Renormalization of the quark mass matrix
NASA Astrophysics Data System (ADS)
Chiu, S. H.; Kuo, T. K.
2016-05-01
Using a set of rephasing-invariant variables, it is shown that the renormalization group equations for quark mixing parameters can be written in a form that is compact, in addition to having simple properties under flavor permutation. We also found approximate solutions to these equations if the quark masses are hierarchical or nearly degenerate.
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.
Mass renormalization in cavity QED
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.
Renormalization constants for 2-twist operators in twisted mass QCD
Alexandrou, C.; Constantinou, M.; Panagopoulos, H.; Stylianou, F.; Korzec, T.
2011-01-01
Perturbative and nonperturbative results on the renormalization constants of the fermion field and the twist-2 fermion bilinears are presented with emphasis on the nonperturbative evaluation of the one-derivative twist-2 vector and axial-vector operators. Nonperturbative results are obtained using the twisted mass Wilson fermion formulation employing two degenerate dynamical quarks and the tree-level Symanzik improved gluon action. The simulations have been performed for pion masses in the range of about 450-260 MeV and at three values of the lattice spacing a corresponding to {beta}=3.9, 4.05, 4.20. Subtraction of O(a{sup 2}) terms is carried out by performing the perturbative evaluation of these operators at 1-loop and up to O(a{sup 2}). The renormalization conditions are defined in the RI{sup '}-MOM scheme, for both perturbative and nonperturbative results. The renormalization factors, obtained for different values of the renormalization scale, are evolved perturbatively to a reference scale set by the inverse of the lattice spacing. In addition, they are translated to MS at 2 GeV using 3-loop perturbative results for the conversion factors.
Renormalization group analysis of the gluon mass equation
NASA Astrophysics Data System (ADS)
Aguilar, A. C.; Binosi, D.; Papavassiliou, J.
2014-04-01
We carry out a systematic study of the renormalization properties of the integral equation that determines the momentum evolution of the effective gluon mass in pure Yang-Mills theory, without quark effects taken into account. A detailed, all-order analysis of the complete kernel appearing in this particular equation, derived in the Landau gauge, reveals that the renormalization procedure may be accomplished through the sole use of ingredients known from the standard perturbative treatment of the theory, with no additional assumptions. However, the subtle interplay of terms operating at the level of the exact equation gets distorted by the approximations usually employed when evaluating the aforementioned kernel. This fact is reflected in the form of the obtained solutions, for which the deviations from the correct behavior are best quantified by resorting to appropriately defined renormalization-group invariant quantities. This analysis, in turn, provides a solid guiding principle for improving the form of the kernel, and furnishes a well-defined criterion for discriminating between various possibilities. Certain renormalization-group inspired Ansätze for the kernel are then proposed, and their numerical implications are explored in detail. One of the solutions obtained fulfills the theoretical expectations to a high degree of accuracy, yielding a gluon mass that is positive definite throughout the entire range of physical momenta, and displays in the ultraviolet the so-called "power-law" running, in agreement with standard arguments based on the operator product expansion. Some of the technical difficulties thwarting a more rigorous determination of the kernel are discussed, and possible future directions are briefly mentioned.
Critical mass renormalization in renormalized ϕ4 theories in two and three dimensions
NASA Astrophysics Data System (ADS)
Pelissetto, Andrea; Vicari, Ettore
2015-12-01
We consider the O (N)-symmetric ϕ4 theory in two and three dimensions and determine the nonperturbative mass renormalization needed to obtain the ϕ4 continuum theory. The required nonperturbative information is obtained by resumming high-order perturbative series in the massive renormalization scheme, taking into account their Borel summability and the known large-order behavior of the coefficients. The results are in good agreement with those obtained in lattice calculations.
Infrared Renormalization-Group Flow for Heavy-Quark Masses
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.
Remark on the subtractive renormalization of the quadratically divergent scalar mass
Fujikawa, Kazuo
2011-05-15
The quadratically divergent scalar mass is subtractively renormalized unlike other divergences which are multiplicatively renormalized. We reexamine some technical aspects of the subtractive renormalization, in particular, the mass-independent renormalization of massive {lambda}{phi}{sup 4} theory with higher derivative regularization. We then discuss an unconventional scheme to introduce the notion of renormalization point {mu} to the subtractive renormalization in a theory defined by a large fixed cutoff M. The resulting renormalization group equation generally becomes inhomogeneous, but it is transformed to be homogeneous. The renormalized scalar mass consists of two components in this scheme, one with the ordinary anomalous dimension and the other which is proportional to the renormalization scale {mu}. This scheme interpolates between the theory defined by dimensional regularization and the theory with unsubtracted quadratic divergences.
Renormalized entanglement entropy flow in mass-deformed ABJM theory
NASA Astrophysics Data System (ADS)
Kim, Kyung Kiu; Kwon, O.-Kab; Park, Chanyong; Shin, Hyeonjoon
2014-08-01
We investigate a mass deformation effect on the renormalized entanglement entropy (REE) near the UV fixed point in (2+1)-dimensional field theory. In the context of the gauge/gravity duality, we use the Lin-Lunin-Maldacena geometries corresponding to the vacua of the mass-deformed ABJM theory. We analytically compute the small mass effect for various droplet configurations and show in holographic point of view that the REE is monotonically decreasing, positive, and stationary at the UV fixed point. These properties of the REE in (2+1)-dimensions are consistent with the Zamolodchikov c-function proposed in (1+1)-dimensional conformal field theory.
Renormalization of a two-loop neutrino mass model
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.
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.
Clothed particle representation in quantum field theory: Mass renormalization
NASA Astrophysics Data System (ADS)
Korda, V. Yu.; Shebeko, A. V.
2004-10-01
We consider the neutral pion and nucleon fields interacting via the pseudoscalar (PS) Yukawa-type coupling. The method of unitary clothing transformations is used to handle the so-called clothed particle representation, where the total field Hamiltonian and the three boost operators in the instant form of relativistic dynamics take on the same sparse structure in the Hilbert space of hadronic states. In this approach the mass counterterms are cancelled (at least, partly) by commutators of the generators of clothing transformations and the field interaction operator. This allows the pion and nucleon mass shifts to be expressed through the corresponding three-dimensional integrals whose integrands depend on certain covariant combinations of the relevant three-momenta. The property provides the momentum independence of mass renormalization. The present results prove to be equivalent to the results obtained by Feynman techniques.
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.
Clothed particle representation in quantum field theory: mass renormalization
NASA Astrophysics Data System (ADS)
Korda, V. Yu.; Shebeko, A. V.
2007-06-01
The method of unitary clothing transformations is used to handling the so-called clothed particle representation (CPR) (see [A.V. Shebeko and M.I. Shirokov, Phys. Part. Nucl. 32 (2001) 31; nucl-th/0102037, V.Yu. Korda and A.V. Shebeko, Phys. Rev. D 70 (2004) 085011, V.Yu. Korda, L. Canton and A.V. Shebeko, doi:10.1016/j.aop.2006.07.010, Ann. Phys. (2006) in press; nucl-th/060325] and refs. therein), where the total field Hamiltonian H and the three boost operators in the instant form of relativistic dynamics take on the same sparse structure in the Hilbert space of hadronic states. In this approach the mass counterterms are cancelled by commutators of the generators of clothing transformations and the field interaction operator. This allows the pion and nucleon mass shifts to be expressed through the corresponding three-dimensional integrals whose integrands are proved to be dependent on certain covariant combinations of the relevant three-momenta. The property provides the momentum independence of mass renormalization.
Discrete translational invariance and mass-renormalization in the two-dimensional sine-Gordon model
NASA Astrophysics Data System (ADS)
Neudecker, Bernhard
1982-06-01
We consider the sine-Gordon model as a field-theory in which the interaction has a discrete translational invariance. It is shown that apart from a Gaussian contribution the Helmholtz free-energy exhibits this symmetry as well. Thus in an originally massless theory, the insertion of a mass term can be considered as a rather “weak” symmetry-breaking. Within the Amit-Goldschmidt-Grinstein renormalization-scheme we show that mass-renormalization is trivial.
Masses of doubly charmed baryons in the extended on-mass-shell renormalization scheme
NASA Astrophysics Data System (ADS)
Sun, Zhi-Feng; Vacas, M. J. Vicente
2016-05-01
In this work, we investigate the mass corrections of the doubly charmed baryons up to N2L O in the extended-on-mass-shell (EOMS) renormalization scheme, comparing with the results of heavy baryon chiral perturbation theory. We find that the terms from the heavy baryon approach are a subset of those obtained in the EOMS scheme. By fitting the lattice data, we can determine the parameters m ˜, α , c1 and c7 from the Lagrangian, while in the heavy baryon approach no information on c1 can be obtained from the baryons mass. Correspondingly, the masses of mΞcc and mΩcc are predicted, in the EOMS scheme, extrapolating the results from different values of the charm quark and the pion masses of the lattice QCD calculations.
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.
NASA Astrophysics Data System (ADS)
Blossier, BenoÃ®t.; Brinet, Mariane; Guichon, Pierre; Morénas, Vincent; Pène, Olivier; Rodríguez-Quintero, Jose; Zafeiropoulos, Savvas
2015-06-01
We present a precise nonperturbative determination of the renormalization constants in the mass independent RI'-MOM scheme. The lattice implementation uses the Iwasaki gauge action and four degenerate dynamical twisted-mass fermions. The gauge configurations are provided by the ETM Collaboration. Renormalization constants for scalar, pseudoscalar, vector and axial operators, as well as the quark propagator renormalization, are computed at three different values of the lattice spacing, two volumes and several twisted-mass parameters. The method we developed allows for a precise cross-check of the running, thanks to the particular proper treatment of hypercubic artifacts. Results for the twist-2 operator O44 are also presented.
Two-loop perturbative quark mass renormalization from large {beta} Monte Carlo
Keisuke Jimmy Juge
2001-02-14
We present the calculation of heavy Wilson quark mass renormalization constants from large beta Monte Carlo simulations. Simulations were performed at various beta larger than 9, each on several spatial lattice sizes to allow for an infinite volume extrapolation. We use twisted boundary conditions to suppress tunneling and work in Coulomb gauge with appropriate adjustments for the temporal links. The one-loop coefficient obtained from this method is in agreement with the analytical result and a preliminary result for the second order coefficient is reported.
Renormalization of quark propagators from twisted-mass lattice QCD at N{sub f}=2
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
NASA Astrophysics Data System (ADS)
Santander-Syro, A. F.; Bareille, C.; Fortuna, F.; Copie, O.; Gabay, M.; Bertran, F.; Taleb-Ibrahimi, A.; Le Fèvre, P.; Herranz, G.; Reyren, N.; Bibes, M.; Barthélémy, A.; Lecoeur, P.; Guevara, J.; Rozenberg, M. J.
2012-09-01
We study, using angle-resolved photoemission spectroscopy, the two-dimensional electron gas (2DEG) at the surface of KTaO3 (KTO), a wide-gap insulator with strong spin-orbit coupling (SOC). We find that this 2DEG is a genuinely different physical state with respect to the bulk: the orbital symmetries of its subbands are entirely reconstructed and their masses are renormalized. This occurs because the values of the SOC, the Fermi energy, and the subband splittings become comparable in the 2DEG. Additionally, we identify an F-center-like heavy band resulting from the polar nature of the KTO surface.
NASA Astrophysics Data System (ADS)
Borowka, S.; Hahn, T.; Heinemeyer, S.; Heinrich, G.; Hollik, W.
2015-09-01
Reaching a theoretical accuracy in the prediction of the lightest MSSM Higgs-boson mass, , at the level of the current experimental precision requires the inclusion of momentum-dependent contributions at the two-loop level. Recently two groups presented the two-loop QCD momentum-dependent corrections to (Borowka et al., Eur Phys J C 74(8):2994, 2014; Degrassi et al., Eur Phys J C 75(2):61, 2015), using a hybrid on-shell- scheme, with apparently different results. We show that the differences can be traced back to a different renormalization of the top-quark mass, and that the claim in Ref. Degrassi et al. (Eur Phys J C 75(2):61, 2015) of an inconsistency in Ref. Borowka et al. (Eur Phys J C 74(8):2994, 2014) is incorrect. We furthermore compare consistently the results for obtained with the top-quark mass renormalized on-shell and . The latter calculation has been added to the FeynHiggs package and can be used to estimate missing higher-order corrections beyond the two-loop level.
NASA Astrophysics Data System (ADS)
Shchadilova, Yulia E.; Grusdt, Fabian; Rubtsov, Alexey N.; Demler, Eugene
2016-04-01
We propose a class of variational Gaussian wave functions to describe Fröhlich polarons at finite momenta. Our wave functions give polaron energies that are in excellent agreement with the existing Monte Carlo results for a broad range of interactions. We calculate the effective mass of polarons and find smooth crossover between weak- and intermediate-coupling strength. Effective masses that we obtain are considerably larger than those predicted by the mean-field method. A prediction based on our variational wave functions is a special pattern of correlations between host atoms that can be measured in time-of-flight experiments.
Direct observation of the mass renormalization in SrVO3 by angle resolved photoemission spectroscopy
Yoshida, t.
2010-05-03
We have performed an angle-resolved photoemission study of the three-dimensional perovskite-type SrVO{sub 3}. Observed spectral weight distribution of the coherent part in the momentum space shows cylindrical Fermi surfaces consisting of the V 3d t{sub 2g} orbitals as predicted by local-density approximation (LDA) band-structure calculation. The observed energy dispersion shows a moderately enhanced effective mass compared to the LDA results, corresponding to the effective mass enhancement seen in the thermodynamic properties. Contributions from the bulk and surface electronic structures to the observed spectra are discussed based on model calculations.
Simulating heat addition via mass addition in constant area compressible flows
NASA Astrophysics Data System (ADS)
Heiser, W. H.; McClure, W. B.; Wood, C. W.
1995-01-01
A study conducted demonstrated the striking similarity between the influence of heat addition and mass addition on compressible flows. These results encourage the belief that relatively modest laboratory experiments employing mass addition can be devised that will reproduce the leading phenomena of heat addition, such as the axial variation of properties, choking, and wall-boundary-layer separation. These suggest that some aspects of the complex behavior of dual-mode ramjet/scramjet combustors could be experimentally evaluated or demonstrated by replacing combustion with less expensive, more easily controlled, and safer mass addition.
Renormalization group in internal space
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.
RENORM predictions of diffraction at LHC confirmed
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.
Improvement of modal scaling factors using mass additive technique
NASA Technical Reports Server (NTRS)
Zhang, Qiang; Allemang, Randall J.; Wei, Max L.; Brown, David L.
1987-01-01
A general investigation into the improvement of modal scaling factors of an experimental modal model using additive technique is discussed. Data base required by the proposed method consists of an experimental modal model (a set of complex eigenvalues and eigenvectors) of the original structure and a corresponding set of complex eigenvalues of the mass-added structure. Three analytical methods,i.e., first order and second order perturbation methods, and local eigenvalue modification technique, are proposed to predict the improved modal scaling factors. Difficulties encountered in scaling closely spaced modes are discussed. Methods to compute the necessary rotational modal vectors at the mass additive points are also proposed to increase the accuracy of the analytical prediction.
Renormalized action improvements
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.
Chishtie, F. A.; Jia, J.; Hanif, T.; Mann, R. B.; McKeon, D. G. C.; Sherry, T. N.; Steele, T. G.
2011-05-15
We consider the effective potential V in the standard model with a single Higgs doublet in the limit that the only mass scale {mu} present is radiatively generated. Using a technique that has been shown to determine V completely in terms of the renormalization group (RG) functions when using the Coleman-Weinberg renormalization scheme, we first sum leading-log (LL) contributions to V using the one loop RG functions, associated with five couplings (the top quark Yukawa coupling x, the quartic coupling of the Higgs field y, the SU(3) gauge coupling z, and the SU(2)xU(1) couplings r and s). We then employ the two loop RG functions with the three couplings x, y, z to sum the next-to-leading-log (NLL) contributions to V and then the three to five loop RG functions with one coupling y to sum all the N{sup 2}LL...N{sup 4}LL contributions to V. In order to compute these sums, it is necessary to convert those RG functions that have been originally computed explicitly in the minimal subtraction scheme to their form in the Coleman-Weinberg scheme. The Higgs mass can then be determined from the effective potential: the LL result is m{sub H}=219 GeV/c{sup 2} and decreases to m{sub H}=188 GeV/c{sup 2} at N{sup 2}LL order and m{sub H}=163 GeV/c{sup 2} at N{sup 4}LL order. No reasonable estimate of m{sub H} can be made at orders V{sub NLL} or V{sub N}{sup 3}{sub LL} since the method employed gives either negative or imaginary values for the quartic scalar coupling. The fact that we get reasonable values for m{sub H} from the LL, N{sup 2}LL, and N{sup 4}LL approximations is taken to be an indication that this mechanism for spontaneous symmetry breaking is in fact viable, though one in which there is slow convergence towards the actual value of m{sub H}. The mass 163 GeV/c{sup 2} is argued to be an upper bound on m{sub H}.
Simple Approach to Renormalize the Cabibbo-Kobayashi-Maskawa Matrix
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.
Mass spectral characterization of petroleum dyes, tracers, and additives
Youngless, T.L.; Swansiger, J.T.; Danner, D.A.; Greco, M.
1985-08-01
Petroleum dyes, additives, and tracers are important for identifying gasolines in spill and contamination problems. High-resolution mass spectrometry (HRMS) was used for the characterization of 21 commercial petroleum dyes. Many contained common chromophores, typically azo or anthraquinone groups, and often differed only in their degree of alkyl substitution. Few dyes were pure and typically contained several chromogens with homologous series of substituents. A separation method was developed to concentrate the polar fractions containing the additives. Subsequent characterization of the polar fraction by GC/MS showed distinct differences between different gasolines. Various colorless tracers were evaluated in terms of detectability, soil adsorption, and cost. Many tracers exhibited soil adsorption and interferences which limited their detectability. Alcohols in the C8-C10 range were found to be the most suitable tracers with GC/MS detection limits of 1 ppm. 22 references, 4 figures, 3 tables.
Entanglement Renormalization and Wavelets.
Evenbly, Glen; White, Steven R
2016-04-01
We establish a precise connection between discrete wavelet transforms and entanglement renormalization, a real-space renormalization group transformation for quantum systems on the lattice, in the context of free particle systems. Specifically, we employ Daubechies wavelets to build approximations to the ground state of the critical Ising model, then demonstrate that these states correspond to instances of the multiscale entanglement renormalization ansatz (MERA), producing the first known analytic MERA for critical systems. PMID:27104687
Entanglement Renormalization and Wavelets
NASA Astrophysics Data System (ADS)
Evenbly, Glen; White, Steven R.
2016-04-01
We establish a precise connection between discrete wavelet transforms and entanglement renormalization, a real-space renormalization group transformation for quantum systems on the lattice, in the context of free particle systems. Specifically, we employ Daubechies wavelets to build approximations to the ground state of the critical Ising model, then demonstrate that these states correspond to instances of the multiscale entanglement renormalization ansatz (MERA), producing the first known analytic MERA for critical systems.
Novel formulations of CKM matrix renormalization
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.
Assassi, Valentin; Baumann, Daniel; Green, Daniel; Zaldarriaga, Matias E-mail: dbaumann@damtp.cam.ac.uk E-mail: matiasz@ias.edu
2014-08-01
This paper provides a systematic study of renormalization in models of halo biasing. Building on work of McDonald, we show that Eulerian biasing is only consistent with renormalization if non-local terms and higher-derivative contributions are included in the biasing model. We explicitly determine the complete list of required bias parameters for Gaussian initial conditions, up to quartic order in the dark matter density contrast and at leading order in derivatives. At quadratic order, this means including the gravitational tidal tensor, while at cubic order the velocity potential appears as an independent degree of freedom. Our study naturally leads to an effective theory of biasing in which the halo density is written as a double expansion in fluctuations and spatial derivatives. We show that the bias expansion can be organized in terms of Galileon operators which aren't renormalized at leading order in derivatives. Finally, we discuss how the renormalized bias parameters impact the statistics of halos.
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
Renormalization and plasma physics
Krommes, J.A.
1980-02-01
A review is given of modern theories of statistical dynamics as applied to problems in plasma physics. The derivation of consistent renormalized kinetic equations is discussed, first heuristically, later in terms of powerful functional techniques. The equations are illustrated with models of various degrees of idealization, including the exactly soluble stochastic oscillator, a prototype for several important applications. The direct-interaction approximation is described in detail. Applications discussed include test particle diffusion and the justification of quasilinear theory, convective cells, E vector x B vector turbulence, the renormalized dielectric function, phase space granulation, and stochastic magnetic fields.
Contractor renormalization group and the Haldane conjecture
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.
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.
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.
Renormalization Group in the Standard Model
Kielanowski, P.; Juarez W, S. R.
2007-11-27
We discuss two applications of the renormalization group method in the Standard Model. In the first one we present some theorems about the running of the Cabibbo-Kobayashi-Maskawa matrix and show that the evolution depends on one function of energy only. In the second one we discuss the properties of the running of the Higgs potential and derive the limits for the Higgs mass.
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.
Renormalization group functional equations
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.
Renormalizing Entanglement Distillation.
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. PMID:26824532
Mixed Meson Mass for Domain-Wall Valence and Staggered Sea Fermions
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.
Nonperturbative renormalization of scalar quantum electrodynamics in d=3
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.
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.
Gutzwiller renormalization group
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
Renormalized Lie perturbation theory
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.
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.
The Physical Renormalization of Quantum Field Theories
Binger, Michael William.; /Stanford U., Phys. Dept. /SLAC
2007-02-20
The profound revolutions in particle physics likely to emerge from current and future experiments motivates an improved understanding of the precise predictions of the Standard Model and new physics models. Higher order predictions in quantum field theories inevitably requires the renormalization procedure, which makes sensible predictions out of the naively divergent results of perturbation theory. Thus, a robust understanding of renormalization is crucial for identifying and interpreting the possible discovery of new physics. The results of this thesis represent a broad set of investigations in to the nature of renormalization. The author begins by motivating a more physical approach to renormalization based on gauge-invariant Green's functions. The resulting effective charges are first applied to gauge coupling unification. This approach provides an elegant formalism for understanding all threshold corrections, and the gauge couplings unify in a more physical manner compared to the usual methods. Next, the gauge-invariant three-gluon vertex is studied in detail, revealing an interesting and rich structure. The effective coupling for the three-gluon vertex, {alpha}(k{sub 1}{sup 2}, k{sub 2}{sup 2}, k{sub 3}{sup 2}), depends on three momentum scales and gives rise to an effective scale Q{sub eff}{sup 2}(k{sub 1}{sup 2}, k{sub 2}{sup 2}, k{sub 3}{sup 2}) which governs the (sometimes surprising) behavior of the vertex. The effects of nonzero internal masses are important and have a complicated threshold and pseudo-threshold structure. The pinch-technique effective charge is also calculated to two-loops and several applications are discussed. The Higgs boson mass in Split Supersymmetry is calculated to two-loops, including all one-loop threshold effects, leading to a downward shift in the Higgs mass of a few GeV. Finally, the author discusses some ideas regarding the overall structure of perturbation theory. This thesis lays the foundation for a comprehensive multi
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.
Spatial correlations, additivity, and fluctuations in conserved-mass transport processes
NASA Astrophysics Data System (ADS)
Das, Arghya; Chatterjee, Sayani; Pradhan, Punyabrata
2016-06-01
We exactly calculate two-point spatial correlation functions in steady state in a broad class of conserved-mass transport processes, which are governed by chipping, diffusion, and coalescence of masses. We find that the spatial correlations are in general short-ranged and, consequently, on a large scale, these transport processes possess a remarkable thermodynamic structure in the steady state. That is, the processes have an equilibrium-like additivity property and, consequently, a fluctuation-response relation, which help us to obtain subsystem mass distributions in the limit of subsystem size large.
IMPROVEMENT AND RENORMALIZATION CONSTANTS IN O(a) IMPROVED LATTICE QCD
T. BHATTACHARYA; ET AL
2000-12-01
We present results at {beta} = 6.0 and 6.2 for the O(a) improvement and renormalization constants for bilinear operators using axial and vector Ward identities. We discuss the extraction of the mass dependence of the renormalization constants and the coefficients of the equation of motion operators.
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.
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.
Kalyniak, P.; Sundaresan, M.K. . Dept. of Physics)
1988-01-01
In this paper, the one loop radiative corrections for the process e/sup +/e/sup -/ {yields} W/sup +/W/sup -/ are re-examined adopting the on-mass shell subtraction scheme. The main purpose of the paper is to present the details of this procedure. A complete computer program for the calculation of the radiative corrections based on this scheme is being developed to analyze the experimental data.
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.
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.
Renormalization plasma shielding effects on scattering entanglement fidelity in dense plasmas
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.
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.
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.
NASA Astrophysics Data System (ADS)
Thirupathaiah, S.; Fink, J.; Maheshwari, P. K.; Kishore, V. V. Ravi; Liu, Z.-H.; Rienks, E. D. L.; Büchner, B.; Awana, V. P. S.; Sarma, D. D.
2016-05-01
Using angle-resolved photoemission spectroscopy (ARPES), we studied the effect of the impurity potential on the electronic structure of FeTe0.5Se0.5 superconductor by substituting 10% of Ni for Fe, which leads to an electron doping of the system. We could resolve three hole pockets near the zone center and an electron pocket near the zone corner in the case of FeTe0.5Se0.5 , whereas only two hole pockets near the zone center and an electron pocket near the zone corner are resolved in the case of Fe0.9Ni0.1Te0.5Se0.5 , suggesting that the hole pocket having predominantly the x y orbital character is very sensitive to the impurity scattering. Upon electron doping, the size of the hole pockets decreases and the size of the electron pockets increases as compared to the host compound. However, the observed changes in the size of the electron and hole pockets are not consistent with the rigid-band model. Moreover, the effective mass of the hole pockets is reduced near the zone center and of the electron pockets is increased near the zone corner in the doped Fe0.9Ni0.1Te0.5Se0.5 as compared to FeTe0.5Se0.5 . We refer these observations to the changes of the spectral function due to the effect of the impurity potential of the dopants.
Dimensional renormalization: Ladders and rainbows
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.}
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.
Renormalization group invariant of lepton Yukawa couplings
NASA Astrophysics Data System (ADS)
Tsuyuki, Takanao
2015-04-01
By using quark Yukawa matrices only, we can construct renormalization invariants that are exact at the one-loop level in the standard model. One of them, Iq, is accidentally consistent with unity, even though quark masses are strongly hierarchical. We calculate a lepton version of the invariant Il for Dirac and Majorana neutrino cases and find that Il can also be close to unity. For the Dirac neutrino and inverted hierarchy case, if the lightest neutrino mass is 3.0 meV to 8.8 meV, an equality Iq=Il can be satisfied. These invariants are not changed even if new particles couple to the standard model particles, as long as those couplings are generation independent.
Renormalization in Coulomb gauge QCD
NASA Astrophysics Data System (ADS)
Andraši, A.; Taylor, John C.
2011-04-01
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.
Renormalization group in quantum mechanics
Polony, J.
1996-12-01
The running coupling constants are introduced in quantum mechanics and their evolution is described with the help of the renormalization group equation. The harmonic oscillator and the propagation on curved spaces are presented as examples. The Hamiltonian and the Lagrangian scaling relations are obtained. These evolution equations are used to construct low energy effective models. Copyright {copyright} 1996 Academic Press, Inc.
