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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kampf, Karol; Institute of Particle and Nuclear Physics, Faculty of Mathematics and Physics, Charles University in Prague, V Holesovickach 2, 18000 Prague; Novotny, Jiri

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 tomore » 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.« less

Path-Integration Computation of the Transport Properties of Polymers Nanoparticles and Complex Biological Structures

NASA Astrophysics Data System (ADS)

Douglas, Jack

2014-03-01

One of the things that puzzled me when I was a PhD student working under Karl Freed was the curious unity between the theoretical descriptions of excluded volume interactions in polymers, the hydrodynamic properties of polymers in solution, and the critical properties of fluid mixtures, gases and diverse other materials (magnets, superfluids,etc.) when these problems were formally expressed in terms of Wiener path integration and the interactions treated through a combination of epsilon expansion and renormalization group (RG) theory. It seemed that only the interaction labels changed from one problem to the other. What do these problems have in common? Essential clues to these interrelations became apparent when Karl Freed, myself and Shi-Qing Wang together began to study polymers interacting with hyper-surfaces of continuously variable dimension where the Feynman perturbation expansions could be performed through infinite order so that we could really understand what the RG theory was doing. It is evidently simply a particular method for resuming perturbation theory, and former ambiguities no longer existed. An integral equation extension of this type of exact calculation to ``surfaces'' of arbitrary fixed shape finally revealed the central mathematical object that links these diverse physical models- the capacity of polymer chains, whose value vanishes at the critical dimension of 4 and whose magnitude is linked to the friction coefficient of polymer chains, the virial coefficient of polymers and the 4-point function of the phi-4 field theory,...Once this central object was recognized, it then became possible solve diverse problems in material science through the calculation of capacity, and related ``virials'' properties, through Monte Carlo sampling of random walk paths. The essential ideas of this computational method are discussed and some applications given to non-trivial problems: nanotubes treated as either rigid rods or ensembles worm-like chains having finite cross-section, DNA, nanoparticles with grafted chain layers and knotted polymers. The path-integration method, which grew up from research in Karl Freed's group, is evidently a powerful tool for computing basic transport properties of complex-shaped objects and should find increasing application in polymer science, nanotechnological applications and biology.

Renormalization group analysis of B →π form factors with B -meson light-cone sum rules

NASA Astrophysics Data System (ADS)

Shen, Yue-Long; Wei, Yan-Bing; Lü, Cai-Dian

2018-03-01

Within the framework of the B -meson light-cone sum rules, we review the calculation of radiative corrections to the three B →π transition form factors at leading power in Λ /mb. To resum large logarithmic terms, we perform the complete renormalization group evolution of the correlation function. We employ the integral transformation which diagonalizes evolution equations of the jet function and the B -meson light-cone distribution amplitude to solve these evolution equations and obtain renormalization group improved sum rules for the B →π form factors. Results of the form factors are extrapolated to the whole physical q2 region and are compared with that of other approaches. The effect of B -meson three-particle light-cone distribution amplitudes, which will contribute to the form factors at next-to-leading power in Λ /mb at tree level, is not considered in this paper.

Renormalized asymptotic enumeration of Feynman diagrams

NASA Astrophysics Data System (ADS)

Borinsky, Michael

2017-10-01

A method to obtain all-order asymptotic results for the coefficients of perturbative expansions in zero-dimensional quantum field is described. The focus is on the enumeration of the number of skeleton or primitive diagrams of a certain QFT and its asymptotics. The procedure heavily applies techniques from singularity analysis. To utilize singularity analysis, a representation of the zero-dimensional path integral as a generalized hyperelliptic curve is deduced. As applications the full asymptotic expansions of the number of disconnected, connected, 1PI and skeleton Feynman diagrams in various theories are given.

Path integration: effect of curved path complexity and sensory system on blindfolded walking.

PubMed

Koutakis, Panagiotis; Mukherjee, Mukul; Vallabhajosula, Srikant; Blanke, Daniel J; Stergiou, Nicholas

2013-02-01

Path integration refers to the ability to integrate continuous information of the direction and distance traveled by the system relative to the origin. Previous studies have investigated path integration through blindfolded walking along simple paths such as straight line and triangles. However, limited knowledge exists regarding the role of path complexity in path integration. Moreover, little is known about how information from different sensory input systems (like vision and proprioception) contributes to accurate path integration. The purpose of the current study was to investigate how sensory information and curved path complexity affect path integration. Forty blindfolded participants had to accurately reproduce a curved path and return to the origin. They were divided into four groups that differed in the curved path, circle (simple) or figure-eight (complex), and received either visual (previously seen) or proprioceptive (previously guided) information about the path before they reproduced it. The dependent variables used were average trajectory error, walking speed, and distance traveled. The results indicated that (a) both groups that walked on a circular path and both groups that received visual information produced greater accuracy in reproducing the path. Moreover, the performance of the group that received proprioceptive information and later walked on a figure-eight path was less accurate than their corresponding circular group. The groups that had the visual information also walked faster compared to the group that had proprioceptive information. Results of the current study highlight the roles of different sensory inputs while performing blindfolded walking for path integration. Copyright © 2012 Elsevier B.V. All rights reserved.

Local renormalization group functions from quantum renormalization group and holographic bulk locality

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nakayama, Yu

Here, 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 N = 4 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 holographicmore » 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 N = 4 super Yang-Mills theory.« less

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.

Signs and stability in higher-derivative gravity

NASA Astrophysics Data System (ADS)

Narain, Gaurav

2018-02-01

Perturbatively renormalizable higher-derivative gravity in four space-time dimensions with arbitrary signs of couplings has been considered. Systematic analysis of the action with arbitrary signs of couplings in Lorentzian flat space-time for no-tachyons, fixes the signs. Feynman + i𝜖 prescription for these signs further grants necessary convergence in path-integral, suppressing the field modes with large action. This also leads to a sensible wick rotation where quantum computation can be performed. Running couplings for these sign of parameters make the massive tensor ghost innocuous leading to a stable and ghost-free renormalizable theory in four space-time dimensions. The theory has a transition point arising from renormalization group (RG) equations, where the coefficient of R2 diverges without affecting the perturbative quantum field theory (QFT). Redefining this coefficient gives a better handle over the theory around the transition point. The flow equations push the flow of parameters across the transition point. The flow beyond the transition point is analyzed using the one-loop RG equations which shows that the regime beyond the transition point has unphysical properties: there are tachyons, the path-integral loses positive definiteness, Newton’s constant G becomes negative and large, and perturbative parameters become large. These shortcomings indicate a lack of completeness beyond the transition point and need of a nonperturbative treatment of the theory beyond the transition point.

From Constructive Field Theory to Fractional Stochastic Calculus. (II) Constructive Proof of Convergence for the Lévy Area of Fractional Brownian Motion with Hurst Index {{alpha} {in} ((1)/(8),(1)/(4))}

NASA Astrophysics Data System (ADS)

Magnen, Jacques; Unterberger, Jérémie

2012-03-01

{Let $B=(B_1(t),...,B_d(t))$ be a $d$-dimensional fractional Brownian motion with Hurst index $\\alpha<1/4$, or more generally a Gaussian process whose paths have the same local regularity. Defining properly iterated integrals of $B$ is a difficult task because of the low H\\"older regularity index of its paths. Yet rough path theory shows it is the key to the construction of a stochastic calculus with respect to $B$, or to solving differential equations driven by $B$. We intend to show in a series of papers how to desingularize iterated integrals by a weak, singular non-Gaussian perturbation of the Gaussian measure defined by a limit in law procedure. Convergence is proved by using "standard" tools of constructive field theory, in particular cluster expansions and renormalization. These powerful tools allow optimal estimates, and call for an extension of Gaussian tools such as for instance the Malliavin calculus. After a first introductory paper \\cite{MagUnt1}, this one concentrates on the details of the constructive proof of convergence for second-order iterated integrals, also known as L\\'evy area.

Connecting dissipation and noncommutativity: A Bateman system case study

NASA Astrophysics Data System (ADS)

Pal, Sayan Kumar; Nandi, Partha; Chakraborty, Biswajit

2018-06-01

We present an approach to the problem of quantization of the damped harmonic oscillator. To start with, we adopt the standard method of doubling the degrees of freedom of the system (Bateman form) and then, by introducing some new parameters, we get a generalized coupled set of equations from the Bateman form. Using the corresponding time-independent Lagrangian, quantum effects on a pair of Bateman oscillators embedded in an ambient noncommutative space (Moyal plane) are analyzed by using both path integral and canonical quantization schemes within the framework of the Hilbert-Schmidt operator formulation. Our method is distinct from those existing in the literature and where the ambient space was taken to be commutative. Our quantization shows that we end up again with a Bateman system except that the damping factor undergoes renormalization. Strikingly, the corresponding expression shows that the renormalized damping factor can be nonzero even if "bare" one is zero to begin with. In other words, noncommutativity can act as a source of dissipation. Conversely, the noncommutative parameter θ , taken to be a free one now, can be fine tuned to get a vanishing renormalized damping factor. This indicates in some sense a "duality" between dissipation and noncommutativity. Our results match the existing results in the commutative limit.

Leading isospin-breaking corrections to meson masses on the lattice

NASA Astrophysics Data System (ADS)

Giusti, Davide; Lubicz, Vittorio; Martinelli, Guido; Sanfilippo, Francesco; Simula, Silvano; Tantalo, Nazario; Tarantino, Cecilia

2018-03-01

We present a study of the isospin-breaking (IB) corrections to pseudoscalar (PS) meson masses using the gauge configurations produced by the ETM Collaboration with Nf = 2+1+1 dynamical quarks at three lattice spacings varying from 0.089 to 0.062 fm. Our method is based on a combined expansion of the path integral in powers of the small parameters (m⌢d-m⌢u)/ΛQCD and αem, where m⌢f is the renormalized quark mass and αem the renormalized fine structure constant. We obtain results for the pion, kaon and Dmeson mass splitting; for the Dashen's theorem violation parameters εγ(MM, 2 GeV), επ0 εK0(MS, 2 GeV) for the light quark masses (m⌢d-m⌢u)(MS¯,2 GeV),(m⌢u/m⌢d)(MS¯,2 GeV); for the flavour symmetry breaking parameters R(MS, 2 GeV) and Q(MS, 2 GeV) and for the strong IB effects on the kaon decay constants.

