)

    Liu, Junjie; Liu, Sha; Li, Nianbei; Li, Baowen; Wu, Changqin

    2015-04-01

    We propose a variational approach to study renormalized phonons in momentum-conserving nonlinear lattices with either symmetric or asymmetric potentials. To investigate the influence of pressure for phonon properties, we derive an inequality which provides both the lower and upper bound of the Gibbs free energy as the associated variational principle. This inequality is a direct extension to the Gibbs-Bogoliubov inequality. Taking the symmetry effect into account, the reference system for the variational approach is chosen to be harmonic with an asymmetric quadratic potential which contains variational parameters. We demonstrate the power of this approach by applying it to one-dimensional nonlinear lattices with a symmetric or asymmetric Fermi-Pasta-Ulam-type potential. For a system with a symmetric potential and zero pressure, we recover existing results. For other systems which are beyond the scope of existing theories, including those having symmetric potential and pressure and those having the asymmetric potential with or without pressure, we also obtain accurate sound velocity.

  6. XY-sliding phases - mirage of the Renormalization Group

    NASA Astrophysics Data System (ADS)

    Vayl, Steven; Kuklov, Anatoly; Oganesyan, Vadim

    The so called sliding XY phases in layered systems are predicted to occur if the one loop renormalization group (RG) flow renders the interlayer Josephson coupling irrelevant, while each layer still features broken U(1) symmetry. In other words, such a layered system remains essentially two-dimensional despite the presence of inter-layer Josephson coupling. We have analyzed numerically a layered system consisting of groups of asymmetric layers where the RG analysis predicts sliding phases to occur. Monte Carlo simulations of such a system have been conducted in the dual representation by Worm Algorithm in terms of the closed loops of J-currents for layer sizes varying from 4 ×4 to 640 ×640 and the number of layers - from 2 to 40. The resulting flow of the inter-layer XY-stiffness has been found to be inconsistent with the RG prediction and fully consistent with the behavior of the 3D standard XY model where the bare inter-layer Josephson coupling is much smaller than the intra-layer stiffness. This result emphasizes the importance of the compactness of the U(1) variable for 2D to 3D transformation. This work was supported by the NSF Grant PHY1314469.

  7. Bimetric renormalization group flows in quantum Einstein gravity

    SciTech Connect

    Manrique, Elisa; Reuter, Martin; Saueressig, Frank

    2011-02-15

    Research Highlights: > Gravitational Effective Action in the bimetric truncation. > First study of the full gravitational flow with a bimetric structure. > The non-trivial gravitational RG fixed point persists under bimetric truncations. > Second non-trivial fixed point emerges, which may control the IR behavior of the theory. - Abstract: The formulation of an exact functional renormalization group equation for quantum Einstein gravity necessitates that the underlying effective average action depends on two metrics, a dynamical metric giving the vacuum expectation value of the quantum field, and a background metric supplying the coarse graining scale. The central requirement of 'background independence' is met by leaving the background metric completely arbitrary. This bimetric structure entails that the effective average action may contain three classes of interactions: those built from the dynamical metric only, terms which are purely background, and those involving a mixture of both metrics. This work initiates the first study of the full-fledged gravitational RG flow, which explicitly accounts for this bimetric structure, by considering an ansatz for the effective average action which includes all three classes of interactions. It is shown that the non-trivial gravitational RG fixed point central to the asymptotic safety program persists upon disentangling the dynamical and background terms. Moreover, upon including the mixed terms, a second non-trivial fixed point emerges, which may control the theory's IR behavior.

  8. Renormalization group studies of many-body localization

    NASA Astrophysics Data System (ADS)

    Altman, Ehud

    2015-03-01

    Quantum correlations do not usually persist for long in systems at finite energy density and disappear once the system thermalizes. But many-body localization offers an alternative paradigm, whereby quantum matter can evade the usual fate of thermal equilibrium and retain retrievable quantum correlations even at high energies. I will survey a dynamical renormalization group (RG) approach used to characterize the novel dynamics and entanglement structures, which develop in the localized phase in lieu of classical thermalization. Then I will present a theory of the transition between the ergodic and the many-body localized phase based on a novel RG framework. Here eigenstate entanglement entropy emerges as a natural scaling variable; the RG describes a change from area-law to volume law entanglement through an intriguing critical point, where the distribution of entanglement entropy becomes maximally broad. The ergodic phase established near the critical point is a Griffiths phase, which exhibits sub-diffusive energy transport and sub-ballistic entanglement propagation. The anomalous diffusion exponent vanishes continuously at the critical point. Before closing I will discuss recent progress in confronting the emerging theoretical understanding of many-body localization with experimental tests. This research is supported in part by the ERC synergy grant UQUAM.

  9. Interleaved numerical renormalization group as an efficient multiband impurity solver

    NASA Astrophysics Data System (ADS)

    Stadler, K. M.; Mitchell, A. K.; von Delft, J.; Weichselbaum, A.

    2016-06-01

    Quantum impurity problems can be solved using the numerical renormalization group (NRG), which involves discretizing the free conduction electron system and mapping to a "Wilson chain." It was shown recently that Wilson chains for different electronic species can be interleaved by use of a modified discretization, dramatically increasing the numerical efficiency of the RG scheme [Phys. Rev. B 89, 121105(R) (2014), 10.1103/PhysRevB.89.121105]. Here we systematically examine the accuracy and efficiency of the "interleaved" NRG (iNRG) method in the context of the single impurity Anderson model, the two-channel Kondo model, and a three-channel Anderson-Hund model. The performance of iNRG is explicitly compared with "standard" NRG (sNRG): when the average number of states kept per iteration is the same in both calculations, the accuracy of iNRG is equivalent to that of sNRG but the computational costs are significantly lower in iNRG when the same symmetries are exploited. Although iNRG weakly breaks SU(N ) channel symmetry (if present), both accuracy and numerical cost are entirely competitive with sNRG exploiting full symmetries. iNRG is therefore shown to be a viable and technically simple alternative to sNRG for high-symmetry models. Moreover, iNRG can be used to solve a range of lower-symmetry multiband problems that are inaccessible to sNRG.

  10. Magnetic moments induce strong phonon renormalization in FeSi.

    PubMed

    Krannich, S; Sidis, Y; Lamago, D; Heid, R; Mignot, J-M; Löhneysen, H v; Ivanov, A; Steffens, P; Keller, T; Wang, L; Goering, E; Weber, F

    2015-01-01

    The interactions of electronic, spin and lattice degrees of freedom in solids result in complex phase diagrams, new emergent phenomena and technical applications. While electron-phonon coupling is well understood, and interactions between spin and electronic excitations are intensely investigated, only little is known about the dynamic interactions between spin and lattice excitations. Noncentrosymmetric FeSi is known to undergo with increasing temperature a crossover from insulating to metallic behaviour with concomitant magnetic fluctuations, and exhibits strongly temperature-dependent phonon energies. Here we show by detailed inelastic neutron-scattering measurements and ab initio calculations that the phonon renormalization in FeSi is linked to its unconventional magnetic properties. Electronic states mediating conventional electron-phonon coupling are only activated in the presence of strong magnetic fluctuations. Furthermore, phonons entailing strongly varying Fe-Fe distances are damped via dynamic coupling to the temperature-induced magnetic moments, highlighting FeSi as a material with direct spin-phonon coupling and multiple interaction paths. PMID:26611619

  11. Fast and simultaneous determination of eleven synthetic color additives in flour and meat products by liquid chromatography coupled with diode-array detector and tandem mass spectrometry.

    PubMed

    Qi, Ping; Lin, Zi-hao; Chen, Gui-yun; Xiao, Jian; Liang, Zhi-an; Luo, Li-ni; Zhou, Jun; Zhang, Xue-wu

    2015-08-15

    In this study, an efficient, fast and sensitive method for the simultaneous determination of eleven synthetic color additives (Allura red, Amaranth, Azo rubine, Brilliant blue, Erythrosine, Indigotine, Ponceau 4R, New red, Sunset yellow, Quinoline yellow and Tartrazine) in flour and meat foodstuffs is developed and validated using HPLC coupled with DAD and MS/MS. The color additives were extracted with ammonia-methanol and was further purified with SPE procedure using Strata-AW column in order to reduce matrix interference. This HPLC-DAD method is intended for a comprehensive survey of color additives in foods. HPLC-MS/MS method was used as the further confirmation and identification. Validation data showed the good recoveries in the range of 75.2-113.8%, with relative standard deviations less than 15%. These methods are suitable for the routine monitoring analysis of eleven synthetic color additives due to its sensitivity, reasonable time and cost.

  12. Constraining bilinear R-parity violation from neutrino masses

    SciTech Connect

    Gozdz, Marek; Kaminski, Wieslaw A.

    2008-10-01

    We confront the R-parity violating minimal supersymmetric standard model with the neutrino oscillation data. Investigating the 1-loop particle-sparticle diagrams with additional bilinear insertions on the external neutrino lines we construct the relevant contributions to the neutrino mass matrix. A comparison of the so-obtained matrices with the experimental ones assuming normal or inverted hierarchy and taking into account possible CP-violating phases allows to set constraints on the values of the bilinear coupling constants. A similar calculation is presented with the input from the Heidelberg-Moscow neutrinoless double beta decay experiment. We base our analysis on the renormalization group evolution of the minimal supersymmetric standard model parameters which are unified at the grand unified theory scale. Using the obtained bounds we calculate the contributions to the Majorana neutrino transition magnetic moments.

  13. Predictions for the top-quark forward-backward asymmetry at high invariant pair mass using the principle of maximum conformality

    NASA Astrophysics Data System (ADS)

    Wang, Sheng-Quan; Wu, Xing-Gang; Si, Zong-Guo; Brodsky, Stanley J.

    2016-01-01

    The D0 collaboration at FermiLab has recently measured the top-quark pair forward-backward asymmetry in p ¯p →t t ¯X reactions as a function of the t t ¯ invariant mass Mt t ¯. The D0 result for AFB(Mt t ¯>650 GeV ) is smaller than AFB(Mt t ¯) obtained for small values of Mt t ¯, which may indicate an "increasing-decreasing" behavior for AFB(Mt t ¯>Mcut) . This behavior is not explained using conventional renormalization scale setting, or even by a next-to-next-to-leading order (N2LO ) QCD calculation—one predicts a monotonically increasing behavior. In the conventional scale-setting method, one simply guesses a single renormalization scale μr for the argument of the QCD running coupling and then varies it over an arbitrary range. However, the conventional method has inherent difficulties. For example, the resulting perturbative quantum chromodynamics (pQCD) predictions depend on the choice of renormalization scheme, in contradiction to the principle of "renormalization scheme invariance"—predictions for physical observables cannot depend on a theoretical convention. The error estimate obtained by varying μr is unreliable since it is only sensitive to perturbative contributions involving the pQCD β -function. Worse, guessing the renormalization scale gives predictions for precision QED observables which are in contradiction to results obtained using the standard Gell-Mann-Low method. In contrast, if one fixes the scale using the principle of maximum conformality (PMC), the resulting pQCD predictions are renormalization-scheme independent since all of the scheme-dependent {βi}-terms in the QCD perturbative series are resummed into the QCD running couplings at each order. The {βi}-terms at each order can be unambiguously identified using renormalization group methods such as the Rδ method. The PMC then determines the renormalization scales of the running coupling at each order and provides unambiguous scale-fixed and scheme-independent predictions

  14. Gate-tunable Kondo resistivity and dephasing rate in graphene studied by numerical renormalization group calculations

    NASA Astrophysics Data System (ADS)

    Lo, Po-Wei; Guo, Guang-Yu; Anders, Frithjof B.

    2014-05-01

    Motivated by the recent observation of the Kondo effect in graphene in transport experiments, we investigate the resistivity and dephasing rate in the Kondo regime due to magnetic impurities in graphene with different chemical potentials (μ). The Kondo effect due to either carbon vacancies or magnetic adatoms in graphene is described by the single-orbital pseudogap asymmetric Anderson impurity model which is solved by the accurate numerical renormalization group method. We find that although the Anderson impurity model considered here is a mixed-valence system, it can be driven into either the Kondo [μ >μc (critical value) >0], mixed-valency (μ ≈μc), or empty-orbital (μ <μc) regime by a gate voltage, giving rise to characteristic features in resistivity and dephasing rate in each regime. Specifically, in the case of μ <μc, the shapes of the resistivity (dephasing rate) curves for different μ are nearly identical. However, as temperature decreases, they start to increase to their maxima at a lower T /TK, but more rapidly [as (TK/T)3/2] than in normal metals [here, T (TK) denotes the (Kondo) temperature]. As T further decreases, after reaching the maximum, the dephasing rate drops more quickly than in normal metals, behaving as (T/TK)3 instead of (T/TK)2. Furthermore, the resistivity has a distinct peak above the saturation value near TK. In the case of μ >μc, in contrast, the resistivity curve has an additional broad shoulder above 10TK and the dephasing rate exhibits an interesting shoulder-peak shape. In the narrow boundary region (μ ≈μc), both the resistivity and dephasing rate curves are similar to the corresponding ones in normal metals. This explains the conventional Kondo-like resistivity from recent experiments on graphene with defects, although the distinct features in the resistivity in the other cases (μ <μc or μ >μc) were not seen in the experiments. The interesting features in the resistivity and dephasing rate are analyzed in

  15. Hadamard renormalization of the stress-energy tensor for a quantized scalar field in a general spacetime of arbitrary dimension

    SciTech Connect

    Decanini, Yves; Folacci, Antoine

    2008-08-15

    We develop the Hadamard renormalization of the stress-energy tensor for a massive scalar field theory defined on a general spacetime of arbitrary dimension. Our formalism could be helpful in treating some aspects of the quantum physics of extra spatial dimensions. More precisely, for spacetime dimensions up to six, we explicitly describe the Hadamard renormalization procedure and for spacetime dimensions from 7 to 11, we provide the framework permitting the interested reader to perform this procedure explicitly in a given spacetime. We complete our study (i) by considering the ambiguities of the Hadamard renormalization of the stress-energy tensor and the corresponding ambiguities for the trace anomaly, (ii) by providing the expressions of the gravitational counterterms involved in the renormalization process, and (iii) by discussing the connections between Hadamard renormalization and renormalization in the effective action. All our results are expanded on standard bases for Riemann polynomials constructed from group theoretical considerations and thus given on irreducible forms.

  16. Kardar-Parisi-Zhang equation with spatially correlated noise: a unified picture from nonperturbative renormalization group.

    PubMed

    Kloss, Thomas; Canet, Léonie; Delamotte, Bertrand; Wschebor, Nicolás

    2014-02-01

    We investigate the scaling regimes of the Kardar-Parisi-Zhang (KPZ) equation in the presence of spatially correlated noise with power-law decay D(p) ∼ p(-2ρ) in Fourier space, using a nonperturbative renormalization group approach. We determine the full phase diagram of the system as a function of ρ and the dimension d. In addition to the weak-coupling part of the diagram, which agrees with the results from Europhys. Lett. 47, 14 (1999) and Eur. Phys. J. B 9, 491 (1999), we find the two fixed points describing the short-range- (SR) and long-range- (LR) dominated strong-coupling phases. In contrast with a suggestion in the references cited above, we show that, for all values of ρ, there exists a unique strong-coupling SR fixed point that can be continuously followed as a function of d. We show in particular that the existence and the behavior of the LR fixed point do not provide any hint for 4 being the upper critical dimension of the KPZ equation with SR noise.

  17. Density-matrix renormalization group algorithm with multi-level active space.

    PubMed

    Ma, Yingjin; Wen, Jing; Ma, Haibo

    2015-07-21

    The density-matrix renormalization group (DMRG) method, which can deal with a large active space composed of tens of orbitals, is nowadays widely used as an efficient addition to traditional complete active space (CAS)-based approaches. In this paper, we present the DMRG algorithm with a multi-level (ML) control of the active space based on chemical intuition-based hierarchical orbital ordering, which is called as ML-DMRG with its self-consistent field (SCF) variant ML-DMRG-SCF. Ground and excited state calculations of H2O, N2, indole, and Cr2 with comparisons to DMRG references using fixed number of kept states (M) illustrate that ML-type DMRG calculations can obtain noticeable efficiency gains. It is also shown that the orbital re-ordering based on hierarchical multiple active subspaces may be beneficial for reducing computational time for not only ML-DMRG calculations but also DMRG ones with fixed M values. PMID:26203012

  18. Turbulent magnetic Prandtl number in helical kinematic magnetohydrodynamic turbulence: two-loop renormalization group result.

    PubMed

    Jurčišinová, E; Jurčišin, M; Remecký, R; Zalom, P

    2013-04-01

    Using the field theoretic renormalization group technique, the influence of helicity (spatial parity violation) on the turbulent magnetic Prandtl number in the kinematic magnetohydrodynamic turbulence is investigated in the two-loop approximation. It is shown that the presence of helicity decreases the value of the turbulent magnetic Prandtl number and, at the same time, the two-loop helical contribution to the turbulent magnetic Prandtl number is at most 4.2% (in the case with the maximal helicity) of its nonhelical value. These results demonstrate, on one hand, the potential importance of the presence of asymmetries in processes in turbulent environments and, on the other hand, the rather strong stability of the properties of diffusion processes of the magnetic field in the conductive turbulent environment with the spatial parity violation in comparison to the corresponding systems without the spatial parity violation. In addition, obtained results are compared to the corresponding results found for the two-loop turbulent Prandtl number in the model of passively advected scalar field. It is shown that the turbulent Prandtl number and the turbulent magnetic Prandtl number, which are the same in fully symmetric isotropic turbulent systems, are essentially different when one considers the spatial parity violation. It means that the properties of the diffusion processes in the turbulent systems with a given symmetry breaking can considerably depend on the internal tensor structure of advected quantities.

  19. A driven similarity renormalization group approach to quantum many-body problems

    SciTech Connect

    Evangelista, Francesco A.

    2014-08-07

    Applications of the similarity renormalization group (SRG) approach [F. Wegner, Ann. Phys. 506, 77 (1994) and S. D. Głazek and K. G. Wilson, Phys. Rev. D 49, 4214 (1994)] to the formulation of useful many-body theories of electron correlation are considered. In addition to presenting a production-level implementation of the SRG based on a single-reference formalism, a novel integral version of the SRG is reported, in which the flow of the Hamiltonian is driven by a source operator. It is shown that this driven SRG (DSRG) produces a Hamiltonian flow that is analogous to that of the SRG. Compared to the SRG, which requires propagating a set of ordinary differential equations, the DSRG is computationally advantageous since it consists of a set of polynomial equations. The equilibrium distances, harmonic vibrational frequencies, and vibrational anharmonicities of a series of diatomic molecules computed with the SRG and DSRG approximated with one- and two-body normal ordered operators are in good agreement with benchmark values from coupled cluster with singles, doubles, and perturbative triples. Particularly surprising results are found when the SRG and DSRG methods are applied to C{sub 2} and F{sub 2}. In the former case, both methods fail to converge, while in the latter case an unbound potential energy curve is obtained. A modified commutator approximation is shown to correct these problems in the case of the DSRG method.

  20. Tensor Renormalization Group Study of the General Spin-S Blume-Capel Model

    NASA Astrophysics Data System (ADS)

    Yang, Li-Ping; Xie, Zhi-Yuan

    2016-10-01

    We focus on the special situation of D = 2J in the general spin-S Blume-Capel model on a square lattice. Under an infinitesimal external magnetic field, the phase transition behaviors due to the thermal fluctuations are investigated by the newly developed tensor renormalization group method. We clearly demonstrate the phase transition process: in the case of an integer spin-S, there are S first-order phase transitions with the stepwise magnetizations M = S,S - 1, ldots ,0; in the case of a half-odd integer spin-S, there are S - 1/2 first-order phase transitions with corresponding M = S,S - 1, ldots ,1/2 in addition to one continuous phase transition due to spin-flip Z2 symmetry breaking. At low temperatures, all first-order phase transitions are accompanied by the successive disappearance of the spin-component pairs (±s); furthermore, the transition temperature for the nth first-order phase transition is the same, independent of the value of the spin-S. In the absence of a magnetic field, a visualization parameter characterizing the intrinsic degeneracy of the different phases provides a different reference for the phase transition process.

  1. UHPLC-high-resolution mass spectrometry determination of bisphenol A and plastic additives released by polycarbonate tableware: influence of ageing and surface damage.

    PubMed

    Bignardi, Chiara; Cavazza, Antonella; Laganà, Carmen; Salvadeo, Paola; Corradini, Claudio

    2015-10-01

    A new UHPLC-ESI-Orbitrap method for the identification and the quantitative determination of bisphenol A and some common additives employed in plastic manufacturing has been developed and validated. The method has been applied to evaluate the migration from 14 samples of tableware of different age and degree of surface damage, in both ethanol and isooctane (used as food simulants according to EU plastic regulation). Bisphenol A, three UV light absorbers, and one whitening agent were detected and quantified. Data were analyzed with the aim of exploring a possible correlation between bisphenol A and additives release, ageing, and surface integrity. A high correlation between age of samples, surface damage, and bisphenol A migration has been evaluated, while the release of additives was not correlated with other parameters. Obtained data showed for the first time that the release of bisphenol A seems to be more connected to ageing than to scratches and cracks occurrence. Graphical Abstract Bisphenol A and additives released by polycarbonate tableware: influence of ageing and surface damage.

  2. Scalar-Tensor gravity with system-dependent potential and its relation with Renormalization Group extended General Relativity

    SciTech Connect

    Rodrigues, Davi C.; Piattella, Oliver F.; Chauvineau, Bertrand E-mail: Bertrand.Chauvineau@oca.eu

    2015-09-01

    We show that Renormalization Group extensions of the Einstein-Hilbert action for large scale physics are not, in general, a particular case of standard Scalar-Tensor (ST) gravity. We present a new class of ST actions, in which the potential is not necessarily fixed at the action level, and show that this extended ST theory formally contains the Renormalization Group case. We also propose here a Renormalization Group scale setting identification that is explicitly covariant and valid for arbitrary relativistic fluids.