A novel formulation of Cabibbo-Kobayashi-Maskawa matrix renormalization
NASA Astrophysics Data System (ADS)
Kniehl, Bernd A.; Sirlin, Alberto
2009-03-01
We present a gauge-independent quark mass counterterm for the on-shell renormalization of the Cabibbo-Kobayashi-Maskawa (CKM) matrix in the Standard Model that is directly expressed in terms of the Lorentz-invariant self-energy functions, and automatically satisfies the hermiticity constraints of the mass matrix. It is very convenient for practical applications and leads to a gauge-independent CKM counterterm matrix that preserves unitarity and satisfies other highly desirable theoretical properties, such as flavor democracy.
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. PMID:24607030
NASA Astrophysics Data System (ADS)
Chen, Fu-Lin; Vanderpool, Robert; Williams, Ronald; Dimmick, Fred; Grover, Brett D.; Long, Russell; Murdoch, Robert
2011-08-01
The US Environmental Protection Agency (EPA) published a National Ambient Air Quality Standard (NAAQS) and the accompanying Federal Reference Method (FRM) for PM 10 in 1987. The EPA revised the particle standards and FRM in 1997 to include PM 2.5. In 2005, EPA proposed revisions to this NAAQS to include PM 10-2.5 but only finalized revisions with a PM 2.5 FRM and the development of a national monitoring network in 2006. Presently, no EPA designated reference or equivalent method sampler has the ability to directly measure the mass concentrations of PM 10, PM 10-2.5, and PM 2.5 simultaneously. An additive approach has been used for samplers like the dichotomous monitors to calculate PM 10 mass concentrations from independent measures of PM 10-2.5 and PM 2.5 (i.e. PM 10 = PM 10-2.5 + PM 2.5). A differential approach has been used to calculate PM 10-2.5 from identical collocated PM 10 and PM 2.5 samplers (i.e. PM 10-2.5 = PM 10-PM 2.5). Since these two approaches have been used widely for PM measurements, it is informative to evaluate their precision and comparability. EPA performed collocated tests of five different particle samplers in the Research Triangle Park area of North Carolina to evaluate the comparability and to characterize the additive and differential approaches used to determine particle mass concentrations. The intra-sampler precision of MiniVol, Omni, and dichotomous samplers was less than 8.4%. The precision of PM 10 measurements using the additive approach with dichotomous samplers was less than 3.5%. The poorest precision of the various PM 10-2.5 differential approaches was less than 15.1%. No zero or negative PM 10-2.5 concentrations were calculated using the differential approach. A coefficient of determination of 0.81 or higher was obtained for all paired comparison of PM 10-2.5. The reported test results show that concentrations calculated from both the additive and differential approaches generally agree among the portable samplers, the more
More on the renormalization group limit cycle in QCD
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.
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
Xiao, Shun; Qian, Shuai; Wang, Yi; Zhang, Yufeng; Cheng, Yiyu
2013-03-21
The response of many previously low-detectable or undetectable compounds in electrospray ionization mass spectrometry (ESI-MS) has been enhanced by the addition of a simple, homemade needle into the traditional ESI interface. The needle located between the ESI emitter and the ion sweep cone (inlet of the detector) would ionize those neutral gaseous compounds, formed during electrospray, by a corona discharge process. The mobile phases, ESI parameters and positions of the needle were investigated and optimized. Several groups of compounds and herbal extracts were tested using the homemade set-up. Both the results of the flow injection and the hyphenated MS analyses showed significant enhancement effects of our homemade needle. The advantages of the proposed method include low cost, simplicity and practicality. PMID:23364279
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.
Algebraic Lattices in QFT Renormalization
NASA Astrophysics Data System (ADS)
Borinsky, Michael
2016-04-01
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.
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.
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.
[The role of additives in bio-mass coal briquette on sulfur retention enhancement].
Lu, Yongqi; Xu, Kangfu; Ma, Yongliang; Wei, Tiejun; Hao, Jiming
2002-01-30
The research first conducted the sulfur-fixing experiment of bio-mass coal briquette in a tubular furnace. The impacts of three additives Al2O3, Fe2O3 and MnO2 on the sulfur retention by calcium-based sorbent in briquette were investigated, and only Al2O3 displayed the enhancement of sulfur retention. The TGA experiment was further carried out, and proved that the high-temperature decomposition of CaSO4 in the deoxidization atmosphere was effectively inhibited with the addition of Al2O3. The XPS and XRD analyses of briquette ash showed that due to the interaction among Al2O3, CaSO4 and CaO, the composite CaSO4.3CaO.3Al2O3 which has more thermal stability was formed. With its wrapping or binding onto the surface of CaSO4 crystal, the decomposition of CaSO4 was mitigated. PMID:11987400
Global Existence of Renormalized Solutions to Entropy-Dissipating Reaction-Diffusion Systems
NASA Astrophysics Data System (ADS)
Fischer, J.
2015-10-01
In the present work we introduce the notion of a renormalized solution for reaction-diffusion systems with entropy-dissipating reactions. We establish the global existence of renormalized solutions. In the case of integrable reaction terms our notion of a renormalized solution reduces to the usual notion of a weak solution. Our existence result in particular covers all reaction-diffusion systems involving a single reversible reaction with mass-action kinetics and (possibly species-dependent) Fick-law diffusion; more generally, it covers the case of systems of reversible reactions with mass-action kinetics which satisfy the detailed balance condition. For such equations the existence of any kind of solution in general was an open problem, thereby motivating the study of renormalized solutions.
Quark lepton complementarity and renormalization group effects
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.
Scale invariance in the causal approach to renormalization theory
NASA Astrophysics Data System (ADS)
Grigore, Dan R.
2001-06-01
The dilation invariance is studied in the framework of Epstein-Glaser approach to renormalization theory. Some analogues of the Callan-Symanzik equations are found and they are applied to the scalar field theory and to Yang-Mills models. We find the interesting result that, if all fields of the theory have zero masses, then from purely cohomological consideration, one can obtain the anomalous terms of logarithmic type.
LETTER: Fisher renormalization for logarithmic corrections
NASA Astrophysics Data System (ADS)
Kenna, Ralph; Hsu, Hsiao-Ping; von Ferber, Christian
2008-10-01
For continuous phase transitions characterized by power-law divergences, Fisher renormalization prescribes how to obtain the critical exponents for a system under constraint from their ideal counterparts. In statistical mechanics, such ideal behaviour at phase transitions is frequently modified by multiplicative logarithmic corrections. Here, Fisher renormalization for the exponents of these logarithms is developed in a general manner. As for the leading exponents, Fisher renormalization at the logarithmic level is seen to be involutory and the renormalized exponents obey the same scaling relations as their ideal analogues. The scheme is tested in lattice animals and the Yang-Lee problem at their upper critical dimensions, where predictions for logarithmic corrections are made.
Effect of cinnamon powder addition during conching on the flavor of dark chocolate mass.
Albak, F; Tekin, A R
2015-04-01
In the present study, refined dark chocolate mix was conched with the addition of finely powdered cinnamon in a laboratory-style conching machine to evaluate its aroma profile both analytically and sensorially. The analytical determinations were carried out by a combination of solid phase micro extraction (SPME)-gas chromatography (GC)-mass spectroscopy (MS) and-olfactometry(O), while the sensory evaluation was made with trained panelists. The optimum conditions for the SPME were found to be CAR/PDMS as the fiber, 60 °C as the temperature, and 60 min as the time. SPME analyses were carried out at 60 °C for 60 min with toluene as an internal standard. 26 compounds were monitored before and after conching. The unconched sample had a significantly higher fruity odor value than the conched sample. This new product was highly acceptable according to the overall inclination test. However some of textural properties, such as coarseness, and hardness were below the general preference. PMID:25829576
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.
Renormalized reaction and relaxation rates
NASA Astrophysics Data System (ADS)
Gorbachev, Yuriy E.
2016-06-01
Impact of the non-equilibrium on the reaction and relaxation rates (called as generalized relaxation rates - GRR), for the spatially inhomogeneous gas mixture is considered. Discarding the assumption that the 'chemical' part of the collisional integral is a small correction to non-reactive part, the expression for the zero-order GRR is derived. They are represented as a renormalization of the traditional reaction and relaxation rates, which means mixing of all corresponding processes. Thus all reactions and relaxation processes are entangled.
Renormalization in momentum dependent resummations
Jakovac, Antal
2006-10-15
At finite temperature and in nonequilibrium environments we have to resum perturbation theory to avoid infrared divergences. Since resummation shuffles the perturbative orders, renormalizability is a nontrivial issue. In this paper we demonstrate that one can modify any type of resummations--even if it is momentum dependent, or it resums higher point functions - in a way that it is renormalizable with the usual zero temperature counterterms. To achieve this goal we reformulate resummation in form of a renormalization scheme. We apply this technique to perform a 2PI resummation in the six dimensional cubic scalar model in equilibrium.
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
Considerations affecting the additional weight required in mass balance of ailerons
NASA Technical Reports Server (NTRS)
Diehl, W S
1937-01-01
This paper is essentially a consideration of mass balance of ailerons from a preliminary design standpoint, in which the extra weight of the mass counterbalance is the most important phase of the problem. Equations are developed for the required balance weight for a simple aileron and this weight is correlated with the mass-balance coefficient. It is concluded the location of the c.g. of the basic aileron is of paramount importance and that complete mass balance imposes no great weight penalty if the aileron is designed to have its c.g. inherently near to the hinge axis.
Renormalization effects on the MSSM from a calculable model of a strongly coupled hidden sector
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.
A site-renormalized molecular fluid theory
NASA Astrophysics Data System (ADS)
Dyer, Kippi M.; Perkyns, John S.; Pettitt, B. Montgomery
2007-11-01
The orientation-dependent pair distribution function for molecular fluids on site-site potentials is expanded in a topological analog of the diagrammatically proper site-site theory of liquids [D. Chandler et al., Mol. Phys. 46, 1335 (1982)]. The resulting functions are then used to diagrammatically renormalize the molecular fluid theory. A result is that the diagrammatically proper interaction site model theory is shown to be a linearized, minimal angular basis set approximation to this site-renormalized molecular theory. This framework is used to propose a new, exact, and proper closure to the diagrammatically proper interaction site model theory. The resulting equation system contains a bridge function expansion in the proper site-site theory. In addition, the construction of the theory is such that the molecular pair distribution function, in full dimensionality, is intrinsic to the theory. Furthermore, the theory is equivalent to the molecular Ornstein-Zernike treatment of site-site molecules in the basis set expansion of Blum and Torruella [J. Chem. Phys. 56, 303 (1971)]. A significant formal result of the theory is the demonstration that certain classes of diagrams which would otherwise be considered improper in the interaction site model formalism are included in the angular expansion of molecular interactions. Numerical results for several apolar homonuclear models and an apolar heteronuclear model are shown to quantitatively improve upon those of reference interaction site model and our recent proper variant with respect to simulation. Significant numerical results are that the various thermodynamic quantities obey the exact symmetries and sum rules within numerical error for the different sites in the heteronuclear case, even for the low order approximation used in this work, and the theory is independent of the so-called auxiliary site problem common to previous site-site theories.
Renormalization of the chromomagnetic operator on the lattice
NASA Astrophysics Data System (ADS)
Constantinou, M.; Costa, M.; Frezzotti, R.; Lubicz, V.; Martinelli, G.; Meloni, D.; Panagopoulos, H.; Simula, S.; ETM Collaboration
2015-08-01
We present our study of the renormalization of the chromomagnetic operator, OCM , which appears in the effective Hamiltonian describing Δ S =1 transitions in and beyond the Standard Model. We have computed, perturbatively to one loop, the relevant Green's functions with two (quark-quark) and three (quark-quark-gluon) external fields, at nonzero quark masses, using both the lattice and dimensional regularizations. The perturbative computation on the lattice is carried out using the maximally twisted-mass action for the fermions, while for the gluons we employed the Symanzik improved gauge action for different sets of values of the Symanzik coefficients. We have identified all the operators which can possibly mix with OCM , including lower-dimensional and nongauge invariant operators, and we have calculated those elements of the mixing matrix which are relevant for the renormalization of OCM. We have also performed numerical lattice calculations to determine nonperturbatively the mixings of the chromomagnetic operator with lower-dimensional operators, through proper renormalization conditions. For the first time, the 1 /a2-divergent mixing of the chromomagnetic operator with the scalar density has been determined nonperturbatively with high precision. Moreover, the 1 /a -divergent mixing with the pseudoscalar density, due to the breaking of parity within the twisted-mass regularization of QCD, has been calculated nonperturbatively and found to be smaller than its one-loop perturbative estimate. The QCD simulations have been carried out using the gauge configurations produced by the European Twisted Mass Collaboration with Nf=2 +1 +1 dynamical quarks, which include in the sea, besides two light mass degenerate quarks, also the strange and charm quarks with masses close to their physical values.
Renormalization Group and Phase Transitions in Spin, Gauge, and QCD Like Theories
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).
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
Coriolis Force Mass-Flow Meter Composed of a Straight Pipe and an Additional Resonance-Vibrator
NASA Astrophysics Data System (ADS)
Tsutsui, Hirohide; Tomikawa, Yoshiro
1993-05-01
This paper deals with a new construction for a mass-flow meter using Coriolis force, and its basic experimental results. Some Coriolis force mass-flow meters, proposed up to now, are of a twin construction of, for example, a U-type pipe or a straight-type pipe, where the mass-flow is determined by measuring the relative displacement between the pipes. Therefore, their structure is too complex. To improve this situation, the authors propose a new mass-flow meter using one straight pipe, together with an additional flexural resonance-vibrator. The experimental results prove that a mass-flow meter can be realized by such a simple construction as dealt with here.
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.
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...
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.
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.
NASA Astrophysics Data System (ADS)
Nakayama, Yu
2015-06-01
The bulk locality in the constructive holographic renormalization group requires miraculous cancellations among various local renormalization group functions. The cancellation is not only from the properties of the spectrum but from more detailed aspects of operator product expansions in relation to conformal anomaly. It is remarkable that one-loop computation of the universal local renormalization group functions in the weakly coupled limit of the super Yang-Mills theory fulfils the necessary condition for the cancellation in the strongly coupled limit in its SL(2, Z) duality invariant form. From the consistency between the quantum renormalization group and the holographic renormalization group, we determine some unexplored local renormalization group functions (e.g. diffusive term in the beta function for the gauge coupling constant) in the strongly coupled limit of the planar super Yang-Mills theory.
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
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.
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.
Supersymmetry-breaking parameters from renormalization group invariants at the LHC
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.
Renormalization in Periodically Driven Quantum Dots.
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
Higher spin versus renormalization group equations
NASA Astrophysics Data System (ADS)
Sachs, Ivo
2014-10-01
We present a variation of earlier attempts to relate renormalization group equations to higher spin equations. We work with a scalar field theory in 3 dimensions. In this case we show that the classical renormalization group equation is a variant of the Vasiliev higher spin equations with Kleinians on AdS4 for a certain subset of couplings. In the large N limit this equivalence extends to the quantum theory away from the conformal fixed points.
NASA Astrophysics Data System (ADS)
Liu, Zhaofeng; Chen, Ying; Dong, Shao-Jing; Glatzmaier, Michael; Gong, Ming; Li, Anyi; Liu, Keh-Fei; Yang, Yi-Bo; Zhang, Jian-Bo; χQCD Collaboration
2014-08-01
We present renormalization constants of overlap quark bilinear operators on 2+1-flavor domain wall fermion configurations. This setup is being used by the χQCD Collaboration in calculations of physical quantities such as strangeness in the nucleon and the strange and charm quark masses. The scale-independent renormalization constant for the axial-vector current is computed using the Ward identity. The renormalization constants for scalar, pseudoscalar, and vector currents are calculated in the RI-MOM scheme. Results in the MS ¯ scheme are also given. The step scaling function of quark masses in the RI-MOM scheme is computed as well. The analysis uses, in total, six different ensembles of three sea quarks, each on two lattices with sizes 243×64 and 323×64 at spacings a =(1.73 GeV)-1 and (2.28 GeV)-1, respectively.
Euclidean Epstein-Glaser renormalization
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.
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.
From dynamical systems to renormalization
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.
2MASS J154043.42-510135.7: a new addition to the 5 pc population
NASA Astrophysics Data System (ADS)
Pérez Garrido, A.; Lodieu, N.; Béjar, V. J. S.; Ruiz, M. T.; Gauza, B.; Rebolo, R.; Zapatero Osorio, M. R.
2014-07-01
Aims: The aim of the project is to find the stars closest to the Sun and to contribute to the completion of the stellar and substellar census of the solar neighbourhood. Methods: We identified a new late-M dwarf within 5 pc, looking for high proper motion sources in the 2MASS-WISE cross-match. We collected astrometric and photometric data available from public large-scale surveys. We complemented this information with low-resolution (R ~ 500) optical (600-1000 nm) and near-infrared (900-2500 nm) spectroscopy with instrumentation on the European Southern Observatory New Technology Telescope to confirm the nature of our candidate. We also present a high-quality medium-resolution VLT/X-shooter spectrum covering the 400 to 2500 nm wavelength range. Results: We classify this new neighbour as an M7.0 ± 0.5 dwarf using spectral templates from the Sloan Digital Sky Survey and spectral indices. Lithium absorption at 670.8 nm is not detected in the X-shooter spectrum, indicating that the M7 dwarf is older than 600 Myr and more massive than 0.06 M⊙. We also derive a trigonometric distance of 4.4+0.5-0.4 pc, in agreement with the spectroscopic distance estimate, making 2MASS J154043.42-510135.7 (2M1540) the nearest M7 dwarf to the Sun. This trigonometric distance is somewhat closer than the ~6 pc distance reported by the ALLWISE team, who independently identified this object recently. This discovery represents an increase by 25% in the number of M7-M8 dwarfs already known at distances closer than 8 pc from our Sun. We derive a density of ρ = 1.9 ± 0.9 × 10-3 pc-3 for M7 dwarfs in the 8 pc volume, a value similar to those quoted in the literature. Conclusions: This new ultracool dwarf is among the 50 closest systems to the Sun, demonstrating that our current knowledge of the stellar census within the 5 pc sample remains incomplete. 2M1540 represents a unique opportunity to search for extrasolar planets around ultracool dwarfs due to its proximity and brightness. Based on
An analysis method for multistage transonic turbines with coolant mass flow addition
Mildner, F.; Gallus, H.E.
1998-10-01
The subject of this paper is a numerical method for the calculation of the transonic flow field of multistage turbines, taking high coolant flow into account. To reduce the processing time, a throughflow method based on the principles of Wu is used for the hub-to-tip calculation. The flow field is obtained by an iterative solution between a three-dimensional inviscid hyperbolic time-dependent algorithm with an implicit finite volume method for the blade-to-blade calculations using C-meshes and a single representative meridional S{sub 2m}-stream surface. Along the 2{sub 2m}-plane with respect to nonorthogonal curvilinear coordinates, the stream function equation governing fluid flow is established. The cooling air inflow inside the blade passage forbids the assumption of a constant mass flow along the main stream direction. To consider the change of the aerodynamic and thermodynamic behavior, a cooling air model was developed and implemented in the algorithm, which allows the mixing of radially arbitrarily distributed cooling air in the trailing edge section of each blade row. The viscous effects and the influence of cooling air mixing are considered by the use of selected loss correlations for profile, tip leakage, secondary flow and mixing losses in the S{sub 2m}-plane in terms of entropy. The method is applied to the four-stage high-temperature gas turbine Siemens KWU V84.3. The numerical results obtained are in good agreement with the experimental data.
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
Determining the structure of supersymmetry breaking with renormalization group invariants
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.
Gauge mediation scenario with hidden sector renormalization in MSSM
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.
The One and Two Loops Renormalization Group Equations in the Standard Model
Juarez W, S. Rebeca; Solis R, H. Gabriel; Kielanowski, P.
2006-01-06
In the context of the Standard Model (SM), we compare the analytical and the numerical solutions of the Renormalization Group Equations (RGE) for the relevant couplings to one and two loops. This information will be an important ingredient for the precise evaluation of boundary values on the physical Higgs Mass.
Duality and holographic renormalization group flows
NASA Astrophysics Data System (ADS)
Halmagyi, Nicholas
This thesis contains a detailed study of holographic renormalization group flows in An quiver gauge theories. The flows considered are two fold. Firstly I consider flows generated by mass terms for the adjoint chiral superfields, these flows have conformal fixed point in the ultraviolet as well as the infrared. Two well known flows in this class are the Pilch-Warner flow and the Klebanov-Witten flow, which as deformations of the UV theory lie in the untwisted sector and twisted sector respectively. There is also known to be flows which mix the twisted and untwisted sectors. We study this whole family of flows using field theory methods combined with their M-theory construction. In particular I elaborate on the duality group which acts on this whole family of flows and a subgroup of the full duality group is identified directly in the field theory as Seiberg duality. The structure of the long sought after IIB supergravity solution to the Klebanov-Witten flow is provided, the entire flow is a metric on the singular conifold which we provide up to the solution of one non-linear p.d.e. Further, the IIB string is solved in the Penrose limit of the Pilch-Warner solution. Secondly, we consider flows which are confining in the infrared the same duality group which acts on this RG-flows mentioned above, also acts of this family of flows. A certain universal behaviour is discovered on this large family of flows and is attributed to certain properties of the affine Weyl group.
Wang, H; Wu, Y; Zhao, Y; Sun, W; Ding, L; Guo, B; Chen, B
2012-08-01
Desorption corona beam ionisation (DCBI), the relatively novel ambient mass spectrometry (MS) technique, was utilised to screen for illicit additives in weight-loss food. The five usually abused chemicals - fenfluramine, N-di-desmethyl sibutramine, N-mono-desmethyl sibutramine, sibutramine and phenolphthalein - were detected with the proposed DCBI-MS method. Fast single-sample and high-throughput analysis was demonstrated. Semi-quantification was accomplished based on peak areas in the ion chromatograms. Four illicit additives were identified and semi-quantified in commercial samples. As there was no tedious sample pre-treatment compared with conventional HPLC methods, high-throughput analysis was achieved with DCBI. The results proved that DCBI-MS is a powerful tool for the rapid screening of illicit additives in weight-loss dietary supplements. PMID:22784191
Nonperturbative renormalization group approach for a scalar theory in higher-derivative gravity
Bonanno, A.; Zappala, D.
1997-05-01
A renormalization group study of a scalar theory coupled to gravity through a general functional dependence on the Ricci scalar in the action is discussed. A set of nonperturbative flow equations governing the evolution of the new interaction terms generated in both local potential and wave function renormalization is derived. It is shown for a specific model that these new terms play an important role in determining the scaling behavior of the system above the mass of the inflaton field. {copyright} {ital 1997} {ital The American Physical Society}
The large-N{sub c} renormalization group
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}.
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.
Self-Consistency Requirements of the Renormalization Group for Setting the Renormalization Scale
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 {β^{R}_{i}}-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.
On the Hyperbolicity of Lorenz Renormalization
NASA Astrophysics Data System (ADS)
Martens, Marco; Winckler, Björn
2014-01-01
We consider infinitely renormalizable Lorenz maps with real critical exponent α > 1 of certain monotone combinatorial types. We prove the existence of periodic points of the renormalization operator, and that each map in the limit set of renormalization has an associated two-dimensional strong unstable manifold. For monotone families of Lorenz maps we prove that each infinitely renormalizable combinatorial type has a unique representative within the family. We also prove that each infinitely renormalizable map has no wandering intervals, is ergodic, and has a uniquely ergodic minimal Cantor attractor of measure zero.
Renormalized dissipation in plasmas with finite collisionality
Parker, S.E.; Carati, D.
1995-05-01
A nonlinear truncation procedure for Fourier-Hermite expansion of Boltzmann-type plasma equations is presented which eliminates fine velocity scale, taking into account its effect on coarser scales. The truncated system is then transformed back to (x, v) space which results in a renormalized Boltzmann equation. The resulting equation may allow for coarser velocity space resolution in kinetic simulations while reducing to the original Boltzmann equation when fine velocity scales are resolved. To illustrate the procedure, renormalized equations are derived for one dimensional electrostatic plasmas in which collisions are modeled by the Lenard-Bernstein operator.
Perturbative renormalization of the electric field correlator
NASA Astrophysics Data System (ADS)
Christensen, C.; Laine, M.
2016-04-01
The momentum diffusion coefficient of a heavy quark in a hot QCD plasma can be extracted as a transport coefficient related to the correlator of two colour-electric fields dressing a Polyakov loop. We determine the perturbative renormalization factor for a particular lattice discretization of this correlator within Wilson's SU(3) gauge theory, finding a ∼ 12% NLO correction for values of the bare coupling used in the current generation of simulations. The impact of this result on existing lattice determinations is commented upon, and a possibility for non-perturbative renormalization through the gradient flow is pointed out.
Information geometry and the renormalization group.
Maity, Reevu; Mahapatra, Subhash; Sarkar, Tapobrata
2015-11-01
Information theoretic geometry near critical points in classical and quantum systems is well understood for exactly solvable systems. Here, we show that renormalization group flow equations can be used to construct the information metric and its associated quantities near criticality for both classical and quantum systems in a universal manner. We study this metric in various cases and establish its scaling properties in several generic examples. Scaling relations on the parameter manifold involving scalar quantities are studied, and scaling exponents are identified. The meaning of the scalar curvature and the invariant geodesic distance in information geometry is established and substantiated from a renormalization group perspective. PMID:26651641
Information geometry and the renormalization group
NASA Astrophysics Data System (ADS)
Maity, Reevu; Mahapatra, Subhash; Sarkar, Tapobrata
2015-11-01
Information theoretic geometry near critical points in classical and quantum systems is well understood for exactly solvable systems. Here, we show that renormalization group flow equations can be used to construct the information metric and its associated quantities near criticality for both classical and quantum systems in a universal manner. We study this metric in various cases and establish its scaling properties in several generic examples. Scaling relations on the parameter manifold involving scalar quantities are studied, and scaling exponents are identified. The meaning of the scalar curvature and the invariant geodesic distance in information geometry is established and substantiated from a renormalization group perspective.
Tensor hypercontraction. II. Least-squares renormalization.
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
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.
More on the infrared renormalization group limit cycle in QCD
E. Epelbaum; H.-W. Hammer; Ulf-G. Meissner; A. Nogga
2006-10-01
We present a detailed study of the recently conjectured infrared renormalization group limit cycle in QCD using chiral effective field theory. It was conjectured that small increases in the up and down quark masses can move QCD to the critical trajectory for an infrared limit cycle in the three-nucleon system. At the critical 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. We exemplify three parameter sets where this effect occurs at next-to-leading order in the chiral counting. For one of them, we study the structure of the three-nucleon system in detail using both chiral and contact effective field theories. Furthermore, we investigate the matching of the chiral and contact theories in the critical region and calculate the influence of the limit cycle on three-nucleon scattering observables.
Renormalization group equations for the CKM matrix
Kielanowski, P.; Juarez W, S. R.; Montes de Oca Y, J. H.
2008-12-01
We derive the one loop renormalization group equations for the Cabibbo-Kobayashi-Maskawa (CKM) matrix for the standard model, its two Higgs extension, and the minimal supersymmetric extension in a novel way. The derived equations depend only on a subset of the model parameters of the renormalization group equations for the quark Yukawa couplings so the CKM matrix evolution cannot fully test the renormalization group evolution of the quark Yukawa couplings. From the derived equations we obtain the invariant of the renormalization group evolution for three models which is the angle {phi}{sub 2} of the unitarity triangle. For the special case of the standard model and its extensions with v{sub 1}{approx_equal}v{sub 2} we demonstrate that also the shape of the unitarity triangle and the Buras-Wolfenstein parameters {rho} and {eta} are conserved. The invariance of the angles of the unitarity triangle means that it is not possible to find a model in which the CKM matrix might have a simple, special form at asymptotic energies.
Finite volume renormalization scheme for fermionic operators
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.