The signed permutation group on Feynman graphs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Purkart, Julian, E-mail: purkart@physik.hu-berlin.de

2016-08-15

The Feynman rules assign to every graph an integral which can be written as a function of a scaling parameter L. Assuming L for the process under consideration is very small, so that contributions to the renormalization group are small, we can expand the integral and only consider the lowest orders in the scaling. The aim of this article is to determine specific combinations of graphs in a scalar quantum field theory that lead to a remarkable simplification of the first non-trivial term in the perturbation series. It will be seen that the result is independent of the renormalization schememore » and the scattering angles. To achieve that goal we will utilize the parametric representation of scalar Feynman integrals as well as the Hopf algebraic structure of the Feynman graphs under consideration. Moreover, we will present a formula which reduces the effort of determining the first-order term in the perturbation series for the specific combination of graphs to a minimum.« less

Mutual information, neural networks and the renormalization group

NASA Astrophysics Data System (ADS)

Koch-Janusz, Maciej; Ringel, Zohar

2018-06-01

Physical systems differing in their microscopic details often display strikingly similar behaviour when probed at macroscopic scales. Those universal properties, largely determining their physical characteristics, are revealed by the powerful renormalization group (RG) procedure, which systematically retains `slow' degrees of freedom and integrates out the rest. However, the important degrees of freedom may be difficult to identify. Here we demonstrate a machine-learning algorithm capable of identifying the relevant degrees of freedom and executing RG steps iteratively without any prior knowledge about the system. We introduce an artificial neural network based on a model-independent, information-theoretic characterization of a real-space RG procedure, which performs this task. We apply the algorithm to classical statistical physics problems in one and two dimensions. We demonstrate RG flow and extract the Ising critical exponent. Our results demonstrate that machine-learning techniques can extract abstract physical concepts and consequently become an integral part of theory- and model-building.

QCD as a Theory of Hadrons

NASA Astrophysics Data System (ADS)

Narison, Stephan

2004-05-01

About Stephan Narison; Outline of the book; Preface; Acknowledgements; Part I. General Introduction: 1. A short flash on particle physics; 2. The pre-QCD era; 3. The QCD story; 4. Field theory ingredients; Part II. QCD Gauge Theory: 5. Lagrangian and gauge invariance; 6. Quantization using path integral; 7. QCD and its global invariance; Part III. MS scheme for QCD and QED: Introduction; 8. Dimensional regularization; 9. The MS renormalization scheme; 10. Renormalization of operators using the background field method; 11. The renormalization group; 12. Other renormalization schemes; 13. MS scheme for QED; 14. High-precision low-energy QED tests; Part IV. Deep Inelastic Scattering at Hadron Colliders: 15. OPE for deep inelastic scattering; 16. Unpolarized lepton-hadron scattering; 17. The Altarelli-Parisi equation; 18. More on unpolarized deep inelastic scatterings; 19. Polarized deep-inelastic processes; 20. Drell-Yan process; 21. One 'prompt photon' inclusive production; Part V. Hard Processes in e+e- Collisions: Introduction; 22. One hadron inclusive production; 23. gg scatterings and the 'spin' of the photon; 24. QCD jets; 25. Total inclusive hadron productions; Part VI. Summary of QCD Tests and as Measurements; Part VII. Power Corrections in QCD: 26. Introduction; 27. The SVZ expansion; 28. Technologies for evaluating Wilson coefficients; 29. Renormalons; 30. Beyond the SVZ expansion; Part VIII. QCD Two-Point Functions: 31. References guide to original works; 32. (Pseudo)scalar correlators; 33. (Axial-)vector two-point functions; 34. Tensor-quark correlator; 35. Baryonic correlators; 36. Four-quark correlators; 37. Gluonia correlators; 38. Hybrid correlators; 39. Correlators in x-space; Part IX. QCD Non-Perturbative Methods: 40. Introduction; 41. Lattice gauge theory; 42. Chiral perturbation theory; 43. Models of the QCD effective action; 44. Heavy quark effective theory; 45. Potential approaches to quarkonia; 46. On monopole and confinement; Part X. QCD Spectral Sum Rules: 47. Introduction; 48. Theoretical foundations; 49. Survey of QCD spectral sum rules; 50. Weinberg and DMO sum rules; 51. The QCD coupling as; 52. The QCD condensates; 53. Light and heavy quark masses, etc.; 54. Hadron spectroscopy; 55. D, B and Bc exclusive weak decays; 56. B0(s)-B0(s) mixing, kaon CP violation; 57. Thermal behaviour of QCD; 58. More on spectral sum rules; Part XI. Appendix A: physical constants and unites; Appendix B: weight factors for SU(N)c; Appendix C: coordinates and momenta; Appendix D: Dirac equation and matrices; Appendix E: Feynman rules; Appendix F: Feynman integrals; Appendix G: useful formulae for the sum rules; Bibliography; Index.

QCD as a Theory of Hadrons

NASA Astrophysics Data System (ADS)

Narison, Stephan

2007-07-01

About Stephan Narison; Outline of the book; Preface; Acknowledgements; Part I. General Introduction: 1. A short flash on particle physics; 2. The pre-QCD era; 3. The QCD story; 4. Field theory ingredients; Part II. QCD Gauge Theory: 5. Lagrangian and gauge invariance; 6. Quantization using path integral; 7. QCD and its global invariance; Part III. MS scheme for QCD and QED: Introduction; 8. Dimensional regularization; 9. The MS renormalization scheme; 10. Renormalization of operators using the background field method; 11. The renormalization group; 12. Other renormalization schemes; 13. MS scheme for QED; 14. High-precision low-energy QED tests; Part IV. Deep Inelastic Scattering at Hadron Colliders: 15. OPE for deep inelastic scattering; 16. Unpolarized lepton-hadron scattering; 17. The Altarelli-Parisi equation; 18. More on unpolarized deep inelastic scatterings; 19. Polarized deep-inelastic processes; 20. Drell-Yan process; 21. One 'prompt photon' inclusive production; Part V. Hard Processes in e+e- Collisions: Introduction; 22. One hadron inclusive production; 23. gg scatterings and the 'spin' of the photon; 24. QCD jets; 25. Total inclusive hadron productions; Part VI. Summary of QCD Tests and as Measurements; Part VII. Power Corrections in QCD: 26. Introduction; 27. The SVZ expansion; 28. Technologies for evaluating Wilson coefficients; 29. Renormalons; 30. Beyond the SVZ expansion; Part VIII. QCD Two-Point Functions: 31. References guide to original works; 32. (Pseudo)scalar correlators; 33. (Axial-)vector two-point functions; 34. Tensor-quark correlator; 35. Baryonic correlators; 36. Four-quark correlators; 37. Gluonia correlators; 38. Hybrid correlators; 39. Correlators in x-space; Part IX. QCD Non-Perturbative Methods: 40. Introduction; 41. Lattice gauge theory; 42. Chiral perturbation theory; 43. Models of the QCD effective action; 44. Heavy quark effective theory; 45. Potential approaches to quarkonia; 46. On monopole and confinement; Part X. QCD Spectral Sum Rules: 47. Introduction; 48. Theoretical foundations; 49. Survey of QCD spectral sum rules; 50. Weinberg and DMO sum rules; 51. The QCD coupling as; 52. The QCD condensates; 53. Light and heavy quark masses, etc.; 54. Hadron spectroscopy; 55. D, B and Bc exclusive weak decays; 56. B0(s)-B0(s) mixing, kaon CP violation; 57. Thermal behaviour of QCD; 58. More on spectral sum rules; Part XI. Appendix A: physical constants and unites; Appendix B: weight factors for SU(N)c; Appendix C: coordinates and momenta; Appendix D: Dirac equation and matrices; Appendix E: Feynman rules; Appendix F: Feynman integrals; Appendix G: useful formulae for the sum rules; Bibliography; Index.

Novel demonstration of the renormalization group invariance of the fixed-order predictions using the principle of maximum conformality and the C -scheme coupling

NASA Astrophysics Data System (ADS)

Wu, Xing-Gang; Shen, Jian-Ming; Du, Bo-Lun; Brodsky, Stanley J.

2018-05-01

As a basic requirement of the renormalization group invariance, any physical observable must be independent of the choice of both the renormalization scheme and the initial renormalization scale. In this paper, we show that by using the newly suggested C -scheme coupling, one can obtain a demonstration that the principle of maximum conformality prediction is scheme-independent to all-orders for any renormalization schemes, thus satisfying all of the conditions of the renormalization group invariance. We illustrate these features for the nonsinglet Adler function and for τ decay to ν + hadrons at the four-loop level.

Renormalization of Coulomb interactions in a system of two-dimensional tilted Dirac fermions

NASA Astrophysics Data System (ADS)

Lee, Yu-Wen; Lee, Yu-Li

2018-01-01

We investigate the effects of long-ranged Coulomb interactions in a tilted Dirac semimetal in two dimensions by using the perturbative renormalization-group (RG) method. Depending on the magnitude of the tilting parameter, the undoped system can have either Fermi points (type I) or Fermi lines (type II). Previous studies usually performed the renormalization-group transformations by integrating out the modes with large momenta. This is problematic when the Fermi surface is open, like type-II Dirac fermions. In this work we study the effects of Coulomb interactions, following the spirit of Shankar [Rev. Mod. Phys. 66, 129 (1994), 10.1103/RevModPhys.66.129], by introducing a cutoff in the energy scale around the Fermi surface and integrating out the high-energy modes. For type-I Dirac fermions, our result is consistent with that of the previous work. On the other hand, we find that for type-II Dirac fermions, the magnitude of the tilting parameter increases monotonically with lowering energies. This implies the stability of type-II Dirac fermions in the presence of Coulomb interactions, in contrast with previous results. Furthermore, for type-II Dirac fermions, the velocities in different directions acquire different renormalization even if they have the same bare values. By taking into account the renormalization of the tilting parameter and the velocities due to the Coulomb interactions, we show that while the presence of a charged impurity leads only to charge redistribution around the impurity for type-I Dirac fermions, for type-II Dirac fermions, the impurity charge is completely screened, albeit with a very long screening length. The latter indicates that the temperature dependence of physical observables are essentially determined by the RG equations we derived. We illustrate this by calculating the temperature dependence of the compressibility and specific heat of the interacting tilted Dirac fermions.

Real-space decoupling transformation for quantum many-body systems.

PubMed

Evenbly, G; Vidal, G

2014-06-06

We propose a real-space renormalization group method to explicitly decouple into independent components a many-body system that, as in the phenomenon of spin-charge separation, exhibits separation of degrees of freedom at low energies. Our approach produces a branching holographic description of such systems that opens the path to the efficient simulation of the most entangled phases of quantum matter, such as those whose ground state violates a boundary law for entanglement entropy. As in the coarse-graining transformation of Vidal [Phys. Rev. Lett. 99, 220405 (2007).

Comprehensive renormalization group analysis of the littlest seesaw model

NASA Astrophysics Data System (ADS)

Geib, Tanja; King, Stephen F.

2018-04-01

We present a comprehensive renormalization group analysis of the littlest seesaw model involving two right-handed neutrinos and a very constrained Dirac neutrino Yukawa coupling matrix. We perform the first χ2 analysis of the low energy masses and mixing angles, in the presence of renormalization group corrections, for various right-handed neutrino masses and mass orderings, both with and without supersymmetry. We find that the atmospheric angle, which is predicted to be near maximal in the absence of renormalization group corrections, may receive significant corrections for some nonsupersymmetric cases, bringing it into close agreement with the current best fit value in the first octant. By contrast, in the presence of supersymmetry, the renormalization group corrections are relatively small, and the prediction of a near maximal atmospheric mixing angle is maintained, for the studied cases. Forthcoming results from T2K and NO ν A will decisively test these models at a precision comparable to the renormalization group corrections we have calculated.