  3. Body dissatisfaction and body mass in girls and boys transitioning from early to mid-adolescence: additional role of self-esteem and eating habits

    PubMed Central

    2012-01-01

    Background In the transition from early to mid-adolescence, gender differences in pubertal development become significant. Body dissatisfaction is often associated with body mass, low self-esteem and abnormal eating habits. The majority of studies investigating body dissatisfaction and its associations have been conducted on female populations. However, some evidence suggests that males also suffer from these problems and that gender differences might already be observed in adolescence. Aims To examine body dissatisfaction and its relationship with body mass, as well as self-esteem and eating habits, in girls and boys in transition from early to mid-adolescence. Methods School nurses recorded the heights and weights of 659 girls and 711 boys with a mean age of 14.5 years. The Rosenberg Self-Esteem Scale and the Body Dissatisfaction subscale of the Eating Disorder Inventory were used as self-appraisal scales. Eating data were self-reported. Results The girls were less satisfied with their bodies than boys were with theirs (mean score (SD): 30.6 (SD 12.2) vs. 18.9 (SD 9.5); p < 0.001). The girls expressed most satisfaction with their bodies when they were underweight, more dissatisfaction when they were of normal weight and most dissatisfaction when they had excess body weight. The boys also expressed most satisfaction when they were underweight and most dissatisfaction when they had excess body weight. The boys reported higher levels of self-esteem than did the girls (mean (SD): 31.3 (4.8) vs. 28.0 (5.9); p < 0.001). The adolescents self-reporting abnormal eating habits were less satisfied with their bodies than those describing normal eating habits (mean (SD): 33.0 (12.9) vs. 21.2 (10.2); p < 0.001). Conclusions Body mass, self-esteem and eating habits revealed a significant relationship with body dissatisfaction in the transitional phase from early to mid-adolescence in girls and boys, but significant gender differences were also found. PMID:22540528

  4. Shaping frequency response of a vibrating plate for passive and active control applications by simultaneous optimization of arrangement of additional masses and ribs. Part I: Modeling

    NASA Astrophysics Data System (ADS)

    Wrona, Stanislaw; Pawelczyk, Marek

    2016-03-01

    An ability to shape frequency response of a vibrating plate according to precisely defined demands has a very high practical potential. It can be applied to improve acoustic radiation of the plate for required frequencies or enhance acoustic isolation of noise barriers and device casings by using both passive and active control. The proposed method is based on mounting severaladditional ribs and masses (passive and/or active) to the plate surface at locations followed from an optimization process. This paper, Part I, concerns derivation of a mathematical model of the plate with attached elements in the function of their shape and placement. The model is validated by means of simulations and laboratory experiments, and compared with models known from the literature. This paper is followed by a companion paper, Part II, where the optimization process is described. It includes arrangement of passive elements as well as actuators and sensors to improve controllability and observability measures, if active control is concerned.

  5. Planet hunters. VII. Discovery of a new low-mass, low-density planet (PH3 C) orbiting Kepler-289 with mass measurements of two additional planets (PH3 B and D)

    SciTech Connect

    Schmitt, Joseph R.; Fischer, Debra A.; Wang, Ji; Margossian, Charles; Brewer, John M.; Giguere, Matthew J.; Agol, Eric; Deck, Katherine M.; Rogers, Leslie A.; Gazak, J. Zachary; Holman, Matthew J.; Jek, Kian J.; Omohundro, Mark R.; Winarski, Troy; Lintott, Chris; Simpson, Robert; Lynn, Stuart; Parrish, Michael; Schawinski, Kevin; Schwamb, Megan E.; and others

    2014-11-10

    We report the discovery of one newly confirmed planet (P = 66.06 days, R {sub P} = 2.68 ± 0.17 R {sub ⊕}) and mass determinations of two previously validated Kepler planets, Kepler-289 b (P = 34.55 days, R {sub P} = 2.15 ± 0.10 R {sub ⊕}) and Kepler-289-c (P = 125.85 days, R {sub P} = 11.59 ± 0.10 R {sub ⊕}), through their transit timing variations (TTVs). We also exclude the possibility that these three planets reside in a 1:2:4 Laplace resonance. The outer planet has very deep (∼1.3%), high signal-to-noise transits, which puts extremely tight constraints on its host star's stellar properties via Kepler's Third Law. The star PH3 is a young (∼1 Gyr as determined by isochrones and gyrochronology), Sun-like star with M {sub *} = 1.08 ± 0.02 M {sub ☉}, R {sub *} = 1.00 ± 0.02 R {sub ☉}, and T {sub eff} = 5990 ± 38 K. The middle planet's large TTV amplitude (∼5 hr) resulted either in non-detections or inaccurate detections in previous searches. A strong chopping signal, a shorter period sinusoid in the TTVs, allows us to break the mass-eccentricity degeneracy and uniquely determine the masses of the inner, middle, and outer planets to be M = 7.3 ± 6.8 M {sub ⊕}, 4.0 ± 0.9M {sub ⊕}, and M = 132 ± 17 M {sub ⊕}, which we designate PH3 b, c, and d, respectively. Furthermore, the middle planet, PH3 c, has a relatively low density, ρ = 1.2 ± 0.3 g cm{sup –3} for a planet of its mass, requiring a substantial H/He atmosphere of 2.1{sub −0.3}{sup +0.8}% by mass, and joins a growing population of low-mass, low-density planets.

  6. Renormalization group constructions of topological quantum liquids and beyond

    NASA Astrophysics Data System (ADS)

    Swingle, Brian; McGreevy, John

    2016-01-01

    We give a detailed physical argument for the area law for entanglement entropy in gapped phases of matter arising from local Hamiltonians. Our approach is based on renormalization group (RG) ideas and takes a resource oriented perspective. We report four main results. First, we argue for the "weak area law": any gapped phase with a unique ground state on every closed manifold obeys the area law. Second, we introduce an RG based classification scheme and give a detailed argument that all phases within the classification scheme obey the area law. Third, we define a special subclass of gapped phases, topological quantum liquids, which captures all examples of current physical relevance, and we rigorously show that topological quantum liquids obey an area law. Fourth, we show that all topological quantum liquids have MERA representations which achieve unit overlap with the ground state in the thermodynamic limit and which have a bond dimension scaling with system size L as ec logd(1+δ )(L ) for all δ >0 . For example, we show that chiral phases in d =2 dimensions have an approximate MERA with bond dimension ec log2(1+δ )(L ). We discuss extensively a number of subsidiary ideas and results necessary to make the main arguments, including field theory constructions. While our argument for the general area law rests on physically motivated assumptions (which we make explicit) and is therefore not rigorous, we may conclude that "conventional" gapped phases obey the area law and that any gapped phase which violates the area law must be a dragon.

  7. Tensor renormalization group methods for spin and gauge models

    NASA Astrophysics Data System (ADS)

    Zou, Haiyuan

    The analysis of the error of perturbative series by comparing it to the exact solution is an important tool to understand the non-perturbative physics of statistical models. For some toy models, a new method can be used to calculate higher order weak coupling expansion and modified perturbation theory can be constructed. However, it is nontrivial to generalize the new method to understand the critical behavior of high dimensional spin and gauge models. Actually, it is a big challenge in both high energy physics and condensed matter physics to develop accurate and efficient numerical algorithms to solve these problems. In this thesis, one systematic way named tensor renormalization group method is discussed. The applications of the method to several spin and gauge models on a lattice are investigated. theoretically, the new method allows one to write an exact representation of the partition function of models with local interactions. E.g. O(N) models, Z2 gauge models and U(1) gauge models. Practically, by using controllable approximations, results in both finite volume and the thermodynamic limit can be obtained. Another advantage of the new method is that it is insensitive to sign problems for models with complex coupling and chemical potential. Through the new approach, the Fisher's zeros of the 2D O(2) model in the complex coupling plane can be calculated and the finite size scaling of the results agrees well with the Kosterlitz-Thouless assumption. Applying the method to the O(2) model with a chemical potential, new phase diagram of the models can be obtained. The structure of the tensor language may provide a new tool to understand phase transition properties in general.

  8. Numerical Contractor Renormalization applied to strongly correlated systems

    NASA Astrophysics Data System (ADS)

    Capponi, Sylvain

    2006-02-01

    We demonstrate the utility of effective Hamilonians for studying strongly correlated systems, such as quantum spin systems. After defining local relevant degrees of freedom, the numerical Contractor Renormalization (CORE) method is applied in two steps: (i) building an effective Hamiltonian with longer ranged interactions up to a certain cut-off using the CORE algorithm and (ii) solving this new model numerically on finite clusters by exact diagonalization and performing finite-size extrapolations to obtain results in the thermodynamic limit. This approach, giving complementary information to analytical treatments of the CORE Hamiltonian, can be used as a semi-quantitative numerical method. For ladder type geometries, we explicitely check the accuracy of the effective models by increasing the range of the effective interactions until reaching convergence. Our results both in the doped and undoped case are in good agreement with previously established results. In two dimensions we consider the plaquette lattice and the kagomé lattice as non-trivial test cases for the numerical CORE method. As it becomes more difficult to extend the range of the effective interactions in two dimensions, we propose diagnostic tools (such as the density matrix of the local building block) to ascertain the validity of the basis truncation. On the plaquette lattice we have an excellent description of the system in both the disordered and the ordered phases, thereby showing that the CORE method is able to resolve quantum phase transitions. On the kagomé lattice we find that the previously proposed twofold degenerate S = 1/2 basis can account for a large number of phenomena of the spin 1/2 kagomé system and gives a good starting point to study the doped case.

  9. Long-term renormalization of chromatic mechanisms following cataract surgery

    PubMed Central

    Delahunt, Peter B.; Webster, Michael A.; Ma, Lei; Werner, John S.

    2008-01-01

    The optical density of the human crystalline lens progressively increases with age, the greatest increase in the visible spectrum being at short wavelengths. This produces a gradual shift in the spectral distribution of the light reaching the retina, yet color appearance remains relatively stable across the life span, implying that the visual system adapts to compensate for changes in spectral sensitivity. We explored properties of this adaptive renormalization by measuring changes in color appearance following cataract surgery. When the lens is removed, cataract patients often report a large perceptual shift in color appearance that can last for months. This change in color appearance was quantified for four cataract patients (63–84 years) by determining the chromaticity of stimuli that appeared achromatic before surgery, and at various intervals after surgery for up to 1 year. Stimuli were presented on a calibrated CRT as 9.5-deg spots, with 3-s duration and 3-s interstimulus intervals (ISIs). Chromaticity was adjusted by the subjects in CIE L*a*b* color space with luminance fixed at 32 cd/m2, on a dark background. We also estimated the optical density of the cataractous lens by comparing absolute scotopic thresholds from 410 nm to 600 nm before and after surgery. The results demonstrated that immediately following surgery there is a large increase in the short-wave light reaching the retina, mainly below 500 nm. The achromatic settings generally showed an initial large shift in the “yellow” direction after surgery that gradually (but never fully) returned to the original achromatic point before surgery. The shifts in the achromatic point occur over a number of months and appear to occur independently of the fellow eye. PMID:15518204

  10. Modeling turbulent flow over fractal trees with renormalized numerical simulation

    NASA Astrophysics Data System (ADS)

    Chester, Stuart; Meneveau, Charles; Parlange, Marc B.

    2007-07-01

    High-Reynolds number flow over tree-like fractals is considered, with emphasis on the drag forces produced. Fractal objects display large scale-disparity and complexity while being amenable to a simple and standardized description. Hence, they offer an elegant idealization of the actual boundaries in practical applications where turbulence interacts with boundaries that are characterized by multiple length-scales. First, using large-eddy-simulation of flow over prefractal shapes with increasing numbers of branch generations, the dependence of the tree drag on the inner cutoff-scale of the fractal is studied. It is found that the convergence of the drag coefficient towards a value that is independent of inner cutoff-scale is very slow. In order to address this fundamental difficulty and avoid the need to resolve all the small-scale branches of the fractal, a new numerical modeling technique called renormalized numerical simulation (RNS) is introduced. RNS models the drag of the unresolved branches using drag coefficients measured from both resolved branches and unresolved branches as modeled in previous iterations of the procedure. The RNS technique and its convergence properties are tested by means of a series of simulations using different levels of resolution. Then, RNS is used to investigate the influence of the tree fractal dimension on the drag coefficient. The increase of the drag with fractal dimension is quantified for two types of tree geometry, in two flow configurations. Results illustrate that RNS enables numerical modeling of physical processes associated with fractal geometries using affordable computational resolution.

  11. Mass transport in low Tg azo-polymers: Effect on the surface relief grating induction and stability of additional side chain groups able to generate physical interactions

    NASA Astrophysics Data System (ADS)

    Luca, Alina Raicu; Moleavin, Ioana-Andreea; Hurduc, Nicolae; Hamel, Matthieu; Rocha, Licinio

    2014-01-01

    The nanostructuration ability of low glass transition temperature (Tg) azo-polysiloxanes films is investigated at working temperatures close or higher than the film Tg. The behavior of materials incorporating additional side chain nitrobenzene or naphthalene groups and as a result presenting different Tg is compared in terms of the surface modulation dynamics and stability of the induced topographic modifications. This comparison is carried out under light exposure and in dark environment. We demonstrate the ability to optically generate surface modulations on these materials even at operating temperatures corresponding to the film Tg. Along with a modification of the opto-mechanic properties correlated with the materials chemical structure, a collapse of the surface structures occurring with different dynamics in materials of similar Tg is highlighted. These observations suggest the existence of an additional mechanism rather than a purely thermal redistribution of the polymer chains in the films.

  12. Enhanced performance of starter lighting ignition type lead-acid batteries with carbon nanotubes as an additive to the active mass

    NASA Astrophysics Data System (ADS)

    Marom, Rotem; Ziv, Baruch; Banerjee, Anjan; Cahana, Beni; Luski, Shalom; Aurbach, Doron

    2015-11-01

    Addition of various carbon materials into lead-acid battery electrodes was studied and examined in order to enhance the power density, improve cycle life and stability of both negative and positive electrodes in lead acid batteries. High electrical-conductivity, high-aspect ratio, good mechanical properties and chemical stability of multi-wall carbon nanotubes (MWCNT, unmodified and mofified with carboxylic groups) position them as viable additives to enhance the electrodes' electrical conductivity, to mitigate the well-known sulfation failure mechanism and improve the physical integration of the electrodes. In this study, we investigated the incorporation-effect of carbon nanotubes (CNT) to the positive and the negative active materials in lead-acid battery prototypes in a configuration of flooded cells, as well as gelled cells. The cells were tested at 25% and 30% depth-of-discharge (DOD). The positive effect of the carbon nanotubes (CNT) utilization as additives to both positive and negative electrodes of lead-acid batteries was clearly demonstrated and is explained herein based on microscopic studies.

  13. Food additives

    PubMed Central

    Spencer, Michael

    1974-01-01

    Food additives are discussed from the food technology point of view. The reasons for their use are summarized: (1) to protect food from chemical and microbiological attack; (2) to even out seasonal supplies; (3) to improve their eating quality; (4) to improve their nutritional value. The various types of food additives are considered, e.g. colours, flavours, emulsifiers, bread and flour additives, preservatives, and nutritional additives. The paper concludes with consideration of those circumstances in which the use of additives is (a) justified and (b) unjustified. PMID:4467857

  14. Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms

    NASA Astrophysics Data System (ADS)

    Chan, Garnet Kin-Lic; Keselman, Anna; Nakatani, Naoki; Li, Zhendong; White, Steven R.

    2016-07-01

    Current descriptions of the ab initio density matrix renormalization group (DMRG) algorithm use two superficially different languages: an older language of the renormalization group and renormalized operators, and a more recent language of matrix product states and matrix product operators. The same algorithm can appear dramatically different when written in the two different vocabularies. In this work, we carefully describe the translation between the two languages in several contexts. First, we describe how to efficiently implement the ab initio DMRG sweep using a matrix product operator based code, and the equivalence to the original renormalized operator implementation. Next we describe how to implement the general matrix product operator/matrix product state algebra within a pure renormalized operator-based DMRG code. Finally, we discuss two improvements of the ab initio DMRG sweep algorithm motivated by matrix product operator language: Hamiltonian compression, and a sum over operators representation that allows for perfect computational parallelism. The connections and correspondences described here serve to link the future developments with the past and are important in the efficient implementation of continuing advances in ab initio DMRG and related algorithms.

  15. Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms.

    PubMed

    Chan, Garnet Kin-Lic; Keselman, Anna; Nakatani, Naoki; Li, Zhendong; White, Steven R

    2016-07-01

    Current descriptions of the ab initio density matrix renormalization group (DMRG) algorithm use two superficially different languages: an older language of the renormalization group and renormalized operators, and a more recent language of matrix product states and matrix product operators. The same algorithm can appear dramatically different when written in the two different vocabularies. In this work, we carefully describe the translation between the two languages in several contexts. First, we describe how to efficiently implement the ab initio DMRG sweep using a matrix product operator based code, and the equivalence to the original renormalized operator implementation. Next we describe how to implement the general matrix product operator/matrix product state algebra within a pure renormalized operator-based DMRG code. Finally, we discuss two improvements of the ab initio DMRG sweep algorithm motivated by matrix product operator language: Hamiltonian compression, and a sum over operators representation that allows for perfect computational parallelism. The connections and correspondences described here serve to link the future developments with the past and are important in the efficient implementation of continuing advances in ab initio DMRG and related algorithms.

  16. Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms.

    PubMed

    Chan, Garnet Kin-Lic; Keselman, Anna; Nakatani, Naoki; Li, Zhendong; White, Steven R

    2016-07-01

    Current descriptions of the ab initio density matrix renormalization group (DMRG) algorithm use two superficially different languages: an older language of the renormalization group and renormalized operators, and a more recent language of matrix product states and matrix product operators. The same algorithm can appear dramatically different when written in the two different vocabularies. In this work, we carefully describe the translation between the two languages in several contexts. First, we describe how to efficiently implement the ab initio DMRG sweep using a matrix product operator based code, and the equivalence to the original renormalized operator implementation. Next we describe how to implement the general matrix product operator/matrix product state algebra within a pure renormalized operator-based DMRG code. Finally, we discuss two improvements of the ab initio DMRG sweep algorithm motivated by matrix product operator language: Hamiltonian compression, and a sum over operators representation that allows for perfect computational parallelism. The connections and correspondences described here serve to link the future developments with the past and are important in the efficient implementation of continuing advances in ab initio DMRG and related algorithms. PMID:27394094

  17. Block-diagonal similarity renormalization group and effective nucleon-nucleon interactions

    NASA Astrophysics Data System (ADS)

    Szpigel, S.; Timóteo, V. S.; Ruiz Arriola, E.

    2016-04-01

    We apply the block-diagonal similarity renormalization group to a simple toy-model for the nucleon-nucleon (NN) interaction in the 1 S 0 channel, aiming to analyze the complementarity between the explicit and the implicit renormalization approaches in nuclear physics. By explicit renormalization we mean the methods based on the wilsonian renormalization group in which high-energy modes above a given cutoff scale are integrated out while their effects are replaced by scale dependent effective interactions consistently generated in the process. We call implicit renormalization the usual procedure of cutoff effective theories in which the high-energy modes above the cutoff scale are simply removed and their effects are included through parametrized cutoff dependent counterterms whose strengths are fixed by fitting low-energy data. We compare the effective interactions obtained in both schemes and find a wide range of cutoff scales where they overlap. We further analyze the role played by the one-pion exchange (OPE) considering a δ-shell plus OPE representation for the NN interaction.

  18. Gauge-independent overline{MS} renormalization in the 2HDM

    NASA Astrophysics Data System (ADS)

    Denner, Ansgar; Jenniches, Laura; Lang, Jean-Nicolas; Sturm, Christian

    2016-09-01

    We present a consistent renormalization scheme for the CP-conserving Two-Higgs-Doublet Model based on overline{MS} renormalization of the mixing angles and the soft- Z 2-symmetry-breaking scale M sb in the Higgs sector. This scheme requires to treat tadpoles fully consistently in all steps of the calculation in order to provide gauge-independent S-matrix elements. We show how bare physical parameters have to be defined and verify the gauge independence of physical quantities by explicit calculations in a general R ξ -gauge. The procedure is straightforward and applicable to other models with extended Higgs sectors. In contrast to the proposed scheme, the overline{MS} renormalization of the mixing angles combined with popular on-shell renormalization schemes gives rise to gauge-dependent results already at the one-loop level. We present explicit results for electroweak NLO corrections to selected processes in the appropriately renormalized Two-Higgs-Doublet Model and in particular discuss their scale dependence.

  19. Two-Band Fibonacci Quasicrystal with Hybridization:. Exact Local GREEN’S Function Using the Renormalization-Group Method

    NASA Astrophysics Data System (ADS)

    Chakrabarti, A.; Karmakar, S. N.; Moitra, R. K.

    In this paper we present a study of the electronic properties of a one-dimensional Fibonacci chain with two hybridizing bands. Our study is motivated by recent experiments with quasicrystals in which transition metal atoms occupy positions of icosahedral symmetry. Using a recently proposed real space renormalization group scheme we make an exact analytical study of the two-band problem. We examine the effect of hybridization on the energy spectrum, the wave functions and the density of states of the Fibonacci chain. We find that the spectrum continues to remain a Cantor set even in the presence of hybridization. We conclude therefore this property of the spectrum is a purely structural effect. We present our results on the electronic density of states and show how hybridization produces additional structures in the energy spectrum.

  20. Tail effect in gravitational radiation reaction: Time nonlocality and renormalization group evolution

    NASA Astrophysics Data System (ADS)

    Galley, Chad R.; Leibovich, Adam K.; Porto, Rafael A.; Ross, Andreas

    2016-06-01

    We use the effective field theory (EFT) framework to calculate the tail effect in gravitational radiation reaction, which enters at the fourth post-Newtonian order in the dynamics of a binary system. The computation entails a subtle interplay between the near (or potential) and far (or radiation) zones. In particular, we find that the tail contribution to the effective action is nonlocal in time and features both a dissipative and a "conservative" term. The latter includes a logarithmic ultraviolet (UV) divergence, which we show cancels against an infrared (IR) singularity found in the (conservative) near zone. The origin of this behavior in the long-distance EFT is due to the point-particle limit—shrinking the binary to a point—which transforms a would-be infrared singularity into an ultraviolet divergence. This is a common occurrence in an EFT approach, which furthermore allows us to use renormalization group (RG) techniques to resum the resulting logarithmic contributions. We then derive the RG evolution for the binding potential and total mass/energy, and find agreement with the results obtained imposing the conservation of the (pseudo) stress-energy tensor in the radiation theory. While the calculation of the leading tail contribution to the effective action involves only one diagram, five are needed for the one-point function. This suggests logarithmic corrections may be easier to incorporate in this fashion. We conclude with a few remarks on the nature of these IR/UV singularities, the (lack of) ambiguities recently discussed in the literature, and the completeness of the analytic post-Newtonian framework.

  1. Functional renormalization group analysis of the soft mode at the QCD critical point

    NASA Astrophysics Data System (ADS)

    Yokota, Takeru; Kunihiro, Teiji; Morita, Kenji

    2016-07-01

    We make an intensive investigation of the soft mode at the quantum chromodynamics (QCD) critical point on the basis of the functional renormalization group (FRG) method in the local potential approximation. We calculate the spectral functions ρ_{σ, π}(ω, p) in the scalar (σ) and pseudoscalar (π) channels beyond the random phase approximation in the quark-meson model. At finite baryon chemical potential μ with a finite quark mass, the baryon-number fluctuation is coupled to the scalar channel and the spectral function in the σ channel has a support not only in the time-like (ω > p) but also in the space-like (ω < p) regions, which correspond to the mesonic and the particle-hole phonon excitations, respectively. We find that the energy of the peak position of the latter becomes vanishingly small with the height being enhanced as the system approaches the QCD critical point, which is a manifestation of the fact that the phonon mode is the soft mode associated with the second-order transition at the QCD critical point, as has been suggested by some authors. Moreover, our extensive calculation of the spectral function in the (ω, p) plane enables us to see that the mesonic and phonon modes have the respective definite dispersion relations ω_{σ.ph}(p), and it turns out that ω_{σ}(p) crosses the light-cone line into the space-like region, and then eventually merges into the phonon mode as the system approaches the critical point more closely. This implies that the sigma-mesonic mode also becomes soft at the critical point. We also provide numerical stability conditions that are necessary for obtaining the accurate effective potential from the flow equation.