Renormalized Energy Concentration in Random Matrices
NASA Astrophysics Data System (ADS)
Borodin, Alexei; Serfaty, Sylvia
2013-05-01
We define a "renormalized energy" as an explicit functional on arbitrary point configurations of constant average density in the plane and on the real line. The definition is inspired by ideas of Sandier and Serfaty (From the Ginzburg-Landau model to vortex lattice problems, 2012; 1D log-gases and the renormalized energy, 2013). Roughly speaking, it is obtained by subtracting two leading terms from the Coulomb potential on a growing number of charges. The functional is expected to be a good measure of disorder of a configuration of points. We give certain formulas for its expectation for general stationary random point processes. For the random matrix β-sine processes on the real line ( β = 1,2,4), and Ginibre point process and zeros of Gaussian analytic functions process in the plane, we compute the expectation explicitly. Moreover, we prove that for these processes the variance of the renormalized energy vanishes, which shows concentration near the expected value. We also prove that the β = 2 sine process minimizes the renormalized energy in the class of determinantal point processes with translation invariant correlation kernels.
Renormalization for breakup of invariant tori
NASA Astrophysics Data System (ADS)
Apte, A.; Wurm, A.; Morrison, P. J.
2005-01-01
We present renormalization group operators for the breakup of invariant tori with winding numbers that are quadratic irrationals. We find the simple fixed points of these operators and interpret the map pairs with critical invariant tori as critical fixed points. Coordinate transformations on the space of maps relate these fixed points, and also induce conjugacies between the corresponding operators.
Lectures on renormalization and asymptotic safety
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.
Elliptical galaxies kinematics within general relativity with renormalization group effects
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)
Garrido Frenich, Antonia; Martínez Vidal, José Luis; Fernández Moreno, José Luis; Romero-González, R
2009-06-01
One of the major problems in quantitative analysis of pesticide residues in food samples by gas chromatography-tandem mass spectrometry (GC-MS/MS) is the enhancement or the suppression, of the target analyte signals in matrix extracts. Potentially positive samples, which had previously been identified by a rapid screening method, were quantified using standard addition to compensate matrix effects. As example we performed a systematic study on the application of the standard addition calibration (SAC) method for the determination of 12 pesticides (acephate, bromopropylate, chlorpyrifos, cypermethrin, diazinon, etrimfos, heptenophos, iprodione, methamidophos, procymidone, tetradifon, and triadimefon) in two matrices (cucumber and orange) in the range of initial concentrations of 10-200 microg kg(-1). The influence of some factors, such as the minimum number of standard additions used (single, two, three or four points calibration), as well as the known amount of analyte added to the sample, is evaluated in order to obtain reliable results. Accurate quantification is achieved when a single point SAC at 200 microg kg(-1) was used, obtaining for all the cases recoveries between 70 and 120%. The proposed analytical approach only needs two injections per sample (blank and spiked extracted sample) to determine the final concentration of pesticide in positive samples. PMID:19406413
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.
Un-renormalized classical electromagnetism
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.
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.
Simple on-shell renormalization framework for the Cabibbo-Kobayashi-Maskawa matrix
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.
Pergantis, S A; Heithmar, E M; Hinners, T A
1997-10-01
Phenylarsonic compounds have been used as poultry and swine feed additives for the purpose of growth promotion and disease prevention. Owing to the lack of suitable analytical methods, however, knowledge of their metabolism, environmental fate and impact remains incomplete. In order to compensate for this, analytical procedures were developed that allow the speciation of arsenic animal feed additives by using microbore high-performance liquid chromatography (microHPLC) coupled on-line with ICP-MS. More specifically, reversed-phase (RP) chromatographic methods were optimised to achieve the separation of various phenylarsonic acids from each other and from the more toxic inorganic arsenic compounds. This mode of chromatography, however, exhibits limitations, especially in the presence of naturally occurring organoarsenic compounds. The application of RP ion-pairing chromatography eliminates such shortcomings by minimising the co-elution of arsenic species. In general, the microHPLC-ICP-MS methods developed in this study provide high selectivity, extremely good sensitivity, low limits of detection (low-ppb or sub-pg amounts of As), require small sample volumes (< 1 microliter), minimise waste and operate most efficiently under low mobile-phase flow rates (15-40 microliters min-1), which are compatible for use with other types of mass spectrometers, e.g., electrospray. Reference materials containing naturally occurring arsenic compounds were spiked with phenylarsonic compounds and then analysed by using the procedures developed in this study. PMID:9463956
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.
Renormalization of stochastic lattice models: epitaxial surfaces.
Haselwandter, Christoph A; Vvedensky, Dimitri D
2008-06-01
We present the application of a method [C. A. Haselwandter and D. D. Vvedensky, Phys. Rev. E 76, 041115 (2007)] for deriving stochastic partial differential equations from atomistic processes to the morphological evolution of epitaxial surfaces driven by the deposition of new material. Although formally identical to the one-dimensional (1D) systems considered previously, our methodology presents substantial additional technical issues when applied to two-dimensional (2D) surfaces. Once these are addressed, subsequent coarse-graining is accomplished as before by calculating renormalization-group (RG) trajectories from initial conditions determined by the regularized atomistic models. Our applications are to the Edwards-Wilkinson (EW) model [S. F. Edwards and D. R. Wilkinson, Proc. R. Soc. London, Ser. A 381, 17 (1982)], the Wolf-Villain (WV) model [D. E. Wolf and J. Villain, Europhys. Lett. 13, 389 (1990)], and a model with concurrent random deposition and surface diffusion. With our rules for the EW model no appreciable crossover is obtained for either 1D or 2D substrates. For the 1D WV model, discussed previously, our analysis reproduces the crossover sequence known from kinetic Monte Carlo (KMC) simulations, but for the 2D WV model, we find a transition from smooth to unstable growth under repeated coarse-graining. Concurrent surface diffusion does not change this behavior, but can lead to extended transient regimes with kinetic roughening. This provides an explanation of recent experiments on Ge(001) with the intriguing conclusion that the same relaxation mechanism responsible for ordered structures during the early stages of growth also produces an instability at longer times that leads to epitaxial breakdown. The RG trajectories calculated for concurrent random deposition and surface diffusion reproduce the crossover sequences observed with KMC simulations for all values of the model parameters, and asymptotically always approach the fixed point corresponding
Renormalization of stochastic lattice models: Epitaxial surfaces
NASA Astrophysics Data System (ADS)
Haselwandter, Christoph A.; Vvedensky, Dimitri D.
2008-06-01
We present the application of a method [C. A. Haselwandter and D. D. Vvedensky, Phys. Rev. E 76, 041115 (2007)] for deriving stochastic partial differential equations from atomistic processes to the morphological evolution of epitaxial surfaces driven by the deposition of new material. Although formally identical to the one-dimensional (1D) systems considered previously, our methodology presents substantial additional technical issues when applied to two-dimensional (2D) surfaces. Once these are addressed, subsequent coarse-graining is accomplished as before by calculating renormalization-group (RG) trajectories from initial conditions determined by the regularized atomistic models. Our applications are to the Edwards-Wilkinson (EW) model [S. F. Edwards and D. R. Wilkinson, Proc. R. Soc. London, Ser. A 381, 17 (1982)], the Wolf-Villain (WV) model [D. E. Wolf and J. Villain, Europhys. Lett. 13, 389 (1990)], and a model with concurrent random deposition and surface diffusion. With our rules for the EW model no appreciable crossover is obtained for either 1D or 2D substrates. For the 1D WV model, discussed previously, our analysis reproduces the crossover sequence known from kinetic Monte Carlo (KMC) simulations, but for the 2D WV model, we find a transition from smooth to unstable growth under repeated coarse-graining. Concurrent surface diffusion does not change this behavior, but can lead to extended transient regimes with kinetic roughening. This provides an explanation of recent experiments on Ge(001) with the intriguing conclusion that the same relaxation mechanism responsible for ordered structures during the early stages of growth also produces an instability at longer times that leads to epitaxial breakdown. The RG trajectories calculated for concurrent random deposition and surface diffusion reproduce the crossover sequences observed with KMC simulations for all values of the model parameters, and asymptotically always approach the fixed point corresponding
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.
Holographic renormalization group and cosmology in theories with quasilocalized gravity
Csaki, Csaba; Erlich, Joshua; Hollowood, Timothy J.; Terning, John
2001-03-15
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.
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.
Spectral renormalization group theory on nonspatial networks
NASA Astrophysics Data System (ADS)
Tuncer, Asli; Erzan, Ayse
We recently proposed a ``spectral renormalization group'' scheme, for non-spatial networks with no metric defined on them. We implemented the spectral renormalization group on two deterministic non-spatial networks without translational invariance, namely the Cayley tree and diamond lattice . The thermodynamic critical exponents for the Gaussian model are only functions of the spectral dimension, d ~. The Gaussian fixed point is stable with respect to a Ψ4 perturbation up to second order on these lattices with d ~ = 2 , the lower critical dimension for the Ising universality class. This is expected for the Cayley tree, but for the diamond lattice it is an indication that the perturbation expansion up to second order breaks down at d ~ = 2 , as it does for the Wilson scheme on the square lattice. On generalized diamond lattices, with 2 < d ~ < 4 , we find non-Gaussian fixed points with non-trivial exponents. For d ~ > 4 , the critical behavior is once again mean field.
Renormalized vacuum polarization of rotating black holes
NASA Astrophysics Data System (ADS)
Ferreira, Hugo R. C.
2015-04-01
Quantum field theory on rotating black hole spacetimes is plagued with technical difficulties. Here, we describe a general method to renormalize and compute the vacuum polarization of a quantum field in the Hartle-Hawking state on rotating black holes. We exemplify the technique with a massive scalar field on the warped AdS3 black hole solution to topologically massive gravity, a deformation of (2 + 1)-dimensional Einstein gravity. We use a "quasi-Euclidean" technique, which generalizes the Euclidean techniques used for static spacetimes, and we subtract the divergences by matching to a sum over mode solutions on Minkowski spacetime. This allows us, for the first time, to have a general method to compute the renormalized vacuum polarization, for a given quantum state, on a rotating black hole, such as the physically relevant case of the Kerr black hole in four dimensions.
Renormalized Resonance Quartets in Dispersive Wave Turbulence
NASA Astrophysics Data System (ADS)
Lee, Wonjung; Kovačič, Gregor; Cai, David
2009-07-01
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.
Renormalization of gauge theories without cohomology
NASA Astrophysics Data System (ADS)
Anselmi, Damiano
2013-07-01
We investigate the renormalization of gauge theories without assuming cohomological properties. We define a renormalization algorithm that preserves the Batalin-Vilkovisky master equation at each step and automatically extends the classical action till it contains sufficiently many independent parameters to reabsorb all divergences into parameter-redefinitions and canonical transformations. The construction is then generalized to the master functional and the field-covariant proper formalism for gauge theories. Our results hold in all manifestly anomaly-free gauge theories, power-counting renormalizable or not. The extension algorithm allows us to solve a quadratic problem, such as finding a sufficiently general solution of the master equation, even when it is not possible to reduce it to a linear (cohomological) problem.
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.
Renormalization group for non-relativistic fermions.
Shankar, R
2011-07-13
A brief introduction is given to the renormalization group for non-relativistic fermions at finite density. It is shown that Landau's theory of the Fermi liquid arises as a fixed point (with the Landau parameters as marginal couplings) and its instabilities as relevant perturbations. Applications to related areas, nuclear matter, quark matter and quantum dots, are briefly discussed. The focus will be on explaining the main ideas to people in related fields, rather than addressing the experts. PMID:21646269
Renormalized strong-coupling quenched QED in four dimensions
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}
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.
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.
Yang, Y.-G.; Qian, S.-B.; Soonthornthum, B. E-mail: qsb@ynao.ac.cn
2012-05-15
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{sub 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) Multiplication-Sign 10{sup -8} days yr{sup -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{sub spin} > (1/3)J{sub orb}.
Magnus expansion and in-medium similarity renormalization group
NASA Astrophysics Data System (ADS)
Morris, T. D.; Parzuchowski, N. M.; Bogner, S. K.
2015-09-01
We present an improved variant of the in-medium similarity renormalization group (IM-SRG) based on the Magnus expansion. In the new formulation, one solves flow equations for the anti-Hermitian operator that, upon exponentiation, yields the unitary transformation of the IM-SRG. The resulting flow equations can be solved using a first-order Euler method without any loss of accuracy, resulting in substantial memory savings and modest computational speedups. Since one obtains the unitary transformation directly, the transformation of additional operators beyond the Hamiltonian can be accomplished with little additional cost, in sharp contrast to the standard formulation of the IM-SRG. Ground state calculations of the homogeneous electron gas (HEG) and 16O nucleus are used as test beds to illustrate the efficacy of the Magnus expansion.
The standard model and its generalizations in the Epstein-Glaser approach to renormalization theory
NASA Astrophysics Data System (ADS)
Grigore, D. R.
2000-12-01
We continue our study of non-Abelian gauge theories in the framework of the Epstein-Glaser approach to renormalization theory. We consider the case when massive spin-1 bosons are present in the theory and we modify appropriately the analysis of the origin of the gauge invariance performed in a preceding paper in the case of null-mass spin-1 bosons. Then we are able to extend a result of Dütsch and Scharf concerning the uniqueness of the standard model, consistent with renormalization theory. In fact we consider the most general case, i.e. the consistent interaction of r spin-1 bosons, and we do not impose any restrictions on the gauge group and the mass spectrum of the theory. We show that, besides the natural emergence of a group structure (as in the massless case), we obtain new conditions of a group theoretical nature, namely the existence of a certain representation of the gauge group associated to the Higgs fields. Some other mass relations connecting the structure constants of the gauge group and the masses of the bosons emerge naturally. The proof is carried out using the Epstein-Glaser approach to renormalization theory.
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.
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. PMID:25524762
Renormalizing Operator-Stable Lagrangian Velocities for Microbial Dynamics Simulations
NASA Astrophysics Data System (ADS)
Cushman, J. H.; Park, M.
2008-05-01
In previous works we've developed upscaling methodologies for stable Levy Lagrangian velocities in fractal media. The renormalization tools were generalized central limit theorems which are equivalent to a renormalization group approach. Here we extend these ides to operator-stable Lagrangian velocities and apply the results to microbial dynamics in multi-scale geologic formations. Renormalized Fokker-Planck equations are presented at each scale.
Chris Quigg
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.
Nonperturbative renormalization and the electron{close_quote}s anomalous moment in large-{alpha} QED
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}
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.
Recent progress in ab initio density matrix renormalization group methodology
NASA Astrophysics Data System (ADS)
Hachmann, Johannes; Dorando, Jonathan J.; Kin-Lic Chan, Garnet
2008-03-01
We present some recent developments in the ab initio density matrix renormalization group (DMRG) method for quantum chemical problems, in particular our local, quadratic scaling algorithm [1] for low dimensional systems. This method is particularly suited for the description of strong nondynamic correlation, and allows us to compute numerically exact (FCI) correlated energies for large active spaces, up to one order of magnitude larger then can be done by conventional CASCI techniques. Other features of this method are its inherent multireference nature, compactness, variational results, size-consistency and size-extensivity. In addition we will review the problems (predominantly organic electronic materials) on which we applied the ab initio DMRG: 1) metal-insulator transition in hydrogen chains [1] 2) all-trans polyacetylene [1] 3) acenes [2] 4) polydiacetylenes [3]. References [1] Hachmann, Cardoen, Chan, JCP 125 (2006), 144101. [2] Hachmann, Dorando, Avil'es, Chan, JCP 127 (2007), 134309. [3] unpublished.
Extreme-value distributions and renormalization group.
Calvo, Iván; Cuchí, Juan C; Esteve, J G; Falceto, Fernando
2012-10-01
In the classical theorems of extreme value theory the limits of suitably rescaled maxima of sequences of independent, identically distributed random variables are studied. The vast majority of the literature on the subject deals with affine normalization. We argue that more general normalizations are natural from a mathematical and physical point of view and work them out. The problem is approached using the language of renormalization-group transformations in the space of probability densities. The limit distributions are fixed points of the transformation and the study of its differential around them allows a local analysis of the domains of attraction and the computation of finite-size corrections. PMID:23214531
Renormalization group analysis in nonrelativistic QCD for colored scalars
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.
Dennis, Elise A; Gundlach-Graham, Alexander W; Ray, Steven J; Enke, Christie G; Barinaga, Charles J; Koppenaal, David W; Hieftje, Gary M
2014-11-01
In this study, we demonstrate the performance of a new mass spectrometry concept called zoom time-of-flight mass spectrometry (zoom-TOFMS). In our zoom-TOFMS instrument, we combine two complementary types of TOFMS: conventional, constant-energy acceleration (CEA) TOFMS and constant-momentum acceleration (CMA) TOFMS to provide complete mass-spectral coverage as well as enhanced resolution and duty factor for a narrow, targeted mass region, respectively. Alternation between CEA- and CMA-TOFMS requires only that electrostatic instrument settings (i.e., reflectron and ion optics) and ion acceleration conditions be changed. The prototype zoom-TOFMS instrument has orthogonal-acceleration geometry, a total field-free distance of 43 cm, and a direct-current glow-discharge ionization source. Experimental results demonstrate that the CMA-TOFMS "zoom" mode offers resolution enhancement of 1.6 times over single-stage acceleration CEA-TOFMS. For the atomic mass range studied here, the maximum resolving power at full-width half-maximum observed for CEA-TOFMS was 1,610 and for CMA-TOFMS the maximum was 2,550. No difference in signal-to-noise (S/N) ratio was observed between the operating modes of zoom-TOFMS when both were operated at equivalent repetition rates. For a 10-kHz repetition rate, S/N values for CEA-TOFMS varied from 45 to 990 and from 67 to 10,000 for CMA-TOFMS. This resolution improvement is the result of a linear TOF-to-mass scale and the energy-focusing capability of CMA-TOFMS. Use of CMA also allows ions outside a given m/z range to be rejected by simple ion-energy barriers to provide a substantial improvement in duty factor. PMID:24866712
CALL FOR PAPERS: Special issue on Renormalization Group 2005
NASA Astrophysics Data System (ADS)
Honkonen, Juha; Kazakov, Dmitri; Diehl, Hans Werner
2005-10-01
This is a call for contributions to a special issue of Journal of Physics A: Mathematical and General dedicated to the subject of the Renormalization Group as featured in the international workshop Renormalization Group 2005, Helsinki, Finland 30 August-3 September 2005 (http://theory.physics.helsinki.fi/~rg2005/). Participants at that meeting as well as other researchers working in the field are invited to submit a research paper to this issue. The Editorial Board has invited Juha Honkonen, Dmitri Kazakov and Hans Werner Diehl to serve as Guest Editors for the special issue. Their criteria for acceptance of contributions are as follows: The subject of the paper should relate to the subject of the workshop. Contributions will be refereed and processed according to the usual procedure of the journal. Conference papers may be based on already published work but should eithercontain significant additional new results and/or insights orgive a survey of the present state of the art, a critical assessment of the present understanding of a topic, and a discussion of open problems Papers submitted by non-participants should be original and contain substantial new results. The guidelines for the preparation of contributions are as follows: The DEADLINE for submission of contributions is 1 December 2005. This deadline will allow the special issue to appear in June 2006. There is a nominal page limit of 16 printed pages per contribution. For papers exceeding this limit, the Guest Editors reserve the right to request a reduction in length. Further advice on publishing your work in Journal of Physics A: Mathematical and General may be found at www.iop.org/Journals/jphysa. Contributions to the special issue should, if possible, be submitted electronically by web upload at www.iop.org/Journals/jphysa or by e-mail to jphysa@iop.org, quoting `JPhysA Special Issue—Renormalization Group 2005'. Submissions should ideally be in standard LaTeX form. Please see the web site for further
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.
The Magnus expansion and the in-medium similarity renormalization group
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.
The Renormalization Group Running of the Higgs Quartic Coupling: Unification vs. Phenomenology
Montes de Oca Y, J. H.; Juarez W, S. R.; Kielanowski, P.
2007-02-09
Within the framework of the standard model (SM) of elementary particles, we obtained numerical solutions for the running Higgs mass, considering the renormalization group equations at the one and two loop approximation. Through the triviality condition (TC) and stability condition (SC) on the Higgs quartic coupling {lambda}H the bounds on the Higgs running mass have been fixed. The numerical results are presented for two special cases. One considering an unification of the three gauge couplings at the energy EU 1013 GeV and the other using the current experimental data for the gauge couplings.
Widder, Lukas; Brennerb, Josef; Huttera, Herbert
2014-01-01
To develop new products and to apply measures of quality control quick and simple accessibility of additive composition in automo- tive lubrication is important. The aim of this study was to investigate the possibility of analyzing organic friction modifier additives by means of atmospheric pressure matrix-assisted laser desorption/ionization mass spectrometry [AP-MALDI-MS] from lubricant solu- tions without the use of additional separation techniques. Analyses of selected friction modifier ethoxylated tallow amines and oleic acid amide were compared using two ionization methods, positive-ion electrospray ionization (ESI) and AP-MALDI, using a LTQ Orbitrap mass spectrometer. Pure additives were characterized from solvent solutions, as well as from synthetic and mineral base oil mixtures. Detected ions of pure additive samples consisted mainly of [M + H]+, but also alkaLi metal adducts [M + Na]+ and [M + K]+ could be seen. Characterizations of blends of both friction modifiers from the base oil mixtures were carried out as well and showed significant inten- sities for several additive peaks. Thus, this work shows a method to directly analyze friction modifier additives used in the automotive industry from an oil blend via the use of AP-MALDI without any further separation steps. The method presented will further simplify the acquisition of data on lubricant composition and additives. Furthermore, it allows the perspective of analyzing additive reaction products directly from formulated oil blends. PMID:25507326
Widder, Lukas; Brennerb, Josef; Huttera, Herbert
2014-01-01
To develop new products and to apply measures of quality control quick and simple accessibility of additive composition in automo- tive lubrication is important. The aim of this study was to investigate the possibility of analyzing organic friction modifier additives by means of atmospheric pressure matrix-assisted laser desorption/ionization mass spectrometry [AP-MALDI-MS] from lubricant solu- tions without the use of additional separation techniques. Analyses of selected friction modifier ethoxylated tallow amines and oleic acid amide were compared using two ionization methods, positive-ion electrospray ionization (ESI) and AP-MALDI, using a LTQ Orbitrap mass spectrometer. Pure additives were characterized from solvent solutions, as well as from synthetic and mineral base oil mixtures. Detected ions of pure additive samples consisted mainly of [M + H]+, but also alkaLi metal adducts [M + Na]+ and [M + K]+ could be seen. Characterizations of blends of both friction modifiers from the base oil mixtures were carried out as well and showed significant inten- sities for several additive peaks. Thus, this work shows a method to directly analyze friction modifier additives used in the automotive industry from an oil blend via the use of AP-MALDI without any further separation steps. The method presented will further simplify the acquisition of data on lubricant composition and additives. Furthermore, it allows the perspective of analyzing additive reaction products directly from formulated oil blends. PMID:25420342
Functional renormalization group approach to noncollinear magnets
NASA Astrophysics Data System (ADS)
Delamotte, B.; Dudka, M.; Mouhanna, D.; Yabunaka, S.
2016-02-01
A functional renormalization group approach to d -dimensional, N -component, noncollinear magnets is performed using various truncations of the effective action relevant to study their long distance behavior. With help of these truncations we study the existence of a stable fixed point for dimensions between d =2.8 and d =4 for various values of N focusing on the critical value Nc(d ) that, for a given dimension d , separates a first-order region for N
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.
Semihard processes with BLM renormalization scale setting
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.
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.
Manifestly diffeomorphism invariant classical Exact Renormalization Group
NASA Astrophysics Data System (ADS)
Morris, Tim R.; Preston, Anthony W. H.
2016-06-01
We construct a manifestly diffeomorphism invariant Wilsonian (Exact) Renor-malization Group for classical gravity, and begin the construction for quantum gravity. We demonstrate that the effective action can be computed without gauge fixing the diffeo-morphism invariance, and also without introducing a background space-time. We compute classical contributions both within a background-independent framework and by perturbing around a fixed background, and verify that the results are equivalent. We derive the exact Ward identities for actions and kernels and verify consistency. We formulate two forms of the flow equation corresponding to the two choices of classical fixed-point: the Gaussian fixed point, and the scale invariant interacting fixed point using curvature-squared terms. We suggest how this programme may completed to a fully quantum construction.
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.
Neutrino anarchy and renormalization group evolution
NASA Astrophysics Data System (ADS)
Brdar, Vedran; König, Matthias; Kopp, Joachim
2016-05-01
The observed pattern of neutrino mixing angles is in good agreement with the hypothesis of neutrino anarchy, which posits that nature has chosen the entries of the leptonic mixing matrix at random. In this paper we investigate how stable this conclusion is under renormalization group (RG) effects. Working in the simplest type-I seesaw model and two variants of the inverse seesaw model we study how the statistical distributions of the neutrino mixing parameters evolve between the grand unification scale and the electroweak scale. Especially in the inverse seesaw case we find significant distortions: Mixing angles tend to be smaller after RG running, and the Dirac C P phase tends to be closer to zero. The p -value describing the compatibility between the observed mixing angles and the anarchy hypothesis increases by 10%-20%. This illustrates that RG effects are highly relevant for quantitative studies of the anarchy scenario.
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.
Physics implications of the diphoton excess from the perspective of renormalization group flow
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
Importance of proper renormalization scale-setting for QCD testing at colliders
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
Importance of proper renormalization scale-setting for QCD testing at colliders
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 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 tt¯ invariant mass. At lower
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
Hilbert space renormalization for the many-electron problem
NASA Astrophysics Data System (ADS)
Li, Zhendong; Chan, Garnet Kin-Lic
2016-02-01
Renormalization is a powerful concept in the many-body problem. Inspired by the highly successful density matrix renormalization group (DMRG) algorithm, and the quantum chemical graphical representation of configuration space, we introduce a new theoretical tool: Hilbert space renormalization, to describe many-electron correlations. While in DMRG, the many-body states in nested Fock subspaces are successively renormalized, in Hilbert space renormalization, many-body states in nested Hilbert subspaces undergo renormalization. This provides a new way to classify and combine configurations. The underlying wavefunction Ansatz, namely, the Hilbert space matrix product state (HS-MPS), has a very rich and flexible mathematical structure. It provides low-rank tensor approximations to any configuration interaction (CI) space through restricting either the "physical indices" or the coupling rules in the HS-MPS. Alternatively, simply truncating the "virtual dimension" of the HS-MPS leads to a family of size-extensive wave function Ansätze that can be used efficiently in variational calculations. We make formal and numerical comparisons between the HS-MPS, the traditional Fock-space MPS used in DMRG, and traditional CI approximations. The analysis and results shed light on fundamental aspects of the efficient representation of many-electron wavefunctions through the renormalization of many-body states.
NASA Astrophysics Data System (ADS)
Constantinou, M.; Horsley, R.; Panagopoulos, H.; Perlt, H.; Rakow, P. E. L.; Schierholz, G.; Schiller, A.; Zanotti, J. M.
2015-01-01
The renormalization factors of local quark-bilinear operators are computed nonperturbatively for Nf=3 flavors of stout link nonperturbative clover (SLiNC) fermions, with emphasis on the various procedures for the chiral and continuum extrapolations. The simulations are performed at a lattice spacing a =0.074 fm , and for five values of the pion mass in the range of 290-465 MeV, allowing a safe and stable chiral extrapolation. Emphasis is given in the subtraction of the well-known pion pole which affects the renormalization factor of the pseudoscalar current. We also compute the inverse propagator and the Green's functions of the local bilinears to one loop in perturbation theory. We investigate lattice artifacts by computing them perturbatively to second order as well as to all orders in the lattice spacing. The renormalization conditions are defined in the RI'-MOM scheme, for both the perturbative and nonperturbative results. The renormalization factors, obtained at different values of the renormalization scale, are translated to the MS ¯ scheme and are evolved perturbatively to 2 GeV. Any residual dependence on the initial renormalization scale is eliminated by an extrapolation to the continuum limit. We also study the various sources of systematic errors. Particular care is taken in correcting the nonperturbative estimates by subtracting lattice artifacts computed to one-loop perturbation theory using the same action. We test two different methods, by subtracting either the O (g2a2) contributions, or the complete (all orders in a ) one-loop lattice artifacts.