An integral-factorized implementation of the driven similarity renormalization group second-order multireference perturbation theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hannon, Kevin P.; Li, Chenyang; Evangelista, Francesco A., E-mail: francesco.evangelista@emory.edu

2016-05-28

We report an efficient implementation of a second-order multireference perturbation theory based on the driven similarity renormalization group (DSRG-MRPT2) [C. Li and F. A. Evangelista, J. Chem. Theory Comput. 11, 2097 (2015)]. Our implementation employs factorized two-electron integrals to avoid storage of large four-index intermediates. It also exploits the block structure of the reference density matrices to reduce the computational cost to that of second-order Møller–Plesset perturbation theory. Our new DSRG-MRPT2 implementation is benchmarked on ten naphthyne isomers using basis sets up to quintuple-ζ quality. We find that the singlet-triplet splittings (Δ{sub ST}) of the naphthyne isomers strongly depend onmore » the equilibrium structures. For a consistent set of geometries, the Δ{sub ST} values predicted by the DSRG-MRPT2 are in good agreements with those computed by the reduced multireference coupled cluster theory with singles, doubles, and perturbative triples.« less

Renormalization Group Invariance of the Pole Mass in the Multi-Higgs System

NASA Astrophysics Data System (ADS)

Kim, Chungku

2018-06-01

We have investigated the renormalization group running of the pole mass in the multi-Higgs theory in two different types of gauge fixing conditions. The pole mass, when expressed in terms of the Lagrangian parameters, turns out to be invariant under the renormalization group with the beta and gamma functions of the symmetric phase.

Time-dependent spectral renormalization method

NASA Astrophysics Data System (ADS)

Cole, Justin T.; Musslimani, Ziad H.

2017-11-01

The spectral renormalization method was introduced by Ablowitz and Musslimani (2005) as an effective way to numerically compute (time-independent) bound states for certain nonlinear boundary value problems. In this paper, we extend those ideas to the time domain and introduce a time-dependent spectral renormalization method as a numerical means to simulate linear and nonlinear evolution equations. The essence of the method is to convert the underlying evolution equation from its partial or ordinary differential form (using Duhamel's principle) into an integral equation. The solution sought is then viewed as a fixed point in both space and time. The resulting integral equation is then numerically solved using a simple renormalized fixed-point iteration method. Convergence is achieved by introducing a time-dependent renormalization factor which is numerically computed from the physical properties of the governing evolution equation. The proposed method has the ability to incorporate physics into the simulations in the form of conservation laws or dissipation rates. This novel scheme is implemented on benchmark evolution equations: the classical nonlinear Schrödinger (NLS), integrable PT symmetric nonlocal NLS and the viscous Burgers' equations, each of which being a prototypical example of a conservative and dissipative dynamical system. Numerical implementation and algorithm performance are also discussed.

Two-loop renormalization of the quark propagator in the light-cone gauge

NASA Astrophysics Data System (ADS)

Williams, James Daniel

The divergent parts of the five two-loop quark self- energy diagrams of quantum chromodynamics are evaluated in the noncovariant light-cone gauge. Most of the Feynman integrals are computed by means of the powerful matrix integration method, originally developed for the author's Master's thesis. From the results of the integrations, it is shown how to renormalize the quark mass and wave function in such a way that the effective quark propagator is rendered finite at two-loop order. The required counterterms turn out to be local functions of the quark momentum, due to cancellation of the nonlocal divergent parts of the two-loop integrals with equal and opposite contributions from one-loop counterterm subtraction diagrams. The final form of the counterterms is seen to be consistent with the renormalization framework proposed by Bassetto, Dalbosco, and Soldati, in which all noncovariant divergences are absorbed into the wave function normalizations. It also turns out that the mass renormalization d m is the same in the light-cone gauge as it is in a general covariant gauge, at least up to two-loop order.

Charge modulation as fingerprints of phase-string triggered interference

NASA Astrophysics Data System (ADS)

Zhu, Zheng; Tian, Chushun; Jiang, Hong-Chen; Qi, Yang; Weng, Zheng-Yu; Zaanen, Jan

2015-07-01

Charge order appears to be an ubiquitous phenomenon in doped Mott insulators, which is currently under intense experimental and theoretical investigations particularly in the high Tc cuprates. This phenomenon is conventionally understood in terms of Hartree-Fock-type mean-field theory. Here we demonstrate a mechanism for charge modulation which is rooted in the many-particle quantum physics arising in the strong coupling limit. Specifically, we consider the problem of a single hole in a bipartite t -J ladder. As a remnant of the fermion signs, the hopping hole picks up subtle phases pending the fluctuating spins, the so-called phase-string effect. We demonstrate the presence of charge modulations in the density matrix renormalization group solutions which disappear when the phase strings are switched off. This form of charge modulation can be understood analytically in a path-integral language with a mean-field-like approximation adopted, showing that the phase strings give rise to constructive interferences leading to self-localization. When the latter occurs, left- and right-moving propagating modes emerge inside the localization volume and their interference is responsible for the real space charge modulation.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhu, Zheng; Tian, Chushun; Jiang, Hong-Chen

Charge order appears to be an ubiquitous phenomenon in doped Mott insulators, which is currently under intense experimental and theoretical investigations particularly in the high T c cuprates. This phenomenon is conventionally understood in terms of Hartree-Fock-type mean-field theory. Here we demonstrate a mechanism for charge modulation which is rooted in the many-particle quantum physics arising in the strong coupling limit. Specifically, we consider the problem of a single hole in a bipartite t - J ladder. As a remnant of the fermion signs, the hopping hole picks up subtle phases pending the fluctuating spins, the so-called phase-string effect. Wemore » demonstrate the presence of charge modulations in the density matrix renormalization group solutions which disappear when the phase strings are switched off. This form of charge modulation can be understood analytically in a path-integral language with a mean-field-like approximation adopted, showing that the phase strings give rise to constructive interferences leading to self-localization. When the latter occurs, left- and right-moving propagating modes emerge inside the localization volume and their interference is responsible for the real space charge modulation.« less

Renormalization group approach to power-law modeling of complex metabolic networks.

PubMed

Hernández-Bermejo, Benito

2010-08-07

In the modeling of complex biological systems, and especially in the framework of the description of metabolic pathways, the use of power-law models (such as S-systems and GMA systems) often provides a remarkable accuracy over several orders of magnitude in concentrations, an unusually broad range not fully understood at present. In order to provide additional insight in this sense, this article is devoted to the renormalization group analysis of reactions in fractal or self-similar media. In particular, the renormalization group methodology is applied to the investigation of how rate-laws describing such reactions are transformed when the geometric scale is changed. The precise purpose of such analysis is to investigate whether or not power-law rate-laws present some remarkable features accounting for the successes of power-law modeling. As we shall see, according to the renormalization group point of view the answer is positive, as far as power-laws are the critical solutions of the renormalization group transformation, namely power-law rate-laws are the renormalization group invariant solutions. Moreover, it is shown that these results also imply invariance under the group of concentration scalings, thus accounting for the reported power-law model accuracy over several orders of magnitude in metabolite concentrations. Copyright 2010 Elsevier Ltd. All rights reserved.

A renormalization group approach to identifying the local quantum numbers in a many-body localized system

NASA Astrophysics Data System (ADS)

Pekker, David; Clark, Bryan K.; Oganesyan, Vadim; Refael, Gil; Tian, Binbin

Many-body localization is a dynamical phase of matter that is characterized by the absence of thermalization. One of the key characteristics of many-body localized systems is the emergence of a large (possibly maximal) number of local integrals of motion (local quantum numbers) and corresponding conserved quantities. We formulate a robust algorithm for identifying these conserved quantities, based on Wegner's flow equations - a form of the renormalization group that works by disentangling the degrees of freedom of the system as opposed to integrating them out. We test our algorithm by explicit numerical comparison with more engineering based algorithms - Jacobi rotations and bi-partite matching. We find that the Wegner flow algorithm indeed produces the more local conserved quantities and is therefore more optimal. A preliminary analysis of the conserved quantities produced by the Wegner flow algorithm reveals the existence of at least two different localization lengthscales. Work was supported by AFOSR FA9550-10-1-0524 and FA9550-12-1-0057, the Kaufmann foundation, and SciDAC FG02-12ER46875.

Products of composite operators in the exact renormalization group formalism

NASA Astrophysics Data System (ADS)

Pagani, C.; Sonoda, H.

2018-02-01

We discuss a general method of constructing the products of composite operators using the exact renormalization group formalism. Considering mainly the Wilson action at a generic fixed point of the renormalization group, we give an argument for the validity of short-distance expansions of operator products. We show how to compute the expansion coefficients by solving differential equations, and test our method with some simple examples.

Functional Renormalization Group Flows on Friedman-Lemaître-Robertson-Walker backgrounds

NASA Astrophysics Data System (ADS)

Platania, Alessia; Saueressig, Frank

2018-06-01

We revisit the construction of the gravitational functional renormalization group equation tailored to the Arnowitt-Deser-Misner formulation emphasizing its connection to the covariant formulation. The results obtained from projecting the renormalization group flow onto the Einstein-Hilbert action are reviewed in detail and we provide a novel example illustrating how the formalism may be connected to the causal dynamical triangulations approach to quantum gravity.

The ab-initio density matrix renormalization group in practice.

PubMed

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

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.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rodrigues, Davi C.; Piattella, Oliver F.; Chauvineau, Bertrand, E-mail: davi.rodrigues@cosmo-ufes.org, E-mail: Bertrand.Chauvineau@oca.eu, E-mail: oliver.piattella@pq.cnpq.br

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

NLO renormalization in the Hamiltonian truncation

NASA Astrophysics Data System (ADS)

Elias-Miró, Joan; Rychkov, Slava; Vitale, Lorenzo G.

2017-09-01

Hamiltonian truncation (also known as "truncated spectrum approach") is a numerical technique for solving strongly coupled quantum field theories, in which the full Hilbert space is truncated to a finite-dimensional low-energy subspace. The accuracy of the method is limited only by the available computational resources. The renormalization program improves the accuracy by carefully integrating out the high-energy states, instead of truncating them away. In this paper, we develop the most accurate ever variant of Hamiltonian Truncation, which implements renormalization at the cubic order in the interaction strength. The novel idea is to interpret the renormalization procedure as a result of integrating out exactly a certain class of high-energy "tail states." We demonstrate the power of the method with high-accuracy computations in the strongly coupled two-dimensional quartic scalar theory and benchmark it against other existing approaches. Our work will also be useful for the future goal of extending Hamiltonian truncation to higher spacetime dimensions.