  2. Renormalization group estimates of transport coefficients in the advection of a passive scalar by incompressible turbulence

    NASA Technical Reports Server (NTRS)

    Zhou, YE; Vahala, George

    1993-01-01

    The advection of a passive scalar by incompressible turbulence is considered using recursive renormalization group procedures in the differential sub grid shell thickness limit. It is shown explicitly that the higher order nonlinearities induced by the recursive renormalization group procedure preserve Galilean invariance. Differential equations, valid for the entire resolvable wave number k range, are determined for the eddy viscosity and eddy diffusivity coefficients, and it is shown that higher order nonlinearities do not contribute as k goes to 0, but have an essential role as k goes to k(sub c) the cutoff wave number separating the resolvable scales from the sub grid scales. The recursive renormalization transport coefficients and the associated eddy Prandtl number are in good agreement with the k-dependent transport coefficients derived from closure theories and experiments.

  3. Numerical Real Space Renormalization of a 2D Random Boson Model

    NASA Astrophysics Data System (ADS)

    Iyer, Shankar; Refael, Gil

    2011-03-01

    Interest in the random boson problem originated in experiments on Helium adsorbed in Vycor, but the problem arises in many contexts, including Josephson junction arrays and disordered cold atom systems. Recently, Altman, Kafri, Polkovnikov, and Refael have studied a rotor model description of interacting bosons subjected to quenched disorder in one dimension. Using a real space renormalization approach, they have identified a random fixed point that marks the transition between superfluid and Mott-glass phases. Here, we describe work that numerically extends their approach to the random boson problem in two dimensions. We first test the validity of the real space renormalization by comparison to exact diagonalization of small systems. Then, we move to larger systems and explore what the renormalization scheme can tell us about the nature of the insulating and superfluid phases.

  4. A simple method for one-loop renormalization in curved space-time

    SciTech Connect

    Markkanen, Tommi; Tranberg, Anders E-mail: anders.tranberg@uis.no

    2013-08-01

    We present a simple method for deriving the renormalization counterterms from the components of the energy-momentum tensor in curved space-time. This method allows control over the finite parts of the counterterms and provides explicit expressions for each term separately. As an example, the method is used for the self-interacting scalar field in a Friedmann-Robertson-Walker metric in the adiabatic approximation, where we calculate the renormalized equation of motion for the field and the renormalized components of the energy-momentum tensor to fourth adiabatic order while including interactions to one-loop order. Within this formalism the trace anomaly, including contributions from interactions, is shown to have a simple derivation. We compare our results to those obtained by two standard methods, finding agreement with the Schwinger-DeWitt expansion but disagreement with adiabatic subtractions for interacting theories.

  5. Non-renormalization of the V c bar c-vertices in N = 1 supersymmetric theories

    NASA Astrophysics Data System (ADS)

    Stepanyantz, K. V.

    2016-08-01

    Using the Slavnov-Taylor identities we prove that the three-point ghost vertices with a single line of the quantum gauge superfield are not renormalized in all loops in N = 1 supersymmetric gauge theories. This statement is verified by the explicit one-loop calculation made by the help of the BRST invariant version of the higher covariant derivative regularization. Using the restrictions to the renormalization constants which are imposed by the non-renormalization of the considered vertices we express the exact NSVZ β-function in terms of the anomalous dimensions of the Faddeev-Popov ghosts and of the quantum gauge superfield. In the expression for the NSVZ β-function obtained in this way the contributions of the Faddeev-Popov ghosts and of the matter superfields have the same structure.

  6. Strong disorder renormalization group primer and the superfluid-insulator transition

    NASA Astrophysics Data System (ADS)

    Refael, Gil; Altman, Ehud

    2013-10-01

    This brief review introduces the method and application of real-space renormalization group to strongly disordered quantum systems. The focus is on recent applications of the strong disorder renormalization group to the physics of disordered-boson systems and the superfluid-insulator transition in one dimension. The fact that there is also a well-understood weak disorder theory for this problem allows us to illustrate what aspects of the physics change at strong disorder. In particular, the strong disorder RG analysis suggests that the transitions at weak disorder and strong disorder belong to distinct universality classes, but this question remains under debate and is not fully resolved to date. Further applications of the strong disorder renormalization group to higher-dimensional Bose systems and to bosons coupled to dissipation are also briefly reviewed.

  7. Systematic renormalization scheme in light-front dynamics with Fock space truncation

    SciTech Connect

    Karmanov, V. A.; Smirnov, A. V.; Mathiot, J.-F.

    2008-04-15

    Within the framework of the covariant formulation of light-front dynamics, we develop a general nonperturbative renormalization scheme based on the Fock decomposition of the state vector and its truncation. The counterterms and bare parameters needed to renormalize the theory depend on the Fock sectors. We present a general strategy in order to calculate these quantities, as well as state vectors of physical systems, in a truncated Fock space. The explicit dependence of our formalism on the orientation of the light-front plane is essential in order to analyze the structure of the counterterms. We apply our formalism to the two-body (one fermion and one boson) truncation in the Yukawa model and in QED, and to the three-body truncation in a scalar model. In QED, we recover analytically, without any perturbative expansion, the renormalization of the electric charge, according to the requirements of the Ward identity.

  8. Renormalization-group approach to the vulcanization transition

    PubMed

    Peng; Goldbart

    2000-04-01

    The vulcanization transition-the cross-link-density-controlled equilibrium phase transition from the liquid to the amorphous solid state-is explored analytically from a renormalization-group perspective. The analysis centers on a minimal model which has previously been shown to yield a rich and informative picture of vulcanized matter at the mean-field level, including a connection with mean-field percolation theory (i.e., random graph theory). This minimal model accounts for both the thermal motion of the constituents and the quenched random constraints imposed on their motion by the cross-links, as well as particle-particle repulsion which suppresses density fluctuations and plays a pivotal role in determining the symmetry structure (and hence properties) of the model. A correlation function involving fluctuations of the amorphous solid order parameter, the behavior of which signals the vulcanization transition, is examined, its physical meaning is elucidated, and the associated susceptibility is constructed and analyzed. A Ginzburg criterion for the width (in cross-link density) of the critical region is derived and is found to be consistent with a prediction due to de Gennes. Inter alia, this criterion indicates that the upper critical dimension for the vulcanization transition is 6. Certain universal critical exponents characterizing the vulcanization transition are computed, to lowest nontrivial order, within the framework of an expansion around the upper critical dimension. This expansion shows that the connection between vulcanization and percolation extends beyond mean-field theory, surviving the incorporation of fluctuations in the sense that pairs of physically analogous quantities (one percolation related and one vulcanization related) are found to be governed by identical critical exponents, at least to first order in the departure from the upper critical dimension (and presumably beyond). The relationship between the present approach to vulcanized

  9. Multiresidue method for the simultaneous determination of veterinary medicinal products, feed additives and illegal dyes in eggs using liquid chromatography-tandem mass spectrometry.

    PubMed

    Piatkowska, Marta; Jedziniak, Piotr; Zmudzki, Jan

    2016-04-15

    A multiclass method was developed for the simultaneous determination of 120 analytes in fresh eggs. The method covers the analytes from the groups of tetracyclines (6), fluoroquinolones (11), sulphonamides (17), nitroimidazoles (9), amphenicols (2), cephalosporins (7), penicillins (8), macrolides (8), benzimidazoles (20), coccidiostats (14), insecticides (3), dyes (12) and others (3). Samples were extracted using 0.1% formic acid in acetonitrile:water (8:2) with the addition of EDTA and cleaned using solid phase extraction with Hybrid SPE cartridges. The chromatographic separation was achieved on C8 column using mobile phase consisting of (A) methanol:acetonitrile (8:2) - (B) 0.1% formic acid in a gradient mode. Validation results according to the Commission Decision 2002/657/EC are as follows: linearity (r⩾0.99), recovery (75-108%), repeatability (CV 1.60-15.9%), reproducibility (CV 2.60-15%), decision limit (CCα 2.25-1156 μg/kg) and detection capability (CCβ 2.04-1316 μg/kg). The presented method was used for analysis of 150 real eggs samples taken from monitoring control program. PMID:26616990

  10. Multiresidue method for the simultaneous determination of veterinary medicinal products, feed additives and illegal dyes in eggs using liquid chromatography-tandem mass spectrometry.

    PubMed

    Piatkowska, Marta; Jedziniak, Piotr; Zmudzki, Jan

    2016-04-15

    A multiclass method was developed for the simultaneous determination of 120 analytes in fresh eggs. The method covers the analytes from the groups of tetracyclines (6), fluoroquinolones (11), sulphonamides (17), nitroimidazoles (9), amphenicols (2), cephalosporins (7), penicillins (8), macrolides (8), benzimidazoles (20), coccidiostats (14), insecticides (3), dyes (12) and others (3). Samples were extracted using 0.1% formic acid in acetonitrile:water (8:2) with the addition of EDTA and cleaned using solid phase extraction with Hybrid SPE cartridges. The chromatographic separation was achieved on C8 column using mobile phase consisting of (A) methanol:acetonitrile (8:2) - (B) 0.1% formic acid in a gradient mode. Validation results according to the Commission Decision 2002/657/EC are as follows: linearity (r⩾0.99), recovery (75-108%), repeatability (CV 1.60-15.9%), reproducibility (CV 2.60-15%), decision limit (CCα 2.25-1156 μg/kg) and detection capability (CCβ 2.04-1316 μg/kg). The presented method was used for analysis of 150 real eggs samples taken from monitoring control program.

  11. Setting the Renormalization Scale in QCD: The Principle of Maximum Conformality

    SciTech Connect

    Brodsky, Stanley J.; Di Giustino, Leonardo; /SLAC

    2011-08-19

    A key problem in making precise perturbative QCD predictions is the uncertainty in determining the renormalization scale {mu} of the running coupling {alpha}{sub s}({mu}{sup 2}): The purpose of the running coupling in any gauge theory is to sum all terms involving the {beta} function; in fact, when the renormalization scale is set properly, all non-conformal {beta} {ne} 0 terms in a perturbative expansion arising from renormalization are summed into the running coupling. The remaining terms in the perturbative series are then identical to that of a conformal theory; i.e., the corresponding theory with {beta} = 0. The resulting scale-fixed predictions using the 'principle of maximum conformality' (PMC) are 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 is also the theoretical principle underlying the BLM procedure, commensurate scale relations between observables, and the scale-setting method used in lattice gauge theory. The number of active flavors nf in the QCD {beta} function is also correctly determined. We discuss several methods for determining the PMC/BLM scale for QCD processes. We show that a single global PMC scale, valid at leading order, can be derived from basic properties of the perturbative QCD cross section. The elimination of the renormalization scheme ambiguity using the PMC will not only increase the precision of QCD tests, but it will also increase the sensitivity of collider experiments to new physics beyond the Standard Model.

  12. Eliminating the Renormalization Scale Ambiguity for Top-Pair Production Using the Principle of Maximum Conformality

    SciTech Connect

    Brodsky, Stanley J.; Wu, Xing-Gang; /Chongqing U.

    2012-04-02

    The uncertainty in setting the renormalization scale in finite-order perturbative QCD predictions using standard methods substantially reduces the precision of tests of the Standard Model in collider experiments. It is conventional to choose a typical momentum transfer of the process as the renormalization scale and take an arbitrary range to estimate the uncertainty in the QCD prediction. However, predictions using this procedure depend on the choice of renormalization scheme, leave a non-convergent renormalon perturbative series, and moreover, one obtains incorrect results when applied to QED processes. In contrast, if one fixes the renormalization scale using the Principle of Maximum Conformality (PMC), all non-conformal {l_brace}{beta}{sub i}{r_brace}-terms in the perturbative expansion series are summed into the running coupling, and one obtains a unique, scale-fixed, scheme-independent prediction at any finite order. The PMC renormalization scale {mu}{sub R}{sup PMC} and the resulting finite-order PMC prediction are both to high accuracy independent of choice of the initial renormalization scale {mu}{sub R}{sup init}, consistent with renormalization group invariance. Moreover, after PMC scale-setting, the n!-growth of the pQCD expansion is eliminated. Even the residual scale-dependence at fixed order due to unknown higher-order {l_brace}{beta}{sub i}{r_brace}-terms is substantially suppressed. As an application, we apply the PMC procedure to obtain NNLO predictions for the t{bar t}-pair hadroproduction cross-section at the Tevatron and LHC colliders. There are no renormalization scale or scheme uncertainties, thus greatly improving the precision of the QCD prediction. The PMC prediction for {sigma}{sub t{bar t}} is larger in magnitude in comparison with the conventional scale-setting method, and it agrees well with the present Tevatron and LHC data. We also verify that the initial scale-independence of the PMC prediction is satisfied to high accuracy at the

  13. Dimensional versus cut-off renormalization and the nucleon-nucleon interaction

    NASA Astrophysics Data System (ADS)

    Ghosh, Angsula; Adhikari, Sadhan K.; Talukdar, B.

    1998-10-01

    The role of dimensional regularization is discussed and compared with that of cut-off regularization in some quantum mechanical problems with ultraviolet divergence in two and three dimensions with special emphasis on the nucleon-nucleon interaction. Both types of renormalizations are performed for attractive divergent one- and two-term separable potentials, a divergent tensor potential, and the sum of a delta function and its derivatives. We allow energy-dependent couplings, and determine the form that these couplings should take if equivalence between the two regularization schemes is to be enforced. We also perform renormalization of an attractive separable potential superposed on an analytic divergent potential.

  14. Decoherence in a double-dot Aharonov-Bohm interferometer: Numerical renormalization group study

    NASA Astrophysics Data System (ADS)

    Kubala, Björn; Roosen, David; Sindel, Michael; Hofstetter, Walter; Marquardt, Florian

    2014-07-01

    Coherence in electronic interferometers is typically believed to be restored fully in the limit of small voltages, frequencies, and temperatures. However, it is crucial to check this essentially perturbative argument by nonperturbative methods. Here we use the numerical renormalization group to study ac transport and decoherence in an experimentally realizable model interferometer, a parallel double quantum dot coupled to a phonon mode. The model allows us to clearly distinguish renormalization effects from decoherence. We discuss finite-frequency transport and confirm the restoration of coherence in the dc limit.

  15. Symmetric blocking and renormalization in lattice N=4 super Yang-Mills

    NASA Astrophysics Data System (ADS)

    Giedt, Joel; Catterall, Simon

    2015-04-01

    The form of the long distance effective action of the twisted lattice N = 4 super Yang-Mills theory depends on having a real space renormalization group transformation that preserves the original lattice properties, both the symmetries and the geometric interpretation of the fields. We have found such a transformation and have exhibited its behavior through a preliminary Monte Carlo renormalization group calculation. Other results regarding the number of counterterms are also obtained by considering rescalings of the lattice fields. Supported by Department of Energy, Office of Science, Office of High Energy Physics Grants DE-FG02-08ER41575 and SC0009998.

  16. Renormalization in charged colloids: non-monotonic behaviour with the surface charge.

    PubMed

    Haro-Pérez, C; Quesada-Pérez, M; Callejas-Fernández, J; Schurtenberger, P; Hidalgo-Álvarez, R

    2006-07-19

    The static structure factor S(q) is measured for a set of deionized latex dispersions with different numbers of ionizable surface groups per particle and similar diameters. For a given volume fraction, the height of the main peak of S(q), which is a direct measure of the spatial ordering of latex particles, does not increase monotonically with the number of ionizable groups. This behaviour cannot be described using the classical renormalization scheme based on the cell model. We analyse our experimental data using a renormalization model based on the jellium approximation, which predicts the weakening of the spatial order for moderate and large particle charges.

  17. Hopf-algebraic renormalization of QED in the linear covariant gauge

    NASA Astrophysics Data System (ADS)

    Kißler, Henry

    2016-09-01

    In the context of massless quantum electrodynamics (QED) with a linear covariant gauge fixing, the connection between the counterterm and the Hopf-algebraic approach to renormalization is examined. The coproduct formula of Green's functions contains two invariant charges, which give rise to different renormalization group functions. All formulas are tested by explicit computations to third loop order. The possibility of a finite electron self-energy by fixing a generalized linear covariant gauge is discussed. An analysis of subdivergences leads to the conclusion that such a gauge only exists in quenched QED.

  18. Dynamical and anharmonic effects on the electron-phonon coupling and the zero-point renormalization of the electronic structure

    NASA Astrophysics Data System (ADS)

    Antonius, G.; Poncé, S.; Lantagne-Hurtubise, E.; Auclair, G.; Gonze, X.; Côté, M.

    2015-08-01

    The renormalization of the band structure at zero temperature due to electron-phonon coupling is explored in diamond, BN, LiF, and MgO crystals. We implement a dynamical scheme to compute the frequency-dependent self-energy and the resulting quasiparticle electronic structure. Our calculations reveal the presence of a satellite band below the Fermi level of LiF and MgO. We show that the renormalization factor (Z ), which is neglected in the adiabatic approximation, can reduce the zero-point renormalization (ZPR) by as much as 40 % . Anharmonic effects in the renormalized eigenvalues at finite atomic displacements are explored with the frozen-phonon method. We use a nonperturbative expression for the ZPR, going beyond the Allen-Heine-Cardona theory. Our results indicate that high-order electron-phonon coupling terms contribute significantly to the zero-point renormalization for certain materials.

  19. Many-Body Effects on Bandgap Shrinkage, Effective Masses, and Alpha Factor

    NASA Technical Reports Server (NTRS)

    Li, Jian-Zhong; Ning, C. Z.; Woo, Alex C. (Technical Monitor)

    2000-01-01

    Many-body Coulomb effects influence the operation of quantum-well (QW) laser diode (LD) strongly. In the present work, we study a two-band electron-hole plasma (EHP) within the Hatree-Fock approximation and the single plasmon pole approximation for static screening. Full inclusion of momentum dependence in the many-body effects is considered. An empirical expression for carrier density dependence of the bandgap renormalization (BGR) in an 8 nm GaAs/Al(0.3)G(4.7)As single QW will be given, which demonstrates a non-universal scaling behavior for quasi-two-dimension structures, due to size-dependent efficiency of screening. In addition, effective mass renormalization (EMR) due to momentum-dependent self-energy many-body correction, for both electrons and holes is studied and serves as another manifestation of the many-body effects. Finally, the effects on carrier density dependence of the alpha factor is evaluated to assess the sensitivity of the full inclusion of momentum dependence.

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

    SciTech Connect

    Ambroso, Michael; Ovrut, Burt A.

    2011-04-10

    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.

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

    DOE PAGES

    Ambroso, Michael; Ovrut, Burt A.

    2011-04-10

    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 anmore » 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.« less

  2. Self-interaction in the Bopp–Podolsky electrodynamics: Can the observable mass of a charged particle depend on its acceleration?

    SciTech Connect

    Zayats, Alexei E.

    2014-03-15

    In this paper we obtain the expression for the self-force in the model with the Lagrangian containing additional terms, quadratic in Maxwell tensor derivatives (so-called Bopp–Podolsky electrodynamics). Features of this force are analyzed for various limiting cases. When a charged particle moves along straight line with a uniform acceleration, an explicit formula is found. In the framework of the considered model, an observable renormalized particle mass is shown to depend on its acceleration. This dependence allows, in principle, to extract experimentally a value of the particle bare mass. -- Highlights: •An expression for the self-force in the Bopp–Podolsky electrodynamics is given. •For a uniformly accelerated charged particle an explicit formula for the self-force is obtained. •Dependence between the observable mass of a charged particle and its acceleration is found.

  3. Global fits of the two-loop renormalized Two-Higgs-Doublet model with soft Z 2 breaking

    NASA Astrophysics Data System (ADS)

    Chowdhury, Debtosh; Eberhardt, Otto

    2015-11-01

    We determine the next-to-leading order renormalization group equations for the Two-Higgs-Doublet model with a softly broken Z 2 symmetry and CP conservation in the scalar potential. We use them to identify the parameter regions which are stable up to the Planck scale and find that in this case the quartic couplings of the Higgs potential cannot be larger than 1 in magnitude and that the absolute values of the S-matrix eigenvalues cannot exceed 2 .5 at the electroweak symmetry breaking scale. Interpreting the 125 GeV resonance as the light CP -even Higgs eigenstate, we combine stability constraints, electroweak precision and flavour observables with the latest ATLAS and CMS data on Higgs signal strengths and heavy Higgs searches in global parameter fits to all four types of Z 2 symmetry. We quantify the maximal deviations from the alignment limit and find that in type II and Y the mass of the heavy CP -even ( CP -odd) scalar cannot be smaller than 340 GeV (360 GeV). Also, we pinpoint the physical parameter regions compatible with a stable scalar potential up to the Planck scale. Motivated by the question how natural a Higgs mass of 125 GeV can be in the context of a Two-Higgs-Doublet model, we also address the hierarchy problem and find that the Two-Higgs-Doublet model does not offer a perturbative solution to it beyond 5 TeV.

  4. No-core Monte Carlo shell model calculations with unitary correlation operator method and similarity renormalization group

    NASA Astrophysics Data System (ADS)

    Liu, Lang

    2015-05-01

    The unitary correlation operator method (UCOM) and the similarity renormalization group theory (SRG) are compared and discussed in the framework of the no-core Monte Carlo shell model (MCSM) calculations for 3H and 4He. The treatment of spurious center-of-mass motion by Lawson's prescription is performed in the MCSM calculations. These results with both transformed interactions show good suppression of spurious center-of-mass motion with proper Lawson's prescription parameter βc.m. values. The UCOM potentials obtain faster convergence of total energy for the ground state than that of SRG potentials in the MCSM calculations, which differs from the cases in the no-core shell model calculations (NCSM). These differences are discussed and analyzed in terms of the truncation scheme in the MCSM and NCSM, as well as the properties of the potentials of SRG and UCOM. Supported by Fundamental Research Funds for the Central Universities (JUSRP1035), National Natural Science Foundation of China (11305077)

  5. Density matrix renormalization group with efficient dynamical electron correlation through range separation

    SciTech Connect

    Hedegård, Erik Donovan Knecht, Stefan; Reiher, Markus; Kielberg, Jesper Skau; Jensen, Hans Jørgen Aagaard

    2015-06-14

    We present a new hybrid multiconfigurational method based on the concept of range-separation that combines the density matrix renormalization group approach with density functional theory. This new method is designed for the simultaneous description of dynamical and static electron-correlation effects in multiconfigurational electronic structure problems.

  6. The energy localization problem and the renormalized vacuum energy in static Robertson-Walker universes

    NASA Astrophysics Data System (ADS)

    Baym, Selçuk Ş.

    1994-10-01

    We calculate the renormalized quantum vacuum energy inside a spherical boundary for the massless conformal scalar field in curved background Robertson-Walker geometry. We use the mode sum method with an exponential cutoff. In our calculations we do not make assumptions about the exterior geometry or the global topology of the universe.