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
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 R_{δ}-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 R_{e+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 {β_{i}}-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.
An Approximate KAM-Renormalization-Group Scheme for Hamiltonian Systems
NASA Astrophysics Data System (ADS)
Chandre, C.; Jauslin, H. R.; Benfatto, G.
1999-01-01
We construct an approximate renormalization scheme for Hamiltonian systems with two degrees of freedom. This scheme is a combination of Kolmogorov-Arnold-Moser (KAM) theory and renormalization-group techniques. It makes the connection between the approximate renormalization procedure derived by Escande and Doveil and a systematic expansion of the transformation. In particular, we show that the two main approximations, consisting in keeping only the quadratic terms in the actions and the two main resonances, keep the essential information on the threshold of the breakup of invariant tori.
Nucleon-nucleon scattering within a multiple subtractive renormalization approach
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.
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.
Thermodynamics of the two-dimensional XY model from functional renormalization
NASA Astrophysics Data System (ADS)
Jakubczyk, P.; Eberlein, A.
2016-06-01
We solve the nonperturbative renormalization-group flow equations for the two-dimensional XY model at the truncation level of the (complete) second-order derivative expansion. We compute the thermodynamic properties in the high-temperature phase and compare the nonuniversal features specific to the XY model with results from Monte Carlo simulations. In particular, we study the position and magnitude of the specific-heat peak as a function of temperature. The obtained results compare well with Monte Carlo simulations. We additionally gauge the accuracy of simplified nonperturbative renormalization-group treatments relying on ϕ4-type truncations. Our computation indicates that such an approximation is insufficient in the high-T phase and a correct analysis of the specific-heat profile requires account of an infinite number of interaction vertices.
Constraints on supersymmetric soft phases from renormalization group relations
Garisto, R.; Wells, J.D.
1997-02-01
By using relations derived from renormalization group equations (RGEs), we find that strong indirect constraints can be placed on the top squark mixing phase in A{sub t} from the electric dipole moment of the neutron (d{sub n}). Since m{sub t} is large, any GUT-scale phase in A{sub t} feeds into other weak scale phases through RGEs, which in turn contribute to d{sub n}. Thus CP-violating effects due to a weak-scale A{sub t} are strongly constrained. We find that {vert_bar}ImA{sub t}{sup EW}{vert_bar} must be smaller than or of order {vert_bar}ImB{sup EW}{vert_bar}, making the electric dipole moment of the top quark unobservably small in most models. Quantitative estimates of the contributions to d{sub n} from A{sub u}, A{sub d}, and B show that substantial fine-tuning is still required to satisfy the experimental bound on d{sub n}. While the low energy phases of the A{close_quote}s are not as strongly constrained as the phase of B{sup EW}, we note that the phase of a universal A{sup GUT} induces large contributions in the phase of B{sup EW} through RGEs, and is thus still strongly constrained in most models with squark masses below a TeV. {copyright} {ital 1997} {ital The American Physical Society}
Livshits, Gideon I.
2014-02-15
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.
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.
Renormalization group flow of entanglement entropy on spheres
NASA Astrophysics Data System (ADS)
Ben-Ami, Omer; Carmi, Dean; Smolkin, Michael
2015-08-01
We explore entanglement entropy of a cap-like region for a generic quantum field theory residing in the Bunch-Davies vacuum on de Sitter space. Entanglement entropy in our setup is identical with the thermal entropy in the static patch of de Sitter, and we derive a simple relation between the vacuum expectation value of the energy-momentum tensor trace and the RG flow of entanglement entropy. In particular, renormalization of the bare couplings and logarithmic divergence of the entanglement entropy are interrelated in our setup. We confirm our findings by recovering known universal contributions for a free field theory deformed by a mass operator as well as obtain correct universal behaviour at the fixed points. Simple examples of entanglement entropy flows are elaborated in d=2 ,3 ,4. Inthreedimensionswefindthatwhiletherenormalizedentanglemententropy is stationary at the fixed points, it is not monotonic. We provide a computational evidence that the universal `area law' for a conformally coupled scalar is different from the known result in the literature, and argue that this difference survives in the limit of flat space. Finally, we carry out the spectral decomposition of entanglement entropy flow and discuss its application to the F-theorem.
Renormalization-group methods for the spectra of disordered chains
NASA Astrophysics Data System (ADS)
Robbins, Mark O.; Koiller, Belita
1983-06-01
A family of real-space renormalization techniques for calculating the Green's functions of disordered chains is developed and explored. The techniques are based on a recently proposed renormalization method which is rederived here and shown to be equivalent to a virtual-crystal approximation on a renormalized Hamiltonian. The derivation suggests how other conventional alloy methods can be coupled to the renormalization concept. Various examples are discussed. Short-range order in the occupation of alloy sites and very general disorder in the Hamiltonian-diagonal, off-diagonal, and environmental-are readily incorporated. The techniques are exact in the limits of high and low concentration and of complete short-range order and for the Lloyd model. All states are found to be localized, in agreement with exact treatments. Results for the alloy density of states are presented for various cases and compared to numerical simulations on long chains (105 atoms).
Renormalization-scheme-invariant perturbation theory: Miracle or mirage
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.
Renormalization and power counting of chiral nuclear forces
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.
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.
Renormalization of the Polyakov loop with gradient flow
NASA Astrophysics Data System (ADS)
Petreczky, P.; Schadler, H.-P.
2015-11-01
We use the gradient flow for the renormalization of the Polyakov loop in various representations. Using 2 +1 flavor QCD with highly improved staggered quarks and lattices with temporal extents of Nτ=6 , 8, 10 and 12 we calculate the renormalized Polyakov loop in many representations including fundamental, sextet, adjoint, decuplet, 15-plet, 24-plet and 27-plet. This approach allows for the calculations of the renormalized Polyakov loops over a large temperature range from T =116 MeV up to T =815 MeV , with small errors not only for the Polyakov loop in fundamental representation, but also for the Polyakov loops in higher representations. We compare our results with standard renormalization schemes and discuss the Casimir scaling of the Polyakov loops.
Renormalization of the Brazilian chiral nucleon-nucleon potential
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.
Nikolov, Nikolay M.
2010-06-17
The deviation from commutativity of the renormalization and the action of all linear partial differential operators is the main source of the anomalies in quantum field theory, including the renormalization group action. This deviation is characterized by certain 'renormalization cocycles' that are related to cohomologies of the so called (ordered) configuration spaces. Cohomological differential equations that determine the renormalization cocycles up to the renormalization freedom are obtained. The solution of these equations requires introducing transcendental extensions related to higher-dimensional polylogarithms.
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
Renormalization in Coulomb-gauge QCD within the Lagrangian formalism
Niegawa, A.
2006-08-15
We study renormalization of Coulomb-gauge QCD within the Lagrangian, second-order, formalism. We derive a Ward identity and the Zinn-Justin equation, and, with the help of the latter, we give a proof of algebraic renormalizability of the theory. Through diagrammatic analysis, we show that, in the strict Coulomb gauge, g{sup 2}D{sup 00} is invariant under renormalization. (D{sup 00} is the time-time component of the gluon propagator.)
Renormalization of curvature elastic constants for elastic and fluid membranes
NASA Astrophysics Data System (ADS)
Ami, S.; Kleinert, H.
1987-02-01
We study the fluctuations of membranes with area and curvature elasticity and calculate the renormalization of the curvature elastic constants due to thermal fluctuations. For the mean curvature elastic constant the result is the same as obtained previously for “ideal membranes” which resist only to curvature deformations. The renormalization of the gaussian curvature, on the other hand, depends on the elastic contants. In an incompressible membrane, it is five times weaker than in an ideal membrane.
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.
Hanh, Vu Thi; Kobayashi, Yutaro; Maebuchi, Motohiro; Nakamori, Toshihiro; Tanaka, Mitsuru; Matsui, Toshiro
2016-01-01
The aim of this study was to establish, through a standard addition method, a convenient quantification assay for dipeptides (GY, YG, SY, YS, and IY) in soybean hydrolysate using 2,4,6-trinitrobenzene sulfonate (TNBS) derivatization-aided LC-TOF-MS. Soybean hydrolysate samples (25.0 mg mL(-1)) spiked with target standards were subjected to TNBS derivatization. Under the optimal LC-MS conditions, five target dipeptides derivatized with TNBS were successfully detected. Examination of the standard addition curves, with a correlation coefficient of r(2) > 0.979, provided a reliable quantification of the target dipeptides, GY, YG, SY, YS, and IY, in soybean hydrolysate to be 424 ± 20, 184 ± 9, 2188 ± 199, 327 ± 16, and 2211 ± 133 μg g(-1) of hydrolysate, respectively. The proposed LC-MS assay is a reliable and convenient assay method, with no interference from matrix effects in hydrolysate, and with no requirement for the use of an isotope labeled internal standard. PMID:26212980
DLA with two species: Renormalization-group method renormalization-group method
NASA Astrophysics Data System (ADS)
Chang, Fuxuan; Li, Houqiang; Liu, De; Lin, Libin
1998-12-01
In this paper, we have studied the structure of DLA with two species by using the kinetic real-space renormalization group method introduced by Wang. Following the RG rules and growth processor, We have gained the configuration of 2×2 cell, calculated the fractal dimensions, multifractal spectra, and free energy when different value of p are applied. And we studied the problem of phase transition with different value of p. Our results demonstrate that the change of p doesn't affect the fractal dimension, but can affect the multifractal spectrum and the phase transition.
Renormalization of stochastic lattice models: basic formulation.
Haselwandter, Christoph A; Vvedensky, Dimitri D
2007-10-01
We describe a general method for the multiscale analysis of stochastic lattice models. Beginning with a lattice Langevin formulation of site fluctuations, we derive stochastic partial differential equations by regularizing the transition rules of the model. Subsequent coarse graining is accomplished by calculating renormalization-group (RG) trajectories from initial conditions determined by the regularized atomistic models. The RG trajectories correspond to hierarchies of continuum equations describing lattice models over expanding length and time scales. These continuum equations retain a quantitative connection over different scales, as well as to the underlying atomistic dynamics. This provides a systematic method for the derivation of continuum equations from the transition rules of lattice models for any length and time scales. As an illustration we consider the one-dimensional (1D) Wolf-Villain (WV) model [Europhys. Lett. 13, 389 (1990)]. The RG analysis of this model, which we develop in detail, is generic and can be applied to a wide range of conservative lattice models. The RG trajectory of the 1D WV model shows a complex crossover sequence of linear and nonlinear stochastic differential equations, which is in excellent agreement with kinetic Monte Carlo simulations of this model. We conclude by discussing possible applications of the multiscale method described here to other nonequilibrium systems. PMID:17994944
Applying Renormalization Group Techniques to Nuclear Reactions
NASA Astrophysics Data System (ADS)
Eldredge, Zachary; Bogner, Scott; Nunes, Filomena
2013-10-01
Nuclear reactions are commonly used to explore the physics of unstable nuclei. Therefore, it is important that accurate, computationally favorable methods exist to describe them. Reaction models often make use of effective nucleon-nucleus potentials (optical potentials) which fit low-energy scattering data and include an imaginary component to account for the removal of flux from the elastic channel. When describing reactions in momentum space, the coupling between low- and high-momentum states can pose a technical challenge. We would like potentials which allow us to compute low-momentum interactions without including highly virtual momentum states. A solution to this problem is to apply renormalization group (RG) techniques to produce a new effective potential in which high and low momentum degrees of freedom are decoupled, so that we need only consider momenta below some cutoff. This poster will present results relating to an implementation of RG techniques on optical potentials, including complex potentials and spin-orbit effects. We show that our evolved optical potentials reproduce bound states and scattering phase shifts without the inclusion of any momenta above a selected cutoff, and compare new potentials to old ones to examine the effect of transformation.
Polarizable Embedding Density Matrix Renormalization Group.
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
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.
Wendelboe, Mette Høegh; Thomsen, Jesper Skovhus; Henriksen, Kim; Vegger, Jens Bay; Brüel, Annemarie
2016-06-01
In rodents, lactation is associated with a considerable and very rapid bone loss, which almost completely recovers after weaning. The aim of the present study was to investigate whether the bisphosphonate Zoledronate (Zln) can inhibit lactation induced bone loss, and if Zln interferes with recovery of bone mass after lactation has ceased. Seventy-six 10-weeks-old NMRI mice were divided into the following groups: Baseline, Pregnant, Lactation, Lactation+Zln, Recovery, Recovery+Zln, and Virgin Control (age-matched). The lactation period was 12days, then the pups were removed, and thereafter recovery took place for 28days. Zln, 100μg/kg, was given s.c. on the day of delivery, and again 4 and 8days later. Mechanical testing, μCT, and dynamic histomorphometry were performed. At L4, lactation resulted in a substantial loss of bone strength (-55% vs. Pregnant, p<0.01), BV/TV (-40% vs. Pregnant, p<0.01), and trabecular thickness (Tb.Th) (-29% vs. Pregnant, p<0.001). Treatment with Zln completely prevented lactation induced loss of bone strength, BV/TV, and Tb.Th at L4. Full recovery of micro-architectural and mechanical properties was found 28days after weaning in vehicle-treated mice. Interestingly, the recovery group treated with Zln during the lactation period had higher BV/TV (+45%, p<0.01) and Tb.Th (+16%, p<0.05) compared with virgin controls. Similar results were found at the proximal tibia and femur. This indicates that Zln did not interfere with the bone formation taking place after weaning. On this background, we conclude that post-lactation bone formation is not dependent on a preceding lactation induced bone loss. PMID:27021151
Ackerman, L K; Noonan, G O; Begley, T H
2009-12-01
The ambient ionization technique direct analysis in real time (DART) was characterized and evaluated for the screening of food packaging for the presence of packaging additives using a benchtop mass spectrometer (MS). Approximate optimum conditions were determined for 13 common food-packaging additives, including plasticizers, anti-oxidants, colorants, grease-proofers, and ultraviolet light stabilizers. Method sensitivity and linearity were evaluated using solutions and characterized polymer samples. Additionally, the response of a model additive (di-ethyl-hexyl-phthalate) was examined across a range of sample positions, DART, and MS conditions (temperature, voltage and helium flow). Under optimal conditions, molecular ion (M+H+) was the major ion for most additives. Additive responses were highly sensitive to sample and DART source orientation, as well as to DART flow rates, temperatures, and MS inlet voltages, respectively. DART-MS response was neither consistently linear nor quantitative in this setting, and sensitivity varied by additive. All additives studied were rapidly identified in multiple food-packaging materials by DART-MS/MS, suggesting this technique can be used to screen food packaging rapidly. However, method sensitivity and quantitation requires further study and improvement. PMID:19753496
Lopez-Aguilar, F.; Costa-Quintana, J. )
1992-07-10
In this paper, the authors give a method for obtaining the renormalized electronic structure of the Hubbard systems. The first step is the determination of the self-energy beyond the Hartree-Fock approximation. This self-energy is constructed from several dielectric response functions. The second step is the determination of the quasiparticle band structure calculation which is performed from an appropriate modification of the augmented plane wave method. The third step consists in the determination of the renormalized density of states deduced from the spectral functions. The analysis of the renormalized density of states of the strongly correlated systems leads to the conclusion that there exist three types of resonances in their electronic structures, the lower energy resonances (LER), the middle energy resonances (MER) and the upper energy resonances (UER). In addition, the authors analyze the conditions for which the Luttinger theorem is satisfied. All of these questions are determined in a characteristic example which allows to test the theoretical method.
Renormalized Two-Fluid Hydrodynamics of Cosmic-Ray--modified Shocks
NASA Astrophysics Data System (ADS)
Malkov, M. A.; Voelk, H. J.
1996-12-01
A simple two-fluid model of diffusive shock acceleration, introduced by Axford, Leer, & Skadron and Drury & Völk, is revisited. This theory became a chief instrument in the studies of shock modification due to particle acceleration. Unfortunately its most intriguing steady state prediction about a significant enhancement of the shock compression and a corresponding increase of the cosmic-ray production violates assumptions which are critical for the derivation of this theory. In particular, for strong shocks the spectral flattening makes a cutoff-independent definition of pressure and energy density impossible and therefore causes an additional closure problem. Confining ourselves for simplicity to the case of plane shocks, assuming reacceleration of a preexisting cosmic-ray population, we argue that also under these circumstances the kinetic solution has a rather simple form. It can be characterized by only a few parameters, in the simplest case by the slope and the magnitude of the momentum distribution at the upper momentum cutoff. We relate these parameters to standard hydrodynamic quantities like the overall shock compression ratio and the downstream cosmic-ray pressure. The two-fluid theory produced in this way has the traditional form but renormalized closure parameters. By solving the renormalized Rankine-Hugoniot equations, we show that for the efficient stationary solution, most significant for cosmic-ray acceleration, the renormalization is needed in the whole parameter range of astrophysical interest.
NASA Astrophysics Data System (ADS)
Yi, H.; Choi, Y.; Park, H.
2012-12-01
In case of expanding mine galleries on redeveloping mine to gain the remaining minerals, commencing stability assessment is required because the sites could be in an unstable state in rock mechanics by occurrence of stress relaxation due to long-unattended existing galleries and other facilities. The paper presents the case study, which consider cause of errors occurrence and correct estimation result, to conduct multi-criteria indicator kriging using drilling log and electro-resistivity data for stability assessment on redeveloping mine. The study area is Gagok mine, which is one of the recent redeveloped mining sites in Korea. For suitable analyzing to the site, two correction methods were proposed that supplemented the indicator kriging method. The FIEG method was used in order to reduce the error of the results from the electro-resistivity survey influenced by infrastructures and mine galleries. In addition, the CARI method was chosen as a technique to resolve the distortions in the results from the indirect data, which were used due to external factors and decreased accuracy in statistical techniques. As a result, 73 % of the data for verifying were showed correct RMR class by estimation results and 1 % of the result were overestimated. Sensitivity of the FIEG was 3.5 %, that of the linear-CARI was 56 to 60 % and that of the logarithm-CARI was 61 to 65 %. In conclusion, the presented methods showed considerably effect increasing the accuracy of the RMR estimation, and remarkably reducing the ratio for overestimation. This paper could be used for the stability analyzing at redeveloping mines not only with increasing accuracy, but also without any further survey data or additional costs.
Renormalization group evolution of the universal theories EFT
NASA Astrophysics Data System (ADS)
Wells, James D.; Zhang, Zhengkang
2016-06-01
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, but 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. 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.
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.
Renormalization group running of neutrino parameters.
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
Renormalization group running of neutrino parameters
NASA Astrophysics Data System (ADS)
Ohlsson, Tommy; Zhou, Shun
2014-10-01
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.
(Non)renormalization of anomalous conductivities and holography
NASA Astrophysics Data System (ADS)
Gürsoy, Umut; Jansen, Aron
2014-10-01
The chiral magnetic and the chiral vortical effects are recently discovered phenomena arising from chiral gauge and gravitational anomalies that lead to generation of electric currents in presence of magnetic field or vorticity. The magnitude of these effects is determined by the anomalous conductivities. These conductivities can be calculated by the linear response theory, and in the strong coupling limit this calculation can be carried out by the holographic techniques. Earlier calculations in case of conformal field theories indicate non-renormalization of these conductivities where the holographic calculation agrees with the free field limit. We extend this holographic study to non-conformal theories exhibiting mass-gap and confinement-deconfinement type transitions in a holographic model based on the analytic black hole solution of Gao and Zhang. We show that radiative corrections are also absent in these non-conformal theories confirming indirect arguments of Jensen et al. in a direct and non-trivial fashion. There are various indications in field theory that such radiative corrections should arise when contribution of dynamical gluon fields to the chiral anomaly is present. Motivated by this, we seek for such corrections in the holographic picture and argue that such corrections indeed arise through mixing of the background and its fluctuations with the axion and the one-form fields that couple to the flavor and probe gauge branes through the Wess-Zumino terms. These corrections are non-vanishing when the flavor to color ratio N f /N c is finite, therefore they are only visible in the Veneziano limit at large N c .
The ab-initio density matrix renormalization group in practice
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.
Renormalization group and the superconducting susceptibility of a Fermi liquid
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.
Emergent geometry from field theory: Wilson's renormalization group revisited
NASA Astrophysics Data System (ADS)
Kim, Ki-Seok; Park, Chanyong
2016-06-01
We find a geometrical description from a field theoretical setup based on Wilson's renormalization group in real space. We show that renormalization group equations of coupling parameters encode the metric structure of an emergent curved space, regarded to be an Einstein equation for the emergent gravity. Self-consistent equations of local order-parameter fields with an emergent metric turn out to describe low-energy dynamics of a strongly coupled field theory, analogous to the Maxwell equation of the Einstein-Maxwell theory in the AdSd +2 /CFTd +1 duality conjecture. We claim that the AdS3 /CFT2 duality may be interpreted as Landau-Ginzburg theory combined with Wilson's renormalization group, which introduces vertex corrections into the Landau-Ginzburg theory in the large-Ns limit, where Ns is the number of fermion flavors.
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.
NASA Astrophysics Data System (ADS)
Luo, Shu
2012-01-01
Enlightened by the idea of the 3×3 Cabibbo-Kobayashi-Maskawa angle matrix proposed recently by Harrison , we introduce the Dirac angle matrix Φ and the Majorana angle matrix Ψ in the lepton sector for Dirac and Majorana neutrinos, respectively. We show that in the presence of CP violation, the angle matrix Φ or Ψ is entirely equivalent to the complex Maki-Nakagawa-Sakata matrix V itself, but has the advantage of being real, phase rephasing invariant, directly associated to the leptonic unitarity triangles and do not depend on any particular parametrization of V. In this paper, we further analyzed how the angle matrices evolve with the energy scale. The one-loop renormalization group equations of Φ, Ψ and some other rephasing invariant parameters are derived and a numerical analysis is performed to compare between the case of Dirac and Majorana neutrinos. Different neutrino mass spectra are taken into account in our calculation. We find that apparently different from the case of Dirac neutrinos, for Majorana neutrinos the renormalization group equation evolutions of Φ, Ψ and J strongly depend on the Majorana-type CP-violating parameters and are more sensitive to the sign of Δm312. They may receive significant radiative corrections in the minimal supersymmetric standard model with large tanβ if three neutrino masses are nearly degenerate.
Peripheral NN scattering from subtractive renormalization of chiral interactions
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}.
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.
Renormalizations and Wandering Jordan Curves of Rational Maps
NASA Astrophysics Data System (ADS)
Cui, Guizhen; Peng, Wenjuan; Tan, Lei
2016-04-01
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.
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.
Nonlinear Reynolds stress models and the renormalization group
NASA Technical Reports Server (NTRS)
Rubinstein, Robert; Barton, J. Michael
1990-01-01
The renormalization group is applied to derive a nonlinear algebraic Reynolds stress model of anisotropic turbulence in which the Reynolds stresses are quadratic functions of the mean velocity gradients. The model results from a perturbation expansion that is truncated systematically at second order with subsequent terms contributing no further information. The resulting turbulence model applied to both low and high Reynolds number flows without requiring wall functions or ad hoc modifications of the equations. All constants are derived from the renormalization group procedure; no adjustable constants arise. The model permits inequality of the Reynolds normal stresses, a necessary condition for calculating turbulence-driven secondary flows in noncircular ducts.
Renormalized dissipation in the nonconservatively forced Burgers equation
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.
Renormalization Group Reduction of Non Integrable Hamiltonian Systems
Stephan I. Tzenov
2002-05-09
Based on Renormalization Group method, a reduction of non integratable multi-dimensional Hamiltonian systems has been performed. The evolution equations for the slowly varying part of the angle-averaged phase space density and for the amplitudes of the angular modes have been derived. It has been shown that these equations are precisely the Renormalization Group equations. As an application of the approach developed, the modulational diffusion in one-and-a-half degrees of freedom dynamical system has been studied in detail.
Screening of heterogeneous surfaces: charge renormalization of Janus particles.
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
On the renormalization of the Gibbons-Hawking boundary term
NASA Astrophysics Data System (ADS)
Jacobson, Ted; Satz, Alejandro
2014-03-01
The bulk (Einstein-Hilbert) and boundary (Gibbons-Hawking) terms in the gravitational action are generally renormalized differently when integrating out quantum fluctuations. The former is affected by nonminimal couplings, while the latter is affected by boundary conditions. We use the heat kernel method to analyze this behavior for a nonminimally coupled scalar field, the Maxwell field, and the graviton field. Allowing for Robin boundary conditions, we examine in which cases the renormalization preserves the ratio of boundary and bulk terms required for the effective action to possess a stationary point. The implications for field theory and black hole entropy computations are discussed.
Nika, Heinz; Nieves, Edward; Hawke, David H.; Angeletti, Ruth Hogue
2013-01-01
We previously adapted the β-elimination/Michael addition chemistry to solid-phase derivatization on reversed-phase supports, and demonstrated the utility of this reaction format to prepare phosphoseryl peptides in unfractionated protein digests for mass spectrometric identification and facile phosphorylation-site determination. Here, we have expanded the use of this technique to β-N-acetylglucosamine peptides, modified at serine/threonine, phosphothreonyl peptides, and phosphoseryl/phosphothreonyl peptides, followed in sequence by proline. The consecutive β-elimination with Michael addition was adapted to optimize the solid-phase reaction conditions for throughput and completeness of derivatization. The analyte remained intact during derivatization and was recovered efficiently from the silica-based, reversed-phase support with minimal sample loss. The general use of the solid-phase approach for enzymatic dephosphorylation was demonstrated with phosphoseryl and phosphothreonyl peptides and was used as an orthogonal method to confirm the identity of phosphopeptides in proteolytic mixtures. The solid-phase approach proved highly suitable to prepare substrates from low-level amounts of protein digests for phosphorylation-site determination by chemical-targeted proteolysis. The solid-phase protocol provides for a simple, robust, and efficient tool to prepare samples for phosphopeptide identification in MALDI mass maps of unfractionated protein digests, using standard equipment available in most biological laboratories. The use of a solid-phase analytical platform is expected to be readily expanded to prepare digest from O-glycosylated- and O-sulfonated proteins for mass spectrometry-based structural characterization. PMID:23997661
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.
Renormalization Group Analysis of the Stability of Turbulent Flows in Porous Media
NASA Astrophysics Data System (ADS)
Avramenko, A. A.; Dmitrenko, N. P.; Tyrinov, A. I.
2016-06-01
The concept of renormalization groups for modeling the parameters of flow in porous media is considered. An algorithm for the renormalization of the equations from the k-ɛ model of turbulence is given. An expression is obtained for the coefficient of renormalized viscosity. Based on the model developed, conditions of the turbulent flow instability in a porous medium have been analyzed.
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). PMID:25748540
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
Renormalization of interactions of ultracold atoms in simulated Rashba gauge fields
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.
Pairing renormalization and regularization within the local density approximation
Borycki, P.J.; Dobaczewski, J.; Nazarewicz, W.; Stoitsov, M.V.
2006-04-15
We discuss methods used in mean-field theories to treat pairing correlations within the local density approximation. Pairing renormalization and regularization procedures are compared in spherical and deformed nuclei. Both prescriptions give fairly similar results, although the theoretical motivation, simplicity, and stability of the regularization procedure make it a method of choice for future applications.