Renormalization of position space amplitudes in a massless QFT

NASA Astrophysics Data System (ADS)

Todorov, Ivan

2017-03-01

Ultraviolet renormalization of position space massless Feynman amplitudes has been shown to yield associate homogeneous distributions. Their degree is determined by the degree of divergence while their order—the highest power of logarithm in the dilation anomaly—is given by the number of (sub)divergences. In the present paper we review these results and observe that (convergent) integration over internal vertices does not alter the total degree of (superficial) ultraviolet divergence. For a conformally invariant theory internal integration is also proven to preserve the order of associate homogeneity. The renormalized 4-point amplitudes in the φ4 theory (in four space-time dimensions) are written as (non-analytic) translation invariant functions of four complex variables with calculable conformal anomaly. Our conclusion concerning the (off-shell) infrared finiteness of the ultraviolet renormalized massless φ4 theory agrees with the old result of Lowenstein and Zimmermann [23].

Spectral functions with the density matrix renormalization group: Krylov-space approach for correction vectors

DOE Office of Scientific and Technical Information (OSTI.GOV)

None, None

Frequency-dependent correlations, such as the spectral function and the dynamical structure factor, help illustrate condensed matter experiments. Within the density matrix renormalization group (DMRG) framework, an accurate method for calculating spectral functions directly in frequency is the correction-vector method. The correction vector can be computed by solving a linear equation or by minimizing a functional. Our paper proposes an alternative to calculate the correction vector: to use the Krylov-space approach. This paper also studies the accuracy and performance of the Krylov-space approach, when applied to the Heisenberg, the t-J, and the Hubbard models. The cases we studied indicate that themore » Krylov-space approach can be more accurate and efficient than the conjugate gradient, and that the error of the former integrates best when a Krylov-space decomposition is also used for ground state DMRG.« less

Spectral functions with the density matrix renormalization group: Krylov-space approach for correction vectors

DOE PAGES

None, None

2016-11-21

Frequency-dependent correlations, such as the spectral function and the dynamical structure factor, help illustrate condensed matter experiments. Within the density matrix renormalization group (DMRG) framework, an accurate method for calculating spectral functions directly in frequency is the correction-vector method. The correction vector can be computed by solving a linear equation or by minimizing a functional. Our paper proposes an alternative to calculate the correction vector: to use the Krylov-space approach. This paper also studies the accuracy and performance of the Krylov-space approach, when applied to the Heisenberg, the t-J, and the Hubbard models. The cases we studied indicate that themore » Krylov-space approach can be more accurate and efficient than the conjugate gradient, and that the error of the former integrates best when a Krylov-space decomposition is also used for ground state DMRG.« less

Drude weight of the spin-(1)/(2) XXZ chain: Density matrix renormalization group versus exact diagonalization

NASA Astrophysics Data System (ADS)

Karrasch, C.; Hauschild, J.; Langer, S.; Heidrich-Meisner, F.

2013-06-01

We revisit the problem of the spin Drude weight D of the integrable spin-1/2 XXZ chain using two complementary approaches, exact diagonalization (ED) and the time-dependent density-matrix renormalization group (tDMRG). We pursue two main goals. First, we present extensive results for the temperature dependence of D. By exploiting time translation invariance within tDMRG, one can extract D for significantly lower temperatures than in previous tDMRG studies. Second, we discuss the numerical quality of the tDMRG data and elaborate on details of the finite-size scaling of the ED results, comparing calculations carried out in the canonical and grand-canonical ensembles. Furthermore, we analyze the behavior of the Drude weight as the point with SU(2)-symmetric exchange is approached and discuss the relative contribution of the Drude weight to the sum rule as a function of temperature.

Diagram reduction in problem of critical dynamics of ferromagnets: 4-loop approximation

NASA Astrophysics Data System (ADS)

Adzhemyan, L. Ts; Ivanova, E. V.; Kompaniets, M. V.; Vorobyeva, S. Ye

2018-04-01

Within the framework of the renormalization group approach to the models of critical dynamics, we propose a method for a considerable reduction of the number of integrals needed to calculate the critical exponents. With this method we perform a calculation of the critical exponent z of model A at 4-loop level, where our method allows one to reduce the number of integrals from 66 to 17. The way of constructing the integrand in a Feynman representation of such diagrams is discussed. Integrals were estimated numerically with a sector decomposition technique.

Threshold and flavor effects in the renormalization group equations of the MSSM: Dimensionless couplings

NASA Astrophysics Data System (ADS)

Box, Andrew D.; Tata, Xerxes

2008-03-01

In a theory with broken supersymmetry, gaugino couplings renormalize differently from gauge couplings, as do higgsino couplings from Higgs boson couplings. As a result, we expect the gauge (Higgs boson) couplings and the corresponding gaugino (higgsino) couplings to evolve to different values under renormalization group evolution. We reexamine the renormalization group equations (RGEs) for these couplings in the minimal supersymmetric standard model (MSSM). To include threshold effects, we calculate the β functions using a sequence of (nonsupersymmetric) effective theories with heavy particles decoupled at the scale of their mass. We find that the difference between the SM couplings and their SUSY cousins that is ignored in the literature may be larger than two-loop effects which are included, and further that renormalization group evolution induces a nontrivial flavor structure in gaugino interactions. We present here the coupled set of RGEs for these dimensionless gauge and Yukawa-type couplings. The RGEs for the dimensionful soft-supersymmetry-breaking parameters of the MSSM will be presented in a companion paper.

Collision group and renormalization of the Boltzmann collision integral.

PubMed

Saveliev, V L; Nanbu, K

2002-05-01

On the basis of a recently discovered collision group [V. L. Saveliev, in Rarefied Gas Dynamics: 22nd International Symposium, edited by T. J. Bartel and M. Gallis, AIP Conf. Proc. No. 585 (AIP, Melville, NY, 2001), p. 101], the Boltzmann collision integral is exactly rewritten in two parts. The first part describes the scattering of particles with small angles. In this part the infinity due to the infinite cross sections is extracted from the Boltzmann collision integral. Moreover, the Boltzmann collision integral is represented as a divergence of the flow in velocity space. Owing to this, the role of collisions in the kinetic equation can be interpreted in terms of the nonlocal friction force that depends on the distribution function.

Collision group and renormalization of the Boltzmann collision integral

NASA Astrophysics Data System (ADS)

Saveliev, V. L.; Nanbu, K.

2002-05-01

On the basis of a recently discovered collision group [V. L. Saveliev, in Rarefied Gas Dynamics: 22nd International Symposium, edited by T. J. Bartel and M. Gallis, AIP Conf. Proc. No. 585 (AIP, Melville, NY, 2001), p. 101], the Boltzmann collision integral is exactly rewritten in two parts. The first part describes the scattering of particles with small angles. In this part the infinity due to the infinite cross sections is extracted from the Boltzmann collision integral. Moreover, the Boltzmann collision integral is represented as a divergence of the flow in velocity space. Owing to this, the role of collisions in the kinetic equation can be interpreted in terms of the nonlocal friction force that depends on the distribution function.

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

PubMed

Mejía-Monasterio, Carlos; Muratore-Ginanneschi, Paolo

2012-07-01

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

Renormalization-group theory of plasma microturbulence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carati, D.; Chriaa, K.; Balescu, R.

1994-08-01

The dynamical renormalization-group methods are applied to the gyrokinetic equation describing drift-wave turbulence in plasmas. As in both magnetohydrodynamic and neutral turbulence, small-scale fluctuations appear to act as effective dissipative processes on large-scale phenomena. A linear renormalized gyrokinetic equation is derived. No artificial forcing is introduced into the equations and all the renormalized corrections are expressed in terms of the fluctuating electric potential. The link with the quasilinear limit and the direct interaction approximation is investigated. Simple analytical expressions for the anomalous transport coefficients are derived by using the linear renormalized gyrokinetic equation. Examples show that both quasilinear and Bohmmore » scalings can be recovered depending on the spectral amplitude of the electric potential fluctuations.« less

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

NASA Astrophysics Data System (ADS)

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

2016-07-01

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

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

PubMed

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

2016-07-07

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.

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 independence of Cosmological Attractors

NASA Astrophysics Data System (ADS)

Fumagalli, Jacopo

2017-06-01

The large class of inflationary models known as α- and ξ-attractors gives identical cosmological predictions at tree level (at leading order in inverse power of the number of efolds). Working with the renormalization group improved action, we show that these predictions are robust under quantum corrections. This means that for all the models considered the inflationary parameters (ns , r) are (nearly) independent on the Renormalization Group flow. The result follows once the field dependence of the renormalization scale, fixed by demanding the leading log correction to vanish, satisfies a quite generic condition. In Higgs inflation (which is a particular ξ-attractor) this is indeed the case; in the more general attractor models this is still ensured by the renormalizability of the theory in the effective field theory sense.

Influence of Fröhlich polaron coupling on renormalized electron bands in polar semiconductors: Results for zinc-blende GaN

NASA Astrophysics Data System (ADS)

Nery, Jean Paul; Allen, Philip B.

2016-09-01

We develop a simple method to study the zero-point and thermally renormalized electron energy ɛk n(T ) for k n the conduction band minimum or valence maximum in polar semiconductors. We use the adiabatic approximation, including an imaginary broadening parameter i δ to suppress noise in the density-functional integrations. The finite δ also eliminates the polar divergence which is an artifact of the adiabatic approximation. Nonadiabatic Fröhlich polaron methods then provide analytic expressions for the missing part of the contribution of the problematic optical phonon mode. We use this to correct the renormalization obtained from the adiabatic approximation. Test calculations are done for zinc-blende GaN for an 18 ×18 ×18 integration grid. The Fröhlich correction is of order -0.02 eV for the zero-point energy shift of the conduction band minimum, and +0.03 eV for the valence band maximum; the correction to renormalization of the 3.28 eV gap is -0.05 eV, a significant fraction of the total zero point renormalization of -0.15 eV.

Renormalization group flows and continual Lie algebras

NASA Astrophysics Data System (ADS)

Bakas, Ioannis

2003-08-01

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

Geometry of the theory space in the exact renormalization group formalism

NASA Astrophysics Data System (ADS)

Pagani, C.; Sonoda, H.

2018-01-01

We consider the theory space as a manifold whose coordinates are given by the couplings appearing in the Wilson action. We discuss how to introduce connections on this theory space. A particularly intriguing connection can be defined directly from the solution of the exact renormalization group (ERG) equation. We advocate a geometric viewpoint that lets us define straightforwardly physically relevant quantities invariant under the changes of a renormalization scheme.

Renormalization group contraction of tensor networks in three dimensions

NASA Astrophysics Data System (ADS)

García-Sáez, Artur; Latorre, José I.

2013-02-01

We present a new strategy for contracting tensor networks in arbitrary geometries. This method is designed to follow as strictly as possible the renormalization group philosophy, by first contracting tensors in an exact way and, then, performing a controlled truncation of the resulting tensor. We benchmark this approximation procedure in two dimensions against an exact contraction. We then apply the same idea to a three-dimensional quantum system. The underlying rational for emphasizing the exact coarse graining renormalization group step prior to truncation is related to monogamy of entanglement.

Effective-field renormalization-group method for Ising systems

NASA Astrophysics Data System (ADS)

Fittipaldi, I. P.; De Albuquerque, D. F.