  7. Renormalized entropy solutions of the Cauchy problem for a first-order inhomogeneous quasilinear equation

    SciTech Connect

    Panov, E Yu

    2013-10-31

    The concept of a renormalized entropy solution of the Cauchy problem for an inhomogeneous quasilinear equation of the first order is introduced. Existence and uniqueness theorems are proved, together with a comparison principle. Connections with generalized entropy solutions are investigated. Bibliography: 10 titles.

  8. Electron-Phonon Renormalization of Electronic Band Structures of C Allotropes and BN Polymorphs

    NASA Astrophysics Data System (ADS)

    Tutchton, Roxanne M.; Marchbanks, Christopher; Wu, Zhigang

    The effect of lattice vibration on electronic band structures has been mostly neglected in first-principles calculations because the electron-phonon (e-ph) renormalization of quasi-particle energies is often small (< 100 meV). However, in certain materials, such as diamond, the electron-phonon coupling reduces the band gap by nearly 0.5 eV, which is comparable to the many-body corrections of the electronic band structures calculated using the density functional theory (DFT). In this work, we compared two implementations of the Allen-Heine-Cardona theory in the EPW code and the ABINIT package respectively. Our computations of Si and diamond demonstrate that the ABINIT implementation converges much faster. Using this method, the e-ph renormalizations of electronic structures of three C allotropes (diamond, graphite, graphene) and four BN polymorphs (zincblend, wurtzite, mono-layer, and layered-hexagonal) were calculated. Our results suggest that (1) all of the zero-point renormalizations of band gaps in these materials, except for graphene, are larger than 100 meV, and (2) there are large variations in e-ph renormalization of band gaps due to differences in crystal structure. This work was supported by a U.S. DOE Early Career Award (Grant No. DE-SC0006433). Computations were carried out at the Golden Energy Computing Organization at CSM and the National Energy Research Scientific Computing Center (NERSC).

  9. Phase diagram and critical end point in nonlocal PNJL models with wavefunction renormalization

    SciTech Connect

    Contrera, Gustavo A.; Orsaria, Milva G.; Scoccola, Norberto N.

    2010-11-12

    We study the chiral phase transition at finite temperature and chemical potential considering a non-local chiral quark model which includes wave-function renormalization and coupling to the Polyakov loop. In particular, we determine the position of the Critical End Point as well as the value of the associated critical exponents for different model parameterizations.

  10. Global solutions to two nonlinear perturbed equations by renormalization group method

    NASA Astrophysics Data System (ADS)

    Kai, Yue

    2016-02-01

    In this paper, according to the theory of envelope, the renormalization group (RG) method is applied to obtain the global approximate solutions to perturbed Burger's equation and perturbed KdV equation. The results show that the RG method is simple and powerful for finding global approximate solutions to nonlinear perturbed partial differential equations arising in mathematical physics.

  11. Solutions of the renormalization-group equations for minimal supergravity SU(5) grand unified theory and strong constraints on its parameters

    SciTech Connect

    Matsumoto, M.; Arafune, J. ); Tanaka, H. ); Shiraishi, K. )

    1992-11-01

    A minimal {ital N}=1 supergravity SU(5) grand unified theory (GUT) is studied for a heavy top-quark mass ({ital m}{sub {ital t}}{ge}90 GeV). Renormalization-group equations are solved without neglecting the Yukawa couplings for the third generation of quarks and leptons. The solutions for mass parameters are expressed as linear combinations of the initial-value parameters of the model at the GUT scale and the coefficients are numerically obtained. This semianalytical expression of the solutions makes it easy to use the results for low-energy phenomenology. Approximate analytical solutions valid for small tan{beta} ({lt}8) are also given. Combining theoretical considerations with experimental restrictions due to the CERN {ital e}{sup +}{ital e{minus}} collider LEP, the Collider Detector at Fermilab (CDF), and the proton decay experiments of Kamiokande, we can show that the very limited supersymmetric parameter space remains allowed.

  12. Phosphazene additives

    DOEpatents

    Harrup, Mason K; Rollins, Harry W

    2013-11-26

    An additive comprising a phosphazene compound that has at least two reactive functional groups and at least one capping functional group bonded to phosphorus atoms of the phosphazene compound. One of the at least two reactive functional groups is configured to react with cellulose and the other of the at least two reactive functional groups is configured to react with a resin, such as an amine resin of a polycarboxylic acid resin. The at least one capping functional group is selected from the group consisting of a short chain ether group, an alkoxy group, or an aryloxy group. Also disclosed are an additive-resin admixture, a method of treating a wood product, and a wood product.

  13. Potlining Additives

    SciTech Connect

    Rudolf Keller

    2004-08-10

    In this project, a concept to improve the performance of aluminum production cells by introducing potlining additives was examined and tested. Boron oxide was added to cathode blocks, and titanium was dissolved in the metal pool; this resulted in the formation of titanium diboride and caused the molten aluminum to wet the carbonaceous cathode surface. Such wetting reportedly leads to operational improvements and extended cell life. In addition, boron oxide suppresses cyanide formation. This final report presents and discusses the results of this project. Substantial economic benefits for the practical implementation of the technology are projected, especially for modern cells with graphitized blocks. For example, with an energy savings of about 5% and an increase in pot life from 1500 to 2500 days, a cost savings of $ 0.023 per pound of aluminum produced is projected for a 200 kA pot.

  14. Long range dynamics of shallow water: renormalization, modulation and long cycles.

    NASA Astrophysics Data System (ADS)

    Gurarie, David

    2000-11-01

    Long-range dynamics of rotating shallow water (RSW) in the low Rossby-Froude regime, Ro = Fr ll1, exhibits multiscale structure with oscillations on different scales, from fast (gravity), to slower ``eddy turnover" , and yet slower ``long weather cycles". We search for an effective theory, that would ``average" fast oscillations on each scale, to produce higher level ``slow evolution". The principal source of fast gravity waves - dominant linear dispersion, could be eliminated by passing to the amplitude equations. In nonlinear systems, however, it does not remove oscillations completely, but transplants them to nonlinear terms. We implement the Bogoliubov-Mitropolskii averaging (BM) to produce renormalized system (RN-RSW), made of the resonant quadratic part of RSW, plus order(Ro) - cubic, and O(Ro^2) - quartic corrections. Renormalized system evolves on the first slow scale. Next we conduct the detailed analysis of RN-RSW for a single 9D-Lorenz-type triad. The triad system allows to implement second renormalization (from ``first slow" to ``second slow" time), based on its 5 adiabatic invariants: two conserved integrals of QGS-oscillator (a 3D subsystem, solvable in Jacobi elliptic functions), and three wave-intensities. The adiabatic invariants evolve on the second slow scale, and describe slow modulation of the basic QGS (Jacobi) parameters: modulus, period, magnitude. The off-shot of our two-step renormalization (BM followed by ``adiabatic averaging") are ``modulated oscillations" of the vortical and gravity modes. We verify the modulation phenomena by numeric simulations of (i) complete RSW-triad, vs. (ii) renormalized system (RN-RSW), vs. (iii) its ``modulated (adiabatic) approximation". All three show good qualitative agreement in their gross features. The analysis of adiabatic system explains some long range phases of the RSW-dynamics, like nonlinear ``relaxation", and ``intensification" regimes, and pinpoints ``modulation" as the principal long

  15. Constraining the MSSM sfermion mass matrices with light fermion masses

    SciTech Connect

    Crivellin, Andreas; Girrbach, Jennifer

    2010-04-01

    We study the finite supersymmetric loop corrections to fermion masses and mixing matrices in the generic MSSM. In this context the effects of non-decoupling chirally-enhanced self-energies are studied beyond leading order in perturbation theory. These NLO corrections are not only necessary for the renormalization of the CKM matrix to be unitary, they are also numerically important for the light fermion masses. Focusing on the trilinear A-terms with generic flavor-structure we derive very strong bounds on the chirality-changing mass insertions {delta}{sub IJ}{sup fLR,RL} by applying 't Hooft's naturalness criterion. In particular, the NLO corrections to the up quark mass allow us to constrain the unbounded element {delta}{sub 13}{sup uRL} if at the same time {delta}{sub 13}{sup uLR} is unequal to zero. Our result is important for single-top production at the LHC.

  16. Liquid chromatography coupled to different atmospheric pressure ionization sources-quadrupole-time-of-flight mass spectrometry and post-column addition of metal salt solutions as a powerful tool for the metabolic profiling of Fusarium oxysporum.

    PubMed

    Cirigliano, Adriana M; Rodriguez, M Alejandra; Gagliano, M Laura; Bertinetti, Brenda V; Godeas, Alicia M; Cabrera, Gabriela M

    2016-03-25

    Fusarium oxysporum L11 is a non-pathogenic soil-borne fungal strain that yielded an extract that showed antifungal activity against phytopathogens. In this study, reversed-phase high-performance liquid chromatography (RP-HPLC) coupled to different atmospheric pressure ionization sources-quadrupole-time-of-flight mass spectrometry (API-QTOF-MS) was applied for the comprehensive profiling of the metabolites from the extract. The employed sources were electrospray (ESI), atmospheric pressure chemical ionization (APCI) and atmospheric pressure photoionization (APPI). Post-column addition of metal solutions of Ca, Cu and Zn(II) was also tested using ESI. A total of 137 compounds were identified or tentatively identified by matching their accurate mass signals, suggested molecular formulae and MS/MS analysis with previously reported data. Some compounds were isolated and identified by NMR. The extract was rich in cyclic peptides like cyclosporins, diketopiperazines and sansalvamides, most of which were new, and are reported here for the first time. The use of post-column addition of metals resulted in a useful strategy for the discrimination of compound classes since specific adducts were observed for the different compound families. This technique also allowed the screening for compounds with metal binding properties. Thus, the applied methodology is a useful choice for the metabolic profiling of extracts and also for the selection of metabolites with potential biological activities related to interactions with metal ions.

  17. Liquid chromatography coupled to different atmospheric pressure ionization sources-quadrupole-time-of-flight mass spectrometry and post-column addition of metal salt solutions as a powerful tool for the metabolic profiling of Fusarium oxysporum.

    PubMed

    Cirigliano, Adriana M; Rodriguez, M Alejandra; Gagliano, M Laura; Bertinetti, Brenda V; Godeas, Alicia M; Cabrera, Gabriela M

    2016-03-25

    Fusarium oxysporum L11 is a non-pathogenic soil-borne fungal strain that yielded an extract that showed antifungal activity against phytopathogens. In this study, reversed-phase high-performance liquid chromatography (RP-HPLC) coupled to different atmospheric pressure ionization sources-quadrupole-time-of-flight mass spectrometry (API-QTOF-MS) was applied for the comprehensive profiling of the metabolites from the extract. The employed sources were electrospray (ESI), atmospheric pressure chemical ionization (APCI) and atmospheric pressure photoionization (APPI). Post-column addition of metal solutions of Ca, Cu and Zn(II) was also tested using ESI. A total of 137 compounds were identified or tentatively identified by matching their accurate mass signals, suggested molecular formulae and MS/MS analysis with previously reported data. Some compounds were isolated and identified by NMR. The extract was rich in cyclic peptides like cyclosporins, diketopiperazines and sansalvamides, most of which were new, and are reported here for the first time. The use of post-column addition of metals resulted in a useful strategy for the discrimination of compound classes since specific adducts were observed for the different compound families. This technique also allowed the screening for compounds with metal binding properties. Thus, the applied methodology is a useful choice for the metabolic profiling of extracts and also for the selection of metabolites with potential biological activities related to interactions with metal ions. PMID:26655791

  18. Pion and η -meson mass splitting at the two-flavor chiral crossover

    NASA Astrophysics Data System (ADS)

    Heller, Markus; Mitter, Mario

    2016-10-01

    We study the splitting in the screening mass of pions and the η -meson across the chiral crossover. This splitting is determined by the 't Hooft determinant. We use results for the renormalization group scale dependence of the 't Hooft determinant obtained within the functional renormalization group in quenched QCD with two flavors. The scale dependence of the 't Hooft determinant is mapped to its temperature dependence with the help of a Polyakov-quark-meson model. As a result we obtain the temperature dependence of the splitting in the screening mass of pions and the η -meson.

  19. PyR@TE. Renormalization group equations for general gauge theories

    NASA Astrophysics Data System (ADS)

    Lyonnet, F.; Schienbein, I.; Staub, F.; Wingerter, A.

    2014-03-01

    Although the two-loop renormalization group equations for a general gauge field theory have been known for quite some time, deriving them for specific models has often been difficult in practice. This is mainly due to the fact that, albeit straightforward, the involved calculations are quite long, tedious and prone to error. The present work is an attempt to facilitate the practical use of the renormalization group equations in model building. To that end, we have developed two completely independent sets of programs written in Python and Mathematica, respectively. The Mathematica scripts will be part of an upcoming release of SARAH 4. The present article describes the collection of Python routines that we dubbed PyR@TE which is an acronym for “Python Renormalization group equations At Two-loop for Everyone”. In PyR@TE, once the user specifies the gauge group and the particle content of the model, the routines automatically generate the full two-loop renormalization group equations for all (dimensionless and dimensionful) parameters. The results can optionally be exported to LaTeX and Mathematica, or stored in a Python data structure for further processing by other programs. For ease of use, we have implemented an interactive mode for PyR@TE in form of an IPython Notebook. As a first application, we have generated with PyR@TE the renormalization group equations for several non-supersymmetric extensions of the Standard Model and found some discrepancies with the existing literature. Catalogue identifier: AERV_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERV_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 924959 No. of bytes in distributed program, including test data, etc.: 495197 Distribution format: tar.gz Programming language: Python. Computer

  20. Higher-order mass defect analysis for mass spectra of complex organic mixtures.

    PubMed

    Roach, Patrick J; Laskin, Julia; Laskin, Alexander

    2011-06-15

    Higher-order mass defect analysis is introduced as a unique formula assignment and visualization method for the analysis of complex mass spectra. This approach is an extension of the concepts of Kendrick mass transformation widely used for identification of homologous compounds differing only by a number of base units (e.g., CH(2), H(2), O, CH(2)O, etc.) in complex mixtures. We present an iterative renormalization routine for defining higher-order homologous series and multidimensional clustering of mass spectral features. This approach greatly simplifies visualization of complex mass spectra and increases the number of chemical formulas that can be confidently assigned for given mass accuracy. The potential for using higher-order mass defects for data reduction and visualization is shown. Higher-order mass defect analysis is described and demonstrated through third-order analysis of a deisotoped high-resolution mass spectrum of crude oil containing nearly 13,000 peaks. PMID:21526851

  1. Human exposure assessment to a large set of polymer additives through the analysis of urine by solid phase extraction followed by ultra high performance liquid chromatography coupled to tandem mass spectrometry.

    PubMed

    Pouech, Charlène; Kiss, Agneta; Lafay, Florent; Léonard, Didier; Wiest, Laure; Cren-Olivé, Cécile; Vulliet, Emmanuelle

    2015-12-01

    Polymer items are extensively present in the human environment. Humans may be consequently exposed to some compounds, such as additives, incorporated in these items. The objective of this work is to assess the human exposure to the main additives such as those authorized in the packaging for pharmaceutical products. The urinary matrix was selected to optimally answer this challenge because it has already been proven that the exposure to chemicals can be revealed by the analysis of this biological matrix. A multi-residue analytical method for the trace analysis at ng/mL in human urine was developed, and consisted of an extraction of analytes from urine by solid phase extraction (SPE) and an analysis by ultra-high performance liquid chromatography coupled to a tandem mass spectrometer (UHPLC-MS/MS). Even if the quantification of these compounds was an analytical challenge because of (i) the presence of these substances in the analytical process, (ii) the diversity of their physicochemical properties, and (iii) the complexity of the matrix, the optimized method exhibited quantification limits lower than 25ng/mL and recoveries between 51% and 120% for all compounds. The method was validated and applied to 52 human urines. To the best of our knowledge, this work presents the first study allowing the assessment of the occurrence of more than twenty polymer additives at ng/mL in human urine.

  2. Diffusive mass transfer by nonequilibrium fluctuations: Fick's law revisited.

    PubMed

    Brogioli, D; Vailati, A

    2001-01-01

    Recent experimental and theoretical works have shown that giant fluctuations are present during diffusion in liquid systems. We use linearized fluctuating hydrodynamics to calculate the net mass transfer due to these nonequilibrium fluctuations. Remarkably, the mass flow turns out to coincide with the usual Fick's one. The renormalization of the hydrodynamic equations allows us to quantify the gravitational modifications of the diffusion coefficient induced by the gravitational stabilization of long wavelength fluctuations.

  3. Renormalization group approach to the Fröhlich polaron model: application to impurity-BEC problem

    PubMed Central

    Grusdt, F.; Shchadilova, Y. E.; Rubtsov, A. N.; Demler, E.

    2015-01-01

    When a mobile impurity interacts with a many-body system, such as a phonon bath, a polaron is formed. Despite the importance of the polaron problem for a wide range of physical systems, a unified theoretical description valid for arbitrary coupling strengths is still lacking. Here we develop a renormalization group approach for analyzing a paradigmatic model of polarons, the so-called Fröhlich model, and apply it to a problem of impurity atoms immersed in a Bose-Einstein condensate of ultra cold atoms. Polaron energies obtained by our method are in excellent agreement with recent diagrammatic Monte Carlo calculations for a wide range of interaction strengths. They are found to be logarithmically divergent with the ultra-violet cut-off, but physically meaningful regularized polaron energies are also presented. Moreover, we calculate the effective mass of polarons and find a smooth crossover from weak to strong coupling regimes. Possible experimental tests of our results in current experiments with ultra cold atoms are discussed. PMID:26183614

  4. Radiative corrections to e/sup +/e/sup -/ reactions to all orders in. cap alpha. using the renormalization group

    SciTech Connect

    Tsai, Y.S.

    1983-01-01

    Renormalization group technique is used to improve the accuracy of the lowest order radiative corrections in QED. The exponentiation of infrared terms comes automatically. It also leads to exponentiation of the vertex functions. It predicts the existence of conversion of photons into pairs and the result agrees with the Kroll-Wada relation. Kinoshita-Lee-Nauenberg cancellation of mass singularities occurs to all order in ..cap alpha.. in leading log approximation in the final state if we sum over all the final states. Higher order corrections to the order ..cap alpha../sup 3/ asymmetry is shown to be small. The results are used to derive useful formulas for the radiative corrections to processes such as e/sup +/e/sup -/ ..-->.. ..mu../sup +/..mu../sup -/, e/sup +/e/sup -/ ..-->.. ..mu../sup +/..mu../sup -/..gamma.., e/sup +/e/sup -/ ..-->.. hadron continuum, e/sup +/e/sup -/ ..-->.. very narrow resonance such as phi, and e/sup +/e/sup -/ ..-->.. not very narrow resonance such as Z/sup 0/.

  5. Renormalization group approach to the Fröhlich polaron model: application to impurity-BEC problem.

    PubMed

    Grusdt, F; Shchadilova, Y E; Rubtsov, A N; Demler, E

    2015-07-17

    When a mobile impurity interacts with a many-body system, such as a phonon bath, a polaron is formed. Despite the importance of the polaron problem for a wide range of physical systems, a unified theoretical description valid for arbitrary coupling strengths is still lacking. Here we develop a renormalization group approach for analyzing a paradigmatic model of polarons, the so-called Fröhlich model, and apply it to a problem of impurity atoms immersed in a Bose-Einstein condensate of ultra cold atoms. Polaron energies obtained by our method are in excellent agreement with recent diagrammatic Monte Carlo calculations for a wide range of interaction strengths. They are found to be logarithmically divergent with the ultra-violet cut-off, but physically meaningful regularized polaron energies are also presented. Moreover, we calculate the effective mass of polarons and find a smooth crossover from weak to strong coupling regimes. Possible experimental tests of our results in current experiments with ultra cold atoms are discussed.

  6. Experimental observation of incoherent-coherent crossover and orbital-dependent band renormalization in iron chalcogenide superconductors

    NASA Astrophysics Data System (ADS)

    Liu, Z. K.; Yi, M.; Zhang, Y.; Hu, J.; Yu, R.; Zhu, J.-X.; He, R.-H.; Chen, Y. L.; Hashimoto, M.; Moore, R. G.; Mo, S.-K.; Hussain, Z.; Si, Q.; Mao, Z. Q.; Lu, D. H.; Shen, Z.-X.

    2015-12-01

    The level of electronic correlation has been one of the key questions in understanding the nature of superconductivity. Among the iron-based superconductors, the iron chalcogenide family exhibits the strongest electron correlations. To gauge the correlation strength, we performed a systematic angle-resolved photoemission spectroscopy study on the iron chalcogenide series Fe1 +ySexTe1 -x (0 mass of bands dominated by the dx y orbital character significantly decreases with increasing selenium ratio, as compared to the dx z/dy z orbital-dominated bands. The orbital-dependent change in the correlation level agrees with theoretical calculations on the band structure renormalization, and may help to understand the onset of superconductivity in Fe1 +ySexTe1 -x .

  7. Renormalized Polyakov loop in the deconfined phase of SU(N) gauge theory and gauge-string duality.

    PubMed

    Andreev, Oleg

    2009-05-29

    We use gauge-string duality to analytically evaluate the renormalized Polyakov loop in pure Yang-Mills theories. For SU(3), the result is in quite good agreement with lattice simulations for a broad temperature range.

  8. Renormalized effective actions for the O(N) model at next-to-leading order of the 1/N expansion

    SciTech Connect

    Fejos, G.; Patkos, A.; Szep, Zs.

    2009-07-15

    A fully explicit renormalized quantum action functional is constructed for the O(N) model in the auxiliary field formulation at next-to-leading order (NLO) of the 1/N expansion. Counterterms are consistently and explicitly derived for arbitrary constant vacuum expectation value of the scalar and auxiliary fields. The renormalized NLO pion propagator is exact at this order and satisfies Goldstone's theorem. Elimination of the auxiliary field sector at the level of the functional provides with O(N{sup 0}) accuracy the renormalized effective action of the model in terms of the original variables. Alternative elimination of the pion and sigma propagators provides the renormalized NLO effective potential for the expectation values of the N vector and of the auxiliary field with the same accuracy.

  9. Renormalization group analysis of ultracold Fermi gases with two-body attractive interaction

    NASA Astrophysics Data System (ADS)

    Guo, Xiaoyong; Chi, Zimeng; Zheng, Qiang; Wang, Zaijun

    2016-01-01

    We propose a new functional renormalization group (RG) strategy to investigate the many-body physics of interacting ultracold Fermi gases. By mapping the Ginzburg-Landau (GL) action of Fermi gases onto a complex φ4-model, we can obtain the closed flow equation in the one-loop approximation. An analysis of the emerging RG flow gives the ground state behavior. The Hamiltonian of a Fermi gas with a two-body attractive interaction is used as a demonstration to clarify our treatment. The fixed point structure reveals not only the condensation phase transition, but also the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) crossover. The effect of the imaginary time renormalization is also discussed. It is shown that for the dynamical field configuration our RG procedure can reproduce the well known theoretical results of BCS-BEC crossover, while under a static approximation the phase transition takes place at a higher critical temperature.