SU(3) renormalization group study on parallel computer AP1000
NASA Astrophysics Data System (ADS)
Akemi, K.; de Forcrand, Ph.; Fujisaki, M.; Hashimoto, T.; Hege, H. C.; Hioki, S.; Makino, J.; Miyamura, O.; Nakamura, A.; Okada, M.; Stamatescu, I. O.; Tago, Y.; Takaishi, T.; QCD TARO (QCD on Thousand cell ARay processorOmnipurpose) Collaboration
We report results of a Monte Crlo renormalization group study with b = 2 blocking on a 34 4 lattice in progress. Δβ at β = 6.8 is consistent with previously obtained values at a large β and is smaller than the two-loop asymptotic value.
RENORMALIZATION OF POLYAKOV LOOPS IN FUNDAMENTAL AND HIGHER REPRESENTATIONS
KACZMAREK,O.; GUPTA, S.; HUEBNER, K.
2007-07-30
We compare two renormalization procedures, one based on the short distance behavior of heavy quark-antiquark free energies and the other by using bare Polyakov loops at different temporal entent of the lattice and find that both prescriptions are equivalent, resulting in renormalization constants that depend on the bare coupling. Furthermore these renormalization constants show Casimir scaling for higher representations of the Polyakov loops. The analysis of Polyakov loops in different representations of the color SU(3) group indicates that a simple perturbative inspired relation in terms of the quadratic Casimir operator is realized to a good approximation at temperatures T{approx}>{Tc}, for renormalized as well as bare loops. In contrast to a vanishing Polyakov loop in representations with non-zero triality in the confined phase, the adjoint loops are small but non-zero even for temperatures below the critical one. The adjoint quark-antiquark pairs exhibit screening. This behavior can be related to the binding energy of glue-lump states.
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.
Renormalization of NN Interaction with Relativistic Chiral Two Pion Exchange
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.
Holographic renormalization of 3D minimal massive gravity
NASA Astrophysics Data System (ADS)
Alishahiha, Mohsen; Qaemmaqami, Mohammad M.; Naseh, Ali; Shirzad, Ahmad
2016-01-01
We study holographic renormalization of 3D minimal massive gravity using the Chern-Simons-like formulation of the model. We explicitly present Gibbons- Hawking term as well as all counterterms needed to make the action finite in terms of dreibein and spin-connection. This can be used to find correlation functions of stress tensor of holographic dual field theory.
NASA Astrophysics Data System (ADS)
Adzhemyan, L. Ts.; Hnatič, M.; Kompaniets, M.; Lučivjanský, T.; Mižišin, L.
2016-02-01
The renormalization group theory is used to the study of the directed bond percolation (Gribov process) near its second-order phase transition between absorbing and active state. We present a numerical calculation of the renormalization group functions in the ɛ-expansion where ɛ is the deviation from the upper critical dimension dc = 4. Within this procedure anomalous dimensions γ are expressed in terms of irreducible renormalized Feynman diagrams and thus the calculation of renormalization constants could be entirely skipped. The renormalization group is included by means of the R operation, and for computational purposes we choose the null momentum subtraction scheme.
NASA Astrophysics Data System (ADS)
Rentrop, J. F.; Meden, V.; Jakobs, S. G.
2016-05-01
We study the renormalization group flow of the Luttinger-Ward functional and of its two-particle-irreducible vertex functions, given a cutoff in the two-particle interaction. We derive a conserving approximation to the flow and relate it to the fluctuation exchange approximation as well as to nonconserving approximations introduced in an earlier publication [J. F. Rentrop, S. G. Jakobs, and V. Meden, J. Phys. A: Math. Theor. 48, 145002 (2015), 10.1088/1751-8113/48/14/145002]. We apply the different approximate flow equations to the single-impurity Anderson model in thermal equilibrium at vanishing temperature. Numerical results for the effective mass, the spin susceptibility, the charge susceptibility, and the linear conductance reflect the similarity of the methods to the fluctuation exchange approximation. We find the majority of the approximations to deviate stronger from the exact results than one-particle-irreducible functional renormalization group schemes. However, we identify a simple static two-particle-irreducible flow scheme which performs remarkably well and produces an exponential Kondo-like scale in the renormalized level position.
Tarazona, Pablo; Feussner, Kirstin; Feussner, Ivo
2015-11-01
Within the lipidome of plants a few bulk molecular species hamper the detection of the rest, which are present at relatively low levels. In addition, low-abundance species are often masked by numerous isobaric interferences, such as those caused by isoelemental species and isotopologues. This scenario not only means that minor species are underrepresented, but also leads to potential misidentifications and limits the structural information gathered by lipidomics approaches. In order to overcome these limitations we have developed a multiplexed liquid chromatography-mass spectrometry lipidomics platform able to achieve an enhanced coverage of plant lipidomes. The platform is based on a single extraction step followed by a series of ultra-performance liquid chromatography separations. Post-column flow is then directed to both a triple quadrupole analyzer for targeted profiling and a time-of-flight analyzer for accurate mass analysis. As a proof of concept, plants were subjected to cold or drought, which are known to trigger widespread remodeling events in plant cell membranes. Analysis of the leaf lipidome yielded 393 molecular species within 23 different lipid classes. This enhanced coverage allowed us to identify lipid molecular species and even classes that are altered upon stress, allowing hypotheses on role of glycosylinositolphosphoceramides (GIPC), steryl glycosides (SG) and acylated steryl glycosides (ASG) in drought stress to be addressed and confirming the findings from numerous previous studies with a single, wide-ranging lipidomics approach. This extended our knowledge on membrane remodeling during the drought response, integrating sphingolipids and sterol lipids into the current glycerolipid-based model. PMID:26340975
Mesons in (2+1)-dimensional light front QCD. II. Similarity renormalization approach
NASA Astrophysics Data System (ADS)
Chakrabarti, Dipankar; Harindranath, A.
2002-02-01
Recently, we have studied the Bloch effective Hamiltonian approach to bound states in (2+1)-dimensional gauge theories. Numerical calculations were carried out to investigate the vanishing energy denominator problem. In this work, we study a similarity renormalization approach to the same problem. By performing analytical calculations with a step function form for the similarity factor, we show that, in addition to curing the vanishing energy denominator problem, the similarity approach generates a linear confining interaction for large transverse separations. However, for large longitudinal separations, the generated interaction grows only as the square root of the longitudinal separation and hence produces violations of rotational symmetry in the spectrum. We carry out numerical studies in the Głazek-Wilson and Wegner formalisms and present low-lying eigenvalues and wave functions. We investigate the sensitivity of the spectra to various parametrizations of the similarity factor and other parameters of the effective Hamiltonian, especially the scale σ. Our results illustrate the need for higher-order calculations of the effective Hamiltonian in the similarity renormalization scheme.
Unified theory of electron-phonon renormalization and phonon-assisted optical absorption
NASA Astrophysics Data System (ADS)
Patrick, Christopher E.; Giustino, Feliciano
2014-09-01
We present a theory of electronic excitation energies and optical absorption spectra which incorporates energy-level renormalization and phonon-assisted optical absorption within a unified framework. Using time-independent perturbation theory we show how the standard approaches for studying vibronic effects in molecules and those for addressing electron-phonon interactions in solids correspond to slightly different choices for the non-interacting Hamiltonian. Our present approach naturally leads to the Allen-Heine theory of temperature-dependent energy levels, the Franck-Condon principle, the Herzberg-Teller effect and to phonon-assisted optical absorption in indirect band gap materials. In addition, our theory predicts sub-gap phonon-assisted optical absorption in direct gap materials, as well as an exponential edge which we tentatively assign to the Urbach tail. We also consider a semiclassical approach to the calculation of optical absorption spectra which simultaneously captures energy-level renormalization and phonon-assisted transitions and is especially suited to first-principles electronic structure calculations. We demonstrate this approach by calculating the phonon-assisted optical absorption spectrum of bulk silicon.
Decomposition of density matrix renormalization group states into a Slater determinant basis
NASA Astrophysics Data System (ADS)
Moritz, Gerrit; Reiher, Markus
2007-06-01
The quantum chemical density matrix renormalization group (DMRG) algorithm is difficult to analyze because of the many numerical transformation steps involved. In particular, a decomposition of the intermediate and the converged DMRG states in terms of Slater determinants has not been accomplished yet. This, however, would allow one to better understand the convergence of the algorithm in terms of a configuration interaction expansion of the states. In this work, the authors fill this gap and provide a determinantal analysis of DMRG states upon convergence to the final states. The authors show that upon convergence, DMRG provides the same complete-active-space expansion for a given set of active orbitals as obtained from a corresponding configuration interaction calculation. Additional insight into DMRG convergence is provided, which cannot be obtained from the inspection of the total electronic energy alone. Indeed, we will show that the total energy can be misleading as a decrease of this observable during DMRG microiteration steps may not necessarily be taken as an indication for the pickup of essential configurations in the configuration interaction expansion. One result of this work is that a fine balance can be shown to exist between the chosen orbital ordering, the guess for the environment operators, and the choice of the number of renormalized states. This balance can be well understood in terms of the decomposition of total and system states in terms of Slater determinants.
Decomposition of density matrix renormalization group states into a Slater determinant basis.
Moritz, Gerrit; Reiher, Markus
2007-06-28
The quantum chemical density matrix renormalization group (DMRG) algorithm is difficult to analyze because of the many numerical transformation steps involved. In particular, a decomposition of the intermediate and the converged DMRG states in terms of Slater determinants has not been accomplished yet. This, however, would allow one to better understand the convergence of the algorithm in terms of a configuration interaction expansion of the states. In this work, the authors fill this gap and provide a determinantal analysis of DMRG states upon convergence to the final states. The authors show that upon convergence, DMRG provides the same complete-active-space expansion for a given set of active orbitals as obtained from a corresponding configuration interaction calculation. Additional insight into DMRG convergence is provided, which cannot be obtained from the inspection of the total electronic energy alone. Indeed, we will show that the total energy can be misleading as a decrease of this observable during DMRG microiteration steps may not necessarily be taken as an indication for the pickup of essential configurations in the configuration interaction expansion. One result of this work is that a fine balance can be shown to exist between the chosen orbital ordering, the guess for the environment operators, and the choice of the number of renormalized states. This balance can be well understood in terms of the decomposition of total and system states in terms of Slater determinants. PMID:17614539
Renormalization, Thermodynamic Formalism and Quasi-Crystals in Subshifts
NASA Astrophysics Data System (ADS)
Bruin, Henk; Leplaideur, Renaud
2013-07-01
We examine the thermodynamic formalism for a class of renormalizable dynamical systems which in the symbolic space is generated by the Thue-Morse substitution, and in complex dynamics by the Feigenbaum-Coullet-Tresser map. The basic question addressed is whether fixed points V of a renormalization operator {{R}} acting on the space of potentials are such that the pressure function {β mapsto {P}(-β V)} exhibits phase transitions. This extends the work by Baraviera, Leplaideur and Lopes on the Manneville-Pomeau map, where such phase transitions were indeed detected. In this paper, however, the attractor of renormalization is a Cantor set (rather than a single fixed point), which admits various classes of fixed points of {{R}}, some of which do and some of which do not exhibit phase transitions. In particular, we show it is possible to reach, as a ground state, a quasi-crystal before temperature zero by freezing a dynamical system.
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.
Computing the effective action with the functional renormalization group
NASA Astrophysics Data System (ADS)
Codello, Alessandro; Percacci, Roberto; Rachwał, Lesław; Tonero, Alberto
2016-04-01
The "exact" or "functional" renormalization group equation describes the renormalization group flow of the effective average action Γ _k. The ordinary effective action Γ _0 can be obtained by integrating the flow equation from an ultraviolet scale k=Λ down to k=0. We give several examples of such calculations at one-loop, both in renormalizable and in effective field theories. We reproduce the four-point scattering amplitude in the case of a real scalar field theory with quartic potential and in the case of the pion chiral Lagrangian. In the case of gauge theories, we reproduce the vacuum polarization of QED and of Yang-Mills theory. We also compute the two-point functions for scalars and gravitons in the effective field theory of scalar fields minimally coupled to gravity.
Renormalized interaction of relativistic bosons with delta function potentials
Dogan, Caglar; Turgut, O. Teoman
2010-08-15
We study the interaction of mutually noninteracting Klein-Gordon particles with localized sources on stochastically complete Riemannian surfaces. This asymptotically free theory requires regularization and coupling constant renormalization. Renormalization is performed nonperturbatively using the orthofermion algebra technique and the principal operator {Phi} is found. The principal operator is then used to obtain the bound state spectrum, in terms of binding energies to single Dirac-delta function centers. The heat kernel method allows us to generalize this procedure to compact and Cartan-Hadamard type Riemannian manifolds. We make use of upper and lower bounds on the heat kernel to constrain the ground state energy from below, thus confirming that our neglect of pair creation is justified for certain ranges of parameters in the problem.
Scaling relations and multicritical phenomena from functional renormalization.
Boettcher, Igor
2015-06-01
We investigate multicritical phenomena in O(N)+O(M) models by means of nonperturbative renormalization group equations. This constitutes an elementary building block for the study of competing orders in a variety of physical systems. To identify possible multicritical points in phase diagrams with two ordered phases, we compute the stability of isotropic and decoupled fixed point solutions from scaling potentials of single-field models. We verify the validity of Aharony's scaling relation within the scale-dependent derivative expansion of the effective average action. We discuss implications for the analysis of multicritical phenomena with truncated flow equations. These findings are an important step towards studies of competing orders and multicritical quantum phase transitions within the framework of functional renormalization. PMID:26172666
On a renormalization group scheme for causal dynamical triangulations
NASA Astrophysics Data System (ADS)
Cooperman, Joshua H.
2016-03-01
The causal dynamical triangulations approach aims to construct a quantum theory of gravity as the continuum limit of a lattice-regularized model of dynamical geometry. A renormalization group scheme—in concert with finite size scaling analysis—is essential to this aim. Formulating and implementing such a scheme in the present context raises novel and notable conceptual and technical problems. I explored these problems, and, building on standard techniques, suggested potential solutions in a previous paper (Cooperman, arXiv:gr-qc/1410.0026). As an application of these solutions, I now propose a renormalization group scheme for causal dynamical triangulations. This scheme differs significantly from that studied recently by Ambjørn, Görlich, Jurkiewicz, Kreienbuehl, and Loll.
Renormalization-group study of the four-body problem
Schmidt, Richard; Moroz, Sergej
2010-05-15
We perform a renormalization-group analysis of the nonrelativistic four-boson problem by means of a simple model with pointlike three- and four-body interactions. We investigate in particular the region where the scattering length is infinite and all energies are close to the atom threshold. We find that the four-body problem behaves truly universally, independent of any four-body parameter. Our findings confirm the recent conjectures of others that the four-body problem is universal, now also from a renormalization-group perspective. We calculate the corresponding relations between the four- and three-body bound states, as well as the full bound-state spectrum and comment on the influence of effective range corrections.
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.
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
Electron-phonon renormalization of the electronic structure of diamond
NASA Astrophysics Data System (ADS)
Giustino, Feliciano; Louie, Steven G.; Cohen, Marvin L.
2011-03-01
The calculation of band structures from first-principles has reached a high level of accuracy. Calculations combining density-functional theory with many-body perturbation theory often are in good agreement with measurements by photoemission, tunneling, and other spectroscopic probes. While significant efforts have been devoted to improving the description of electron-electron interactions in these calculations, the effect of lattice vibrations has largely been overlooked so far. In this work we study from first principles the electron-phonon renormalization of the band gap of diamond. The calculated temperature dependence of the gap and the broadening of the absorption edge are in excellent agreement with spectroscopic ellipsometry data. Interestingly we find a gap renormalization due to zero-point vibrations as large as 0.6 eV. We discuss the implications of our findings for the electronic structure of other carbon-based bulk materials and nanostructures.
E-cigarette Marketing and Older Smokers: Road to Renormalization
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
Holographic entanglement entropy of N =2* renormalization group flow
NASA Astrophysics Data System (ADS)
Pang, Da-Wei
2015-10-01
The N =2* theory is obtained by deforming N =4 supersymmetric Yang-Mills theory with two relevant operators of dimensions 2 and 3. We study the holographic entanglement entropy of the N =2* theory along the whole renormalization group flow. We find that in the UV the holographic entanglement entropy for an arbitrary entangling region receives a universal logarithmic correction, which is related to the relevant operator of dimension 3. This universal behavior can be interpreted on the field theory side by perturbatively evaluating the entanglement entropy of a conformal field theory (CFT) under relevant deformations. In the IR regime, we obtain the large R behavior of the renormalized entanglement entropy for both a strip and a sphere entangling region, where R denotes the size of the entangling region. A term proportional to 1 /R is found for both cases, which can be attributed to the emergent CFT5 in the IR.
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.
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.
Consistent closure of renormalization group flow equations in quantum gravity
NASA Astrophysics Data System (ADS)
Codello, Alessandro; D'Odorico, Giulio; Pagani, Carlo
2014-04-01
We construct a consistent closure for the beta functions of the cosmological and Newton's constants by evaluating the influence that the anomalous dimensions of the fluctuating metric and ghost fields have on their renormalization group flow. In this generalized framework we confirm the presence of a UV attractive non-Gaussian fixed point, which we find characterized by real critical exponents. Our closure method is general and can be applied systematically to more general truncations of the gravitational effective average action.
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.
Subtractive Renormalization Group Invariance: Pionless EFT at NLO
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}.
Lattice and continuum wavelets and the block renormalization group
O'Carroll, M. )
1993-05-01
The authors obtain a resolution of the identity operator, for functions on a lattice [var epsilon]Z[sup d], which is derived from the block renormalization group. The authors use eigenfunctions of the terms of the decomposition to form a basis for l[sub 2]([var epsilon]Z[sup d]) and show how the basis is generated from lattice wavelets. The lattice spacing [var epsilon] is taken to zero and continuum wavelets are obtained. 12 refs.
A Renormalized Rough Path over Fractional Brownian Motion
NASA Astrophysics Data System (ADS)
Unterberger, Jérémie
2013-06-01
We construct in this article a rough path over fractional Brownian motion with arbitrary Hurst index by (i) using the Fourier normal ordering algorithm introduced in (Unterberger, Commun Math Phy 298(1):1-36, 2010) to reduce the problem to that of regularizing tree iterated integrals and (ii) applying the Bogolioubov-Parasiuk-Hepp-Zimmermann (BPHZ) renormalization algorithm to Feynman diagrams representing tree iterated integrals.
The Pion Renormalized Light-Cone Wave Function
NASA Astrophysics Data System (ADS)
Trawiński, Arkadiusz P.
2016-06-01
An approximate light-cone wave function for the pion effective quark-antiquark Fock sector corresponding to a small value of the renormalization group parameter is presented. The approximate wave function is motivated by the LF-holography and the quadratic confinement potential in the front form of Hamiltonian dynamics, which is in harmony with the linear confining potential in the instant form. The pion radius, decay constant and form-factor are also presented.
Effect of Zn and Ni impurities on the quasiparticle renormalization of superconducting Bi-2212.
Zabolotnyy, V B; Borisenko, S V; Kordyuk, A A; Fink, J; Geck, J; Koitzsch, A; Knupfer, M; Büchner, B; Berger, H; Erb, A; Lin, C T; Keimer, B; Follath, R
2006-01-27
The Cu substitution by Zn and Ni impurities and its influence on the mass renormalization effects in angle-resolved photoelectron spectra (ARPES) of Bi2Sr2CaCu2O8-delta is addressed. We show that the nonmagnetic Zn atoms have a much stronger effect in both the nodal and antinodal parts of the Brillouin zone than magnetic Ni. The observed changes are consistent with the behavior of the spin resonance mode as seen by inelastic neutron scattering in YBCO. This strongly suggests that the "peak-dip-hump" and the kink in ARPES on the one side and neutron resonance on the other are closely related features. PMID:16486757
The effect of gravitational tidal forces on renormalized quantum fields
NASA Astrophysics Data System (ADS)
Hollowood, Timothy J.; Shore, Graham M.
2012-02-01
The effect of gravitational tidal forces on renormalized quantum fields propagating in curved spacetime is investigated and a generalisation of the optical theorem to curved spacetime is proved. In the case of QED, the interaction of tidal forces with the vacuum polarization cloud of virtual e + e - pairs dressing the renormalized photon has been shown to produce several novel phenomena. In particular, the photon field amplitude can locally increase as well as decrease, corresponding to a negative imaginary part of the refractive index, in apparent violation of unitarity and the optical theorem. Below threshold decays into e + e - pairs may also occur. In this paper, these issues are studied from the point of view of a non-equilibrium initial-value problem, with the field evolution from an initial null surface being calculated for physically distinct initial conditions and for both scalar field theories and QED. It is shown how a generalised version of the optical theorem, valid in curved spacetime, allows a local increase in amplitude while maintaining consistency with unitarity. The picture emerges of the field being dressed and undressed as it propagates through curved spacetime, with the local gravitational tidal forces determining the degree of dressing and hence the amplitude of the renormalized quantum field. These effects are illustrated with many examples, including a description of the undressing of a photon in the vicinity of a black hole singularity.
Unifying renormalization group and the continuous wavelet transform
NASA Astrophysics Data System (ADS)
Altaisky, M. V.
2016-05-01
It is shown that the renormalization group turns to be a symmetry group in a theory initially formulated in a space of scale-dependent functions, i.e., those depending on both the position x and the resolution a . Such a theory, earlier described in [1,2], is finite by construction. The space of scale-dependent functions {ϕa(x )} is more relevant to a physical reality than the space of square-integrable functions L2(Rd); because of the Heisenberg uncertainty principle, what is really measured in any experiment is always defined in a region rather than a point. The effective action Γ(A ) of our theory turns out to be complementary to the exact renormalization group effective action. The role of the regulator is played by the basic wavelet—an "aperture function" of a measuring device used to produce the snapshot of a field ϕ at the point x with the resolution a . The standard renormalization group results for ϕ4 model are reproduced.
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.
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.
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.
Substrate-induced Majorana renormalization in topological nanowires
NASA Astrophysics Data System (ADS)
Das Sarma, S.; Hui, Hoi-Yin; Brydon, P. M. R.; Sau, Jay D.
2015-07-01
We theoretically consider the substrate-induced Majorana localization length renormalization in nanowires in contact with a bulk superconductor in the strong tunnel-coupled regime, showing explicitly that this renormalization depends strongly on the transverse size of the one-dimensional nanowires. For metallic (e.g. Fe on Pb) or semiconducting (e.g. InSb on Nb) nanowires, the renormalization effect is found to be very strong and weak, respectively, because the transverse confinement size in the two situations happens to be 0.5 nm (metallic nanowire) and 20 nm (semiconducting nanowire). Thus, the Majorana localization length could be very short (long) for metallic (semiconducting) nanowires even for the same values of all other parameters (except for the transverse wire size). We also show that any tunneling conductance measurements in such nanowires, carried out at temperatures and/or energy resolutions comparable to the induced superconducting energy gap, cannot distinguish between the existence of the Majorana modes or ordinary subgap fermionic states since both produce very similar broad and weak peaks in the subgap tunneling conductance independent of the localization length involved. Only low temperature (and high resolution) tunneling measurements manifesting sharp zero bias peaks can be considered to be signatures of Majorana modes in topological nanowires.
Strong Disorder Renormalization Group for the Many Body Localization Transition
NASA Astrophysics Data System (ADS)
Refael, Gil; Oganesyan, Vadim; Iyer, Shankar
2012-02-01
The strong disorder renormalization group, originally devised by Ma and Dasgupta to study the random Heisenberg antiferromagnet, has subsequently been used to investigate the low energy physics and quantum phase transitions of a variety of strongly disordered systems. However, recent work by Basko, Aleiner, and Altshuler has focused attention on the many body localization transition, a dynamical quantum phase transition that involves the localization of highly excited eigenstates of a many body system in Fock space. Numerical results from an exact diagonalization study by Pal and Huse suggest that the many body localization transition may exhibit so-called infinite-randomness, a property that implies that a strong disorder renormalization group may be well-suited to study this transition. With the many body localization transition in mind, we therefore outline a strong disorder renormalization procedure that targets the least-localized eigenstate of a model. We then apply this procedure to study disordered quantum Ising and XXZ models. The latter model is similar to the one investigated by Pal and Huse and is expected to contain a dynamical transition between localized and ergodic phases; our principal aim is to use the strong disorder RG to characterize this transition.
Renormalization group and phase transitions in spin, gauge, and QCD like theories
NASA Astrophysics Data System (ADS)
Liu, Yuzhi
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). We use the two dimensional nearest neighbor Ising model to introduce many conventional yet important concepts. We then generalize the model to Dyson's hierarchical model (HM), which has rich phase properties depending on the strength of the interaction. The partition function zeros (Fisher zeros) of the HM model in the complex temperature plane is calculated and their connection with the complex RG flows is discussed. The two lattice matching method is used to construct both the complex RG flows and calculate the discrete beta functions. The motivation of calculating the discrete beta functions for various HM models is to test the matching method and to show how physically relevant fixed points emerge from the complex domain. We notice that the critical exponents calculated from the HM depend on the blocking parameter b. This motivated us to analyze the connection between the discrete and continuous RG transformation. We demonstrate numerical calculations of the ERG equations. We discuss the relation between Litim and Wilson-Polchinski equation and the effect of the cut-off functions in the ERG calculation. We then apply methods developed in the spin models to more complicated and more physically relevant lattice gauge theories and lattice quantum chromodynamics (QCD) like theories. Finite size scaling (FSS) technique is used to analyze the Binder cumulant of the SU(2) lattice gauge model. We calculate the critical exponent nu and omega of the model and show that it is in the same universality class as the three dimensional Ising model. Motivated by the walking technicolor theory, we study the strongly coupled gauge theories with conformal or near conformal properties. We compare
Dryga, Anatoly; Warshel, Arieh
2010-01-01
Simulations of long time process in condensed phases in general and in biomolecules in particular, presents a major challenge that cannot be overcome at present by brute force molecular dynamics (MD) approaches. This work takes the renormalization method, intruded by us sometime ago, and establishes its reliability and potential in extending the time scale of molecular simulations. The validation involves a truncated gramicidin system in the gas phase that is small enough to allow very long explicit simulation and sufficiently complex to present the physics of realistic ion channels. The renormalization approach is found to be reliable and arguably presents the first approach that allows one to exploit the otherwise problematic steered molecular dynamics (SMD) treatments in quantitative and meaningful studies. It is established that we can reproduce the long time behavior of large systems by using Langevin dynamics (LD) simulations of a renormalized implicit model. This is done without spending the enormous time needed to obtain such trajectories in the explicit system. The present study also provides a promising advance in accelerated evaluation of free energy barriers. This is done by adjusting the effective potential in the implicit model to reproduce the same passage time as that obtained in the explicit model, under the influence of an external force. Here having a reasonable effective friction provides a way to extract the potential of mean force (PMF) without investing the time needed for regular PMF calculations. The renormalization approach, which is illustrated here in realistic calculations, is expected to provide a major help in studies of complex landscapes and in exploring long time dynamics of biomolecules. PMID:20836533
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.
Król, Sylwia; Zabiegała, Bożena; Namieśnik, Jacek
2012-08-01
Monitoring of the environmental fate of polybrominated diphenyl ethers (PBDEs) involves determination of their concentration in air, airborne particles and settled dust. This requires the implementation of appropriate analytical tools like measuring instruments, reference materials and analytical procedures. In this study an analytical procedure was developed for determining PBDEs in samples with a complex matrix composition. The efficiencies of three different extraction techniques - Soxhlet extraction (SE), Accelerated Solvent Extraction (ASE) and Ultrasound Assisted Extraction (UAE) - were compared. The study investigated the possibility of using the standard addition method for estimating PBDEs levels. The GC-μECD system was successfully applied as an alternative to low resolution mass spectrometry (LRMS) for determining BDE-209 in dust samples. The developed analytical procedure was then used to analyze dust samples, collected from houses and computer suites in the Tri-city area (Gdansk, Gdynia and Sopot), in order to detect and quantify the presence of polybrominated diphenyl ethers (PBDEs) in the indoor environment. Concentrations of studied congeners (from triBDE to heptaBDE), obtained by chromatographic analysis of dust samples extracts, performed applying two measurement systems (GC-EIMS and GC-μECD) ranged between 331 and 3102 ng g(-1) for house dust and between
Running-mass inflation model and primordial black holes
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.