1992-02-01

A new applicable effective-field renormalization-group (ERFG) scheme for computing critical properties of Ising spins systems is proposed and used to study the phase diagrams of a quenched bond-mixed spin Ising model on square and Kagomé lattices. The present EFRG approach yields results which improves substantially on those obtained from standard mean-field renormalization-group (MFRG) method. In particular, it is shown that the EFRG scheme correctly distinguishes the geometry of the lattice structure even when working with the smallest possible clusters, namely N'=1 and N=2.

Critical behavior of the quantum spin- {1}/{2} anisotropic Heisenberg model

NASA Astrophysics Data System (ADS)

Sousa, J. Ricardo de

A two-step renormalization group approach - a decimation followed by an effective field renormalization group (EFRG) - is proposed in this work to study the critical behavior of the quantum spin- {1}/{2} anisotropic Heisenberg model. The new method is illustrated by employing approximations in which clusters with one, two and three spins are used. The values of the critical parameter and critical exponent, in two- and three-dimensional lattices, for the Ising and isotropic Heisenberg limits are calculated and compared with other renormalization group approaches and exact (or series) results.

An extended approach for computing the critical properties in the two-and three-dimensional lattices within the effective-field renormalization group method

NASA Astrophysics Data System (ADS)

de Albuquerque, Douglas F.; Santos-Silva, Edimilson; Moreno, N. O.

2009-10-01

In this letter we employing the effective-field renormalization group (EFRG) to study the Ising model with nearest neighbors to obtain the reduced critical temperature and exponents ν for bi- and three-dimensional lattices by increasing cluster scheme by extending recent works. The technique follows up the same strategy of the mean field renormalization group (MFRG) by introducing an alternative way for constructing classical effective-field equations of state takes on rigorous Ising spin identities.

Crossing Boundaries: Nativity, Ethnicity, and Mate Selection

PubMed Central

Qian, Zhenchao; Glick, Jennifer E.; Baston, Christie

2016-01-01

The influx of immigrants has increased diversity among ethnic minorities and indicates that they may take multiple integration paths in American society. Previous research on ethnic integration often focuses on panethnic differences and few have explored ethnic diversity within a racial or panethnic context. Using 2000 U.S. census data for Puerto Rican, Mexican, Chinese, and Filipino origin individuals, we examine differences in marriage and cohabitation with whites, with other minorities, within a panethnic group, and within an ethnic group by nativity status. Ethnic endogamy is strong and, to a less extent, so is panethnic endogamy. Yet, marital or cohabiting unions with whites remain an important path of integration but differ significantly by ethnicity, nativity, age at arrival, and educational attainment. Meanwhile, ethnic differences in marriage and cohabitation with other racial or ethnic minorities are strong. Our analysis supports that unions with whites remain a major path of integration, but other paths of integration also become viable options for all ethnic groups. PMID:22350840

Renormalization of concurrence: The application of the quantum renormalization group to quantum-information systems

NASA Astrophysics Data System (ADS)

Kargarian, M.; Jafari, R.; Langari, A.

2007-12-01

We have combined the idea of renormalization group and quantum-information theory. We have shown how the entanglement or concurrence evolve as the size of the system becomes large, i.e., the finite size scaling is obtained. Moreover, we introduce how the renormalization-group approach can be implemented to obtain the quantum-information properties of a many-body system. We have obtained the concurrence as a measure of entanglement, its derivatives and their scaling behavior versus the size of system for the one-dimensional Ising model in transverse field. We have found that the derivative of concurrence between two blocks each containing half of the system size diverges at the critical point with the exponent, which is directly associated with the divergence of the correlation length.

Surface hopping with a manifold of electronic states. II. Application to the many-body Anderson-Holstein model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dou, Wenjie; Subotnik, Joseph E.; Nitzan, Abraham

We investigate a simple surface hopping (SH) approach for modeling a single impurity level coupled to a single phonon and an electronic (metal) bath (i.e., the Anderson-Holstein model). The phonon degree of freedom is treated classically with motion along–and hops between–diabatic potential energy surfaces. The hopping rate is determined by the dynamics of the electronic bath (which are treated implicitly). For the case of one electronic bath, in the limit of small coupling to the bath, SH recovers phonon relaxation to thermal equilibrium and yields the correct impurity electron population (as compared with numerical renormalization group). For the case ofmore » out of equilibrium dynamics, SH current-voltage (I-V) curve is compared with the quantum master equation (QME) over a range of parameters, spanning the quantum region to the classical region. In the limit of large temperature, SH and QME agree. Furthermore, we can show that, in the limit of low temperature, the QME agrees with real-time path integral calculations. As such, the simple procedure described here should be useful in many other contexts.« less

Scaling theory of tunneling diffusion of a heavy particle interacting with phonons

NASA Astrophysics Data System (ADS)

Itai, K.

1988-05-01

The author discusses motion of a heavy particle in a d-dimensional lattice interacting with phonons by different couplings. The models discussed are characterized by the dimension (d) and the set of two indices (λ,ν) which specify the momentum dependence of the dispersion of phonon energy (ω~kν) and of the particle-phonon coupling (~kλ). Scaling equations are derived by eliminating the short-time behavior in a renormalization-group scheme using Feynman's path-integral method, and the technique developed by Anderson, Yuval, and Hamann for the Kondo problem. The scaling equations show that the particle is localized in the strict sense when (2λ+d+2)/ν<2 and is not localized when (2λ+d+2)/ν>2. In the marginal case, i.e., (2λ+d+2)/ν=2, localization occurs for couplings larger than a critical value. This marginal case shows Ohmic dissipation and is a close analogy to the Caldeira-Leggett model for macroscopic quantum tunneling and the hopping models of Schmid's type. For large-enough (2λ+d+2)/ν, the particle is considered practically localized, but the origin of the localization is quite different from that for (2λ+d+2)/ν<=2. .AE

The quantum-field renormalization group in the problem of a growing phase boundary

DOE Office of Scientific and Technical Information (OSTI.GOV)

Antonov, N.V.; Vasil`ev, A.N.

1995-09-01

Within the quantum-field renormalization-group approach we examine the stochastic equation discussed by S.I. Pavlik in describing a randomly growing phase boundary. We show that, in contrast to Pavlik`s assertion, the model is not multiplicatively renormalizable and that its consistent renormalization-group analysis requires introducing an infinite number of counterterms and the respective coupling constants ({open_quotes}charge{close_quotes}). An explicit calculation in the one-loop approximation shows that a two-dimensional surface of renormalization-group points exits in the infinite-dimensional charge space. If the surface contains an infrared stability region, the problem allows for scaling with the nonuniversal critical dimensionalities of the height of the phase boundarymore » and time, {delta}{sub h} and {delta}{sub t}, which satisfy the exact relationship 2 {delta}{sub h}= {delta}{sub t} + d, where d is the dimensionality of the phase boundary. 23 refs., 1 tab.« less

Renormalization-group constraints on Yukawa alignment in multi-Higgs-doublet models

NASA Astrophysics Data System (ADS)

Ferreira, P. M.; Lavoura, L.; Silva, João P.

2010-05-01

We write down the renormalization-group equations for the Yukawa-coupling matrices in a general multi-Higgs-doublet model. We then assume that the matrices of the Yukawa couplings of the various Higgs doublets to right-handed fermions of fixed quantum numbers are all proportional to each other. We demonstrate that, in the case of the two-Higgs-doublet model, this proportionality is preserved by the renormalization-group running only in the cases of the standard type-I, II, X, and Y models. We furthermore show that a similar result holds even when there are more than two Higgs doublets: the Yukawa-coupling matrices to fermions of a given electric charge remain proportional under the renormalization-group running if and only if there is a basis for the Higgs doublets in which all the fermions of a given electric charge couple to only one Higgs doublet.

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.

Dimensional regularization in position space and a Forest Formula for Epstein-Glaser renormalization

NASA Astrophysics Data System (ADS)

Dütsch, Michael; Fredenhagen, Klaus; Keller, Kai Johannes; Rejzner, Katarzyna

2014-12-01

We reformulate dimensional regularization as a regularization method in position space and show that it can be used to give a closed expression for the renormalized time-ordered products as solutions to the induction scheme of Epstein-Glaser. This closed expression, which we call the Epstein-Glaser Forest Formula, is analogous to Zimmermann's Forest Formula for BPH renormalization. For scalar fields, the resulting renormalization method is always applicable, we compute several examples. We also analyze the Hopf algebraic aspects of the combinatorics. Our starting point is the Main Theorem of Renormalization of Stora and Popineau and the arising renormalization group as originally defined by Stückelberg and Petermann.

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.

Renormalization group equations and the Lifshitz point in noncommutative Landau-Ginsburg theory

NASA Astrophysics Data System (ADS)

Chen, Guang-Hong; Wu, Yong-Shi

2002-02-01

A one-loop renormalization group (RG) analysis is performed for noncommutative Landau-Ginsburg theory in an arbitrary dimension. We adopt a modern version of the Wilsonian RG approach, in which a shell integration in momentum space bypasses the potential IR singularities due to UV-IR mixing. The momentum-dependent trigonometric factors in interaction vertices, characteristic of noncommutative geometry, are marginal under RG transformations, and their marginality is preserved at one loop. A negative Θ-dependent anomalous dimension is discovered as a novel effect of the UV-IR mixing. We also found a noncommutative Wilson-Fisher (NCWF) fixed point in less than four dimensions. At large noncommutativity, a momentum space instability is induced by quantum fluctuations, and a consequential first-order phase transition is identified together with a Lifshitz point in the phase diagram. In the vicinity of the Lifshitz point, we introduce two critical exponents νm and βk, whose values are determined to be 1/4 and 1/2, respectively, at mean-field level.

Multiscale unfolding of real networks by geometric renormalization

NASA Astrophysics Data System (ADS)

García-Pérez, Guillermo; Boguñá, Marián; Serrano, M. Ángeles

2018-06-01

Symmetries in physical theories denote invariance under some transformation, such as self-similarity under a change of scale. The renormalization group provides a powerful framework to study these symmetries, leading to a better understanding of the universal properties of phase transitions. However, the small-world property of complex networks complicates application of the renormalization group by introducing correlations between coexisting scales. Here, we provide a framework for the investigation of complex networks at different resolutions. The approach is based on geometric representations, which have been shown to sustain network navigability and to reveal the mechanisms that govern network structure and evolution. We define a geometric renormalization group for networks by embedding them into an underlying hidden metric space. We find that real scale-free networks show geometric scaling under this renormalization group transformation. We unfold the networks in a self-similar multilayer shell that distinguishes the coexisting scales and their interactions. This in turn offers a basis for exploring critical phenomena and universality in complex networks. It also affords us immediate practical applications, including high-fidelity smaller-scale replicas of large networks and a multiscale navigation protocol in hyperbolic space, which betters those on single layers.