  10. Approaching many-body localization from disordered Luttinger liquids via the functional renormalization group

    NASA Astrophysics Data System (ADS)

    Karrasch, C.; Moore, J. E.

    2015-09-01

    We study the interplay of interactions and disorder in a one-dimensional fermion lattice coupled adiabatically to infinite reservoirs. We employ both the functional renormalization group (FRG) as well as matrix product state techniques, which serve as an accurate benchmark for small systems. Using the FRG, we compute the length- and temperature-dependence of the conductance averaged over 104 samples for lattices as large as 105 sites. We identify regimes in which non-Ohmic power law behavior can be observed and demonstrate that the corresponding exponents can be understood by adapting earlier predictions obtained perturbatively for disordered Luttinger liquids. In the presence of both disorder and isolated impurities, the conductance has a universal single-parameter scaling form. This lays the groundwork for an application of the functional renormalization group to the realm of many-body localization.

  11. A renormalization group analysis of lattice models of two-dimensional membranes

    SciTech Connect

    Ambjoern, J.; Durhuus, B.; Froehlich, J.; Joensson, T. )

    1989-04-01

    The authors study lattice models of two-dimensional membranes of interest in statistical physics. The energy functional of a membrane is expressed as a sum of terms proportional to the surface area of the membrane, an extrinsic curvature and an intrinsic curvature quantity, respectively, but they neglect excluded volume effects. They introduce a renormalization transformation for these models which preserves the form of the energy functional, up to nonlocal terms. Their renormalization group construction is used to analyze the phase diagram and the different critical regimes of their models. They find evidence for a crumpling transition, separating a regime where surfaces are crystalline from one where the surfaces collapse to branched polymers, and they find a third genuine random-surface regime.

  12. Dual fermionic variables and renormalization group approach to junctions of strongly interacting quantum wires

    NASA Astrophysics Data System (ADS)

    Giuliano, Domenico; Nava, Andrea

    2015-09-01

    Making a combined use of bosonization and fermionization techniques, we build nonlocal transformations between dual fermion operators, describing junctions of strongly interacting spinful one-dimensional quantum wires. Our approach allows for trading strongly interacting (in the original coordinates) fermionic Hamiltonians for weakly interacting (in the dual coordinates) ones. It enables us to generalize to the strongly interacting regime the fermionic renormalization group approach to weakly interacting junctions. As a result, on one hand, we are able to pertinently complement the information about the phase diagram of the junction obtained within the bosonization approach; on the other hand, we map out the full crossover of the conductance tensors between any two fixed points in the phase diagram connected by a renormalization group trajectory.

  13. Structure of the Broken Phase of the Sine-Gordon Model Using Functional Renormalization

    NASA Astrophysics Data System (ADS)

    Pangon, V.

    We study in this paper the sine-Gordon model using functional renormalization group at local potential approximation using different renormalization group (RG) schemes. In d = 2, using Wegner-Houghton RG we demonstrate that the location of the phase boundary is entirely driven by the relative position to the Coleman fixed point even for strongly coupled bare theories. We show the existence of a set of IR fixed points in the broken phase that are reached independently of the bare coupling. The bad convergence of the Fourier series in the broken phase is discussed and we demonstrate that these fixed points can be found only using a global resolution of the effective potential. We then introduce the methodology for the use of average action method where the regulator breaks periodicity and show that it provides the same conclusions for various regulators. The behavior of the model is then discussed in d≠2 and the absence of the previous fixed points is interpreted.

  14. Giant bandgap renormalization and excitonic effects in a monolayer transition metal dichalcogenide semiconductor

    NASA Astrophysics Data System (ADS)

    Bradley, Aaron; Ugeda, Miguel M.; Shi, Su-Fei; da Jornada, Felipe H.; Zhang, Yi; Qiu, Diana Y.; Ruan, Wei; Mo, Sung-Kwan; Hussain, Zahid; Shen, Zhi-Xun; Wang, Feng; Louie, Steven G.; Crommie, Michael F.

    2015-03-01

    Reduced screening in 2D has been predicted to result in dramatically enhanced Coulomb interactions that should cause giant bandgap renormalization and exotic excitonic effects in single-layer TMD semiconductors. Here we present a direct experimental observation of extraordinarily high exciton binding energy and bandgap renormalization in a single-layer of a semiconducting MoSe2, grown on bilayer graphene, using high-resolution scanning tunneling spectroscopy and photoluminescence spectroscopy. We have measured both the quasiparticle electronic bandgap and the optical transitions, obtaining an exciton binding energy of 0.55 eV - a value orders of magnitude larger than in conventional 3D semiconductors. We have also studied the influence of external dielectric screening by repeating measurements on MoSe2/HOPG. These results are important for room-temperature optoelectronic devices involving 2D TMDs, as well as more complex layered heterostructures.

  15. Magnetic Kronig-Penney-type graphene superlattices: finite energy Dirac points with anisotropic velocity renormalization.

    PubMed

    Qui Le, V; Huy Pham, C; Lien Nguyen, V

    2012-08-29

    We study the energy band structure of magnetic graphene superlattices with delta-function magnetic barriers and zero average magnetic field. The dispersion relation obtained using the T-matrix approach shows the emergence of an infinite number of Dirac-like points at finite energies, while the original Dirac point is still located at the same place as that for pristine graphene. The carrier group velocity at the original Dirac point is isotropically renormalized, but at finite energy Dirac points it is generally anisotropic. An asymmetry in the width between the wells and the barriers of the periodic potential induces a shift of the original Dirac point in the zero-energy plane, keeping the velocity renormalization isotropic.

  16. Gauge invariant composite operators of QED in the exact renormalization group formalism

    NASA Astrophysics Data System (ADS)

    Sonoda, H.

    2014-01-01

    Using the exact renormalization group (ERG) formalism, we study the gauge invariant composite operators in QED. Gauge invariant composite operators are introduced as infinitesimal changes of the gauge invariant Wilson action. We examine the dependence on the gauge fixing parameter of both the Wilson action and gauge invariant composite operators. After defining ‘gauge fixing parameter independence,’ we show that any gauge independent composite operators can be made ‘gauge fixing parameter independent’ by appropriate normalization. As an application, we give a concise but careful proof of the Adler-Bardeen non-renormalization theorem for the axial anomaly in an arbitrary covariant gauge by extending the original proof by A Zee.

  17. Noise spectrum of quantum transport through double quantum dots: Renormalization and non-Markovian effects

    NASA Astrophysics Data System (ADS)

    Shi, Pengqin; Hu, Menghan; Ying, Yaofeng; Jin, Jinshuang

    2016-09-01

    Based on the time-nonlocal particle number-resolved master equation, we investigate the sequential electron transport through the interacting double quantum dots. Our calculations show that there exists the effect of energy renormalization in the dispersion of the bath interaction spectrum and it is sensitive to the the bandwidth of the bath. This effect would strongly affect the stationary current and its zero-frequency shot noise for weak inter-dot coherent coupling strength, but for strong inter-dot coupling regime, it is negligible due to the strong intrinsic Rabi coherent dynamics. Moreover, the possible observable effects of the energy renormalization in the noise spectrum are also investigated through the Rabi coherence signal. Finally, the non-Markovian effect is manifested in the finite-frequency noise spectrum with the appearance of quasisteps, and the magnitude of these quasisteps are modified by the dispersion function.

  18. Many-Body Effects on the Zero-Point Renormalization of the Band Structure

    NASA Astrophysics Data System (ADS)

    Antonius, G.; Poncé, S.; Boulanger, P.; Côté, M.; Gonze, X.

    2014-05-01

    We compute the zero-point renormalization (ZPR) of the optical band gap of diamond from many-body perturbation theory using the perturbative G0W0 approximation as well as quasiparticle self-consistent GW. The electron-phonon coupling energies are found to be more than 40% higher than standard density functional theory when many-body effects are included with the frozen-phonon calculations. A similar increase is observed for the zero-point renormalization in GaAs when G0W0 corrections are applied. We show that these many-body corrections are necessary to accurately predict the temperature dependence of the band gap. The frozen-phonon method also allows us to validate the rigid-ion approximation which is always present in density functional perturbation theory.

  19. Flexoelectricity and thermal fluctuations of lipid bilayer membranes: Renormalization of flexoelectric, dielectric, and elastic properties

    NASA Astrophysics Data System (ADS)

    Liu, L. P.; Sharma, P.

    2013-03-01

    Thermal fluctuations renormalize the bending elasticity of lipid bilayers. This well-studied effect is a cornerstone in the study of several membrane biophysical phenomena. Analogously, nearly all membranes are endowed with an electromechanical coupling called flexoelectricity that admits membrane polarization due to curvature changes. Flexoelectricity is found to be important in a number of biological functions, including hearing, ion transport, and in some situations where mechanotransduction is necessary. Very little is known about the interplay between thermal fluctuations and flexoelectricity. In this work, we explore how the apparent flexoelectricity is altered due to thermal fluctuations and, further, how the elastic and dielectric properties are renormalized due to flexoelectricity. We find that the apparent bending rigidity is softened by flexoelectricity and discuss the ramifications for interpreting existing experimental work.

  20. Renormalization and small-world model of fractal quantum repeater networks.

    PubMed

    Wei, Zong-Wen; Wang, Bing-Hong; Han, Xiao-Pu

    2013-01-01

    Quantum networks provide access to exchange of quantum information. The primary task of quantum networks is to distribute entanglement between remote nodes. Although quantum repeater protocol enables long distance entanglement distribution, it has been restricted to one-dimensional linear network. Here we develop a general framework that allows application of quantum repeater protocol to arbitrary quantum repeater networks with fractal structure. Entanglement distribution across such networks is mapped to renormalization. Furthermore, we demonstrate that logarithmical times of recursive such renormalization transformations can trigger fractal to small-world transition, where a scalable quantum small-world network is achieved. Our result provides new insight into quantum repeater theory towards realistic construction of large-scale quantum networks.

  1. Renormalization and small-world model of fractal quantum repeater networks

    PubMed Central

    Wei, Zong-Wen; Wang, Bing-Hong; Han, Xiao-Pu

    2013-01-01

    Quantum networks provide access to exchange of quantum information. The primary task of quantum networks is to distribute entanglement between remote nodes. Although quantum repeater protocol enables long distance entanglement distribution, it has been restricted to one-dimensional linear network. Here we develop a general framework that allows application of quantum repeater protocol to arbitrary quantum repeater networks with fractal structure. Entanglement distribution across such networks is mapped to renormalization. Furthermore, we demonstrate that logarithmical times of recursive such renormalization transformations can trigger fractal to small-world transition, where a scalable quantum small-world network is achieved. Our result provides new insight into quantum repeater theory towards realistic construction of large-scale quantum networks. PMID:23386977

  2. Renormalization of the BCS-BEC crossover by order-parameter fluctuations

    SciTech Connect

    Bartosch, Lorenz; Kopietz, Peter; Ferraz, Alvaro

    2009-09-01

    We use the functional renormalization group approach with partial bosonization in the particle-particle channel to study the effect of order parameter fluctuations on the BCS-Bose-Einstein condensate (BEC) crossover of superfluid fermions in three dimensions. Our approach is based on a new truncation of the vertex expansion where the renormalization group flow of bosonic two-point functions is closed by means of Dyson-Schwinger equations and the superfluid order parameter is related to the single-particle gap via a Ward identity. We explicitly calculate the chemical potential, the single-particle gap, and the superfluid order parameter at the unitary point and compare our results with experiments and previous calculations.

  3. Logarithms of alpha in QED bound states from the renormalization group

    PubMed

    Manohar; Stewart

    2000-09-11

    The velocity renormalization group is used to determine lnalpha contributions to QED bound state energies. The leading-order anomalous dimension for the potential gives the alpha(5)lnalpha Lamb shift. The next-to-leading-order anomalous dimension determines the alpha(6)lnalpha, alpha(7)ln (2)alpha, and alpha(8)ln (3)alpha corrections to the energy. These are used to obtain the alpha(8)ln (3)alpha Lamb shift and alpha(7)ln (2)alpha hyperfine splitting for hydrogen, muonium, and positronium, as well as the alpha(2)lnalpha and alpha(3)ln (2)alpha corrections to the ortho- and parapositronium lifetimes. This shows for the first time that these logarithms can be computed from the renormalization group.

  4. Renormalization of the graphene dispersion velocity determined from scanning tunneling spectroscopy.

    PubMed

    Chae, Jungseok; Jung, Suyong; Young, Andrea F; Dean, Cory R; Wang, Lei; Gao, Yuanda; Watanabe, Kenji; Taniguchi, Takashi; Hone, James; Shepard, Kenneth L; Kim, Phillip; Zhitenev, Nikolai B; Stroscio, Joseph A

    2012-09-14

    In graphene, as in most metals, electron-electron interactions renormalize the properties of electrons but leave them behaving like noninteracting quasiparticles. Many measurements probe the renormalized properties of electrons right at the Fermi energy. Uniquely for graphene, the accessibility of the electrons at the surface offers the opportunity to use scanned probe techniques to examine the effect of interactions at energies away from the Fermi energy, over a broad range of densities, and on a local scale. Using scanning tunneling spectroscopy, we show that electron interactions leave the graphene energy dispersion linear as a function of excitation energy for energies within ±200  meV of the Fermi energy. However, the measured dispersion velocity depends on density and increases strongly as the density approaches zero near the charge neutrality point, revealing a squeezing of the Dirac cone due to interactions.

  5. Multireference quantum chemistry through a joint density matrix renormalization group and canonical transformation theory.

    PubMed

    Yanai, Takeshi; Kurashige, Yuki; Neuscamman, Eric; Chan, Garnet Kin-Lic

    2010-01-14

    We describe the joint application of the density matrix renormalization group and canonical transformation theory to multireference quantum chemistry. The density matrix renormalization group provides the ability to describe static correlation in large active spaces, while the canonical transformation theory provides a high-order description of the dynamic correlation effects. We demonstrate the joint theory in two benchmark systems designed to test the dynamic and static correlation capabilities of the methods, namely, (i) total correlation energies in long polyenes and (ii) the isomerization curve of the [Cu(2)O(2)](2+) core. The largest complete active spaces and atomic orbital basis sets treated by the joint DMRG-CT theory in these systems correspond to a (24e,24o) active space and 268 atomic orbitals in the polyenes and a (28e,32o) active space and 278 atomic orbitals in [Cu(2)O(2)](2+). PMID:20095661

  6. Renormalization versus strong form factors for one-boson-exchange potentials

    SciTech Connect

    Calle Cordon, A.; Ruiz Arriola, E.

    2010-04-15

    We analyze the one-boson-exchange potential from the point of view of renormalization theory. We show that the nucleon-meson Lagrangian, while predicting the NN force, does not predict the NN scattering matrix nor the deuteron properties unambiguously due to the appearance of short distance singularities. While the problem has traditionally been circumvented by introducing vertex functions via phenomenological strong form factors, we propose to impose physical renormalization conditions on the scattering amplitude at low energies. Working in the large N{sub c} approximation with pi, sigma, rho, and omega mesons we show that, once these conditions are applied, results for low-energy phases of proton-neutron scattering as well as deuteron properties become largely insensitive to the form factors and to the vector mesons yielding reasonable agreement with the data and for realistic values of the coupling constants.

  7. Unraveling the interlayer-related phonon self-energy renormalization in bilayer graphene

    PubMed Central

    Araujo, Paulo T.; Mafra, Daniela L.; Sato, Kentaro; Saito, Riichiro; Kong, Jing; Dresselhaus, Mildred S.

    2012-01-01

    In this letter, we present a step towards understanding the bilayer graphene (2LG) interlayer (IL)-related phonon combination modes and overtones as well as their phonon self-energy renormalizations by using both gate-modulated and laser-energy dependent inelastic scattering spectroscopy. We show that although the IL interactions are weak, their respective phonon renormalization response is significant. Particularly special, the IL interactions are mediated by Van der Waals forces and are fundamental for understanding low-energy phenomena such as transport and infrared optics. Our approach opens up a new route to understanding fundamental properties of IL interactions which can be extended to any graphene-like material, such as MoS2, WSe2, oxides and hydroxides. Furthermore, we report a previously elusive crossing between IL-related phonon combination modes in 2LG, which might have important technological applications. PMID:23264879

  8. Thermal conductivities of one-dimensional anharmonic/nonlinear lattices: renormalized phonons and effective phonon theory

    NASA Astrophysics Data System (ADS)

    Li, Nianbei; Li, Baowen

    2012-12-01

    Heat transport in low-dimensional systems has attracted enormous attention from both theoretical and experimental aspects due to its significance to the perception of fundamental energy transport theory and its potential applications in the emerging field of phononics: manipulating heat flow with electronic anologs. We consider the heat conduction of one-dimensional nonlinear lattice models. The energy carriers responsible for the heat transport have been identified as the renormalized phonons. Within the framework of renormalized phonons, a phenomenological theory, effective phonon theory, has been developed to explain the heat transport in general one-dimensional nonlinear lattices. With the help of numerical simulations, it has been verified that this effective phonon theory is able to predict the scaling exponents of temperature-dependent thermal conductivities quantitatively and consistently.

  9. Entanglement Holographic Mapping of Many-Body Localized System by Spectrum Bifurcation Renormalization Group

    NASA Astrophysics Data System (ADS)

    You, Yi-Zhuang; Qi, Xiao-Liang; Xu, Cenke

    We introduce the spectrum bifurcation renormalization group (SBRG) as a generalization of the real-space renormalization group for the many-body localized (MBL) system without truncating the Hilbert space. Starting from a disordered many-body Hamiltonian in the full MBL phase, the SBRG flows to the MBL fixed-point Hamiltonian, and generates the local conserved quantities and the matrix product state representations for all eigenstates. The method is applicable to both spin and fermion models with arbitrary interaction strength on any lattice in all dimensions, as long as the models are in the MBL phase. In particular, we focus on the 1 d interacting Majorana chain with strong disorder, and map out its phase diagram using the entanglement entropy. The SBRG flow also generates an entanglement holographic mapping, which duals the MBL state to a fragmented holographic space decorated with small blackholes.

  10. Inverse Mellin Transformation of Continuous Singular Value Decomposition: A Route to Holographic Renormalization

    NASA Astrophysics Data System (ADS)

    Matsueda, Hiroaki

    2016-11-01

    We examine holographic renormalization by singular value decomposition (SVD) of matrix data generated by a Monte Carlo snapshot of the two-dimensional (2D) classical Ising model at criticality. Taking the continuous limit of the SVD enables us to find the mathematical form of each SVD component by the inverse Mellin transformation as well as the power-law behavior of the SVD spectrum. We find that each SVD component is characterized by the two-point spin correlator with a finite correlation length. Then, the continuous limit of the decomposition index in the SVD corresponds to the inverse of the correlation length. These features strongly indicate that the SVD contains the same mathematical structure as the holographic renormalization.

  11. Material and Doping Dependence of the Nodal and Anti-Nodal Dispersion Renormalizations in Single- and Multi-Layer Cuprates

    SciTech Connect

    Johnston, S.; Lee, W.S.; Nowadnick, E.A.; Moritz, B.; Shen, Z.-X.; Devereaux, T.P.; /Stanford U., Geballe Lab. /SLAC

    2010-02-15

    In this paper we present a review of bosonic renormalization effects on electronic carriers observed from angle-resolved photoemission spectra in the cuprates. Specifically, we discuss the viewpoint that these renormalizations represent coupling of the electrons to the lattice and review how materials dependence, such as the number of CuO{sub 2} layers, and doping dependence can be understood straightforwardly in terms of several aspects of electron-phonon coupling in layered correlated materials.

  12. Toward Reliable Prediction of Hyperfine Coupling Constants Using Ab Initio Density Matrix Renormalization Group Method: Diatomic (2)Σ and Vinyl Radicals as Test Cases.

    PubMed

    Lan, Tran Nguyen; Kurashige, Yuki; Yanai, Takeshi

    2014-05-13

    The density matrix renormalization group (DMRG) method is used in conjunction with the complete active space (CAS) procedure, the CAS configuration interaction (CASCI), and the CAS self-consistent field (CASSCF) to evaluate hyperfine coupling constants (HFCCs) for a series of diatomic (2)Σ radicals (BO, CO(+), CN, and AlO) and vinyl (C2H3) radical. The electron correlation effects on the computed HFCC values were systematically investigated using various levels of active space, which were increasingly extended from single valence space to large-size model space entailing double valence and at least single polarization shells. In addition, the core correlation was treated by including the core orbitals in active space. Reasonably accurate results were obtained by the DMRG-CASSCF method involving orbital optimization, while DMRG-CASCI calculations with Hartree-Fock orbitals provided poor agreement of the HFCCs with the experimental values. To achieve further insights into the accuracy of HFCC calculations, the orbital contributions to the total spin density were analyzed at a given nucleus, which is directly related to the FC term and is numerically sensitive to the level of correlation treatment and basis sets. The convergence of calculated HFCCs with an increasing number of renormalized states was also assessed. This work serves as the first study on the performance of the ab initio DMRG method for HFCC prediction.

  13. Background field quantization in non-covariant gauges: renormalization and WTST identities

    NASA Astrophysics Data System (ADS)

    Mckeon, G.; Phillips, S. B.; Samant, S. S.; Sherry, T. N.

    1986-04-01

    Background field quantization of pure YM theories in non-covariant gauges is treated with particular emphasis on renormalization. Gauge fixing terms of the form ( {1}/{2α})n · Q aƒ abn · Q b are considered where ƒ ab can assume the forms ƒ ( i) ab = -δ ab (the axial gauge), ƒ ( ii) ab = (n · D(A)) 2ab/n 4 and ƒ ( iii) ab = D 2(A) ab/n 2 (the planar gauge). For the cases where ƒ ab depends explicitly on the background field Aμa the ghost sector is enlarged by the addition of appropriate Nielsen-Kallosh ghost fields. The BRS identities for these gauge choices are derived and solved. The quantum-corrected versions of both the bare background field gauge transformations and the bare quantum field gauge transformations are obtained from the BRS analysis. It is also shown that, to one loop, all the counter terms are determined by the background field independent part of the theory and this result is used, in cases (ii) and (iii), to derive all the counter terms and to show that Kallosh's theorem is verified. The result is also used to demonstrate the pathological nature of case (i) for α ≠ 0, in particular the result that Kallosh's theorem is not applicable. The result that the generating functional of Green functions is independent of the background field Aμa in the absence of all external sources is generalized to the case of non-covariant gauges. The equality established by Abbott between the 1PI generating functionals overlineΓ[A, 0] and Γ c[ overlineQ; A] overlineQ = A , where Γ c is a conventional generating functional in an A-dependent gauge, is analysed. We show that the WTST identities satisfied by Γc reduce, when overlineQ is set equal to A, to the naive Ward-identity satisfied by overlineΓ[A, 0] .

  14. The density matrix renormalization group for strongly correlated electron systems: A generic implementation

    NASA Astrophysics Data System (ADS)

    Alvarez, G.