Variational approach to renormalized phonon in momentum-nonconserving nonlinear lattices
NASA Astrophysics Data System (ADS)
Liu, Junjie; Li, Baowen; Wu, Changqin
2016-05-01
In this letter, we extend a previously proposed variational approach to systematically investigate general momentum-nonconserving nonlinear lattices. Two intrinsic identities characterizing optimal reference systems are firstly revealed, which enables us to derive explicit expressions for optimal variational parameters. The resulting optimal harmonic reference systems provide information for the band gap as well as the dispersion of renormalized phonons in momentum-nonconserving nonlinear lattices. As a demonstration, we consider the one-dimensional φ4 lattice. We show that the phonon band gap endows a simple power-law temperature dependence in the weak stochasticity regime where predicted dispersion is reliable by comparing with numerical results. In addition, an exact relation between ensemble averages of the φ4 lattice in the whole temperature range is found, regardless of the existence of the strong stochasticity threshold.
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.
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.
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.
Bose gases near resonance: Renormalized interactions in a condensate
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.
Renormalization In Quantum Gauge Theory Using Zeta-Function Method
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.
Three-body loss in lithium from functional renormalization
Floerchinger, S.; Schmidt, R.; Wetterich, C.
2009-05-15
We use functional-integral methods for an estimate of the three-body loss in a three-component {sup 6}Li ultracold atom gas. We advocate a simple picture where the loss proceeds by the formation of a three-atom bound trimer state, the trion. In turn, the effective amplitude for the trion formation from three atoms is estimated from a simple effective boson exchange process. The energy gap of the trion and other key quantities for the loss coefficient are computed in a functional renormalization-group framework.
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.
Error estimates and specification parameters for functional renormalization
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.
Renormalized anisotropic exchange for representing heat assisted magnetic recording media
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.
Renormalization of high-energy Lorentz-violating QED
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.
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.
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.
Information-geometric approach to the renormalization group
NASA Astrophysics Data System (ADS)
Bény, Cédric; Osborne, Tobias J.
2015-08-01
We propose a general formulation of the renormalization group (RG) as a family of quantum channels which connect the microscopic physical world to the observable world at some scale. By endowing the set of quantum states with an operationally motivated information geometry, we induce the space of Hamiltonians with a corresponding metric geometry. The resulting structure allows one to quantify information loss along RG flows in terms of the distinguishability of thermal states. In particular, we introduce a family of functions, expressible in terms of two-point correlation functions, which are nonincreasing along the flow. Among those, we study the speed of the flow and its generalization to infinite lattices.
High energy scattering and renormalization in the NS+ string and large N QCD
NASA Astrophysics Data System (ADS)
Rojas Fernandez, Francisco Javier
In this work we study a model of open strings and its low energy limit as a device to understand certain aspects of gauge theory. More specifically, we use the even G-parity sector of the Neveu-Schwarz model with the open strings endpoints attached to a stack of N coincident Dp-branes as our starting point. After various projections, the low energy limit of this string theory is pure Yang-Mills and the field theory limit of the sum of the planar open string diagrams becomes to the sum of the leading diagrams of 't Hooft's large N expansion of QCD. The typical expression for the amplitude we study here, namely for the scattering of open string massless vector bosons, comes in an integral form that shows multiple (spurious) divergences in various corners of the integration region. However, we regularize all of these divergences by momentarily suspending total momentum conservation by an amount p, as first suggested by Goddard and by Neveu and Scherk [1, 2], and construct the appropriate counterterms. We show that all the counterterms we need to introduce, after analytic continuation to p = 0, are all proportional to the tree amplitude which then amounts to a renormalization the string coupling constant. Using this renormalized expression, we also study its high-energy behavior. We obtain the one-loop ( O (g2)) correction to the open string Regge trajectory alpha(t) also as a function of the spacetime dimensionality of the Dp-branes. We also study the field theory limit of the new trajectory which amounts to analyzing the small t behavior of alpha(t). We obtain the exact same answer given by conventional calculations in dimensionally regularized gauge theory which puts the gluon on a Regge trajectory of order g2. We think that this is a useful insight that open string theory provides into the understanding of gauge theory. Additionally we study the behavior of the new trajectory alpha(t) for t away from zero which is relevant for open string physics. Finally we work
Dynamical renormalization group approach to relaxation in quantum field theory
NASA Astrophysics Data System (ADS)
Boyanovsky, D.; de Vega, H. J.
2003-10-01
The real time evolution and relaxation of expectation values of quantum fields and of quantum states are computed as initial value problems by implementing the dynamical renormalization group (DRG). Linear response is invoked to set up the renormalized initial value problem to study the dynamics of the expectation value of quantum fields. The perturbative solution of the equations of motion for the field expectation values of quantum fields as well as the evolution of quantum states features secular terms, namely terms that grow in time and invalidate the perturbative expansion for late times. The DRG provides a consistent framework to resum these secular terms and yields a uniform asymptotic expansion at long times. Several relevant cases are studied in detail, including those of threshold infrared divergences which appear in gauge theories at finite temperature and lead to anomalous relaxation. In these cases the DRG is shown to provide a resummation akin to Bloch-Nordsieck but directly in real time and that goes beyond the scope of Bloch-Nordsieck and Dyson resummations. The nature of the resummation program is discussed in several examples. The DRG provides a framework that is consistent, systematic, and easy to implement to study the non-equilibrium relaxational dynamics directly in real time that does not rely on the concept of quasiparticle widths.
Signal inference with unknown response: calibration-uncertainty renormalized estimator.
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. PMID:25679743
Numerical renormalization group study of a dissipative quantum dot
NASA Astrophysics Data System (ADS)
Glossop, M. T.; Ingersent, K.
2007-03-01
We study the quantum phase transition (QPT) induced by dissipation in a quantum dot device at the degeneracy point. We employ a Bose-Fermi numerical renormalization group approach [1] to study the simplest case of a spinless resonant-level model that couples the charge density on the dot to a dissipative bosonic bath with density of states B(φ)ŝ. In anticipation of future experiments [2] and to assess further the validity of theoretical techniques in this rapidly developing area, we take the conduction-electron leads to have a pseudogap density of states: ρ(φ) |φ|^r, as considered in a very recent perturbative renormalization group study [3]. We establish the conditions on r and s such that a QPT arises with increasing dissipation strength --- from a delocalized phase, where resonant tunneling leads to large charge fluctuations on the dot, to a localized phase where such fluctuations are frozen. We present results for the single-particle spectrum and the response of the system to a local electric field, extracting critical exponents that depend in general on r and s and obey hyperscaling relations. We make full comparison with results of [3] where appropriate. Supported by NSF Grant DMR-0312939. [1] M. T. Glossop and K. Ingersent, PRL 95, 067202 (2005); PRB (2006). [2] L. G. G. V. Dias da Silva, N. P. Sandler, K. Ingersent, and S. E. Ulloa, PRL 97, 096603 (2006). [3] C.-H. Chung, M. Kir'can, L. Fritz, and M. Vojta (2006).
Superfluid phase transition with activated velocity fluctuations: Renormalization group approach.
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
Electron phonon renormalization in N-doped graphene
NASA Astrophysics Data System (ADS)
Podila, Ramakrishna; Ayala, Paola; Spear, John; Pichler, Thomas; Rao, Apparao
2012-02-01
Current research efforts are aimed at controlling the electronic properties graphene sheets using electron (or hole) doping for successful device fabrication. The presence of strong coupling between electronic and vibrational properties in graphene greatly assists Raman spectroscopy in probing the dopant-induced electronic energy changes. Previously, Raman spectroscopy was employed as a tool to probe the electron and phonon renormalization in doped single-walled carbon nanotubes (SWNT). It was found that the increase in electron velocity in?uences lattice vibrations locally near a negatively charged defect. These local renormalization effects were observed to result in a new effectively downshifted (up-shifted) Raman peak below the G' peak for n-doped (p-doped) SWNTs. In case of graphene, we find that the several Raman features for CVD grown N-doped graphene vary depending upon local dopant bonding environment. For instance, non-graphitic dopants (pyridinic, pyrrolic) were observed to result in highly intense D & D'-band unlike the graphitic dopants. We explain these results in terms of the zig-zag (armchair) edges formed by graphitic (non-graphitic) bonding environment of the dopant.
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.
Measuring the aspect ratio renormalization of anisotropic-lattice gluons
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.
Communication: Random phase approximation renormalized many-body perturbation theory
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.
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 .
Generalized similarity, renormalization groups, and nonlinear clocks for multiscaling.
Park, M; O'Malley, D; Cushman, J H
2014-04-01
Fixed points of the renormalization group operator Rp,rX(t)≡X(rt)/rp are said to be p-self-similar. Here X(t) is an arbitrary stochastic process. The concept of a p-self-similar process is generalized via the renormalization group operator RF,GX(t)=F[X(G(t))], where F and G are bijections on (-∞,∞) and [0,∞), respectively. If X(t) is a fixed point of RF,G, then X(t) is said to be (F,G)-self-similar. We say Y(t) is (F,G)-X(t)-similar if RF,GX(t)=Y(t) in distribution. Exit time distributions and finite-size Lyapunov exponents were obtained for these latter processes. A power law multiscaling process is defined with a multipower-law clock. This process is employed to statistically represent diffusion in a nanopore, a monolayer fluid confined between atomically structured surfaces. The tools presented provide a straightforward method to statistically represent any multiscaling process in time. PMID:24827190
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.
Collapse transition of randomly branched polymers: renormalized field theory.
Janssen, Hans-Karl; Stenull, Olaf
2011-05-01
We present a minimal dynamical model for randomly branched isotropic polymers, and we study this model in the framework of renormalized field theory. For the swollen phase, we show that our model provides a route to understand the well-established dimensional-reduction results from a different angle. For the collapse θ transition, we uncover a hidden Becchi-Rouet-Stora supersymmetry, signaling the sole relevance of tree configurations. We correct the long-standing one-loop results for the critical exponents, and we push these results on to two-loop order. For the collapse θ' transition, we find a runaway of the renormalization group flow, which lends credence to the possibility that this transition is a fluctuation-induced first-order transition. Our dynamical model allows us to calculate for the first time the fractal dimension of the shortest path on randomly branched polymers in the swollen phase as well as at the collapse transition and related fractal dimensions. PMID:21728509
Renormalization group improved Yennie-Frautschi-Suura theory for Z/sup 0/ physics
Ward, B.F.L.
1987-06-01
Described is a recently developed renormalization group improved version of the program of Yennie, Frautschi and Suura for the exponentiation of infrared divergences in Abelian gauge theories. Particular attention is paid to the relevance of this renormalization group improved exponentiation to Z/sup 0/ physics at the SLC and LEP.
Renormalization screening and collision-induced quantum interference in dense plasmas
Jung, Young-Dae; Rasheed, A.; Jamil, M.
2014-07-15
The influence of renormalization screening and collision-induced quantum interference in electron-electron collisions is investigated in partially ionized dense hydrogen plasmas. The effective interaction potential with the total spin-states of the collision system is considered to obtain the differential electron-electron scattering cross section. The results show that the renormalization plasma screening effect suppresses the electron-electron scattering cross section, including the quantum interference effect, especially, except for the forward and backward scattering directions. It is also shown that the renormalization plasma screening effect on the scattering cross section decreases with increasing collision energy. However, the renormalization screening effect is found to be important for the forward directions in the scattering cross section neglecting the quantum interference effect. The variations of the renormalization screening and collision-induced quantum interference effects are also discussed.
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.
An exact, finite, gauge-invariant, non-perturbative approach to QCD renormalization
NASA Astrophysics Data System (ADS)
Fried, H. M.; Tsang, P. H.; Gabellini, Y.; Grandou, T.; Sheu, Y.-M.
2015-08-01
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.
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.
An exact, finite, gauge-invariant, non-perturbative approach to QCD renormalization
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.
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.
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.
Implementation of the locally renormalized CCSD(T) approaches for arbitrary reference function.
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
NASA Astrophysics Data System (ADS)
Hammond, Richard T.
2015-03-01
Some physical aspects of negative mass are examined. Several unusual properties, such as the ability of negative mass to penetrate any armor, are analysed. Other surprising effects include the bizarre system of negative mass chasing positive mass, naked singularities and the violation of cosmic censorship, wormholes, and quantum mechanical results as well. In addition, a brief look into the implications for strings is given.
NASA Astrophysics Data System (ADS)
Cvetič, G.; Kim, C. S.
We assume that the standard model (SM) breaks down around some energy Λ and is replaced there by a new (Higgsless) flavor gauge theory (FGT) with fewer input parameters in the interactions corresponding to the Yukawa sector of SM. This would imply more symmetry for the values of the Yukawa (running) parameters of SM at E Λ, possibly by a (approximate) flavor democracy (for the quark mass sector). We investigate this possibility by studying the renormalization group equations (RGE's) for the quark Yukawa couplings of SM with one and two Higgs doublets, by running them from the known physical values at low energies (E 1 GeV) to Λ (> 1 TeV) and comparing the resulting quark masses mq (E Λ) for various mt and υU/υD. Unlike previous investigations of these RGE's, we do not implement the requirement mt(Λpole) = ∞. We found that SM with two Higgs doublets (type 2) is most likely to experience a gradual transition to FGT. Our results also shed more light on the adequacy and deficiencies of the usual RGE approaches within TMSM and related models. We also found that, independent of the assumption of a transition mechanism to FGT, mt phy< ˜ 200 GeV for Λpole≪ ΛPlanck in most cases of SM with two Higgs doublets.
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. PMID:25794727
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.
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.
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.
Renormalized field theory of collapsing directed randomly branched polymers.
Janssen, Hans-Karl; Wevelsiep, Frank; Stenull, Olaf
2009-10-01
We present a dynamical field theory for directed randomly branched polymers and in particular their collapse transition. We develop a phenomenological model in the form of a stochastic response functional that allows us to address several interesting problems such as the scaling behavior of the swollen phase and the collapse transition. For the swollen phase, we find that by choosing model parameters appropriately, our stochastic functional reduces to the one describing the relaxation dynamics near the Yang-Lee singularity edge. This corroborates that the scaling behavior of swollen branched polymers is governed by the Yang-Lee universality class as has been known for a long time. The main focus of our paper lies on the collapse transition of directed branched polymers. We show to arbitrary order in renormalized perturbation theory with epsilon expansion that this transition belongs to the same universality class as directed percolation. PMID:19905335
Local Scale Transformations on the Lattice with Tensor Network Renormalization.
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. PMID:26871313
A renormalization group analysis of two-dimensional magnetohydrodynamic turbulence
NASA Technical Reports Server (NTRS)
Liang, Wenli Z.; Diamond, P. H.
1993-01-01
The renormalization group (RNG) method is used to study the physics of two-dimensional (2D) magnetohydrodynamic (MHD) turbulence. It is shown that, for a turbulent magnetofluid in two dimensions, no RNG transformation fixed point exists on account of the coexistence of energy transfer to small scales and mean-square magnetic flux transfer to large scales. The absence of a fixed point renders the RNG method incapable of describing the 2D MHD system. A similar conclusion is reached for 2D hydrodynamics, where enstrophy flows to small scales and energy to large scales. These analyses suggest that the applicability of the RNG method to turbulent systems is intrinsically limited, especially in the case of systems with dual-direction transfer.
Percolation, renormalization, and quantum computing with nondeterministic gates.
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. PMID:17930565
Time-dependent charge renormalization procedure in QED
NASA Astrophysics Data System (ADS)
Lv, Q. Z.; Betke, J.; Su, Q.; Grobe, R.
2015-09-01
We examine the formation process of the vacuum polarization cloud around a localized charge with space-time resolution permitting us to view the traditional charge renormalization procedure from a dynamical perspective. The asymptotic steady-state charge cloud found in the long-time limit (after the subtraction of a suitable term) matches the distribution predicted by standard perturbative propagator techniques based on Feynman diagrams. This match demonstrates that an alternative (classical-field approximation based) approach can predict the nonlinear properties of the vacuum state. It turns out that some aspects of the polarization dynamics suggest that the vacuum can be viewed as a classical dielectric medium, while other aspects are purely quantum mechanical in nature and cannot be predicted from the Maxwell theory for classical fields.
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.
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.
Renormalization group analysis of anisotropic diffusion in turbulent shear flows
NASA Technical Reports Server (NTRS)
Rubinstein, Robert; Barton, J. Michael
1991-01-01
The renormalization group is applied to compute anisotropic corrections to the scalar eddy diffusivity representation of turbulent diffusion of a passive scalar. The corrections are linear in the mean velocity gradients. All model constants are computed theoretically. A form of the theory valid at arbitrary Reynolds number is derived. The theory applies only when convection of the velocity-scalar correlation can be neglected. A ratio of diffusivity components, found experimentally to have a nearly constant value in a variety of shear flows, is computed theoretically for flows in a certain state of equilibrium. The theoretical value is well within the fairly narrow range of experimentally observed values. Theoretical predictions of this diffusivity ratio are also compared with data from experiments and direct numerical simulations of homogeneous shear flows with constant velocity and scalar gradients.
Space and time renormalization in phase transition dynamics
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
Higher spin Fronsdal equations from the exact renormalization group
NASA Astrophysics Data System (ADS)
Jin, Kewang; Leigh, Robert G.; Parrikar, Onkar
2015-06-01
We show that truncating the exact renormalization group equations of free U( N) vector models in the single-trace sector to the linearized level reproduces the Fronsdal equations on AdS d+1 for all higher spin fields, with the correct boundary conditions. More precisely, we establish canonical equivalence between the linearized RG equations and the familiar local, second order differential equations on AdS d+1, namely the higher spin Fronsdal equations. This result is natural because the second-order bulk equations of motion on AdS simply report the value of the quadratic Casimir of the corresponding conformal modules in the CFT. We thus see that the bulk Hamiltonian dynamics given by the boundary exact RG is in a different but equivalent canonical frame than that which is most natural from the bulk point of view.
The numerical renormalization group and multi-orbital impurity models
NASA Astrophysics Data System (ADS)
Weichselbaum, Andreas; Stadler, K. M.; von Delft, J.; Yin, Z. P.; Kotliar, G.; Mitchell, Andrew
The numerical renormalization group (NRG) is a highly versatile and accurate method for the simulation of (effective) fermionic impurity models. Despite that the cost of NRG is exponential in the number of orbitals, by now, symmetric three-band calculations have become available on a routine level. Here we present a recent detailed study on the spin-orbital separation in a three-band Hund metal with relevance for iron-pnictides via the dynamical mean field theory (DMFT). In cases, finally, where the orbital symmetry is broken, we demonstrate that interleaved NRG still offers an accurate alternative approach within the NRG with dramatically improved numerical efficiency at comparable accuracy relative to conventional NRG.
Central charge and renormalization in supersymmetric theories with vortices
Shizuya, K.
2005-03-15
Some quantum features of vortices in supersymmetric theories in 1+2 dimensions are studied in a manifestly supersymmetric setting of the superfield formalism. A close examination of the supercurrent that accommodates the central charge and super-Poincare charges in a supermultiplet reveals that there is no genuine quantum anomaly in the supertrace identity and in the supercharge algebra, with the central-charge operator given by the bare Fayet-Iliopoulos term alone. The central charge and the vortex spectrum undergo renormalization on taking the expectation value of the central-charge operator. It is shown that the vortex spectrum is exactly determined at one-loop while the spectrum of the elementary excitations receives higher-order corrections.
Stability of renormalization group trajectories and the fermion flavor problem
NASA Astrophysics Data System (ADS)
Goldfain, Ervin
2007-04-01
An outstanding puzzle of the current standard model for particle physics (SM) is that both leptons and quarks arise in replicated patterns. Our work suggests that the number of fermion flavors occurring in the SM may be directly derived from the dynamics of renormalization group equations. The starting point is the system describing the coupling flow in the gauge sector [ dgidt.= βi(gi)=bi(N,nf)gi^3 +O(gi^5 ) ] where i=(1,2,3) labels the gauge group of dimension N, nf is the number of fermion flavors and t the sliding scale. With the help of the Routh-Hurwitz criterion, we find that the SM solution nf=6 follows from demanding stability of the linearized flow about its fixed points.
Algorithms for Entanglement Renormalization: Boundaries, Impurities and Interfaces
NASA Astrophysics Data System (ADS)
Evenbly, G.; Vidal, G.
2014-04-01
We propose algorithms, based on the multi-scale entanglement renormalization ansatz, to obtain the ground state of quantum critical systems in the presence of boundaries, impurities, or interfaces. By exploiting the theory of minimal updates (Evenbly and Vidal, arXiv:1307.0831, 2013), the ground state is completely characterized in terms of a number of variational parameters that is independent of the system size, even though the presence of a boundary, an impurity, or an interface explicitly breaks the translation invariance of the host system. Similarly, computational costs do not scale with the system size, allowing the thermodynamic limit to be studied directly and thus avoiding finite size effects e.g. when extracting the universal properties of the critical system.
Fiori, M; Pierdominici, E; Longo, F; Brambilla, G
1998-05-22
Corticosteroids were proposed as growth promoting agents to improve commercial quality of meat. We developed a liquid chromatography-atmospheric pressure chemical ionisation mass spectrometry (LC-APCI-MS) method able to identify the presence in milk replacers, when given by mouth, of dexamethasone, betamethasone, flumethasone, triamcinolone, predinisotone, prednisolone, methylprednisolone, fludrocortisone and beclomethasone, at levels in the range of 20-100 ppb. C18 solid-phase extraction, LC-RP C8 column separation, data acquisition (positive ions) in the scan range m/z 200-550 allowed us to differentiate and identify compounds by protonated molecules, their methanolic adducts and fragmentation patterns. PMID:9646497
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
Renormalization Group Theory Technique and Subgrid Scale Closure for Fluid and Plasma Turbulence.
NASA Astrophysics Data System (ADS)
Zhou, Ye.
Renormalization group theory is applied to incompressible three-dimension Navier-Stokes turbulence so as to eliminate unresolvable small scales. The renormalized Navier-Stokes equation includes a triple nonlinearity with the eddy viscosity exhibiting a mild cusp behavior, in qualitative agreement with the test-field model results of Kraichnan. For the cusp behavior to arise, not only is the triple nonlinearity necessary but the effects of pressure must be incorporated in the triple term. Renormalization group theory is also applied to a model Alfven wave turbulence equation. In particular, the effect of small unresolvable subgrid scales on the large scales is computed. It is found that the removal of the subgrid scales leads to a renormalized response function. (i) This response function can be calculated analytically via the difference renormalization group technique. Strong absorption can occur around the Alfven frequency for sharply peaked subgrid frequency spectra. (ii) With the epsilon - expansion renormalization group approach, the Lorenzian wavenumber spectrum of Chen and Mahajan can be recovered for finite epsilon , but the nonlinear coupling constant still remains small, fully justifying the neglect of higher order nonlinearities introduced by the renormalization group procedure.
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. PMID:26297463
Food additives are substances that become part of a food product when they are added during the processing or making of that food. "Direct" food additives are often added during processing to: Add nutrients ...
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.
Renormalization of the nonlinear O(3) model with θ-term
NASA Astrophysics Data System (ADS)
Flore, Raphael
2013-05-01
The renormalization of the topological term in the two-dimensional nonlinear O(3) model is studied by means of the Functional Renormalization Group. By considering the topological charge as a limit of a more general operator, it is shown that a finite multiplicative renormalization occurs in the extreme infrared. In order to compute the effects of the zero modes, a specific representation of the Clifford algebra is developed which allows to reformulate the bosonic problem in terms of Dirac operators and to employ the index theorem.
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.
Lebens-Higgins, Z; Scanlon, D O; Paik, H; Sallis, S; Nie, Y; Uchida, M; Quackenbush, N F; Wahila, M J; Sterbinsky, G E; Arena, Dario A; Woicik, J C; Schlom, D G; Piper, L F J
2016-01-15
We have directly measured the band gap renormalization associated with the Moss-Burstein shift in the perovskite transparent conducting oxide (TCO), La-doped BaSnO_{3}, using hard x-ray photoelectron spectroscopy. We determine that the band gap renormalization is almost entirely associated with the evolution of the conduction band. Our experimental results are supported by hybrid density functional theory supercell calculations. We determine that unlike conventional TCOs where interactions with the dopant orbitals are important, the band gap renormalization in La-BaSnO_{3} is driven purely by electrostatic interactions. PMID:26824566
Renormalization-group theory for the eddy viscosity in subgrid modeling
NASA Technical Reports Server (NTRS)
Zhou, YE; Vahala, George; Hossain, Murshed
1988-01-01
Renormalization-group theory is applied to incompressible three-dimensional Navier-Stokes turbulence so as to eliminate unresolvable small scales. The renormalized Navier-Stokes equation now includes a triple nonlinearity with the eddy viscosity exhibiting a mild cusp behavior, in qualitative agreement with the test-field model results of Kraichnan. For the cusp behavior to arise, not only is the triple nonlinearity necessary but the effects of pressure must be incorporated in the triple term. The renormalized eddy viscosity will not exhibit a cusp behavior if it is assumed that a spectral gap exists between the large and small scales.
Renormalization-group theory for Alfvén-wave turbulence
NASA Astrophysics Data System (ADS)
Zhou, Ye; Vahala, George
1988-06-01
є-Expansion renormalization-group theory is applied to a model Alfvén-wave turbulence equation. In particular, the effect of small ‘unresolvable’ subgrid scales on the large scales is computed. It is found that the removal of the subgrid scales leads to a renormalized response function v. The Lorenzian wavenumber spectrum of Chen & Mahajan can be recovered for finite є, but the nonlinear coupling constant still remains small, fully justifying the neglect of higher-order nonlinearities introduced by the renormalization-group procedure.
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.
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.
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
NASA Astrophysics Data System (ADS)
Brambilla, M.; Di Renzo, F.; Hasegawa, M.
2014-07-01
This is the third of a series of papers on three-loop computation of renormalization constants for Lattice QCD. Our main points of interest are results for the regularization defined by the Iwasaki gauge action and Wilson fermions. Our results for quark bilinears renormalized according to the RI'-MOM scheme can be compared to non-perturbative results. The latter are available for twisted mass QCD: being defined in the chiral limit, the renormalization constants must be the same. We also address more general problems. In particular, we discuss a few methodological issues connected to summing the perturbative series such as the effectiveness of boosted perturbation theory and the disentanglement of irrelevant and finite-volume contributions. Discussing these issues we consider not only the new results of this paper, but also those for the regularization defined by the tree-level Symanzik improved gauge action and Wilson fermions, which we presented in a recent paper of ours. We finally comment on the extent to which the techniques we put at work in the NSPT context can provide a fresher look into the lattice version of the RI'-MOM scheme.
Sturm, C.; Soni, A.; Aoki, Y.; Christ, N. H.; Izubuchi, T.; Sachrajda, C. T. C.