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

NASA Technical Reports Server (NTRS)

Zhou, YE; Vahala, George

1993-01-01

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

Renormalization group, normal form theory and the Ising model

NASA Astrophysics Data System (ADS)

Raju, Archishman; Hayden, Lorien; Clement, Colin; Liarte, Danilo; Sethna, James

The results of the renormalization group are commonly advertised as the existence of power law singularities at critical points. Logarithmic and exponential corrections are seen as special cases and dealt with on a case-by-case basis. We propose to systematize computing the singularities in the renormalization group using perturbative normal form theory. This gives us a way to classify all such singularities in a unified framework and to generate a systematic machinery to do scaling collapses. We show that this procedure leads to some new results even in classic cases like the Ising model and has general applicability.

Hypercuboidal renormalization in spin foam quantum gravity

NASA Astrophysics Data System (ADS)

Bahr, Benjamin; Steinhaus, Sebastian

2017-06-01

In this article, we apply background-independent renormalization group methods to spin foam quantum gravity. It is aimed at extending and elucidating the analysis of a companion paper, in which the existence of a fixed point in the truncated renormalization group flow for the model was reported. Here, we repeat the analysis with various modifications and find that both qualitative and quantitative features of the fixed point are robust in this setting. We also go into details about the various approximation schemes employed in the analysis.

The { β}-expansion formalism in perturbative QCD and its extension

NASA Astrophysics Data System (ADS)

Kataev, A. L.; Mikhailov, S. V.

2016-11-01

We discuss the { β}-expansion for renormalization group invariant quantities tracing this expansion to the different contractions of the corresponding incomplete BPHZ R-operation. All of the coupling renormalizations, which follow from these contractions, should be taken into account for the { β}-expansion. We illustrate this feature considering the nonsinglet Adler function D NS in the third order of perturbation. We propose a generalization of the { β}-expansion for the renormalization group covariant quantities — the { β, γ}-expansion.

Variational Approach to Monte Carlo Renormalization Group

NASA Astrophysics Data System (ADS)

Wu, Yantao; Car, Roberto

2017-12-01

We present a Monte Carlo method for computing the renormalized coupling constants and the critical exponents within renormalization theory. The scheme, which derives from a variational principle, overcomes critical slowing down, by means of a bias potential that renders the coarse grained variables uncorrelated. The two-dimensional Ising model is used to illustrate the method.

Tunneling in quantum cosmology and holographic SYM theory

NASA Astrophysics Data System (ADS)

Ghoroku, Kazuo; Nakano, Yoshimasa; Tachibana, Motoi; Toyoda, Fumihiko

2018-03-01

We study the time evolution of the early Universe, which is developed by a cosmological constant Λ4 and supersymmetric Yang-Mills (SYM) fields in the Friedmann-Robertson-Walker space-time. The renormalized vacuum expectation value of the energy-momentum tensor of the SYM theory is obtained in a holographic way. It includes a radiation of the SYM field, parametrized as C . The evolution is controlled by this radiation C and the cosmological constant Λ4. For positive Λ4, an inflationary solution is obtained at late time. When C is added, the quantum mechanical situation at early time is fairly changed. Here we perform the early time analysis in terms of two different approaches, (i) the Wheeler-DeWitt equation and (ii) Lorentzian path integral with the Picard-Lefschetz method by introducing an effective action. The results of two methods are compared.

Entanglement renormalization and topological order.

PubMed

Aguado, Miguel; Vidal, Guifré

2008-02-22

The multiscale entanglement renormalization ansatz (MERA) is argued to provide a natural description for topological states of matter. The case of Kitaev's toric code is analyzed in detail and shown to possess a remarkably simple MERA description leading to distillation of the topological degrees of freedom at the top of the tensor network. Kitaev states on an infinite lattice are also shown to be a fixed point of the renormalization group flow associated with entanglement renormalization. All of these results generalize to arbitrary quantum double models.

Functional renormalization group for the U (1 )-T56 tensorial group field theory with closure constraint

NASA Astrophysics Data System (ADS)

Lahoche, Vincent; Ousmane Samary, Dine

2017-02-01

This paper is focused on the functional renormalization group applied to the T56 tensor model on the Abelian group U (1 ) with closure constraint. For the first time, we derive the flow equations for the couplings and mass parameters in a suitable truncation around the marginal interactions with respect to the perturbative power counting. For the second time, we study the behavior around the Gaussian fixed point, and show that the theory is nonasymptotically free. Finally, we discuss the UV completion of the theory. We show the existence of several nontrivial fixed points, study the behavior of the renormalization group flow around them, and point out evidence in favor of an asymptotically safe theory.

Exact renormalization group equations: an introductory review

NASA Astrophysics Data System (ADS)

Bagnuls, C.; Bervillier, C.

2001-07-01

We critically review the use of the exact renormalization group equations (ERGE) in the framework of the scalar theory. We lay emphasis on the existence of different versions of the ERGE and on an approximation method to solve it: the derivative expansion. The leading order of this expansion appears as an excellent textbook example to underline the nonperturbative features of the Wilson renormalization group theory. We limit ourselves to the consideration of the scalar field (this is why it is an introductory review) but the reader will find (at the end of the review) a set of references to existing studies on more complex systems.

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

DOE PAGES

Bi, Huan -Yu; Wu, Xing -Gang; Ma, Yang; ...

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 satisfymore » 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.« less

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: Personal computer. Operating system: Tested on Fedora 15, MacOS 10 and 11, Ubuntu 12. Classification: 11.1. External routines: SymPy, PyYAML, NumPy, IPython, SciPy Nature of problem: Deriving the renormalization group equations for a general quantum field theory. Solution method: Group theory, tensor algebra Running time: Tens of seconds per model (one-loop), tens of minutes (two-loop)

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hedegård, Erik Donovan, E-mail: erik.hedegard@phys.chem.ethz.ch; Knecht, Stefan; Reiher, Markus, E-mail: markus.reiher@phys.chem.ethz.ch

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.

Strongly correlated fermions after a quantum quench.

PubMed

Manmana, S R; Wessel, S; Noack, R M; Muramatsu, A

2007-05-25

Using the adaptive time-dependent density-matrix renormalization group method, we study the time evolution of strongly correlated spinless fermions on a one-dimensional lattice after a sudden change of the interaction strength. For certain parameter values, two different initial states (e.g., metallic and insulating) lead to observables which become indistinguishable after relaxation. We find that the resulting quasistationary state is nonthermal. This result holds for both integrable and nonintegrable variants of the system.

The Holographic F Theorem

NASA Astrophysics Data System (ADS)

Taylor, Marika; Woodhead, William

2017-12-01

The F theorem states that, for a unitary three dimensional quantum field theory, the F quantity defined in terms of the partition function on a three sphere is positive, stationary at fixed point and decreases monotonically along a renormalization group flow. We construct holographic renormalization group flows corresponding to relevant deformations of three-dimensional conformal field theories on spheres, working to quadratic order in the source. For these renormalization group flows, the F quantity at the IR fixed point is always less than F at the UV fixed point, but F increases along the RG flow for deformations by operators of dimension between 3/2 and 5/2. Therefore the strongest version of the F theorem is in general violated.

Nonperturbative renormalization-group approach preserving the momentum dependence of correlation functions

NASA Astrophysics Data System (ADS)

Rose, F.; Dupuis, N.

2018-05-01

We present an approximation scheme of the nonperturbative renormalization group that preserves the momentum dependence of correlation functions. This approximation scheme can be seen as a simple improvement of the local potential approximation (LPA) where the derivative terms in the effective action are promoted to arbitrary momentum-dependent functions. As in the LPA, the only field dependence comes from the effective potential, which allows us to solve the renormalization-group equations at a relatively modest numerical cost (as compared, e.g., to the Blaizot-Mendéz-Galain-Wschebor approximation scheme). As an application we consider the two-dimensional quantum O(N ) model at zero temperature. We discuss not only the two-point correlation function but also higher-order correlation functions such as the scalar susceptibility (which allows for an investigation of the "Higgs" amplitude mode) and the conductivity. In particular, we show how, using Padé approximants to perform the analytic continuation i ωn→ω +i 0+ of imaginary frequency correlation functions χ (i ωn) computed numerically from the renormalization-group equations, one can obtain spectral functions in the real-frequency domain.

Renormalization group fixed points of foliated gravity-matter systems

NASA Astrophysics Data System (ADS)

Biemans, Jorn; Platania, Alessia; Saueressig, Frank

2017-05-01

We employ the Arnowitt-Deser-Misner formalism to study the renormalization group flow of gravity minimally coupled to an arbitrary number of scalar, vector, and Dirac fields. The decomposition of the gravitational degrees of freedom into a lapse function, shift vector, and spatial metric equips spacetime with a preferred (Euclidean) "time"- direction. In this work, we provide a detailed derivation of the renormalization group flow of Newton's constant and the cosmological constant on a flat Friedmann-Robertson-Walker background. Adding matter fields, it is shown that their contribution to the flow is the same as in the covariant formulation and can be captured by two parameters d g d λ . We classify the resulting fixed point structure as a function of these parameters finding that the existence of non-Gaussian renormalization group fixed points is rather generic. In particular the matter content of the standard model and its most common extensions gives rise to one non-Gaussian fixed point with real critical exponents suitable for Asymptotic Safety. Moreover, we find non-Gaussian fixed points for any number of scalar matter fields, making the scenario attractive for cosmological model building.

Integrability in heavy quark effective theory

NASA Astrophysics Data System (ADS)

Braun, Vladimir M.; Ji, Yao; Manashov, Alexander N.

2018-06-01

It was found that renormalization group equations in the heavy-quark effective theory (HQET) for the operators involving one effective heavy quark and light degrees of freedom are completely integrable in some cases and are related to spin chain models with the Hamiltonian commuting with the nondiagonal entry C( u) of the monodromy matrix. In this work we provide a more complete mathematical treatment of such spin chains in the QISM framework. We also discuss the relation of integrable models that appear in the HQET context with the large-spin limit of integrable models in QCD with light quarks. We find that the conserved charges and the "ground state" wave functions in HQET models can be obtained from the light-quark counterparts in a certain scaling limit.

Controlling sign problems in spin models using tensor renormalization

NASA Astrophysics Data System (ADS)

Denbleyker, Alan; Liu, Yuzhi; Meurice, Y.; Qin, M. P.; Xiang, T.; Xie, Z. Y.; Yu, J. F.; Zou, Haiyuan

2014-01-01

We consider the sign problem for classical spin models at complex β =1/g02 on L ×L lattices. We show that the tensor renormalization group method allows reliable calculations for larger Imβ than the reweighting Monte Carlo method. For the Ising model with complex β we compare our results with the exact Onsager-Kaufman solution at finite volume. The Fisher zeros can be determined precisely with the tensor renormalization group method. We check the convergence of the tensor renormalization group method for the O(2) model on L×L lattices when the number of states Ds increases. We show that the finite size scaling of the calculated Fisher zeros agrees very well with the Kosterlitz-Thouless transition assumption and predict the locations for larger volume. The location of these zeros agree with Monte Carlo reweighting calculation for small volume. The application of the method for the O(2) model with a chemical potential is briefly discussed.