    2009-09-01

    The purpose of this paper is (i) to present a generic and fully functional implementation of the density-matrix renormalization group (DMRG) algorithm, and (ii) to describe how to write additional strongly-correlated electron models and geometries by using templated classes. Besides considering general models and geometries, the code implements Hamiltonian symmetries in a generic way and parallelization over symmetry-related matrix blocks. Program summaryProgram title: DMRG++ Catalogue identifier: AEDJ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDJ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: See file LICENSE No. of lines in distributed program, including test data, etc.: 15 795 No. of bytes in distributed program, including test data, etc.: 83 454 Distribution format: tar.gz Programming language: C++, MPI Computer: PC, HP cluster Operating system: Any, tested on Linux Has the code been vectorized or parallelized?: Yes RAM: 1 GB (256 MB is enough to run included test) Classification: 23 External routines: BLAS and LAPACK Nature of problem: Strongly correlated electrons systems, display a broad range of important phenomena, and their study is a major area of research in condensed matter physics. In this context, model Hamiltonians are used to simulate the relevant interactions of a given compound, and the relevant degrees of freedom. These studies rely on the use of tight-binding lattice models that consider electron localization, where states on one site can be labeled by spin and orbital degrees of freedom. The calculation of properties from these Hamiltonians is a computational intensive problem, since the Hilbert space over which these Hamiltonians act grows exponentially with the number of sites on the lattice. Solution method: The DMRG is a numerical variational technique to study quantum many body Hamiltonians. For one-dimensional and quasi one-dimensional systems, the

  15. Sum-Rule Conserving Spectral Functions from the Numerical Renormalization Group

    NASA Astrophysics Data System (ADS)

    Weichselbaum, Andreas; von Delft, Jan

    2007-08-01

    We show how spectral functions for quantum impurity models can be calculated very accurately using a complete set of discarded numerical renormalization group eigenstates, recently introduced by Anders and Schiller. The only approximation is to judiciously exploit energy scale separation. Our derivation avoids both the overcounting ambiguities and the single-shell approximation for the equilibrium density matrix prevalent in current methods, ensuring that relevant sum rules hold rigorously and spectral features at energies below the temperature can be described accurately.

  16. Point splitting renormalization of Schwinger induced current in de Sitter spacetime

    NASA Astrophysics Data System (ADS)

    Hayashinaka, Takahiro; Yokoyama, Jun'ichi

    2016-07-01

    The covariant and gauge invariant calculation of the current expectation value in the homogeneous electric field in 1+3 dimensional de Sitter spacetime is shown. The result accords with previous work obtained by using adiabatic subtraction scheme. We therefore conclude the counterintuitive behaviors of the current in the infrared (IR) regime such as IR hyperconductivity and negative current are not artifacts of the renormalization scheme, but are real IR effects of the spacetime.

  17. Renormalized second-order perturbation theory for the electron correlation energy: Concept, implementation, and benchmarks

    NASA Astrophysics Data System (ADS)

    Ren, Xinguo; Rinke, Patrick; Scuseria, Gustavo E.; Scheffler, Matthias

    2013-07-01

    We present a renormalized second-order perturbation theory (rPT2), based on a Kohn-Sham (KS) reference state, for the electron correlation energy that includes the random-phase approximation (RPA), second-order screened exchange (SOSEX), and renormalized single excitations (rSE). These three terms all involve a summation of certain types of diagrams to infinite order, and can be viewed as ``renormalization'' of the second-order direct, exchange, and single-excitation (SE) terms of Rayleigh-Schrödinger perturbation theory based on a KS reference. In this work, we establish the concept of rPT2 and present the numerical details of our SOSEX and rSE implementations. A preliminary version of rPT2, in which the renormalized SE (rSE) contribution was treated approximately, has already been benchmarked for molecular atomization energies and chemical reaction barrier heights and shows a well-balanced performance [J. Paier , New J. Phys.1367-263010.1088/1367-2630/14/4/043002 14, 043002 (2012)]. In this work, we present a refined version of rPT2, in which we evaluate the rSE series of diagrams rigorously. We then extend the benchmark studies to noncovalent interactions, including the rare-gas dimers, and the S22 and S66 test sets, as well as the cohesive energy of small copper clusters, and the equilibrium geometry of 10 diatomic molecules. Despite some remaining shortcomings, we conclude that rPT2 gives an overall satisfactory performance across different electronic situations, and is a promising step towards a generally applicable electronic-structure approach.

  18. Emergence of criticality in the transportation passenger flow: scaling and renormalization in the Seoul bus system.

    PubMed

    Goh, Segun; Lee, Keumsook; Choi, Moo Young; Fortin, Jean-Yves

    2014-01-01

    Social systems have recently attracted much attention, with attempts to understand social behavior with the aid of statistical mechanics applied to complex systems. Collective properties of such systems emerge from couplings between components, for example, individual persons, transportation nodes such as airports or subway stations, and administrative districts. Among various collective properties, criticality is known as a characteristic property of a complex system, which helps the systems to respond flexibly to external perturbations. This work considers the criticality of the urban transportation system entailed in the massive smart card data on the Seoul transportation network. Analyzing the passenger flow on the Seoul bus system during one week, we find explicit power-law correlations in the system, that is, power-law behavior of the strength correlation function of bus stops and verify scale invariance of the strength fluctuations. Such criticality is probed by means of the scaling and renormalization analysis of the modified gravity model applied to the system. Here a group of nearby (bare) bus stops are transformed into a (renormalized) "block stop" and the scaling relations of the network density turn out to be closely related to the fractal dimensions of the system, revealing the underlying structure. Specifically, the resulting renormalized values of the gravity exponent and of the Hill coefficient give a good description of the Seoul bus system: The former measures the characteristic dimensionality of the network whereas the latter reflects the coupling between distinct transportation modes. It is thus demonstrated that such ideas of physics as scaling and renormalization can be applied successfully to social phenomena exemplified by the passenger flow.

  19. New applications of the renormalization group method in physics: a brief introduction.

    PubMed

    Meurice, Y; Perry, R; Tsai, S-W

    2011-07-13

    The renormalization group (RG) method developed by Ken Wilson more than four decades ago has revolutionized the way we think about problems involving a broad range of energy scales such as phase transitions, turbulence, continuum limits and bifurcations in dynamical systems. The Theme Issue provides articles reviewing recent progress made using the RG method in atomic, condensed matter, nuclear and particle physics. In the following, we introduce these articles in a way that emphasizes common themes and the universal aspects of the method.

  20. Equation-free dynamic renormalization: Self-similarity in multidimensional particle system dynamics

    SciTech Connect

    Zou Yu; Kevrekidis, Ioannis; Ghanem, Roger

    2005-10-01

    We present an equation-free dynamic renormalization approach to the computational study of coarse-grained, self-similar dynamic behavior in multidimensional particle systems. The approach is aimed at problems for which evolution equations for coarse-scale observables (e.g., particle density) are not explicitly available. Our illustrative example involves Brownian particles in a 2D Couette flow; marginal and conditional inverse cumulative distribution functions (ICDFs) constitute the macroscopic observables of the evolving particle distributions.

  1. Renormalizing Sznajd model on complex networks taking into account the effects of growth mechanisms

    NASA Astrophysics Data System (ADS)

    González, M. C.; Sousa, A. O.; Herrmann, H. J.

    2006-01-01

    We present a renormalization approach to solve the Sznajd opinion formation model on complex networks. For the case of two opinions, we present an expression of the probability of reaching consensus for a given opinion as a function of the initial fraction of agents with that opinion. The calculations reproduce the sharp transition of the model on a fixed network, as well as the recently observed smooth function for the model when simulated on a growing complex networks.

  2. Emergence of criticality in the transportation passenger flow: scaling and renormalization in the Seoul bus system.

    PubMed

    Goh, Segun; Lee, Keumsook; Choi, Moo Young; Fortin, Jean-Yves

    2014-01-01

    Social systems have recently attracted much attention, with attempts to understand social behavior with the aid of statistical mechanics applied to complex systems. Collective properties of such systems emerge from couplings between components, for example, individual persons, transportation nodes such as airports or subway stations, and administrative districts. Among various collective properties, criticality is known as a characteristic property of a complex system, which helps the systems to respond flexibly to external perturbations. This work considers the criticality of the urban transportation system entailed in the massive smart card data on the Seoul transportation network. Analyzing the passenger flow on the Seoul bus system during one week, we find explicit power-law correlations in the system, that is, power-law behavior of the strength correlation function of bus stops and verify scale invariance of the strength fluctuations. Such criticality is probed by means of the scaling and renormalization analysis of the modified gravity model applied to the system. Here a group of nearby (bare) bus stops are transformed into a (renormalized) "block stop" and the scaling relations of the network density turn out to be closely related to the fractal dimensions of the system, revealing the underlying structure. Specifically, the resulting renormalized values of the gravity exponent and of the Hill coefficient give a good description of the Seoul bus system: The former measures the characteristic dimensionality of the network whereas the latter reflects the coupling between distinct transportation modes. It is thus demonstrated that such ideas of physics as scaling and renormalization can be applied successfully to social phenomena exemplified by the passenger flow. PMID:24599221

  3. The δN formula is the dynamical renormalization group

    SciTech Connect

    Dias, Mafalda; Seery, David; Ribeiro, Raquel H. E-mail: RaquelHRibeiro@case.edu

    2013-10-01

    We derive the 'separate universe' method for the inflationary bispectrum, beginning directly from a field-theory calculation. We work to tree-level in quantum effects but to all orders in the slow-roll expansion, with masses accommodated perturbatively. Our method provides a systematic basis to account for novel sources of time-dependence in inflationary correlation functions, and has immediate applications. First, we use our result to obtain the correct matching prescription between the 'quantum' and 'classical' parts of the separate universe computation. Second, we elaborate on the application of this method in situations where its validity is not clear. As a by-product of our calculation we give the leading slow-roll corrections to the three-point function of field fluctuations on spatially flat hypersurfaces in a canonical, multiple-field model.

  4. Renormalization group improved pQCD prediction for Υ(1 S) leptonic decay

    NASA Astrophysics Data System (ADS)

    Shen, Jian-Ming; Wu, Xing-Gang; Ma, Hong-Hao; Bi, Huan-Yu; Wang, Sheng-Quan

    2015-06-01

    The complete next-to-next-to-next-to-leading order short-distance and bound-state QCD corrections to Υ(1 S) leptonic decay rate Γ(Υ(1 S) → ℓ+ℓ-) has been finished by Beneke et al. [8]. Based on those improvements, we present a renormalization group (RG) improved pQCD prediction for Γ(Υ(1 S) → ℓ+ℓ-) by applying the principle of maximum conformality (PMC). The PMC is based on RG-invariance and is designed to solve the pQCD renormalization scheme and scale ambiguities. After applying the PMC, all known-type of β-terms at all orders, which are controlled by the RG-equation, are resummed to determine optimal renormalization scale for its strong running coupling at each order. We then achieve a more convergent pQCD series, a scheme- independent and more accurate pQCD prediction for Υ(1 S) leptonic decay, i.e. keV, where the uncertainty is the squared average of the mentioned pQCD errors. This RG-improved pQCD prediction agrees with the experimental measurement within errors.

  5. Renormalized second-oder perturbation theory for the electron correlation energy: concepts and benchmarks

    NASA Astrophysics Data System (ADS)

    Rinke, Patrick; Ren, Xinguo; Scheffler, Matthias; Scuseria, Gustavo

    2012-02-01

    We present a renormalized second-oder perturbation theory (R2PT) for the electron correlation energy that combines the random-phase approximation (RPA), second-order screened exchange (SOSEX) [1], and renormalized single excitations (rSE) [2]. These three terms all involve a summation of certain types of diagrams to infinite order, and can be viewed as a ``renormalization" of the direct, the exchange and the single excitation (SE) term of 2nd-order Rayleigh-Schr"ordinger perturbation theory based on an (approximate) Kohn-Sham reference state. A preliminary version of R2PT has been benchmarked for covalently-bonded molecular systems and chemical reaction barrier heights [3] and shows an overall well balanced performance. We have extended this, by including ``off-diagonal'' diagrams into the rSE term and expect this refined version of R2PT to be more generally applicable to electronic systems of different bonding characteristics. Extended benchmarks of van-der-Waals-bonded molecules and crystalline solids will be presented. [1] A. Gr"uneis et al., J. Chem. Phys. 131, 154115 (2009). [2] X. Ren et al., Phys. Rev. Lett. 106, 153003 (2011). [3] J. Paier et al., arXiv:cond-mat/1111.0173.

  6. Functional renormalization group approach to electronic structure calculations for systems without translational symmetry

    NASA Astrophysics Data System (ADS)

    Seiler, Christian; Evers, Ferdinand

    2016-10-01

    A formalism for electronic-structure calculations is presented that is based on the functional renormalization group (FRG). The traditional FRG has been formulated for systems that exhibit a translational symmetry with an associated Fermi surface, which can provide the organization principle for the renormalization group (RG) procedure. We here advance an alternative formulation, where the RG flow is organized in the energy-domain rather than in k space. This has the advantage that it can also be applied to inhomogeneous matter lacking a band structure, such as disordered metals or molecules. The energy-domain FRG (ɛ FRG) presented here accounts for Fermi-liquid corrections to quasiparticle energies and particle-hole excitations. It goes beyond the state of the art G W -BSE , because in ɛ FRG the Bethe-Salpeter equation (BSE) is solved in a self-consistent manner. An efficient implementation of the approach that has been tested against exact diagonalization calculations and calculations based on the density matrix renormalization group is presented. Similar to the conventional FRG, also the ɛ FRG is able to signalize the vicinity of an instability of the Fermi-liquid fixed point via runaway flow of the corresponding interaction vertex. Embarking upon this fact, in an application of ɛ FRG to the spinless disordered Hubbard model we calculate its phase boundary in the plane spanned by the interaction and disorder strength. Finally, an extension of the approach to finite temperatures and spin S =1 /2 is also given.

  7. Renormalized dispersion relations of β-Fermi-Pasta-Ulam chains in equilibrium and nonequilibrium states

    NASA Astrophysics Data System (ADS)

    Jiang, Shi-xiao W.; Lu, Hai-hao; Zhou, Douglas; Cai, David

    2014-09-01

    We study the nonlinear dispersive characteristics in β-Fermi-Pasta-Ulam (FPU) chains in both thermal equilibrium and nonequilibrium steady state. By applying a multiple scale analysis to the FPU chain, we analyze the contribution of the trivial and nontrivial resonance to the renormalization of the dispersion relation. Our results show that the contribution of the nontrivial resonance remains significant to the renormalization, in particular, in strongly nonlinear regimes. We contrast our results with the dispersion relations obtained from the Zwanzig-Mori formalism and random phase approximation to further illustrate the role of resonances. Surprisingly, these theoretical dispersion relations can be generalized to describe dispersive characteristics well at the nonequilibrium steady state of the FPU chain with driving-damping in real space. Through numerical simulation, we confirm that the theoretical renormalized dispersion relations are valid for a wide range of nonlinearities in thermal equilibrium as well as in nonequilibrium steady state. We further show that the dispersive characteristics persist in nonequilibrium steady state driven-damped in Fourier space.

  8. Functional renormalization group analysis of tensorial group field theories on Rd

    NASA Astrophysics Data System (ADS)

    Geloun, Joseph Ben; Martini, Riccardo; Oriti, Daniele

    2016-07-01

    Rank-d tensorial group field theories are quantum field theories (QFTs) defined on a group manifold G×d , which represent a nonlocal generalization of standard QFT and a candidate formalism for quantum gravity, since, when endowed with appropriate data, they can be interpreted as defining a field theoretic description of the fundamental building blocks of quantum spacetime. Their renormalization analysis is crucial both for establishing their consistency as quantum field theories and for studying the emergence of continuum spacetime and geometry from them. In this paper, we study the renormalization group flow of two simple classes of tensorial group field theories (TGFTs), defined for the group G =R for arbitrary rank, both without and with gauge invariance conditions, by means of functional renormalization group techniques. The issue of IR divergences is tackled by the definition of a proper thermodynamic limit for TGFTs. We map the phase diagram of such models, in a simple truncation, and identify both UV and IR fixed points of the RG flow. Encouragingly, for all the models we study, we find evidence for the existence of a phase transition of condensation type.

  9. An exact renormalization model for earthquakes and material failure: Statics and dynamics

    SciTech Connect

    Newman, W.I. |; Gabrielov, A.M. |; Durand, T.A.; Phoenix, S.L.; Turcotte, D.L.

    1993-09-12

    Earthquake events are well-known to prams a variety of empirical scaling laws. Accordingly, renormalization methods offer some hope for understanding why earthquake statistics behave in a similar way over orders of magnitude of energy. We review the progress made in the use of renormalization methods in approaching the earthquake problem. In particular, earthquake events have been modeled by previous investigators as hierarchically organized bundles of fibers with equal load sharing. We consider by computational and analytic means the failure properties of such bundles of fibers, a problem that may be treated exactly by renormalization methods. We show, independent of the specific properties of an individual fiber, that the stress and time thresholds for failure of fiber bundles obey universal, albeit different, staling laws with respect to the size of the bundles. The application of these results to fracture processes in earthquake events and in engineering materials helps to provide insight into some of the observed patterns and scaling-in particular, the apparent weakening of earthquake faults and composite materials with respect to size, and the apparent emergence of relatively well-defined stresses and times when failure is seemingly assured.

  10. Calculation of QCD instanton determinant with arbitrary mass

    SciTech Connect

    Dunne, Gerald V.; Hur, Jin; Lee, Choonkyu; Min, Hyunsoo

    2005-04-15

    The precise quark mass dependence of the one-loop effective action in an instanton background has recently been computed [Phys. Rev. Lett. 94, 072001 (2005).]. The result interpolates smoothly between the previously known extreme small and large mass limits. The computational method makes use of the fact that the single instanton background has radial symmetry, so that the computation can be reduced to a sum over partial waves of logarithms of radial determinants, each of which can be computed numerically in an efficient manner. The bare sum over partial waves is divergent and must be regulated and renormalized. In this paper we provide more details of this computation, including both the renormalization procedure and the numerical approach. We conclude with comparisons of our precise numerical results with a simple interpolating function that connects the small and large mass limits, and with the leading order of the derivative expansion.

  11. Stueckelberg massive electromagnetism in curved spacetime: Hadamard renormalization of the stress-energy tensor and the Casimir effect

    NASA Astrophysics Data System (ADS)

    Belokogne, Andrei; Folacci, Antoine

    2016-02-01

    We discuss Stueckelberg massive electromagnetism on an arbitrary four-dimensional curved spacetime and, in particular, (i) the gauge invariance of the classical theory and its covariant quantization; (ii) the wave equations for the massive spin-1 field Aμ , for the auxiliary Stueckelberg scalar field Φ and for the ghost fields C and C*; (iii) Ward identities; (iv) the Hadamard representation of the various Feynman propagators and the covariant Taylor series expansions of the corresponding coefficients. This permits us to construct, for a Hadamard quantum state, the expectation value of the renormalized stress-energy tensor associated with the Stueckelberg theory. We provide two alternative but equivalent expressions for this result. The first one is obtained by removing the contribution of the "Stueckelberg ghost" Φ and only involves state-dependent and geometrical quantities associated with the massive vector field Aμ. The other one involves contributions coming from both the massive vector field and the auxiliary Stueckelberg scalar field, and it has been constructed in such a way that, in the zero-mass limit, the massive vector field contribution reduces smoothly to the result obtained from Maxwell's theory. As an application of our results, we consider the Casimir effect outside a perfectly conducting medium with a plane boundary. We discuss the results obtained using Stueckelberg but also de Broglie-Proca electromagnetism, and we consider the zero-mass limit of the vacuum energy in both theories. We finally compare the de Broglie-Proca and Stueckelberg formalisms and highlight the advantages of the Stueckelberg point of view, even if, in our opinion, the de Broglie-Proca and Stueckelberg approaches of massive electromagnetism are two faces of the same field theory.

  12. Quark mass dependence of two-flavor QCD

    NASA Astrophysics Data System (ADS)

    Creutz, Michael

    2011-01-01

    I explore the rich phase diagram of two-flavor QCD as a function of the quark masses. The theory involves three parameters, including one that is CP violating. As the masses vary, regions of both first- and second-order transitions are expected. For nondegenerate quarks, nonperturbative effects cease to be universal, leaving individual quark mass ratios with a renormalization scheme dependence. This raises complications in matching lattice results with perturbative schemes and demonstrates the tautology of attacking the strong CP problem via a vanishing up-quark mass.

  13. Interplay of the scaling limit and the renormalization group: Implications for symmetry restoration

    NASA Astrophysics Data System (ADS)

    Konik, Robert M.; Saleur, Hubert; Ludwig, Andreas W.

    2002-08-01

    Symmetry restoration is usually understood as a renormalization-group induced phenomenon. In this context, the issue of whether one-loop renormalization-group equations can be trusted in predicting symmetry restoration has recently been the subject of much debate. Here we advocate a more pragmatic point of view and expand the definition of symmetry restoration to encompass all situations where the physical properties have only a weak dependence upon an anisotropy in the bare couplings. Moreover we concentrate on universal properties, and so take a scaling limit where the physics is well described by a field theory. In this context, we find a large variety of models that exhibit, for all practical purposes, symmetry restoration: even if symmetry is not restored in a strict sense, physical properties are surprisingly insensitive to the remaining anisotropy. Although we have adopted an expanded notion of symmetry restoration, we nonetheless emphasize that the scaling limit also has implications for symmetry restoration as a renormalization-group induced phenomenon. In all the models we considered, the scaling limit turns out only to permit bare couplings which are nearly isotropic and small. Then the one-loop β function should contain all the physics and higher loop orders can be neglected. We suggest that this feature generalizes to more complex models. We exhibit a large class of theories with current-current perturbations [of which the SO(8) model of interest in two-leg Hubbard ladders and armchair carbon nanotubes is one] where the one-loop β functions indicate symmetry restoration; thus we argue that these results can be trusted within the scaling limit.