2009-07-01
We extend the Rome-Southampton regularization independent momentum-subtraction renormalization scheme (RI/MOM) for bilinear operators to one with a nonexceptional, symmetric subtraction point. Two-point Green's functions with the insertion of quark bilinear operators are computed with scalar, pseudoscalar, vector, axial-vector and tensor operators at one-loop order in perturbative QCD. We call this new scheme RI/SMOM, where the S stands for 'symmetric'. Conversion factors are derived, which connect the RI/SMOM scheme and the MS scheme and can be used to convert results obtained in lattice calculations into the MS scheme. Such a symmetric subtraction point involves nonexceptional momenta implying a lattice calculation with substantially suppressed contamination from infrared effects. Further, we find that the size of the one-loop corrections for these infrared improved kinematics is substantially decreased in the case of the pseudoscalar and scalar operator, suggesting a much better behaved perturbative series. Therefore it should allow us to reduce the error in the determination of the quark mass appreciably.
NASA Astrophysics Data System (ADS)
Chen, Z.; Jones, C. M.
2002-05-01
Microchemistry of fish otoliths (fish ear bones) is a very useful tool for monitoring aquatic environments and fish migration. However, determination of the elemental composition in fish otolith by ICP-MS has been limited to either analysis of dissolved sample solution or measurement of limited number of trace elements by laser ablation (LA)- ICP-MS due to low sensitivity, lack of available calibration standards, and complexity of polyatomic molecular interference. In this study, a method was developed for in situ determination of trace elements in fish otoliths by laser ablation double focusing sector field ultra high sensitivity Finnigan Element 2 ICP-MS using a solution standard addition calibration method. Due to the lack of matrix-match solid calibration standards, sixteen trace elements (Na, Mg, P, Cr, Mn, Fe, Ni, Cu, Rb, Sr, Y, Cd, La, Ba, Pb and U) were determined using a solution standard calibration with Ca as an internal standard. Flexibility, easy preparation and stable signals are the advantages of using solution calibration standards. In order to resolve polyatomic molecular interferences, medium resolution (M/delta M > 4000) was used for some elements (Na, Mg, P, Cr, Mn, Fe, Ni, and Cu). Both external calibration and standard addition quantification strategies are compared and discussed. Precision, accuracy, and limits of detection are presented.
Ludwig, B; Heil, B; Flessa, H; Beese, F
2000-01-01
The dynamics of C and N in terrestrial ecosystems are not completely understood and the use of stable isotopes may be useful to gain further insight in the pathways of CO2 emissions and leaching of dissolved organic carbon (DOC) and nitrogen (DON) during decomposition of litter. Objectives were (i) to study the decomposition dynamics of Calamagrostis epigeios, a common grass species in forests, using 13C-depleted and 15N-enriched plants and (ii) to quantify the effect wood ash addition on the decomposition and leaching of DOC and DON. Decomposition was studied for 128 days under aerobic conditions at 8 degrees C and moisture close to field capacity in a spodic dystric Cambisol with mor-moder layer. Variants included control plots and additions of (i) Calamagrostis litter and (ii) Calamagrostis litter plus 4 kg ash m-2. (i) Decomposition of Calamagrostis resulted in a CO2 production of 76.2 g CO2-C m-2 (10% of added C) after 128 days and cumulative DOC production was 14.0 g C m-2 out of which 0.9 g C m-2 was Calamagrostis-derived (0.1% of added C). The specific CO2 formation and specific DOC production from Calamagrostis were 6 times higher (CO2) and 4 times smaller (DOC) than those from the organic layer. The amount of Calamagrostis-derived total N (NH4+, NO3-, DON) leached was 0.7 g N m-2 (4.8% of added N). Cumulative DON production was 0.8 g N m-2 which was slightly higher than for the control. During soil passage, much of the DOC and DON was removed due to sorption or decomposition. DOC and DON releases from the mineral soil (17 cm depth) were 6.3 g C m-2 and 0.5 g N m-2. (ii) Addition of ash resulted in a complete fixing of CO2 for 40 days due to carbonatisation. Afterwards, the CO2 production rates were similar to the variant without ash addition. Production of DOC (98.6 g C m-2) and DON (2.5 g N m-2) was marked, mainly owing to humus decay. However, Calamagrostis-derived DOC and Calamagrostis-derived total N were only 3.9 g C m-2 (0.5% of added C) and 0.5 g N
Nonperturbative renormalization group study of the stochastic Navier-Stokes equation.
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
Noncompact lattice QED with two charges: Phase diagram and renormalization group flow
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.}
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
Attempered renormalization-group scheme for the SU(2)-Higgs model
Callaway, D.J.E.; Furlong, R.C.; Petronzio, R.
1987-06-15
The fact that most renormalization-group blocking schemes include each site link in many block links can generate spurious interactions in the block system. This shortcoming can lead to inconsistent flow diagrams in truncated calculations. A general method for avoiding this problem is formulated and applied to a Monte Carlo renormalization-group study of the SU(2)-Higgs model in four dimensions with scale factor ..sqrt..2 . .AE
Renormalization of high-energy Lorentz-violating four-fermion models
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.
NASA Astrophysics Data System (ADS)
Nakhleh, Charles W.
2013-03-01
This paper uses elementary techniques drawn from renormalization theory to derive the Lorentz-Dirac equation for the relativistic classical electron from the Maxwell-Lorentz equations for a classical charged particle coupled to the electromagnetic field. I show that the resulting effective theory, valid for electron motions that change over distances large compared to the classical electron radius, reduces naturally to the Landau-Lifshitz equation. No familiarity with renormalization or quantum field theory is assumed.
Persistence-length renormalization of polymers in a crowded environment of hard disks.
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
Renormalized perturbation theory - Vlasov-Poisson system, weak turbulence limit, and gyrokinetics
NASA Astrophysics Data System (ADS)
Zhang, Y. Z.; Mahadjan, S. M.
1988-10-01
The self-consistency of the renormalized perturbation theory of Zhang and Mahajan (1985) is demonstrated by applying it to the Vlasov-Poisson system and showing that the theory has the correct weak turbulence limit. Energy conservation is proved to arbitrary high order for the electrostatic drift waves. The theory is applied to derive renormalized equations for a low-beta gyrokinetic system. Comparison of this theory with other current theories is presented.
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
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
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
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
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.
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.
Bimetric renormalization group flows in quantum Einstein gravity
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.
Functional renormalization group - a new approach to frustrated quantum magnetism
NASA Astrophysics Data System (ADS)
Reuther, Johannes
The experimental and theoretical investigation of quantum spin systems has become one of the central disciplines of contemporary condensed matter physics. From an experimental viewpoint, the field has been significantly fueled by the recent synthesis of novel strongly correlated materials with exotic magnetic or quantum paramagnetic ground states. From a theoretical perspective, however, the numerical treatment of realistic models for quantum magnetism in two and three spatial dimensions still constitutes a serious challenge. This particularly applies to frustrated systems, which complicate the employment of established methods. This talk intends to propagate the pseudofermion functional renormalization group (PFFRG) as a novel approach to determine large size ground state correlations of a wide class of spin Hamiltonians. Using a diagrammatic pseudofermion representation for quantum spin models, the PFFRG performs systematic summations in all two-particle fermionic interaction channels, capturing the correct balance between classical magnetic ordering and quantum fluctuations. Numerical results for various frustrated spin models on different 2D and 3D lattices are reviewed, and benchmarked against other methods if available.
Exploration of similarity renormalization group generators in 1-dimensional potentials
NASA Astrophysics Data System (ADS)
Heinz, Matthias
2015-10-01
The Similarity Renormalization Group (SRG) is used in nuclear theory to decouple high- and low-momentum components of potentials to improve convergence and thus reduce the computational requirements of many-body calculations. The SRG is a series of unitary transformations defined by a differential equation for the Hamiltonian. It includes a matrix called the generator that defines how the transformation will change the Hamiltonian. The commonly used SRG generators evolve the Hamiltonian into a band-diagonal shape. Evolving potentials using SRG induces many-body forces. If these forces are truncated at the N-body level, this systematically introduces errors from omitted (N+1)-body forces when modeling many-body systems. While established generators are fairly successful, alternative generators may converge faster, be faster to calculate, or lead to smaller many-body forces. In particular, recent findings suggest that a block diagonal generator may induce smaller many-body forces. We use 1-dimensional systems of two, three, and four bosons as a theoretical laboratory for studying how these alternative generators perform, and to observe how they induce many-body forces.
Phase transitions in two dimensions and multiloop renormalization group expansions
NASA Astrophysics Data System (ADS)
Sokolov, A. I.
2013-07-01
We discuss using the field theory renormalization group (RG) to study the critical behavior of twodimensional (2D) models. We write the RG functions of the 2D λϕ 4 Euclidean n-vector theory up to five-loop terms, give numerical estimates obtained from these series by Padé-Borel-Leroy resummation, and compare them with their exact counterparts known for n = 1, 0,-1. From the RG series, we then derive pseudo-ɛ-expansions for the Wilson fixed point location g*, critical exponents, and the universal ratio R 6 = g 6 / g 2 , where g 6 is the effective sextic coupling constant. We show that the obtained expansions are "friendler" than the original RG series: the higher-order coefficients of the pseudo-ɛ-expansions for g*, R6, and γ -1 turn out to be considerably smaller than their RG analogues. This allows resumming the pseudo-ɛ-expansions using simple Padé approximants without the Borel-Leroy transformation. Moreover, we find that the numerical estimates obtained using the pseudo-ɛ-expansions for g* and γ -1 are closer to the known exact values than those obtained from the five-loop RG series using the Padé-Borel-Leroy resummation.
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.
Nearest neighbor interaction in the Path Integral Renormalization Group method
NASA Astrophysics Data System (ADS)
de Silva, Wasanthi; Clay, R. Torsten
2014-03-01
The Path Integral Renormalization Group (PIRG) method is an efficient numerical algorithm for studying ground state properties of strongly correlated electron systems. The many-body ground state wave function is approximated by an optimized linear combination of Slater determinants which satisfies the variational principle. A major advantage of PIRG is that is does not suffer the Fermion sign problem of quantum Monte Carlo. Results are exact in the noninteracting limit and can be enhanced using space and spin symmetries. Many observables can be calculated using Wick's theorem. PIRG has been used predominantly for the Hubbard model with a single on-site Coulomb interaction U. We describe an extension of PIRG to the extended Hubbard model (EHM) including U and a nearest-neighbor interaction V. The EHM is particularly important in models of charge-transfer solids (organic superconductors) and at 1/4-filling drives a charge-ordered state. The presence of lattice frustration also makes studying these systems difficult. We test the method with comparisons to small clusters and long one dimensional chains, and show preliminary results for a coupled-chain model for the (TMTTF)2X materials. This work was supported by DOE grant DE-FG02-06ER46315.
Grassman-number tensor network states and its renormalization
NASA Astrophysics Data System (ADS)
Gu, Zhengcheng; Verstraete, Frank; Wen, Xiaogang
2010-03-01
Traditional condensed matter physics is based on two theories: symmetry breaking theory for phases and phase transitions, and Fermi liquid theory for metals. Mean-field theory is a powerful method to describe symmetry breaking phases and phase transitions by assuming the ground state wavefunctions for many- body systems can be approximately described by direct product states. The Fermi liquid theory is another powerful method to study electron systems by assuming that the ground state wavefunctions for the electrons can be approximately described by Slater determinants. In this paper, we propose a new class of states: Grassman-number tensor product states. These states only need polynomial amount of information to approximately encode many-body ground states. Many classes of states, such as matrix/tensor product states (M/TPS), Slater determinant states, etc., are subclasses of Grassman-number tensor product states. However, calculating the physical quantities for these state can be exponential hard in general. To solve this difficulty, we develop the Grassman-tensor- entanglement renormalization group (GTERG) method to efficiently calculate the physical quantities. We demonstrate our algorithm by studying several simple fermion/boson models.
Magnetic moments induce strong phonon renormalization in FeSi
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
Magnetic moments induce strong phonon renormalization in FeSi.
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
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.
Does Multiplicity Replace Renormalization and Link Genetics too?
NASA Astrophysics Data System (ADS)
Goradia, Shantilal
2007-04-01
The substitution of sixty orders of magnitude, the age of the universe in Planck times, for W in entropy equation S = ln W, yields 138, close to the reciprocal of fine-structure constant (137) consistent with (1) Einstein's 1919 retraction of cosmological constant, (2) non-decreasing nature of entropy (3) Gamow's view. I link cosmology and Boltzmann statistics in terms of encryption in sequences of the OPEN and CLOSED states (or their superposition) pictorially shown in fig 1 [1]. I take an algorithmic approach to explain the expression of genetic information in cloning in terms of black hole information theory via Planck scale and flexible Einstein Rosen bridges linking physical particles of genetic tape with spacetime. Einstein's retraction of cosmological constant, long before Hubble's finding, surprised me, possibly you and Mike Turner too, during my last encounter with Mike at NDU. In 1919, Einstein addressed multiplicity, not GR. Unlike later papers on MOND without dark matter, I use no renormalization tricks in v2 of [1]. [1] physics/0210040 v3 (Jan 2007). To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2007.NES07.C1.7
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.
Renormalization group theory for Kondo breakdown in Kondo lattice systems
NASA Astrophysics Data System (ADS)
Ballmann, K.; Nejati, A.; Kroha, J.
2015-03-01
We present a renormalization group (RG) theory for the breakdown of Kondo screening in the Kondo lattice model (KLM) without pre-assumptions about the competition between Kondo effect and magnetic ordering or Fermi surface criticality. We show that the vertex between a single, local Kondo spin and the extended conduction electrons obtains RKKY- induced, non-local contributions in the in-and out-going coordinates of scattering electrons due to scattering at surrounding Kondo sites, but it remains local in the Kondo spin position. This enables the existence of a local Kondo screening scale TK(y) in the KLM, controlled by the effective RKKY coupling parameter y. TK(y) is determined by the RG flow of the local spin exchange coupling in the presence of the self-consistent spin response on surrounding Kondo sites. We show that TK(y) exhibits universal behavior and is suppressed by the antiferromagnetic RKKY coupling. Beyond a maximal RKKY parameter value ymax Kondo screening ceases to exist even without magnetic ordering. The theory opens up the possibility of describing quantum critical scenarios involving spin wave instabilities or local Kondo breakdown on the same footing.
The In-Medium Similarity Renormalization Group: A novel ab initio method for nuclei
NASA Astrophysics Data System (ADS)
Hergert, H.; Bogner, S. K.; Morris, T. D.; Schwenk, A.; Tsukiyama, K.
2016-03-01
We present a comprehensive review of the In-Medium Similarity Renormalization Group (IM-SRG), a novel ab initio method for nuclei. The IM-SRG employs a continuous unitary transformation of the many-body Hamiltonian to decouple the ground state from all excitations, thereby solving the many-body problem. Starting from a pedagogical introduction of the underlying concepts, the IM-SRG flow equations are developed for systems with and without explicit spherical symmetry. We study different IM-SRG generators that achieve the desired decoupling, and how they affect the details of the IM-SRG flow. Based on calculations of closed-shell nuclei, we assess possible truncations for closing the system of flow equations in practical applications, as well as choices of the reference state. We discuss the issue of center-of-mass factorization and demonstrate that the IM-SRG ground-state wave function exhibits an approximate decoupling of intrinsic and center-of-mass degrees of freedom, similar to Coupled Cluster (CC) wave functions. To put the IM-SRG in context with other many-body methods, in particular many-body perturbation theory and non-perturbative approaches like CC, a detailed perturbative analysis of the IM-SRG flow equations is carried out. We conclude with a discussion of ongoing developments, including IM-SRG calculations with three-nucleon forces, the multi-reference IM-SRG for open-shell nuclei, first non-perturbative derivations of shell-model interactions, and the consistent evolution of operators in the IM-SRG. We dedicate this review to the memory of Gerry Brown, one of the pioneers of many-body calculations of nuclei.
NASA Astrophysics Data System (ADS)
Kalagov, G. A.; Kompaniets, M. V.; Nalimov, M. Yu.
2014-11-01
We use quantum-field renormalization group methods to study the phase transition in an equilibrium system of nonrelativistic Fermi particles with the "density-density" interaction in the formalism of temperature Green's functions. We especially attend to the case of particles with spins greater than 1/2 or fermionic fields with additional indices for some reason. In the vicinity of the phase transition point, we reduce this model to a ϕ 4 -type theory with a matrix complex skew-symmetric field. We define a family of instantons of this model and investigate the asymptotic behavior of quantum field expansions in this model. We calculate the β-functions of the renormalization group equation through the third order in the ( 4 ∈)-scheme. In the physical space dimensions D = 2, 3, we resum solutions of the renormalization group equation on trajectories of invariant charges. Our results confirm the previously proposed suggestion that in the system under consideration, there is a first-order phase transition into a superconducting state that occurs at a higher temperature than the classical theory predicts.
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
Berglund, F
1978-01-01
The use of additives to food fulfils many purposes, as shown by the index issued by the Codex Committee on Food Additives: Acids, bases and salts; Preservatives, Antioxidants and antioxidant synergists; Anticaking agents; Colours; Emulfifiers; Thickening agents; Flour-treatment agents; Extraction solvents; Carrier solvents; Flavours (synthetic); Flavour enhancers; Non-nutritive sweeteners; Processing aids; Enzyme preparations. Many additives occur naturally in foods, but this does not exclude toxicity at higher levels. Some food additives are nutrients, or even essential nutritents, e.g. NaCl. Examples are known of food additives causing toxicity in man even when used according to regulations, e.g. cobalt in beer. In other instances, poisoning has been due to carry-over, e.g. by nitrate in cheese whey - when used for artificial feed for infants. Poisonings also occur as the result of the permitted substance being added at too high levels, by accident or carelessness, e.g. nitrite in fish. Finally, there are examples of hypersensitivity to food additives, e.g. to tartrazine and other food colours. The toxicological evaluation, based on animal feeding studies, may be complicated by impurities, e.g. orthotoluene-sulfonamide in saccharin; by transformation or disappearance of the additive in food processing in storage, e.g. bisulfite in raisins; by reaction products with food constituents, e.g. formation of ethylurethane from diethyl pyrocarbonate; by metabolic transformation products, e.g. formation in the gut of cyclohexylamine from cyclamate. Metabolic end products may differ in experimental animals and in man: guanylic acid and inosinic acid are metabolized to allantoin in the rat but to uric acid in man. The magnitude of the safety margin in man of the Acceptable Daily Intake (ADI) is not identical to the "safety factor" used when calculating the ADI. The symptoms of Chinese Restaurant Syndrome, although not hazardous, furthermore illustrate that the whole ADI
A driven similarity renormalization group approach to quantum many-body problems
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.
Consistency of the particle-particle random-phase approximation and renormalization
Dang, Nguyen Dinh
2006-08-15
The consistency condition is tested within the particle-particle random-phase approximation (RPA), renormalized RPA (RRPA), and the self-consistent RPA (SCRPA) making use of the Richardson model of pairing. The two-particle separation energy is calculated in two ways, namely, as the energy of the first addition mode, which adds two particles to a core with N particles, and as the energy of the first removal mode, which removes two particles from the N+2 particle system to get back to the same N-particle core. The corresponding transitions generated by the pairing operators are also calculated. It is found that the results obtained in these two ways of calculations are close to each other only at large values of particle number N and/or small interaction strength. At N{<=}10 for a given value of the interaction strength, the discrepancy between the results obtained in two ways of calculations within the SCRPA is much smaller than those given by the RPA and RRPA.
Density-matrix renormalization group study of the extended Kitaev-Heisenberg model
NASA Astrophysics Data System (ADS)
Shinjo, Kazuya; Sota, Shigetoshi; Tohyama, Takami
2015-02-01
We study an extended Kitaev-Heisenberg model including additional anisotropic couplings by using the two-dimensional density-matrix renormalization group method. Calculating the ground-state energy, entanglement entropy, and spin-spin correlation functions, we make a phase diagram of the extended Kitaev-Heisenberg model around the spin-liquid phase. We find a zigzag antiferromagnetic phase, a ferromagnetic phase, a 120∘ antiferromagnetic phase, and two kinds of incommensurate phases around the Kitaev spin-liquid phase. Furthermore, we study the entanglement spectrum of the model, and we find that entanglement levels in the Kitaev spin-liquid phase are degenerate forming pairs, but those in the magnetically ordered phases are nondegenerate. The Schmidt gap defined as the energy difference between the lowest two levels changes at the phase boundary adjacent to the Kitaev spin-liquid phase. However, we find that phase boundaries between magnetically ordered phases do not necessarily agree with the change of the Schmidt gap.
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. PMID:25353423
Ballesteros-Gómez, Ana; Jonkers, Tim; Covaci, Adrian; de Boer, Jacob
2016-04-01
Plastics are complex mixtures consisting of a polymer and additives with different physico-chemical properties. We developed a broad screening method to elucidate the nature of compounds present in plastics used in electrical/electronic equipment commonly found at homes (e.g., electrical adaptors, computer casings, heaters). The analysis was done by (a) solvent extraction followed by liquid chromatography coupled to high accuracy/resolution time-of-flight mass spectrometry (TOFMS) with different ionization sources or (b) direct analysis of the solid by ambient mass spectrometry high accuracy/resolution TOFMS. The different ionization methods showed different selectivity and sensitivity for the different compound classes and were complementary. A variety of antioxidants, phthalates, UV filters, and flame retardants were found in most samples. Furthermore, some recently reported impurities or degradation products derived from flame retardants were identified, such as hydroxylated triphenyl phosphate and tetrabromobisphenol A monoglycidyl ether. PMID:26758596
Pseudo-ε expansion and renormalized coupling constants at criticality.
Sokolov, A I; Nikitina, M A
2014-05-01
Universal values of dimensional effective coupling constants g(2k) that determine nonlinear susceptibilities χ(2k) and enter the scaling equation of state are calculated for n-vector field theory within the pseudo-ε expansion approach. Pseudo-ε expansions for g(6) and g(8) at criticality are derived for arbitrary n. Analogous series for ratios R(6) = g(6)/g(4)(2) and R(8) = g(8)/g(4)(3) that figure in the equation of state are also found, and the pseudo-ε expansion for Wilson fixed point location g(4)(*) descending from the six-loop renormalization group (RG) expansion for the β function is reported. Numerical results are presented for 0 ≤ n ≤ 64, with the most attention paid to the physically important cases n = 0,1,2,3. Pseudo-ε expansions for quartic and sextic couplings have rapidly diminishing coefficients, so Padé resummation turns out to be sufficient to yield high-precision numerical estimates. Moreover, direct summation of these series with optimal truncation gives values of g(4)(*) and R(6)(*) that are almost as accurate as those provided by the Padé technique. Pseudo-ε expansion estimates for g(8)(*) and R(8)(*) are found to be much worse than those for lower-order couplings independently of the resummation method employed. The numerical effectiveness of the pseudo-ε expansion approach in two dimensions is also studied. Pseudo-ε expansion for g(4)(*) originating from the five-loop RG series for the β function of two-dimensional λϕ(4) field theory is used to get numerical estimates for n ranging from 0 to 64. The approach discussed gives accurate enough values of g(4)(*) down to n = 2 and leads to fair estimates for Ising and polymer (n = 0) models. PMID:25353759
Higher-order renormalization of graphene many-body theory
NASA Astrophysics Data System (ADS)
González, J.
2012-08-01
We study the many-body theory of graphene Dirac quasiparticles interacting via the long-range Coulomb potential, taking as a starting point the ladder approximation to different vertex functions. We test in this way the low-energy behavior of the electron system beyond the simple logarithmic dependence of electronic correlators on the high-energy cutoff, which is characteristic of the large- N approximation. We show that the graphene many-body theory is perfectly renormalizable in the ladder approximation, as all higher powers in the cutoff dependence can be absorbed into the redefinition of a finite number of parameters (namely, the Fermi velocity and the weight of the fields) that remain free of infrared divergences even at the charge neutrality point. We illustrate this fact in the case of the vertex for the current density, where a complete cancellation between the cutoff dependences of vertex and electron self-energy corrections becomes crucial for the preservation of the gauge invariance of the theory. The other potentially divergent vertex corresponds to the staggered (sublattice odd) charge density, which is made cutoff independent by a redefinition in the scale of the density operator. This allows to compute a well-defined, scale invariant anomalous dimension to all orders in the ladder series, which becomes singular at a value of the interaction strength marking the onset of chiral symmetry breaking (and gap opening) in the Dirac field theory. The critical coupling we obtain in this way matches with great accuracy the value found with a quite different method, based on the resolution of the gap equation, thus reassuring the predictability of our renormalization approach.
On higher order geometric and renormalization group flows
NASA Astrophysics Data System (ADS)
Prabhu, Kartik; Das, Sanjit; Kar, Sayan
2011-10-01
Renormalization group (RG) flows of the bosonic nonlinear σ-model are governed, perturbatively, at different orders of α', by perturbatively evaluated β-functions. In regions where {α'}/{Rc2}≪1 ( {1}/{Rc2} represents the curvature scale), the flow equations at various orders in α' can be thought of as approximating the full, non-perturbative RG flow. On the other hand, taking a different viewpoint, we may consider the above-mentioned RG flow equations as viable geometric flows in their own right, without any reference to the RG aspect. Looked at as purely geometric flows where higher order terms appear, we no longer have the perturbative restrictions (small curvatures). In this paper, we perform our analysis from both these perspectives using specific target manifolds such as S2, H2, unwarped S2×H2 and simple warped products. We analyse and solve the higher order RG flow equations within the appropriate perturbative domains and find the corrections arising due to the inclusion of higher order terms. Such corrections, within the perturbative regime, are shown to be small and they provide an estimate of the error that arises when higher orders are ignored. We also investigate higher order geometric flows on the same manifolds and figure out generic features of geometric evolution, the appearance of singularities and solitons. The aim, in this context, is to demonstrate the role of higher order terms in modifying the flow. One interesting aspect of our analysis is that, separable solutions of the higher order flow equations for simple warped spacetimes (of the kind used in bulk-brane models with a single extra dimension), correspond to constant curvature anti de Sitter (AdS) spacetimes, modulo an overall flow parameter dependent scale factor. The functional form of this scale factor (that we obtain) changes on the inclusion of successive higher order terms in the flow.
Pseudo-ɛ expansion and renormalized coupling constants at criticality
NASA Astrophysics Data System (ADS)
Sokolov, A. I.; Nikitina, M. A.
2014-05-01
Universal values of dimensional effective coupling constants g2k that determine nonlinear susceptibilities χ2k and enter the scaling equation of state are calculated for n-vector field theory within the pseudo-ɛ expansion approach. Pseudo-ɛ expansions for g6 and g8 at criticality are derived for arbitrary n. Analogous series for ratios R6=g6/g42 and R8=g8/g43 that figure in the equation of state are also found, and the pseudo-ɛ expansion for Wilson fixed point location g4* descending from the six-loop renormalization group (RG) expansion for the β function is reported. Numerical results are presented for 0≤n≤64, with the most attention paid to the physically important cases n =0,1,2,3. Pseudo-ɛ expansions for quartic and sextic couplings have rapidly diminishing coefficients, so Padé resummation turns out to be sufficient to yield high-precision numerical estimates. Moreover, direct summation of these series with optimal truncation gives values of g4* and R6* that are almost as accurate as those provided by the Padé technique. Pseudo-ɛ expansion estimates for g8* and R8* are found to be much worse than those for lower-order couplings independently of the resummation method employed. The numerical effectiveness of the pseudo-ɛ expansion approach in two dimensions is also studied. Pseudo-ɛ expansion for g4* originating from the five-loop RG series for the β function of two-dimensional λϕ4 field theory is used to get numerical estimates for n ranging from 0 to 64. The approach discussed gives accurate enough values of g4* down to n =2 and leads to fair estimates for Ising and polymer (n =0) models.
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.
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.
Long-term renormalization of chromatic mechanisms following cataract surgery
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
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.
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.
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.
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.
Hamza, A.M.; Sudan, R.N.