Meaning of the field dependence of the renormalization scale in Higgs inflation

NASA Astrophysics Data System (ADS)

Hamada, Yuta; Kawai, Hikaru; Nakanishi, Yukari; Oda, Kin-ya

2017-05-01

We consider the prescription dependence of the Higgs effective potential under the presence of general nonminimal couplings. We evaluate the fermion loop correction to the effective action in a simplified Higgs-Yukawa model whose path integral measure takes simple form either in the Jordan or Einstein frame. The resultant effective action becomes identical in both cases when we properly take into account the quartically divergent term coming from the change of measure. Working in the counterterm formalism, we clarify that the difference between the prescriptions I and II comes from the counter term to cancel the logarithmic divergence. This difference can be absorbed into the choice of tree-level potential from the infinitely many possibilities, including all the higher-dimensional terms. We also present another mechanism to obtain a flat potential by freezing the running of the effective quartic coupling for large field values, using the nonminimal coupling in the gauge kinetic function.

Turbulent transport of a passive-scalar field by using a renormalization-group method

NASA Technical Reports Server (NTRS)

Hossain, Murshed

1992-01-01

A passive-scalar field is considered to evolve under the influence of a turbulent fluid governed by the Navier-Stokes equation. Turbulent-transport coefficients are calculated by small-scale elimination using a renormalization-group method. Turbulent processes couple both the viscosity and the diffusivity. In the absence of any correlation between the passive-scalar fluctuations and any component of the fluid velocity, the renormalized diffusivity is essentially the same as if the fluid velocity were frozen, although the renormalized equation does contain higher-order nonlinear terms involving viscosity. This arises due to the nonlinear interaction of the velocity with itself. In the presence of a finite correlation, the turbulent diffusivity becomes coupled with both the velocity field and the viscosity. There is then a dependence of the turbulent decay of the passive scalar on the turbulent Prandtl number.

Unifying time evolution and optimization with matrix product states

NASA Astrophysics Data System (ADS)

Haegeman, Jutho; Lubich, Christian; Oseledets, Ivan; Vandereycken, Bart; Verstraete, Frank

2016-10-01

We show that the time-dependent variational principle provides a unifying framework for time-evolution methods and optimization methods in the context of matrix product states. In particular, we introduce a new integration scheme for studying time evolution, which can cope with arbitrary Hamiltonians, including those with long-range interactions. Rather than a Suzuki-Trotter splitting of the Hamiltonian, which is the idea behind the adaptive time-dependent density matrix renormalization group method or time-evolving block decimation, our method is based on splitting the projector onto the matrix product state tangent space as it appears in the Dirac-Frenkel time-dependent variational principle. We discuss how the resulting algorithm resembles the density matrix renormalization group (DMRG) algorithm for finding ground states so closely that it can be implemented by changing just a few lines of code and it inherits the same stability and efficiency. In particular, our method is compatible with any Hamiltonian for which ground-state DMRG can be implemented efficiently. In fact, DMRG is obtained as a special case of our scheme for imaginary time evolution with infinite time step.

Glueball spectra from a matrix model of pure Yang-Mills theory

NASA Astrophysics Data System (ADS)

Acharyya, Nirmalendu; Balachandran, A. P.; Pandey, Mahul; Sanyal, Sambuddha; Vaidya, Sachindeo

2018-05-01

We present variational estimates for the low-lying energies of a simple matrix model that approximates SU(3) Yang-Mills theory on a three-sphere of radius R. By fixing the ground state energy, we obtain the (integrated) renormalization group (RG) equation for the Yang-Mills coupling g as a function of R. This RG equation allows to estimate the mass of other glueball states, which we find to be in excellent agreement with lattice simulations.

Group-theoretical model of developed turbulence and renormalization of the Navier-Stokes equation.

PubMed

Saveliev, V L; Gorokhovski, M A

2005-07-01

On the basis of the Euler equation and its symmetry properties, this paper proposes a model of stationary homogeneous developed turbulence. A regularized averaging formula for the product of two fields is obtained. An equation for the averaged turbulent velocity field is derived from the Navier-Stokes equation by renormalization-group transformation.

Functional renormalization group and Kohn-Sham scheme in density functional theory

NASA Astrophysics Data System (ADS)

Liang, Haozhao; Niu, Yifei; Hatsuda, Tetsuo

2018-04-01

Deriving accurate energy density functional is one of the central problems in condensed matter physics, nuclear physics, and quantum chemistry. We propose a novel method to deduce the energy density functional by combining the idea of the functional renormalization group and the Kohn-Sham scheme in density functional theory. The key idea is to solve the renormalization group flow for the effective action decomposed into the mean-field part and the correlation part. Also, we propose a simple practical method to quantify the uncertainty associated with the truncation of the correlation part. By taking the φ4 theory in zero dimension as a benchmark, we demonstrate that our method shows extremely fast convergence to the exact result even for the highly strong coupling regime.

Renormalization group flow of the Higgs potential

NASA Astrophysics Data System (ADS)

Gies, Holger; Sondenheimer, René

2018-01-01

We summarize results for local and global properties of the effective potential for the Higgs boson obtained from the functional renormalization group, which allows one to describe the effective potential as a function of both scalar field amplitude and renormalization group scale. This sheds light onto the limitations of standard estimates which rely on the identification of the two scales and helps in clarifying the origin of a possible property of meta-stability of the Higgs potential. We demonstrate that the inclusion of higher-dimensional operators induced by an underlying theory at a high scale (GUT or Planck scale) can relax the conventional lower bound on the Higgs mass derived from the criterion of absolute stability. This article is part of the Theo Murphy meeting issue `Higgs cosmology'.

Path-integral invariants in abelian Chern-Simons theory

NASA Astrophysics Data System (ADS)

Guadagnini, E.; Thuillier, F.

2014-05-01

We consider the U(1) Chern-Simons gauge theory defined in a general closed oriented 3-manifold M; the functional integration is used to compute the normalized partition function and the expectation values of the link holonomies. The non-perturbative path-integral is defined in the space of the gauge orbits of the connections which belong to the various inequivalent U(1) principal bundles over M; the different sectors of configuration space are labelled by the elements of the first homology group of M and are characterized by appropriate background connections. The gauge orbits of flat connections, whose classification is also based on the homology group, control the non-perturbative contributions to the mean values. The functional integration is carried out in any 3-manifold M, and the corresponding path-integral invariants turn out to be strictly related with the abelian Reshetikhin-Turaev surgery invariants.

Medial temporal lobe roles in human path integration.

PubMed

Yamamoto, Naohide; Philbeck, John W; Woods, Adam J; Gajewski, Daniel A; Arthur, Joeanna C; Potolicchio, Samuel J; Levy, Lucien; Caputy, Anthony J

2014-01-01

Path integration is a process in which observers derive their location by integrating self-motion signals along their locomotion trajectory. Although the medial temporal lobe (MTL) is thought to take part in path integration, the scope of its role for path integration remains unclear. To address this issue, we administered a variety of tasks involving path integration and other related processes to a group of neurosurgical patients whose MTL was unilaterally resected as therapy for epilepsy. These patients were unimpaired relative to neurologically intact controls in many tasks that required integration of various kinds of sensory self-motion information. However, the same patients (especially those who had lesions in the right hemisphere) walked farther than the controls when attempting to walk without vision to a previewed target. Importantly, this task was unique in our test battery in that it allowed participants to form a mental representation of the target location and anticipate their upcoming walking trajectory before they began moving. Thus, these results put forth a new idea that the role of MTL structures for human path integration may stem from their participation in predicting the consequences of one's locomotor actions. The strengths of this new theoretical viewpoint are discussed.

Medial Temporal Lobe Roles in Human Path Integration

PubMed Central

Yamamoto, Naohide; Philbeck, John W.; Woods, Adam J.; Gajewski, Daniel A.; Arthur, Joeanna C.; Potolicchio, Samuel J.; Levy, Lucien; Caputy, Anthony J.

2014-01-01

Path integration is a process in which observers derive their location by integrating self-motion signals along their locomotion trajectory. Although the medial temporal lobe (MTL) is thought to take part in path integration, the scope of its role for path integration remains unclear. To address this issue, we administered a variety of tasks involving path integration and other related processes to a group of neurosurgical patients whose MTL was unilaterally resected as therapy for epilepsy. These patients were unimpaired relative to neurologically intact controls in many tasks that required integration of various kinds of sensory self-motion information. However, the same patients (especially those who had lesions in the right hemisphere) walked farther than the controls when attempting to walk without vision to a previewed target. Importantly, this task was unique in our test battery in that it allowed participants to form a mental representation of the target location and anticipate their upcoming walking trajectory before they began moving. Thus, these results put forth a new idea that the role of MTL structures for human path integration may stem from their participation in predicting the consequences of one's locomotor actions. The strengths of this new theoretical viewpoint are discussed. PMID:24802000

The renormalization group and the implicit function theorem for amplitude equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kirkinis, Eleftherios

2008-07-15

This article lays down the foundations of the renormalization group (RG) approach for differential equations characterized by multiple scales. The renormalization of constants through an elimination process and the subsequent derivation of the amplitude equation [Chen et al., Phys. Rev. E 54, 376 (1996)] are given a rigorous but not abstract mathematical form whose justification is based on the implicit function theorem. Developing the theoretical framework that underlies the RG approach leads to a systematization of the renormalization process and to the derivation of explicit closed-form expressions for the amplitude equations that can be carried out with symbolic computation formore » both linear and nonlinear scalar differential equations and first order systems but independently of their particular forms. Certain nonlinear singular perturbation problems are considered that illustrate the formalism and recover well-known results from the literature as special cases.« less

Renormalization of QCD in the interpolating momentum subtraction scheme at three loops

NASA Astrophysics Data System (ADS)

Gracey, J. A.; Simms, R. M.

2018-04-01

We introduce a more general set of kinematic renormalization schemes than the original momentum subtraction schemes of Celmaster and Gonsalves. These new schemes will depend on a parameter ω , which tags the external momentum of one of the legs of the three-point vertex functions in QCD. In each of the three new schemes, we renormalize QCD in the Landau and maximal Abelian gauges and establish the three-loop renormalization group functions in each gauge. For an application, we evaluate two critical exponents at the Banks-Zaks fixed point and demonstrate that their values appear to be numerically scheme independent in a subrange of the conformal window.

Renormalization group analysis of dipolar Heisenberg model on square lattice

NASA Astrophysics Data System (ADS)

Keleş, Ahmet; Zhao, Erhai

2018-06-01

We present a detailed functional renormalization group analysis of spin-1/2 dipolar Heisenberg model on square lattice. This model is similar to the well-known J1-J2 model and describes the pseudospin degrees of freedom of polar molecules confined in deep optical lattice with long-range anisotropic dipole-dipole interactions. Previous study of this model based on tensor network ansatz indicates a paramagnetic ground state for certain dipole tilting angles which can be tuned in experiments to control the exchange couplings. The tensor ansatz formulated on a small cluster unit cell is inadequate to describe the spiral order, and therefore the phase diagram at high azimuthal tilting angles remains undetermined. Here, we obtain the full phase diagram of the model from numerical pseudofermion functional renormalization group calculations. We show that an extended quantum paramagnetic phase is realized between the Néel and stripe/spiral phases. In this region, the spin susceptibility flows smoothly down to the lowest numerical renormalization group scales with no sign of divergence or breakdown of the flow, in sharp contrast to the flow towards the long-range-ordered phases. Our results provide further evidence that the dipolar Heisenberg model is a fertile ground for quantum spin liquids.