  14. Algorithmic derivation of functional renormalization group equations and Dyson-Schwinger equations

    NASA Astrophysics Data System (ADS)

    Huber, Markus Q.; Braun, Jens

    2012-06-01

    We present the Mathematica application DoFun which allows to derive Dyson-Schwinger equations and renormalization group flow equations for n-point functions in a simple manner. DoFun offers several tools which considerably simplify the derivation of these equations from a given physical action. We discuss the application of DoFun by means of two different types of quantum field theories, namely a bosonic O(N) theory and the Gross-Neveu model. Program summaryProgram title:DoFun Catalogue identifier: AELN_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AELN_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 35 506 No. of bytes in distributed program, including test data, etc.: 571 837 Distribution format: tar.gz Programming language: Mathematica 7 and higher Computer: PCs and workstations Operating system: All on which Mathematica is available (Windows, Unix, MacOS) Classification: 11.1, 11.4, 11.5, 11.6 Nature of problem: Derivation of functional renormalization group equations and Dyson-Schwinger equations from the action of a given theory. Solution method: Implementation of an algorithm to derive functional renormalization group and Dyson-Schwinger equations. Unusual features: The results can be plotted as Feynman diagrams in Mathematica. The output is compatible with the syntax of many other programs and is therefore suitable for further (algebraic) computations. Running time: Seconds to minutes

  15. Apker Award Recipient: Renormalization-Group Study of Helium Mixtures Immersed in a Porous Medium

    NASA Astrophysics Data System (ADS)

    Lopatnikova, Anna

    1998-03-01

    Superfluidity and phase separation in ^3He-^4He mixtures immersed in aerogel are studied by renormalization-group theory. Firstly, the theory is applied to jungle-gym (non-random) aerogel.(A. Lopatnikova and A.N. Berker, Phys. Rev. B 55, 3798 (1997).) This calculation is conducted via the coupled renormalization-group mappings of interactions near and away from aerogel. Superfluidity at very low ^4He concentrations and a depressed tricritical temperature are found at the onset of superfludity. A superfluid-superfluid phase separation, terminating at an isolated critical point, is found entirely within the superfluid phase. Secondly, the theory is applied to true aerogel, which has quenched disorder at both atomic and geometric levels.(A. Lopatnikova and A.N. Berker, Phys. Rev. B 56, 11865 (1997).) This calculation is conducted via the coupled renormalization-group mappings, near and away from aerogel, of quenched probability distributions of random interactions. Random-bond effects on superfluidity onset and random-field effects on superfluid phase separation are seen. The quenched randomness causes the λ line of second-order phase transitions of superfluidity onset to reach zero temperature, in agreement with general prediction and experiments. Based on these studies, the experimentally observed(S.B. Kim, J. Ma, and M.H.W. Chan, Phys. Rev. Lett. 71, 2268 (1993); N. Mulders and M.H.W. Chan, Phys. Rev. Lett. 75, 3705 (1995).) distinctive characteristics of ^3He-^4He mixtures in aerogel are related to the aerogel properties of connectivity, tenuousness, and atomic and geometric randomness.

  16. On stochastic differential equations driven by the renormalized square of the Gaussian white noise

    NASA Astrophysics Data System (ADS)

    Ben Ammou, Bilel Kacem; Lanconelli, Alberto

    2015-11-01

    We investigate the properties of the Wick square of Gaussian white noises through a new method to perform nonlinear operations on Hida distributions. This method lays in between the Wick product interpretation and the usual definition of nonlinear functions. We prove an Itô-type formula and solve stochastic differential equations driven by the renormalized square of the Gaussian white noise. Our approach works with standard assumptions on the coefficients of the equations, global Lipschitz continuity, and produces existence and uniqueness results in the space where the noise lives. The linear case is studied in details and positivity of the solution is proved.

  17. A simpler derivation of Feigenbaum's renormalization group equation for the period-doubling bifurcation sequence

    NASA Astrophysics Data System (ADS)

    Coppersmith, S. N.

    1999-01-01

    One interesting and important property of nonlinear dynamical systems is that they can exhibit universality—behavior that is quantitatively identical for a broad class of systems. The first and most famous example of universality in a dynamical system was identified by Feigenbaum [M. J. Feigenbaum, J. Stat. Phys. 19, 25-52 (1978), 21, 669-706 (1979)] in the period-doubling route to chaos. This note presents a new derivation of Feigenbaum's renormalization group equation, used to understand this universality. The argument, designed for incorporation into an undergraduate dynamical systems course, is simpler than those in standard textbooks.

  18. Renormalization of the Three-Body System with Short-Range Interactions

    NASA Astrophysics Data System (ADS)

    Bedaque, P. F.; Hammer, H.-W.; van Kolck, U.

    1999-01-01

    We discuss renormalization of the nonrelativistic three-body problem with short-range forces. The problem becomes nonperturbative at momenta of the order of the inverse of the two-body scattering length, and an infinite number of graphs must be summed. This summation leads to a cutoff dependence that does not appear in any order in perturbation theory. We argue that this cutoff dependence can be absorbed in a single three-body counterterm and compute the running of the three-body force with the cutoff. We comment on the relevance of this result for the effective field theory program in nuclear and molecular physics.

  19. Charge independence, charge symmetry breaking in the S-wave nucleon-nucleon interaction, and renormalization

    SciTech Connect

    Alvaro Calle Cordon,Manuel Pavon Valderrama,Enrique Ruiz Arriola

    2012-02-01

    We study the interplay between charge symmetry breaking and renormalization in the NN system for S-waves. We find a set of universality relations which disentangle explicitly the known long distance dynamics from low energy parameters and extend them to the Coulomb case. We analyze within such an approach the One-Boson-Exchange potential and the theoretical conditions which allow to relate the proton-neutron, proton-proton and neutron-neutron scattering observables without the introduction of extra new parameters and providing good phenomenological success.

  20. Time-dependent renormalized-natural-orbital theory applied to laser-driven H2 +

    NASA Astrophysics Data System (ADS)

    Hanusch, A.; Rapp, J.; Brics, M.; Bauer, D.

    2016-04-01

    Recently introduced time-dependent renormalized-natural-orbital theory (TDRNOT) is extended towards a multicomponent approach in order to describe H2 + beyond the Born-Oppenheimer approximation. Two kinds of natural orbitals, describing the electronic and the nuclear degrees of freedom are introduced, and the exact equations of motion for them are derived. The theory is benchmarked by comparing numerically exact results of the time-dependent Schrödinger equation for an H2 + model system with the corresponding TDRNOT predictions. Ground-state properties, linear-response spectra, fragmentation, and high-order harmonic generation are investigated.

  1. Renormalization of the fragmentation equation: exact self-similar solutions and turbulent cascades.

    PubMed

    Saveliev, V L; Gorokhovski, M A

    2012-12-01

    Using an approach developed earlier for renormalization of the Boltzmann collision integral [Saveliev and Nanbu, Phys. Rev. E 65, 051205 (2002)], we derive an exact divergence form for the fragmentation operator. Then we reduce the fragmentation equation to the continuity equation in size space, with the flux given explicitly. This allows us to obtain self-similar solutions and to find the integral of motion for these solutions (we call it the bare flux). We show how these solutions can be applied as a description of cascade processes in three- and two-dimensional turbulence. We also suggested an empirical cascade model of impact fragmentation of brittle materials. PMID:23367898

  2. Continuous Multiscale Entanglement Renormalization Ansatz as Holographic Surface-State Correspondence.

    PubMed

    Miyaji, Masamichi; Numasawa, Tokiro; Shiba, Noburo; Takayanagi, Tadashi; Watanabe, Kento

    2015-10-23

    We present how the surface-state correspondence, conjectured by Miyaji and Takayanagi, works in the setup of AdS(3)/CFT(2) by generalizing the formulation of a continuous multiscale entanglement renormalization group ansatz. The boundary states in conformal field theories play a crucial role in our formulation and the bulk diffeomorphism is naturally taken into account. We give an identification of bulk local operators which reproduces correct scalar field solutions on AdS(3) and bulk scalar propagators. We also calculate the information metric for a locally excited state and show that it reproduces the time slice of AdS(3). PMID:26551098

  3. Renormalized scattering series for frequency-domain waveform modelling of strong velocity contrasts

    NASA Astrophysics Data System (ADS)

    Jakobsen, M.; Wu, R. S.

    2016-08-01

    An improved description of scattering and inverse scattering processes in reflection seismology may be obtained on the basis of a scattering series solution to the Helmoltz equation, which allows one to separately model primary and multiple reflections. However, the popular scattering series of Born is of limited seismic modelling value, since it is only guaranteed to converge if the global contrast is relatively small. For frequency-domain waveform modelling of realistic contrasts, some kind of renormalization may be required. The concept of renormalization is normally associated with quantum field theory, where it is absolutely essential for the treatment of infinities in connection with observable quantities. However, the renormalization program is also highly relevant for classical systems, especially when there are interaction effects that act across different length scales. In the scattering series of De Wolf, a renormalization of the Green's functions is achieved by a split of the scattering potential operator into fore- and backscattering parts; which leads to an effective reorganization and partially re-summation of the different terms in the Born series, so that their order better reflects the physics of reflection seismology. It has been demonstrated that the leading (single return) term in the De Wolf series (DWS) gives much more accurate results than the corresponding Born approximation, especially for models with high contrasts that lead to a large accumulation of phase changes in the forward direction. However, the higher order terms in the DWS that are associated with internal multiples have not been studied numerically before. In this paper, we report from a systematic numerical investigation of the convergence properties of the DWS which is based on two new operator representations of the DWS. The first operator representation is relatively similar to the original scattering potential formulation, but more global and explicit in nature. The second

  4. Nonperturbative renormalization of quark bilinear operators and B{sub K} using domain wall fermions

    SciTech Connect

    Aoki, Y.; Dawson, C.; Boyle, P. A.; Tweedie, R. J.; Christ, N. H.; Li, S.; Mawhinney, R. D.; Donnellan, M. A.; Juettner, A.; Sachrajda, C. T.; Izubuchi, T.; Noaki, J.; Soni, A.; Yamaguchi, A.

    2008-09-01

    We present a calculation of the renormalization coefficients of the quark bilinear operators and the K-K mixing parameter B{sub K}. The coefficients relating the bare lattice operators to those in the RI/MOM scheme are computed nonperturbatively and then matched perturbatively to the MS scheme. The coefficients are calculated on the RBC/UKQCD 2+1 flavor dynamical lattice configurations. Specifically we use a 16{sup 3}x32 lattice volume, the Iwasaki gauge action at {beta}=2.13 and domain wall fermions with L{sub s}=16.

  5. Real space renormalization group and totalitarian paradox of majority rule voting

    NASA Astrophysics Data System (ADS)

    Galam, Serge

    2000-09-01

    The effect of majority rule voting in hierarchical structures is studied using the basic concepts from real space renormalization group. It shows in particular that a huge majority can be self-eliminated while climbing up the hierarchy levels. This majority democratic self-elimination articulates around the existence of fixed points in the voting flow. An unstable fixed point determines the critical threshold to full and total power. It can be varied from 50% up to 77% of initial support. Our model could shed new light on the last century eastern European communist collapse.

  6. Improving the In-Medium Similarity Renormalization Group via approximate inclusion of three-body effects

    NASA Astrophysics Data System (ADS)

    Morris, Titus; Bogner, Scott

    2015-10-01

    The In-Medium Similarity Renormalization Group (IM-SRG) has been applied successfully not only to several closed shell finite nuclei, but has recently been used to produce effective shell model interactions that are competitive with phenomenological interactions in the SD shell. A recent alternative method for solving of the IM-SRG equations, called the Magnus expansion, not only provides a computationally feasible route to producing observables, but also allows for approximate handling of induced three-body forces. Promising results for several systems, including finite nuclei, will be presented and discussed.

  7. Dynamical gap generation in graphene with frequency-dependent renormalization effects

    NASA Astrophysics Data System (ADS)

    Carrington, M. E.; Fischer, C. S.; von Smekal, L.; Thoma, M. H.

    2016-09-01

    We study the frequency dependencies in the renormalization of the fermion Green's function for the π -band electrons in graphene and their influence on the dynamical gap generation at sufficiently strong interaction. Adopting the effective QED-like description for the low-energy excitations within the Dirac-cone region, we self-consistently solve the fermion Dyson-Schwinger equation in various approximations for the photon propagator and the vertex function with special emphasis on frequency-dependent Lindhard screening and retardation effects.

  8. Computing Effective Hamiltonians of Doped and Frustrated Antiferromagnets By Contractor Renormalization

    NASA Astrophysics Data System (ADS)

    Auerbach, Assa

    2006-02-01

    A review of the Contractor Renormalization (CORE) method, as a systematic derivation of the low energy effective hamiltonian, is given, with emphasis on its differences and advantages over traditional perturbative (weak/strong links) real space RG. For the low energy physics of the 2D Hubbard model, we derive the plaquette bosons (projected SO(5)) model which connects the microscopic model to phases and phenomenology of high-Tc cuprates. For the S = 1/2 Pyrochlore and Kagomé antiferromagnets, the effective hamiltonians predict spin-disordered, lattice symmetry breaking, ground states with a large density of low energy singlets as found by exact diagonalization of small clusters.

  9. Renormalizing (phi/sup 3/)/sub 6/ theory in curved space-time

    SciTech Connect

    Kodaira, J.; Okada, J.

    1986-05-15

    The renormalization of phi/sup 3/ theory in a six-dimensional conformally flat space-time is discussed at the two-loop level. The background-field method and the momentum-space representation of the Feynman propagator are used to calculate the ultraviolet divergences of the effective action. It is shown that (phi/sup 3/)/sub 6/ theory is renormalizable in a conformally flat space-time at the two-loop level. The counterterms are given to the two-loop order. The next-to-leading-order term in the ..beta.. function for the coupling constant of the Rphi/sup 2/ term is then obtained.

  10. Renormalization-group theory for the phase-field crystal equation

    NASA Astrophysics Data System (ADS)

    Athreya, Badrinarayan P.; Goldenfeld, Nigel; Dantzig, Jonathan A.

    2006-07-01

    We derive a set of rotationally covariant amplitude equations for use in multiscale simulation of the two-dimensional phase-field crystal model by a variety of renormalization-group (RG) methods. We show that the presence of a conservation law introduces an ambiguity in operator ordering in the RG procedure, which we show how to resolve. We compare our analysis with standard multiple-scale techniques, where identical results can be obtained with greater labor, by going to sixth order in perturbation theory, and by assuming the correct scaling of space and time.

  11. Radiation reaction and renormalization in classical electrodynamics of a point particle in any dimension

    NASA Astrophysics Data System (ADS)

    Kazinski, P. O.; Lyakhovich, S. L.; Sharapov, A. A.

    2002-07-01

    The effective equations of motion for a point charged particle taking into account the radiation reaction are considered in various space-time dimensions. The divergences stemming from the pointness of the particle are studied and an effective renormalization procedure is proposed encompassing uniformly the cases of all even dimensions. It is shown that in any dimension the classical electrodynamics is a renormalizable theory if not multiplicatively beyond d=4. For the cases of three and six dimensions the covariant analogues of the Lorentz-Dirac equation are explicitly derived.

  12. Golden mean renormalization for a generalized Harper equation: The Ketoja-Satija orchid

    NASA Astrophysics Data System (ADS)

    Mestel, B. D.; Osbaldestin, A. H.

    2004-12-01

    We provide a rigorous analysis of the fluctuations of localized eigenstates in a generalized Harper equation with golden mean flux and with next-nearest-neighbor interactions. For next-nearest-neighbor interaction above a critical threshold, these self-similar fluctuations are characterized by orbits of a renormalization operator on a universal strange attractor, whose projection was dubbed the "orchid" by Ketoja and Satija [Phys. Rev. Lett. 75, 2762 (1995)]. We show that the attractor is given essentially by an embedding of a subshift of finite type, and give a description of its periodic orbits.

  13. Order parameter evolution in scalar QFT: Renormalization group resummation of secular terms

    SciTech Connect

    de Vega, H.J.; Salgado, J.F.

    1997-11-01

    The quantum evolution equations for the field expectation value are analytically solved to cubic order in the field amplitude and to one-loop level in the {lambda}{phi}{sup 4} model. We adapt and use the renormalization group (RG) method for such nonlinear and nonlocal equations. The time dependence of the field expectation value is explicitly derived integrating the RG equations. It is shown that the field amplitude for late times approaches a finite limit as O(t{sup {minus}3/2}). This limiting value is expressed as a function of the initial field amplitude. {copyright} {ital 1997} {ital The American Physical Society}

  14. Time-dependent renormalized Redfield theory II for off-diagonal transition in reduced density matrix

    NASA Astrophysics Data System (ADS)

    Kimura, Akihiro

    2016-09-01

    In our previous letter (Kimura, 2016), we constructed time-dependent renormalized Redfield theory (TRRT) only for diagonal transition in a reduced density matrix. In this letter, we formulate the general expression for off-diagonal transition in the reduced density matrix. We discuss the applicability of TRRT by numerically comparing the dependencies on the energy gap of the exciton relaxation rate by using the TRRT and the modified Redfield theory (MRT). In particular, we roughly show that TRRT improves MRT for the detailed balance about the excitation energy transfer reaction.

  15. Spectral renormalization group for the Gaussian model and ψ4 theory on nonspatial networks

    NASA Astrophysics Data System (ADS)

    Tuncer, Aslı; Erzan, Ayşe

    2015-08-01

    We implement the spectral renormalization group on different deterministic nonspatial networks without translational invariance. We calculate the thermodynamic critical exponents for the Gaussian model on the Cayley tree and the diamond lattice and find that they are functions of the spectral dimension, d ˜. The results are shown to be consistent with those from exact summation and finite-size scaling approaches. At d ˜=2 , the lower critical dimension for the Ising universality class, the Gaussian fixed point is stable with respect to a ψ4 perturbation up to second order. However, on generalized diamond lattices, non-Gaussian fixed points arise for 2

  16. Top quark and Higgs boson masses from wormhole physics

    SciTech Connect

    Harris, B.A.; Joshi, G.C. )

    1994-11-01

    We bring together quantum field theory on [ital S][sub 4] with the Coleman wormhole hypothesis, which imposes constraints on terms in the gravitational Lagrangian. In particular, we investigate the effect of matter fields on the trace anomaly, which is related to the (curvature)[sup 2] terms, by the use of the renormalization group equations. We consider a toy model of a nonconformally coupled Higgs boson to a single top'' quark. By numerically solving the renormalization group equations for the couplings of the model, we can find preferred values of the particle masses for various values of the bare nonconformal coupling. By making the [ital ad] [ital hoc] assumption that the tree-level, Higgs boson treace anomaly vanishes on shell, a unique prediction can be made within this model for the masses of both the Higgs boson and the top quark.

  17. Additional zinc delivered in a liquid supplement, but not in a fortified porridge, increased fat-free mass accrual among young Peruvian children with mild-to-moderate stunting.

    PubMed

    Arsenault, Joanne E; López de Romaña, Daniel; Penny, Mary E; Van Loan, Marta D; Brown, Kenneth H

    2008-01-01

    The exact mechanism whereby zinc influences growth is unknown, although it has been postulated that zinc may stimulate appetite and energy intake or enhance fat-free mass (FFM) accrual directly. We compared energy intake, reported appetite, and body composition of 6- to 8-mo-old Peruvian children with initial length-for-age Z-score (LAZ) < -0.5 SD who were randomly assigned to receive daily for 6 mo: 1) 3 mg/d zinc in a liquid supplement; 2) 3 mg/d zinc in a fortified porridge; or 3) no extra zinc in either the supplement or porridge. There were no group-wise differences in changes in dietary energy intakes or body composition or in the prevalence of reported poor appetite. However, among children with an initial LAZ less than the median (-1.1 SD), those who received zinc as a liquid supplement had a 0.41 kg greater increase in FFM than those who did not receive zinc (P < 0.05). We concluded that daily provision of 3 mg of supplemental zinc did not affect energy intake or reported appetite. Among children with initial mild-to-moderate stunting, those who received the zinc supplement had a greater increase in FFM than those who did not receive additional zinc. It is possible that the growth-restricted children were more likely to be zinc deficient and that FFM accrual may be an early growth response to supplemental zinc. Zinc supplements may be more efficacious than the same dose of zinc provided in fortified food; therefore, further research is needed on the optimal level of zinc fortification that will result in improved health outcomes in populations with high rates of zinc deficiency.

  18. Additional zinc delivered in a liquid supplement, but not in a fortified porridge, increased fat-free mass accrual among young Peruvian children with mild-to-moderate stunting.

    PubMed

    Arsenault, Joanne E; López de Romaña, Daniel; Penny, Mary E; Van Loan, Marta D; Brown, Kenneth H

    2008-01-01

    The exact mechanism whereby zinc influences growth is unknown, although it has been postulated that zinc may stimulate appetite and energy intake or enhance fat-free mass (FFM) accrual directly. We compared energy intake, reported appetite, and body composition of 6- to 8-mo-old Peruvian children with initial length-for-age Z-score (LAZ) < -0.5 SD who were randomly assigned to receive daily for 6 mo: 1) 3 mg/d zinc in a liquid supplement; 2) 3 mg/d zinc in a fortified porridge; or 3) no extra zinc in either the supplement or porridge. There were no group-wise differences in changes in dietary energy intakes or body composition or in the prevalence of reported poor appetite. However, among children with an initial LAZ less than the median (-1.1 SD), those who received zinc as a liquid supplement had a 0.41 kg greater increase in FFM than those who did not receive zinc (P < 0.05). We concluded that daily provision of 3 mg of supplemental zinc did not affect energy intake or reported appetite. Among children with initial mild-to-moderate stunting, those who received the zinc supplement had a greater increase in FFM than those who did not receive additional zinc. It is possible that the growth-restricted children were more likely to be zinc deficient and that FFM accrual may be an early growth response to supplemental zinc. Zinc supplements may be more efficacious than the same dose of zinc provided in fortified food; therefore, further research is needed on the optimal level of zinc fortification that will result in improved health outcomes in populations with high rates of zinc deficiency. PMID:18156412

  19. PSTAR: Primary and secondary terms analysis and renormalization: A unified approach to building energy simulations and short-term monitoring

    SciTech Connect

    Subbarao, K.

    1988-09-01

    This report presents a unified method of hourly simulation of a building and analysis of performance data. The method is called Primary and Secondary Terms Analysis and Renormalization (PSTAR). In the PSTAR method, renormalized parameters are introduced for the primary terms such that the renormalized energy balance equation is best satisfied in the least squares sense, hence, the name PSTAR. PSTAR allows extraction of building characteristics from short-term tests on a small number of data channels. These can be used for long-term performance prediction (''ratings''), diagnostics, and control of heating, ventilating, and air conditioning systems (HVAC), comparison of design versus actual performance, etc. By combining realistic building models, simple test procedures, and analysis involving linear equations, PSTAR provides a powerful tool for analyzing building energy as well as testing and monitoring. It forms the basis for the Short-Term Energy Monitoring (STEM) project at SERI.

  20. Renormalization and Short Distance Properties of Gauge Invariant Gluonium and Hadron Operators

    NASA Astrophysics Data System (ADS)

    Dorn, H.; Robaschik, D.; Wieczorek, E.

    Various expressions for nonlocal gauge invariant meson, baryon and gluonium operators are considered which differ from one another not only by the colour representations of the phase factors used but also with respect to the underlying contours. Renormalization and short distance properties of these operators turn out to be unique as long as the contours chosen are smooth ones. Anomalous dimensions of mesons and baryons can be expressed in terms of a gauge independent anomalous dimension of the quark field. Furthermore, composite operators distinguished by the absence of renormalization are discussed.Translated AbstractDie Renormierung eichinvarianter Gluonium- und Hadron-Operatoren und ihr Verhalten bei kleinen AbständenEs werden verschiedene nichtlokale eichinvariante Meson-, Baryon- und Gluoniumoperatoren untersucht, die sich sowohl hinsichtlich der gewählten Darstellung der Farbgruppe als auch der zu Grunde liegenden Kurven unterscheiden. Die Renormierung und das Verhalten bei kleinen Abständen sind jedoch unabhängig von dieser Wahl, solange glatte einfache Kurven benutzt werden. Die anomalen Dimensionen der Mesonen und Baryonen erweisen sich als Vielfaches einer eichinvarianten anomalen Dimension des Quarkfeldes. Schließlich werden Operatoren konstruiert, die keiner Renormierung bedürfen.