1995-03-01
The equations governing the nonlinear evolution of density fluctuations in a low-pressure weakly ionized plasma driven unstable by the ExB or gradient-drift instability were derived by Sudan and Keskinen for addressing the electrostatic turbulence in the E and F regions of the Earth`s ionosphere. The authors have developed a subgrid model suitable for the numerical simulation of these equations which is closely related to renormalized diffusion caused by small-scale fluctuation spectrum. {open_quotes}Dynamical Renormalization Group{close_quotes} (RNG) methods are employed to obtain the renormalized diffusion. This procedure computes the long-wavelength, long-time behavior of density correlations generated by the evolution equation for the plasma stirred by a Gaussian random force characterized by a correlation function {proportional_to} k{sup m} where k is the wavenumber of the forcing function. The effect of small scales on the large-scale dynamics in the limit k{yields}0 and infinite Reynolds number can be expressed in the form of renormalized coefficients; in this case, renormalized diffusion. If one assumes the power spectra to be given by the Kolmogorov argument of cascading of energy through k space then one can derive a subgrid model based on the results of RNG. 27 refs.
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.
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
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.
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.
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
Systematic renormalization scheme in light-front dynamics with Fock space truncation
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.
Brodsky-Lepage-Mackenzie optimal renormalization scale setting for semihard processes
NASA Astrophysics Data System (ADS)
Caporale, F.; Ivanov, D. Yu.; Murdaca, B.; Papa, A.
2015-06-01
The Balitsky-Fadin-Kuraev-Lipatov (BFKL) approach for the investigation of semihard processes is plagued by large next-to-leading corrections, both in the kernel of the universal BFKL Green's function and in the process-dependent impact factors, as well as by large uncertainties in the renormalization scale setting. All that calls for an optimization procedure of the perturbative series. In this respect, one of the most common methods is the Brodsky-Lepage-Mackenzie (BLM) one, which eliminates the renormalization scale ambiguity by absorbing the nonconformal β0 terms into the running coupling. In this paper, we apply the BLM scale setting procedure directly to the amplitudes (cross sections) of several semihard processes. We show that, due to the presence of β0 terms in the next-to-leading expressions for the impact factors, the optimal renormalization scale is not universal but depends both on the energy and on the type of process in question.
A simple method for one-loop renormalization in curved space-time
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.
Carrier Plasmon Induced Nonlinear Band Gap Renormalization in Two-Dimensional Semiconductors
NASA Astrophysics Data System (ADS)
Liang, Yufeng; Yang, Li
2015-02-01
In reduced-dimensional semiconductors, doping-induced carrier plasmons can strongly couple with quasiparticle excitations, leading to a significant band gap renormalization. However, the physical origin of this generic effect remains obscure. We develop a new plasmon-pole theory that efficiently and accurately captures this coupling. Using monolayer MoS2 and MoSe2 as prototype two-dimensional (2D) semiconductors, we reveal a striking band gap renormalization above 400 meV and an unusual nonlinear evolution of their band gaps with doping. This prediction significantly differs from the linear behavior that is observed in one-dimensional structures. Notably, our predicted band gap renormalization for MoSe2 is in excellent agreement with recent experimental results. Our developed approach allows for a quantitative understanding of many-body interactions in general doped 2D semiconductors and paves the way for novel band gap engineering techniques.
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.
NASA Astrophysics Data System (ADS)
Abbas, Gauhar; Ananthanarayan, B.; Caprini, Irinel
2013-08-01
We determine the strong coupling constant αs from the τ hadronic width using a renormalization group summed (RGS) expansion of the QCD Adler function. The main theoretical uncertainty in the extraction of αs is due to the manner in which renormalization group invariance is implemented, and the as yet uncalculated higher order terms in the QCD perturbative series. We show that new expansion exhibits good renormalization group improvement and the behavior of the series is similar to that of the standard CIPT expansion. The value of the strong coupling in /lineMS scheme obtained with the RGS expansion is α s(M_τ 2) = 0.338 ± 0.010. The convergence properties of the new expansion can be improved by Borel transformation and analytic continuation in the Borel plane. This is discussed elsewhere in these issues.
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.
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.
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.
Setting the Renormalization Scale in QCD: The Principle of Maximum Conformality
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.
The mass spectra, hierarchy and cosmology of B-L MSSM heterotic compactifications
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.
The mass spectra, hierarchy and cosmology of B-L MSSM heterotic compactifications
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
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.
Renormalization and destruction of 1/γ2 tori in the standard nontwist map
NASA Astrophysics Data System (ADS)
Apte, A.; Wurm, A.; Morrison, P. J.
2003-06-01
Extending the work of del-Castillo-Negrete, Greene, and Morrison [Physica D 91, 1 (1996); 100, 311 (1997)] on the standard nontwist map, the breakup of an invariant torus with winding number equal to the inverse golden mean squared is studied. Improved numerical techniques provide the greater accuracy that is needed for this case. The new results are interpreted within the renormalization group framework by constructing a renormalization operator on the space of commuting map pairs, and by studying the fixed points of the so constructed operator.
Kolmogorov-Arnold-Moser-Renormalization-Group Analysis of Stability in Hamiltonian Flows
NASA Astrophysics Data System (ADS)
Govin, M.; Chandre, C.; Jauslin, H. R.
1997-11-01
We study the stability and breakup of invariant tori in Hamiltonian flows using a combination of Kolmogorov-Arnold-Moser (KAM) theory and renormalization-group techniques. We implement the scheme numerically for a family of Hamiltonians quadratic in the actions to analyze the strong coupling regime. We show that the KAM iteration converges up to the critical coupling at which the torus breaks up. Adding a renormalization consisting of a rescaling of phase space and a shift of resonances allows us to determine the critical coupling with higher accuracy. We determine a nontrivial fixed point and its universality properties.
Momentum subtraction scheme renormalization group functions in the maximal Abelian gauge
NASA Astrophysics Data System (ADS)
Bell, J. M.; Gracey, J. A.
2013-10-01
The one-loop 3-point vertex functions of QCD in the maximal Abelian gauge are evaluated at the fully symmetric point at one loop. As a consequence the theory is renormalized in the various momentum subtraction schemes, which are defined by the trivalent vertices, as well as in the MS¯ scheme. From these the two-loop renormalization group functions in the momentum schemes are derived using the one-loop conversion functions. In parallel we repeat the analysis for the Curci-Ferrari gauge, which corresponds to the maximal Abelian gauge in a specific limit. The relation between the Λ parameters in different schemes is also provided.
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
Renormalization group theory of anomalous transport in systems with Hamiltonian chaos.
Zaslavsky, G. M.
1994-03-01
We present a general scheme to describe particle kinetics in the case of incomplete Hamiltonian chaos when a set of islands of stability forms a complicated fractal space-time dynamics and when there is orbit stickiness to the islands' boundary. This kinetics is alternative to the "normal" Fokker-Planck-Kolmogorov equation. A new kinetic equation describes random wandering in the fractal space-time. Critical exponents of the anomalous kinetics are expressed through dynamical characteristics of a Hamiltonian using the renormalization group approach. Renormalization transformation has been applied simultaneously for space and time and fractional calculus has been exploited. PMID:12780083
Renormalization group theory of anomalous transport in systems with Hamiltonian chaos
NASA Astrophysics Data System (ADS)
Zaslavsky, G. M.
1994-03-01
We present a general scheme to describe particle kinetics in the case of incomplete Hamiltonian chaos when a set of islands of stability forms a complicated fractal space-time dynamics and when there is orbit stickiness to the islands' boundary. This kinetics is alternative to the ``normal'' Fokker-Planck-Kolmogorov equation. A new kinetic equation describes random wandering in the fractal space-time. Critical exponents of the anomalous kinetics are expressed through dynamical characteristics of a Hamiltonian using the renormalization group approach. Renormalization transformation has been applied simultaneously for space and time and fractional calculus has been exploited.
a Renormalization Group Calculation of the Velocity - and Density-Density Correlation Functions.
NASA Astrophysics Data System (ADS)
Cowan, Mark Timothy
The velocity-velocity correlation function of a free field theory is obtained. The renormalization group, along with a 4-varepsilon expansion, is then used to find the leading order behavior of the velocity-velocity correlation function for an interacting field theory in the high temperature phase near the critical point. The details of the calculation of the density-density correlation function for Hedgehogs, in the context of a free field theory, is presented next. Finally the renormalization group, along with a 4-varepsilon expansion, is used to find the leading order behavior of the density-density correlation function for Hedgehogs in an interacting field theory near the critical point.
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.
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. PMID:26554294
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.
NASA Astrophysics Data System (ADS)
Shah, Abhay G.; Friedman, John L.; Keidl, Tobias S.
2012-10-01
This is the first of two papers on computing the self-force in a radiation gauge for a particle of mass m moving in circular, equatorial orbit about a Kerr black hole. In the extreme-mass-ratio inspiral (EMRI) framework, with mode-sum renormalization, we compute the renormalized value of the quantity H≔(1)/(2)hαβuαuβ, gauge-invariant under gauge transformations generated by a helically symmetric gauge vector; here, hαβ is the metric perturbation, uα the particle’s 4-velocity. We find the related order m correction to the particle’s angular velocity at fixed renormalized redshift (and to its redshift at fixed angular velocity), each of which can be written in terms of H. The radiative part of the metric perturbation is constructed from a Hertz potential that is extracted from the Weyl scalar by an algebraic inversion T. S. Keidl , Phys. Rev. D 82, 124012 (2010). We then write the spin-weighted spheroidal harmonics as a sum over spin-weighted spherical harmonics Yℓms and use mode-sum renormalization to find the renormalization coefficients by matching a series in L=ℓ+1/2 to the large-L behavior of the expression for H. The nonradiative parts of the perturbed metric associated with changes in mass and angular momentum are calculated in the Kerr gauge.
Urban, Jan; Hrouzek, Pavel; Stys, Dalibor; Martens, Harald
2013-01-01
Responsivity is a conversion qualification of a measurement device given by the functional dependence between the input and output quantities. A concentration-response-dependent calibration curve represents the most simple experiment for the measurement of responsivity in mass spectrometry. The cyanobacterial hepatotoxin microcystin-LR content in complex biological matrices of food additives was chosen as a model example of a typical problem. The calibration curves for pure microcystin and its mixtures with extracts of green alga and fish meat were reconstructed from the series of measurement. A novel approach for the quantitative estimation of ion competition in ESI is proposed in this paper. We define the correlated responsivity offset in the intensity values using the approximation of minimal correlation given by the matrix to the target mass values of the analyte. The estimation of the matrix influence enables the approximation of the position of a priori unknown responsivity and was easily evaluated using a simple algorithm. The method itself is directly derived from the basic attributes of the theory of measurements. There is sufficient agreement between the theoretical and experimental values. However, some theoretical issues are discussed to avoid misinterpretations and excessive expectations. PMID:23586036
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.
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.
Intuitive understanding of T → 0 behavior of 2d spin glasses via renormalization group analysis
NASA Astrophysics Data System (ADS)
Hartmann, A. K.
2012-07-01
Commentary on 'The nature of the different zero-temperature phases in discrete two-dimensional spin glasses: entropy, universality, chaos and cascades in the renormalization group flow', by Thomas Jörg and Florent Krzakala, 2012 J. Stat. Mech. L01001.
NASA Astrophysics Data System (ADS)
Kholodenko, A. L.; Freed, Karl F.
1983-06-01
The chain conformation space renormalization group method is transformed into a representation where the t'Hooft-Veltman method of dimensional regularization can directly be applied to problems involving polymer excluded volume. This t'Hooft-Veltman-type representation enables a comparison to be made with other direct renormalization methods for polymer excluded volume. In contrast to the latter, the current method and the chain conformation one from which it is derived are not restricted to the asymptotic limit of very long chains and do not require the cumbersome use of insertions to calculate the relevant exponents. Furthermore, the theory emerges directly in polymer language from the traditional excluded volume perturbation expansion which provides the correct weight factors for the diagrams. Special attention is paid to the general diagrammatic structure of the theory and to the renormalization prescription in order that this prescription follows from considerations on measurable quantities. The theory is illustrated by calculation of the mean square end-to-end distance and second virial coefficient to second order including the full crossover dependence on the renormalized strength of the excluded volume interaction and on the chain length. A subsequent paper provides the generalization of the theory to the treatment of excluded volume effects in polyelectrolytes.
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.
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.
NASA Astrophysics Data System (ADS)
Ovidiu Vlad, Marcel
1992-07-01
A new stochastic renormalization approach for multi-step decay phenomena is developed. A simple physical interpretation of the renormalization method is suggested. It consists in grouping successions of variable numbers of decay events into blocks. The law of probability multiplication leads to an exponential random process Y = YX1 + X2 + …0 where both the exponents X1, X2,… and the basis Y0 are random variables. The physically consistent solution of the model corresponds to a “super-strong” renormalization regime. The dependence of the moments of the decay parameter on the number of decay steps q can be exactly determined. It consists in a linear superposition of inverse power laws in q modulated by periodic functions in In q, having different periods. The theory is applied to the renormalization of the bronchial tree. Our computation shows that the lung structure is very tolerant to fluctuations. This result supports the mechanism of morphogenesis of fractal biological organs suggested by West (Ann. Biomed. Eng. 18 (1990) 135). The possibilities of application to the scattering phenomena in one-dimensional disordered media are also investigated.
Phase diagram and critical end point in nonlocal PNJL models with wavefunction renormalization
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.
DeWitt-Schwinger renormalization and vacuum polarization in d dimensions
Thompson, R. T.; Lemos, Jose P. S.
2009-09-15
Calculation of the vacuum polarization, <{phi}{sup 2}(x)>, and expectation value of the stress tensor,
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.
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).
Conformal mass in Einstein-Gauss-Bonnet AdS gravity
NASA Astrophysics Data System (ADS)
Jatkar, Dileep P.; Kofinas, Georgios; Miskovic, Olivera; Olea, Rodrigo
2015-05-01
In this paper, we show that the physical information given by conserved charges for asymptotically AdS spacetimes in Einstein-Gauss-Bonnet AdS gravity is encoded in the electric part of the Weyl tensor. This result generalizes the conformal mass definition by Ashtekar-Magnon-Das (AMD) to a gravity theory with a Gauss-Bonnet term. This proof makes use of the Noether charges obtained from an action renormalized by the addition of counterterms which depend on the extrinsic curvature (Kounterterms). If the asymptotic fall-off behavior of the Weyl tensor is same as the one considered in the AMD method, then the Kounterterm charges and the AMD charges agree in any dimension.
Higher-order mass defect analysis for mass spectra of complex organic mixtures.
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
Döker, Serhat; Boşgelmez, İffet İpek
2015-10-01
A simple and sensitive procedure was developed for extraction and speciation of mercury in fish. Species separation was accomplished with reverse phase-high performance liquid chromatography (HPLC) hyphenated to inductively coupled plasma mass spectrometry (ICP-MS). Oxygen addition into plasma allowed use of organic-rich mobile phase, achieving species separation in 4 min. Mercury species extraction was achieved by microwave exposure for 2 min at mild conditions (60°C, pH 2.0), avoiding necessity of neutralizing sample prior to injection in HPLC, and reducing number of sample preparation steps, analytical source of errors and inter conversion of species. Limit of detection for entire procedure was found to be 0.2 and 0.1 ng g(-1) for mercuric ion and methylmercury, respectively. The method was applied to certified reference materials (TORT-2 and DORM-2) and commercialized fish samples (Mullus barbatus, Sparus aurata, Trachurus mediterraneus, Mugil soiuy, Dicentrarchus labrax, and Pomatomus saltatrix) from Black Sea. PMID:25872437
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
Renormalization group approach to the Fröhlich polaron model: application to impurity-BEC problem
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
Renormalization group approach to the Fröhlich polaron model: application to impurity-BEC problem.
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
Renormalization group approach to the Fröhlich polaron model: application to impurity-BEC problem
NASA Astrophysics Data System (ADS)
Grusdt, F.; Shchadilova, Y. E.; Rubtsov, A. N.; Demler, E.
2015-07-01
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.
One-loop renormalization of the NMSSM in SloopS: The neutralino-chargino and sfermion sectors
NASA Astrophysics Data System (ADS)
Bélanger, G.; Bizouard, V.; Boudjema, F.; Chalons, G.
2016-06-01
We have completed the one-loop renormalisation of the Next-to-Minimal Supersymmetric Standard Model (NMSSM) allowing for and comparing between different renormalisation schemes. A special attention is paid to on-shell schemes. We study a variety of these schemes based on alternative choices of the physical input parameters. In this paper we present our approach to the renormalization of the NMSSM and report on our results for the neutralino-chargino and sfermion sectors. We will borrow some results from our study of the Higgs sector whose full discussion is left for a separate publication. We have implemented the setup for all the sectors of the NMSSM within SloopS, a code for the automatic computation of one-loop corrections initially developed for the standard model and the MSSM. Among the many applications that allows the code, we present here the one-loop corrections to neutralino masses and to partial widths of neutralinos and charginos into final states with one gauge boson. One-loop electroweak and QCD corrections to the partial widths of third generation sfermions into a fermion and a chargino or a neutralino are also computed.
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
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/.
Renormalized effective actions for the O(N) model at next-to-leading order of the 1/N expansion
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.
Renormalized Polyakov loop in the deconfined phase of SU(N) gauge theory and gauge-string duality.
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. PMID:19519096
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.
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.
Domain wall fermion study of scaling in non-perturbative renormalization of quark bilinears and B
NASA Astrophysics Data System (ADS)
Zhestkov, Yuriy Gennadjevich
We develop a non-perturbative scaling technique that connects the results of simulations at different values of coupling β to obtain the renormalization coefficients of scalar and pseudoscalar operators, local vector and axial currents, conserved vector and axial currents over the range of energy scales from 1 to 10 GeV. This technique is then applied to discuss the renormalization of the physically important operator ODS=2LL , central to our understanding of CP violation. We use the domain wall fermion formulation in the quenched approximation at a series of three values of β, 6.0, 6.45, and 7.05, corresponding to lattice spacing scaling by factors of two. The lattice volumes used in the series of simulations are 84 and 164 with the extent in the fifth dimension Ls = 14.
Locally Renormalized Coupled-Cluster Equations for Singly and Doubly Excited Clusters
Kowalski, Karol
2006-07-10
The Numerator-Denominator Connected (NDC) Expansion for the Coupled-Cluster (CC) method [K. Kowalski, P. Piecuch, J. Chem. Phys. 122 (2005) 074107], is used to construct a new set of stationary conditions for approximate coupled-cluster approaches. Several CC approximations based on models involving singles and doubles (CCSD) as well as singles, doubles, and triples (CCSDT) are developed and discussed in the context of ground-state applications. The resulting locally-renormalized CCSD (LR-CCSD) and CCSDT (LR-CCSDT) equations are shown to regularize the expressions for the cluster amplitudes in the challenging situations that occur when the orbital energy differences approach zero. Affordable schemes for handling the local denominators (all-holes-Jn coupling), that naturally appear in locally renormalized formalisms, are also discussed.
Renormalized vacuum polarization on rotating warped AdS3 black holes
NASA Astrophysics Data System (ADS)
Ferreira, Hugo R. C.; Louko, Jorma
2015-01-01
We compute the renormalized vacuum polarization of a massive scalar field in the Hartle-Hawking state on (2 +1 )-dimensional rotating, spacelike stretched black hole solutions to topologically massive gravity, surrounded by a Dirichlet mirror that makes the state well defined. The Feynman propagator is written as a mode sum on the complex Riemannian section of the spacetime, and a Hadamard renormalization procedure is implemented by matching to a mode sum on the complex Riemannian section of a rotating Minkowski spacetime. No analytic continuation in the angular momentum parameter is invoked. Selected numerical results are given, demonstrating the numerical efficacy of the method. We anticipate that this method can be extended to wider classes of rotating black hole spacetimes, in particular to the Kerr spacetime in four dimensions.
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.
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.
Renormalization and small-world model of fractal quantum repeater networks
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
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.
Critical temperature and superfluid gap of the unitary Fermi gas from functional renormalization
NASA Astrophysics Data System (ADS)
Boettcher, Igor; Pawlowski, Jan M.; Wetterich, Christof
2014-05-01
We investigate the superfluid transition of the unitary Fermi gas by means of the functional renormalization group, aiming at quantitative precision. We extract Tc/μ=0.38(2) and Δ /μ=1.04(15) for the critical temperature and the superfluid gap at zero temperature, respectively, within a systematic improvement of the truncation for the effective average action. The key ingredient in comparison to previous approaches consists in the use of regulators which cut off both frequencies and momenta. We incorporate renormalization effects on both the bosonic and the fermionic propagators, include higher-order bosonic scattering processes, and investigate the regulator and specification parameter dependence for an error estimate. The ratio Δ /Tc=2.7(3) becomes less sensitive to the relative cutoff scale of bosons and fermions when improving the truncation. The techniques developed in this work are easily carried over to the cases of finite scattering length, lower dimensionality, and spin imbalance.
Unraveling the interlayer-related phonon self-energy renormalization in bilayer graphene
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
Electronic states on a fractal: Exact Green's-function renormalization approach
NASA Astrophysics Data System (ADS)
Andrade, R. F. S.; Schellnhuber, H. J.
1991-12-01
A nontrivial tight-binding model for electron dynamics on the fractal Koch curve is investigated within the framework of the Green's-function formalism. The key result is the construction of a multiple exact renormalization group that allows one to derive all the rather unusual properties of the model. This group is generated by four nonequivalent decimation operations, which define distinct transformation rules for the 48 relevant parameters to be renormalized. The calculation of the density of states confirms the crucial results that were obtained recently using transfer-matrix methods: local self-affinity, dense gap structure, and singular electronic levels with infinite degeneracy. This demonstrates that the Green's-function approach is not inferior to other techniques even in topologically one-dimensional situations.
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.
NASA Astrophysics Data System (ADS)
Bauer, Carsten; Rückriegel, Andreas; Sharma, Anand; Kopietz, Peter
2015-09-01
Using a nonperturbative functional renormalization group approach, we calculate the renormalized quasiparticle velocity v (k ) and the static dielectric function ɛ (k ) of suspended graphene as functions of an external momentum k . Our numerical result for v (k ) can be fitted by v (k ) /vF=A +B ln(Λ0/k ) , where vF is the bare Fermi velocity, Λ0 is an ultraviolet cutoff, and A =1.37 , B =0.51 for the physically relevant value (e2/vF=2.2 ) of the coupling constant. In contrast to calculations based on the static random-phase approximation, we find that ɛ (k ) approaches unity for k →0 . Our result for v (k ) agrees very well with a recent measurement by Elias et al. [Nat. Phys. 7, 701 (2011), 10.1038/nphys2049].
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.
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.
Alles, B.; D'Elia, M.; Di Giacomo, A.; Pica, C.
2006-11-01
A Ginsparg-Wilson based calibration of the topological charge is used to calculate the renormalization constants which appear in the field-theoretical determination of the topological susceptibility on the lattice. A systematic comparison is made with calculations based on cooling. The two methods agree within present statistical errors (3%-4%). We also discuss the independence of the multiplicative renormalization constant Z from the background topological charge used to determine it.
The δN formula is the dynamical renormalization group
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.
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.
Renormalization group flow of quartic perturbations in graphene: Strong coupling and large- N limits
NASA Astrophysics Data System (ADS)
Drut, Joaquín E.; Son, Dam Thanh
2008-02-01
We explore the renormalization group flow of quartic perturbations in the low-enegy theory of graphene, in the strong Coulomb coupling and large- N limits, where N is the number of fermion flavors. We compute the anomalous dimensions of the quartic couplings u up to leading order in 1/N and find both relevant and irrelevant directions in the space of quartic couplings. We discuss possible phase diagrams and relevance for the physics of graphene.
NASA Astrophysics Data System (ADS)
Chandre, C.; Jauslin, H. R.
1998-12-01
We study an approximate renormalization-group transformation to analyze the breakup of invariant tori for 3 degrees of freedom Hamiltonian systems. The scheme is implemented for the spiral mean torus. We find numerically that the critical surface is the stable manifold of a critical nonperiodic attractor. We compute scaling exponents associated with this fixed set, and find that they can be expected to be universal.
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.
Flow equation of functional renormalization group for three-body scattering problems
NASA Astrophysics Data System (ADS)
Tanizaki, Yuya
2013-11-01
Functional renormalization group (FRG) is applied to the three-body scattering problem in the two-component fermionic system with an attractive contact interaction. We establish an exact flow equation on the basis of FRG and show that our flow equation is consistent with integral equations obtained from the Dyson-Schwinger equation. In particular, the relation of our flow equation and the Skornyakov and Ter-Martirosyan equation for the atom-dimer scattering is made clear.
Equation-free dynamic renormalization: Self-similarity in multidimensional particle system dynamics
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.
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
Renormalization theory of beam-beam interaction in electron-positron colliders
Chin, Y.H.
1989-07-01
This note is devoted to explaining the essence of the renormalization theory of beam-beam interaction for carrying out analytical calculations of equilibrium particle distributions in electron-positron colliding beam storage rings. Some new numerical examples are presented such as for betatron tune dependence of the rms beam size. The theory shows reasonably good agreements with the results of computer simulations. 5 refs., 6 figs.
Goh, Segun; Lee, Keumsook; Choi, MooYoung; 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
Kowalski, Karol; De Jong, Wibe A.
2006-08-31
Noniterative inclusion of the higher=order clusters has been a subject of intensive studies aimed at developing a well balanced description of individual many-body contributions for entire ground-state potential energy surfaces. In traditional approaches, the connected quadruples are estimated directly based on perturbative arguments, which leads to excellent agreement with full CI results near the equilibrium geometry and increasingly worse energies for larger internuclear stretches. As a possible improvement to this situation, two techniques are considered as especially promising: perturbative approaches based on the similarity transformed Hamiltonians and renormalization schemes both in global and local formulation. Following the latter strategy we adopted the recently introduced Numerator-Denominator Connected expansion (NDC) [ K. Kowalski, P. Piecuch, J. Chem. Phys. 122 (2005) [074107] as an effective tool for designing new forms of noniterative corrections accounting for the joint effect of triples and quadruples. The performance of the ensuing locally renormalized CCSD(TQ) approaches (LR-CCSD(TQ) is illustrated on several examples that require either going beyond the triples approximation or describing very subtle effects encountered in Van der Waals complexes. Comparisons with other noniterative approaches are also made and some issues regarding the size-extensivity of the locally renormalized methods are addressed.
An exact renormalization model for earthquakes and material failure: Statics and dynamics
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.
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.
Renormalization group analysis of thermal transport in the disordered Fermi liquid
NASA Astrophysics Data System (ADS)
Schwiete, G.; Finkel'stein, A. M.
2014-10-01
We present a detailed study of thermal transport in the disordered Fermi liquid with short-range interactions. At temperatures smaller than the impurity scattering rate, i.e., in the diffusive regime, thermal conductivity acquires nonanalytic quantum corrections. When these quantum corrections become large at low temperatures, the calculation of thermal conductivity demands a theoretical approach that treats disorder and interactions on an equal footing. In this paper, we develop such an approach by merging Luttinger's idea of using gravitational potentials for the analysis of thermal phenomena with a renormalization group calculation based on the Keldysh nonlinear sigma model. The gravitational potentials are introduced in the action as auxiliary sources that couple to the heat density. These sources are a convenient tool for generating expressions for the heat density and its correlation function from the partition function. Already in the absence of the gravitational potentials, the nonlinear sigma model contains several temperature-dependent renormalization group charges. When the gravitational potentials are introduced into the model, they acquire an independent renormalization group flow. We show that this flow preserves the phenomenological form of the correlation function, reflecting its relation to the specific heat and the constraints imposed by energy conservation. The main result of our analysis is that the Wiedemann-Franz law holds down to the lowest temperatures even in the presence of disorder and interactions and despite the quantum corrections that arise for both the electric and thermal conductivities.