  1. Analytic Dependence is an Unnecessary Requirement in Renormalization of Locally Covariant QFT

    NASA Astrophysics Data System (ADS)

    Khavkine, Igor; Moretti, Valter

    2016-06-01

    Finite renormalization freedom in locally covariant quantum field theories on curved spacetime is known to be tightly constrained, under certain standard hypotheses, to the same terms as in flat spacetime up to finitely many curvature dependent terms. These hypotheses include, in particular, locality, covariance, scaling, microlocal regularity and continuous and analytic dependence on the metric and coupling parameters. The analytic dependence hypothesis is somewhat unnatural, because it requires that locally covariant observables (which are simultaneously defined on all spacetimes) depend continuously on an arbitrary metric, with the dependence strengthened to analytic on analytic metrics. Moreover the fact that analytic metrics are globally rigid makes the implementation of this requirement at the level of local {*}-algebras of observables rather technically cumbersome. We show that the conditions of locality, covariance, scaling and a naturally strengthened microlocal spectral condition, are actually sufficient to constrain the allowed finite renormalizations equally strongly, thus eliminating both the continuity and the somewhat unnatural analyticity hypotheses. The key step in the proof uses the Peetre-Slovák theorem on the characterization of (in general non-linear) differential operators by their locality and regularity properties.

  2. Diffusion on a one-dimensional disordered lattice: A renormalization-group approach

    NASA Astrophysics Data System (ADS)

    Guyer, R. A.

    1984-04-01

    Diffusion of a particle on a one-dimensional disordered lattice is studied using the renormalization-group (RG) procedure of Goncalves da Silva and Koiller

    [Solid State Commun. 40, 215 (1981)]
    . The RG equations are derived and their physical content is discussed. Several examples are studied using the RG equations and a disorder-averaging procedure that permits stepwise averaging of the RG equations. Values of the diffusion constant so calculated, while qualitatively correct, are in poor agreement with the known correct answer. The RG equations are shown to be derivable from a dedecoration carried out on a replica-trick description of the diffusion process. Employing the relationship of the RG equations to dedecoration, a stepwise disorder-averaging procedure is constructed that yields values of the diffusion constant in excellent agreement with expectations. The relationships of the RG equations to the renormalization-group treatment of Machta
    [Phys. Rev. B 24, 5260 (1981)]
    and to the logistic equation are discussed.

  3. Giant bandgap renormalization and excitonic effects in a monolayer transition metal dichalcogenide semiconductor

    NASA Astrophysics Data System (ADS)

    Ugeda, Miguel M.; Bradley, Aaron J.; Shi, Su-Fei; da Jornada, Felipe H.; Zhang, Yi; Qiu, Diana Y.; Ruan, Wei; Mo, Sung-Kwan; Hussain, Zahid; Shen, Zhi-Xun; Wang, Feng; Louie, Steven G.; Crommie, Michael F.

    2014-12-01

    Two-dimensional (2D) transition metal dichalcogenides (TMDs) are emerging as a new platform for exploring 2D semiconductor physics. Reduced screening in two dimensions results in markedly enhanced electron-electron interactions, which have been predicted to generate giant bandgap renormalization and excitonic effects. Here we present a rigorous experimental observation of extraordinarily large exciton binding energy in a 2D semiconducting TMD. We determine the single-particle electronic bandgap of single-layer MoSe2 by means of scanning tunnelling spectroscopy (STS), as well as the two-particle exciton transition energy using photoluminescence (PL) spectroscopy. These yield an exciton binding energy of 0.55 eV for monolayer MoSe2 on graphene—orders of magnitude larger than what is seen in conventional 3D semiconductors and significantly higher than what we see for MoSe2 monolayers in more highly screening environments. This finding is corroborated by our ab initio GW and Bethe-Salpeter equation calculations which include electron correlation effects. The renormalized bandgap and large exciton binding observed here will have a profound impact on electronic and optoelectronic device technologies based on single-layer semiconducting TMDs.

  4. Natural orbitals renormalization group approach to the two-impurity Kondo critical point

    NASA Astrophysics Data System (ADS)

    He, Rong-Qiang; Dai, Jianhui; Lu, Zhong-Yi

    2015-04-01

    The problem of two magnetic impurities in a normal metal exposes the two opposite tendencies in the formation of a singlet ground state, driven respectively by the single-ion Kondo effect with conduction electrons to screen impurity spins or the Ruderman-Kittel-Kasuya-Yosida interaction between the two impurities to directly form impurity spin singlet. However, whether the competition between these two tendencies can lead to a quantum critical point has been debated over more than two decades. Here, we study this problem by applying the newly proposed natural orbitals renormalization group method to a lattice version of the two-impurity Kondo model with a direct exchange K between the two impurity spins. The method allows for unbiased access to the ground state wave functions and low-lying excitations for sufficiently large system sizes. We demonstrate the existence of a quantum critical point, characterized by the power-law divergence of impurity staggered susceptibility with critical exponent γ =0.60 (1 ) , on the antiferromagnetic side of K when the interimpurity distance R is even lattice spacing, while a crossover behavior is recovered when R is odd lattice spacing. These results have ultimately resolved the long-standing discrepancy between the numerical renormalization group and quantum Monte Carlo studies, confirming a link of this two-impurity Kondo critical point to a hidden particle-hole symmetry predicted by the local Fermi liquid theory.

  5. Quasiparticle weight and renormalized Fermi velocity of graphene with long-range Coulomb interactions

    NASA Astrophysics Data System (ADS)

    Tang, Ho-Kin; Leaw, Jia Ning; Rodrigues, J. N. B.; Sengupta, P.; Assaad, F. F.; Adam, S.

    In this work, we study the effects of realistic Coulomb interactions in graphene using a projective quantum Monte Carlo simulation of electrons at half-filing on a honeycomb lattice. We compute the quasiparticle residue, the renormalized Fermi velocity and the antiferromagnetic order parameter as a function of both the long-range and short-range components of the Coulomb potential. We find that the Mott insulator transition is determined mostly by the short-range interaction and is consistent with the Gross-Neveu-Yukawa critical theory. Far from the critical point and in the semi-metallic regime, we find that the Fermi-velocity and quasiparticle residue are influenced by the long-range tail of the Coulomb potential, and for very small interaction strength are consistent with predictions of first order perturbation theory. For experimentally relevant and stronger values of the long-range interaction, our numerical data contradicts prediction from both perturbation theory and the renormalization group approaches. This work was supported by Singapore National Research Foundation (NRF-NRFF2012-01 and CA2DM mid-size Centre), Singapore Ministry of Education(Yale-NUS College R-607-265-01312 and MOE2014-T2-2-112), and DFG Grant No. AS120/9-1.

  6. From short to long distances with Gell-Mann--Low Renormalization group

    NASA Astrophysics Data System (ADS)

    Dunjko, Vanja; Olshanii, Maxim

    2004-05-01

    Computing correlation functions is an important and formidable problem of many-body physics. For 1D gapless systems, Haldane's theory gives exponents of large distance expansions, model details entering through speed of sound. The prefactors depend on high-energy cutoffs, and it is unclear which model-dependent parameters set them. ..We present a method very well-suited for the approximate computation of the leading order prefactor, with short-distance expansion as an input. Our basis is the Gell-Mann--Low Renormalization Group, and optimism about sufficient analyticity of correlation functions. In the test case of Tonks-Girardeau gas, a rare model where both short and long-distance expansions are known, already the first non-zero subleading term of the short-distance expansion gives the long-distance prefactor to within 15%. ..While Wilson's Renormalization Group makes high energy cutoffs irrelevant, we actually determine them for Haldane model. A byproduct of our method is an interpolation between short and long-distance behaviors, which we use to treat interaction-induced decoherence in atom interferometers.

  7. Entanglement entropy renormalization for the noncommutative scalar field coupled to classical BTZ geometry

    NASA Astrophysics Data System (ADS)

    Jurić, Tajron; Samsarov, Andjelo

    2016-05-01

    In this work, we consider a noncommutative (NC) massless scalar field coupled to the classical nonrotational BTZ geometry. In a manner of the theories where the gravity emerges from the underlying scalar field theory, we study the effective action and the entropy derived from this noncommutative model. In particular, the entropy is calculated by making use of the two different approaches, the brick-wall method and the heat kernel method designed for spaces with conical singularity. We show that the UV divergent structures of the entropy obtained through these two different methods agree with each other. It is also shown that the same renormalization condition that removes the infinities from the effective action can also be used to renormalize the entanglement entropy for the same system. Besides, the interesting feature of the NC model considered here is that it allows an interpretation in terms of an equivalent system comprising a commutative massive scalar field but in a modified geometry: that of the rotational BTZ black hole, the result that hints at a duality between the commutative and noncommutative systems in the background of a BTZ black hole.

  8. Ising Models, Universality and the Non Renormalization of the Quantum Anomalies

    NASA Astrophysics Data System (ADS)

    Mastropietro, Vieri

    2010-03-01

    A number of universal relations (proposed by Kadanoff, Luther, Peschel and Haldane) are believed to be true in a wide class of systems with continuously varying indices, among which are interacting planar Ising models, vertex or Ashkin-Teller models, quantum spin chains and 1D Fermi systems; by such relations one can predict several quantities in terms of a few measurable parameters without relying on the specific microscopic details. The validity of such relations can be checked in special solvable models but, despite several attempts, the proof of their general validity was up to now an open problem. A rigorous derivation of several of such relations (for solvable and not solvable models and without any use of exact solutions) has been recently obtained in [8] and [11] through Renormalization Group methods. The proof is based on the representation in terms of Grassmann integrals and the validity of the Adler-Bardeen property of the non renormalization of the quantum anomalies in the asymptotic Ward identities. Gauge invariance is exact only in the scaling limit but the lattice corrections can be rigorously taken into account.

  9. Renormalized effective actions in radially symmetric backgrounds: Partial wave cutoff method

    SciTech Connect

    Dunne, Gerald V.; Hur, Jin; Lee, Choonkyu

    2006-10-15

    The computation of the one-loop effective action in a radially symmetric background can be reduced to a sum over partial-wave contributions, each of which is the logarithm of an appropriate one-dimensional radial determinant. While these individual radial determinants can be evaluated simply and efficiently using the Gel'fand-Yaglom method, the sum over all partial-wave contributions diverges. A renormalization procedure is needed to unambiguously define the finite renormalized effective action. Here we use a combination of the Schwinger proper-time method, and a resummed uniform DeWitt expansion. This provides a more elegant technique for extracting the large partial-wave contribution, compared to the higher-order radial WKB approach which had been used in previous work. We illustrate the general method with a complete analysis of the scalar one-loop effective action in a class of radially separable SU(2) Yang-Mills background fields. We also show that this method can be applied to the case where the background gauge fields have asymptotic limits appropriate to uniform field strengths, such as, for example, in the Minkowski solution, which describes an instanton immersed in a constant background. Detailed numerical results will be presented in a sequel.

  10. A practical approach to the Hamilton-Jacobi formulation of holographic renormalization

    NASA Astrophysics Data System (ADS)

    Elvang, Henriette; Hadjiantonis, Marios

    2016-06-01

    We revisit the subject of holographic renormalization for asymptotically AdS spacetimes. For many applications of holography, one has to handle the divergences associated with the on-shell gravitational action. The brute force approach uses the Fefferman- Graham (FG) expansion near the AdS boundary to identify the divergences, but subsequent reversal of the expansion is needed to construct the infinite counterterms. While in principle straightforward, the method is cumbersome and application/reversal of FG is formally unsatisfactory. Various authors have proposed an alternative method based on the Hamilton-Jacobi equation. However, this approach may appear to be abstract, difficult to implement, and in some cases limited in applicability. In this paper, we clarify the Hamilton-Jacobi formulation of holographic renormalization and present a simple algorithm for its implementation to extract cleanly the infinite counterterms. While the derivation of the method relies on the Hamiltonian formulation of general relativity, the actual application of our algorithm does not. The work applies to any D-dimensional holographic dual with asymptotic AdS boundary, Euclidean or Lorentzian, and arbitrary slicing. We illustrate the method in several examples, including the FGPW model, a holographic model of 3d ABJM theory, and cases with marginal scalars such as a dilaton-axion system.

  11. Running of the contact interactions in chiral N3LO potentials from subtractive renormalization

    NASA Astrophysics Data System (ADS)

    Batista, E. F.; Szpigel, S.; Timóteo, V. S.

    2015-07-01

    In this work a subtracted kernel renormalization procedure (SKM) is applied to the chiral NN potential up to next-to-next-to-next-to-leading-order (N3 LO) to obtain the running of the renormalized contact strengths with the subtraction scale μ and the phase shifts for all uncoupled waves with contact interaction (S,P,D). We use two potentials constructed within the framework of Weinberg's approach to ChEFT, which provide a very accurate description of NN scattering data below laboratory energies E ∼ 350 MeV, namely Epelbaum, Glöckle and Meissner (N3LO-EGM) and Entem and Machleidt (N3LO-EM). For both potentials, we consider a large cutoff (30 fm-1) and analyze the phases and the running of the contact strengths with the subtraction point μ by making a fit of the K-matrix with five subtractions to the K-matrix from the Nijmegen II potential at low energies (E ≤ 20 MeV).

  12. Renormalized Area and Properly Embedded Minimal Surfaces in Hyperbolic 3-Manifolds

    NASA Astrophysics Data System (ADS)

    Alexakis, Spyridon; Mazzeo, Rafe

    2010-08-01

    We study the renormalized area functional {mathcal{A}} in the AdS/CFT correspondence, specifically for properly embedded minimal surfaces in convex cocompact hyperbolic 3-manifolds (and somewhat more broadly, Poincaré-Einstein spaces). Our main results include an explicit formula for the renormalized area of such a minimal surface Y as an integral of local geometric quantities, as well as formulæ for the first and second variations of {mathcal{A}} which are given by integrals of global quantities over the asymptotic boundary loop γ of Y. All of these formulæ are also obtained for a broader class of nonminimal surfaces. The proper setting for the study of this functional (when the ambient space is hyperbolic) requires an understanding of the moduli space of all properly embedded minimal surfaces with smoothly embedded asymptotic boundary. We show that this moduli space is a smooth Banach manifold and develop a {mathbb{Z}} -valued degree theory for the natural map taking a minimal surface to its boundary curve. We characterize the nondegenerate critical points of {mathcal{A}} for minimal surfaces in {mathbb{H}^3} , and finally, discuss the relationship of {mathcal{A}} to the Willmore functional.

  13. Precise estimate of correlation length exponents from simple real-space renormalization group analysis

    NASA Astrophysics Data System (ADS)

    Kubica, Aleksander; Yoshida, Beni

    2014-03-01

    We invent a novel real-space renormalization group (RG) scheme which accurately estimates correlation length exponents ν near criticality of quantum Ising and clock models in higher dimensions. The method, based on a recent proposal by Miyazaki et al., Phys. Rev. E 83, 051103 (2011), is remarkably simple (often analytical), grouping only a few spins into a block spin so that renormalized Hamiltonian has a closed form. A previous difficulty of spatial anisotropy and unwanted terms arising in higher-dimensional RG schemes is avoided by incorporating rotational invariance and internal Zq symmetries of the Hamiltonian. By applying this scheme to (2+1)-dim Ising model on a triangular lattice, we obtained ν = 0 . 6300 which is within statistical error of the current best Monte-Carlo result and ϕ4 theory estimation with seven-loop corrections. We also apply the scheme to higher-dimensional clock (Potts) models for which ordinary Monte-Carlo methods are not efficient due to suppression of quantum fluctuation in first-order phase transition.

  14. Linear response theory for the density matrix renormalization group: Efficient algorithms for strongly correlated excited states

    NASA Astrophysics Data System (ADS)

    Nakatani, Naoki; Wouters, Sebastian; Van Neck, Dimitri; Chan, Garnet Kin-Lic

    2014-01-01

    Linear response theory for the density matrix renormalization group (DMRG-LRT) was first presented in terms of the DMRG renormalization projectors [J. J. Dorando, J. Hachmann, and G. K.-L. Chan, J. Chem. Phys. 130, 184111 (2009)]. Later, with an understanding of the manifold structure of the matrix product state (MPS) ansatz, which lies at the basis of the DMRG algorithm, a way was found to construct the linear response space for general choices of the MPS gauge in terms of the tangent space vectors [J. Haegeman, J. I. Cirac, T. J. Osborne, I. Pižorn, H. Verschelde, and F. Verstraete, Phys. Rev. Lett. 107, 070601 (2011)]. These two developments led to the formulation of the Tamm-Dancoff and random phase approximations (TDA and RPA) for MPS. This work describes how these LRTs may be efficiently implemented through minor modifications of the DMRG sweep algorithm, at a computational cost which scales the same as the ground-state DMRG algorithm. In fact, the mixed canonical MPS form implicit to the DMRG sweep is essential for efficient implementation of the RPA, due to the structure of the second-order tangent space. We present ab initio DMRG-TDA results for excited states of polyenes, the water molecule, and a [2Fe-2S] iron-sulfur cluster.

  15. Low energy threshold corrections to neutrino masses and mixing angles

    NASA Astrophysics Data System (ADS)

    Chankowski, P. H.; Wąsowicz, P.

    2002-03-01

    We compute the low energy threshold corrections to neutrino masses and mixing in the standard model (SM) and its minimal supersymmetric version, using the effective theory technique. We demonstrate that they stabilize the results for neutrino masses and mixing with respect to the choice of the scale to which the renormalization group (RG) equation is integrated. (This confirms the correctness of the recent re-derivation of the RGE for the SM in hep-ph/0108005.) Since, as is known, those corrections are potentially very important for phenomenology we derive for them the explicit formulae that can be applied to specific models of neutrino masses and mixing.

  16. Exploring the renormalization of quantum discord and Bell non-locality in the one-dimensional transverse Ising model

    NASA Astrophysics Data System (ADS)

    Liu, Cheng-cheng; Shi, Jia-dong; Ding, Zhi-yong; Ye, Liu

    2016-08-01

    In this paper, the effect of external magnet field g on the relationship among the quantum discord, Bell non-locality and quantum phase transition by employing quantum renormalization-group (QRG) method in the one-dimensional transverse Ising model is investigated. In our model, external magnet field g can influence the phase diagrams. The results have shown that both the two quantum correlation measures can develop two saturated values, which are associated with two distinct phases: long-ranged ordered Ising phase and the paramagnetic phase with the number of QRG iterations increasing. Additionally, quantum non-locality always existent in the long-ranged ordered Ising phase no matter whatever the value of g is and what times QRG steps are carried out and we conclude that the quantum non-locality always exists not only suitable for the two sites of block, but for nearest-neighbor blocks in the long-ranged ordered Ising phase. However, the block-block correlation in the paramagnetic phase is not strong enough to violate the Bell-CHSH inequality as the size of system becomes large. Furthermore, when the system violates the CHSH inequality, i.e., satisfies quantum non-locality, it needs to be entangled. On the other way, if the system obeys the CHSH inequality, it may be entangled or not. To gain further insight, the non-analytic and scaling behavior of QD and Bell non-locality have also been analyzed in detail and this phenomenon indicates that the behavior of the correlation can perfectly help one to observe the quantum critical properties of the model.

  17. NLO QCD corrections to multi-jet production at the LHC with a centre-of-mass energy of √{ s} = 8 TeV

    NASA Astrophysics Data System (ADS)

    Badger, Simon; Biedermann, Benedikt; Uwer, Peter; Yundin, Valery

    2013-01-01

    We study three and four jet production in hadronic collisions at next-to-leading order accuracy in massless QCD. We cross check results previously obtained by the BLACKHAT Collaboration for the LHC with a centre-of-mass energy of √{ s} = 7 TeV and present new results for the LHC operating at 8 TeV. We find large negative NLO corrections reducing the leading order cross sections by about 40-50%. Furthermore we observe an important reduction of the scale uncertainty. In addition to the cross sections we also present results for differential distributions. The dynamical renormalization/factorization scale used in the calculation leads to a remarkably stable K-factor. The results presented here were obtained with the NJET package (Badger et al., 2012) [1], a publicly available library for the evaluation of one-loop amplitudes in massless QCD.

  18. Analytical mass spectrometry of poly(ethylene glycol) additives in artists' acrylic emulsion media, artists' paints, and microsamples from acrylic paintings using MALDI-MS and nanospray-ESI-MS

    NASA Astrophysics Data System (ADS)

    Hoogland, F. G.; Boon, J. J.

    2009-07-01

    Poly(ethylene glycol) (PEG) compounds in artists' acrylic emulsion paint products from different paint manufacturers, ranging from base emulsions (Rohm and Haas, Röhm and Scott Bader), to modified emulsions and complete paints (Rowney, Winsor and Newton, Golden, Liquitex, Lascaux), were characterised with a newly developed mass spectrometric method which combines data from Matrix assisted laser desorption/ionisation mass spectrometry (MALDI-MS) and nano-electrospray ionisation mass spectrometry (nano-ESI-MS(MS)). MALDI-MS was used for the determination of the molar mass distribution (MMD) and calculation of the molar mass averages (Mw and Mn), the polydispersity index (D) and the relative amount of a specific distribution if multiple PEGs were present. Electrospray ionisation mass spectrometry was used for the end-group analysis. Three different classes of polymers was found being PEG, polypropylene glycol (PPG) and a block copolymer of polyethylene glycol/polypropylene glycol (PEG/PPG) with molar mass averages ranging from 400 to 4200 Da. PEG compounds with a nonylphenyl or an octylphenyl hydrophobic end-group are most common. The hydrophilic end-groups observed are hydroxide and/or sulphate. Water extracts of microsamples from a palette by David Hockney dating from 1970 and samples paintings by Patrick Caulfield (1936-2005) and John Hoyland (born in 1934) were investigated with the same technique. Although some artist paint manufacturers use the same specific base emulsions to make their paints, the composition of the PEG compounds present in the water extracts of the palette and paintings samples made it possible, in some cases, to suggest a specific brand of paint used by the artist.

  19. Application of the renormalization group to the calculation of the vacuum decay rate in flat and curved space-time

    NASA Astrophysics Data System (ADS)

    Metaxas, Dimitrios

    2007-02-01

    I show that an application of renormalization group arguments may lead to significant corrections to the vacuum decay rate for phase transitions in flat and curved space-time. It can also give some information regarding its dependence on the parameters of the theory, including the cosmological constant in the case of decay in curved space-time.

  20. Mass and mixing angle patterns in the Standard Model and its material Supersymmetric Extension

    SciTech Connect

    Ramond, P.

    1992-01-01

    Using renormalization group techniques, we examine several interesting relations among masses and mixing angles of quarks and lepton in the Standard Model of Elementary Particle Interactions as a functionof scale. We extend the analysis to the minimal Supersymmetric Extension to determine its effect on these mass relations. For a heavy to quark, and minimal supersymmetry, most of these relations, can be made to agree at one unification scale.