Renormalization group naturalness of GUT Higgs potentials

NASA Astrophysics Data System (ADS)

Allanach, B. C.; Amelino-Camelia, G.; Philipsen, O.; Pisanti, O.; Rosa, L.

1999-01-01

We analyze the symmetry-breaking patterns of grand unified theories from the point of view of a recently proposed criterion of renormalization-group naturalness. We perform the analysis on simple non-SUSY SU(5) and SO(10) and SUSY SU(5) GUTs. We find that the naturalness criterion can favor spontaneous symmetry breaking in the direction of the smallest of the maximal little groups. Some differences between theories with and without supersymmetry are also emphasized.

Type 0 open string amplitudes and the tensionless limit

NASA Astrophysics Data System (ADS)

Rojas, Francisco

2014-12-01

The sum over planar multiloop diagrams in the NS + sector of type 0 open strings in flat spacetime has been proposed by Thorn as a candidate to resolve nonperturbative issues of gauge theories in the large N limit. With S U (N ) Chan-Paton factors, the sum over planar open string multiloop diagrams describes the 't Hooft limit N →∞ with N gs2 held fixed. By including only planar diagrams in the sum the usual mechanism for the cancellation of loop divergences (which occurs, for example, among the planar and Möbius strip diagrams by choosing a specific gauge group) is not available and a renormalization procedure is needed. In this article the renormalization is achieved by suspending total momentum conservation by an amount p ≡∑ i n ki≠0 at the level of the integrands in the integrals over the moduli and analytically continuing them to p =0 at the very end. This procedure has been successfully tested for the 2 and 3 gluon planar loop amplitudes by Thorn. Gauge invariance is respected and the correct running of the coupling in the limiting gauge field theory was also correctly obtained. In this article we extend those results in two directions. First, we generalize the renormalization method to an arbitrary n -gluon planar loop amplitude giving full details for the 4-point case. One of our main results is to provide a fully renormalized amplitude which is free of both UV and the usual spurious divergences leaving only the physical singularities in it. Second, using the complete renormalized amplitude, we extract the high-energy scattering regime at fixed angle (tensionless limit). Apart from obtaining the usual exponential falloff at high energies, we compute the full dependence on the scattering angle which shows the existence of a smooth connection between the Regge and hard scattering regimes.

Origin of the enhancement of tunneling probability in the nearly integrable system

NASA Astrophysics Data System (ADS)

Hanada, Yasutaka; Shudo, Akira; Ikeda, Kensuke S.

2015-04-01

The enhancement of tunneling probability in the nearly integrable system is closely examined, focusing on tunneling splittings plotted as a function of the inverse of the Planck's constant. On the basis of the analysis using the absorber which efficiently suppresses the coupling, creating spikes in the plot, we found that the splitting curve should be viewed as the staircase-shaped skeleton accompanied by spikes. We further introduce renormalized integrable Hamiltonians and explore the origin of such a staircase structure by investigating the nature of eigenfunctions closely. It is found that the origin of the staircase structure could trace back to the anomalous structure in tunneling tail which manifests itself in the representation using renormalized action bases. This also explains the reason why the staircase does not appear in the completely integrable system.

Covariant Derivatives and the Renormalization Group Equation

NASA Astrophysics Data System (ADS)

Dolan, Brian P.

The renormalization group equation for N-point correlation functions can be interpreted in a geometrical manner as an equation for Lie transport of amplitudes in the space of couplings. The vector field generating the diffeomorphism has components given by the β functions of the theory. It is argued that this simple picture requires modification whenever any one of the points at which the amplitude is evaluated becomes close to any other. This modification necessitates the introduction of a connection on the space of couplings and new terms appear in the renormalization group equation involving covariant derivatives of the β function and the curvature associated with the connection. It is shown how the connection is related to the operator product expansion coefficients, but there remains an arbitrariness in its definition.

Renormalization group flow of the Higgs potential.

PubMed

Gies, Holger; Sondenheimer, René

2018-03-06

We summarize results for local and global properties of the effective potential for the Higgs boson obtained from the functional renormalization group, which allows one to describe the effective potential as a function of both scalar field amplitude and renormalization group scale. This sheds light onto the limitations of standard estimates which rely on the identification of the two scales and helps in clarifying the origin of a possible property of meta-stability of the Higgs potential. We demonstrate that the inclusion of higher-dimensional operators induced by an underlying theory at a high scale (GUT or Planck scale) can relax the conventional lower bound on the Higgs mass derived from the criterion of absolute stability.This article is part of the Theo Murphy meeting issue 'Higgs cosmology'. © 2018 The Author(s).

Dual fermionic variables and renormalization group approach to junctions of strongly interacting quantum wires

NASA Astrophysics Data System (ADS)

Giuliano, Domenico; Nava, Andrea

2015-09-01

Making a combined use of bosonization and fermionization techniques, we build nonlocal transformations between dual fermion operators, describing junctions of strongly interacting spinful one-dimensional quantum wires. Our approach allows for trading strongly interacting (in the original coordinates) fermionic Hamiltonians for weakly interacting (in the dual coordinates) ones. It enables us to generalize to the strongly interacting regime the fermionic renormalization group approach to weakly interacting junctions. As a result, on one hand, we are able to pertinently complement the information about the phase diagram of the junction obtained within the bosonization approach; on the other hand, we map out the full crossover of the conductance tensors between any two fixed points in the phase diagram connected by a renormalization group trajectory.

Renormalization of the fragmentation equation: exact self-similar solutions and turbulent cascades.

PubMed

Saveliev, V L; Gorokhovski, M A

2012-12-01

Using an approach developed earlier for renormalization of the Boltzmann collision integral [Saveliev and Nanbu, Phys. Rev. E 65, 051205 (2002)], we derive an exact divergence form for the fragmentation operator. Then we reduce the fragmentation equation to the continuity equation in size space, with the flux given explicitly. This allows us to obtain self-similar solutions and to find the integral of motion for these solutions (we call it the bare flux). We show how these solutions can be applied as a description of cascade processes in three- and two-dimensional turbulence. We also suggested an empirical cascade model of impact fragmentation of brittle materials.

Conductance scaling of junctions of Luttinger-liquid wires out of equilibrium

NASA Astrophysics Data System (ADS)

Aristov, D. N.; Wölfle, P.

2018-05-01

We develop the renormalization group theory of the conductances of N -lead junctions of spinless Luttinger-liquid wires as functions of bias voltages applied to N independent Fermi-liquid reservoirs. Based on the perturbative results up to second order in the interaction we demonstrate that the conductances obey scaling. The corresponding renormalization group β functions are derived up to second order.

Emergent supersymmetry in the marginal deformations of $$\\mathcal{N}=4$$ SYM

DOE PAGES

Jin, Qingjun

2016-10-24

Here, we study the one loop renormalization group flow of the marginal deformations ofmore » $$\\mathcal{N}=4$$ SYM theory using the a-function. We found that in the planar limit some non-supersymmetric deformations flow to the supersymmetric infrared fixed points described by the Leigh-Strassler theory. This means supersymmetry emerges as a result of renormalization group flow.« less

mr: A C++ library for the matching and running of the Standard Model parameters

NASA Astrophysics Data System (ADS)

Kniehl, Bernd A.; Pikelner, Andrey F.; Veretin, Oleg L.

2016-09-01

We present the C++ program library mr that allows us to reliably calculate the values of the running parameters in the Standard Model at high energy scales. The initial conditions are obtained by relating the running parameters in the MS bar renormalization scheme to observables at lower energies with full two-loop precision. The evolution is then performed in accordance with the renormalization group equations with full three-loop precision. Pure QCD corrections to the matching and running are included through four loops. We also provide a Mathematica interface for this program library. Catalogue identifier: AFAI_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AFAI_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 No. of lines in distributed program, including test data, etc.: 517613 No. of bytes in distributed program, including test data, etc.: 2358729 Distribution format: tar.gz Programming language: C++. Computer: IBM PC. Operating system: Linux, Mac OS X. RAM: 1 GB Classification: 11.1. External routines: TSIL [1], OdeInt [2], boost [3] Nature of problem: The running parameters of the Standard Model renormalized in the MS bar scheme at some high renormalization scale, which is chosen by the user, are evaluated in perturbation theory as precisely as possible in two steps. First, the initial conditions at the electroweak energy scale are evaluated from the Fermi constant GF and the pole masses of the W, Z, and Higgs bosons and the bottom and top quarks including the full two-loop threshold corrections. Second, the evolution to the high energy scale is performed by numerically solving the renormalization group evolution equations through three loops. Pure QCD corrections to the matching and running are included through four loops. Solution method: Numerical integration of analytic expressions Additional comments: Available for download from URL: http://apik.github.io/mr/. The MathLink interface is tested to work with Mathematica 7-9 and, with an additional flag, also with Mathematica 10 under Linux and with Mathematica 10 under Mac OS X. Running time: less than 1 second References: [1] S. P. Martin and D. G. Robertson, Comput. Phys. Commun. 174 (2006) 133-151 [hep-ph/0501132]. [2] K. Ahnert and M. Mulansky, AIP Conf. Proc. 1389 (2011) 1586-1589 [arxiv:1110.3397 [cs.MS

Effective scalar field theory and reduction of couplings

NASA Astrophysics Data System (ADS)

Atance, Mario; Cortés, José Luis

1997-09-01

A general discussion of the renormalization of the quantum theory of a scalar field as an effective field theory is presented. The renormalization group equations in a mass-independent renormalization scheme allow us to identify the possibility to go beyond the renormalizable φ4 theory without losing its predictive power. It is shown that there is a minimal extension with just one additional free parameter (the mass scale of the effective theory expansion) and some of its properties are discussed.

Callan-Symanzik equations for infrared Yang-Mills theory

NASA Astrophysics Data System (ADS)

Weber, Axel; Dall'Olio, Pietro

2017-12-01

Dyson-Schwinger equations have been successful in determining the correlation functions in Yang-Mills theory in the Landau gauge, in the infrared regime. We argue that similar results can be obtained, in a technically simpler way, with Callan-Symanzik renormalization group equations. We present generalizations of the infrared safe renormalization scheme proposed by Tissier and Wschebor in 2011, and show how the renormalization scheme dependence can be used to improve the matching to the existing lattice data for the gluon and ghost propagators.

Renormalization Group scale-setting in astrophysical systems

NASA Astrophysics Data System (ADS)

Domazet, Silvije; Štefančić, Hrvoje

2011-09-01

A more general scale-setting procedure for General Relativity with Renormalization Group corrections is proposed. Theoretical aspects of the scale-setting procedure and the interpretation of the Renormalization Group running scale are discussed. The procedure is elaborated for several highly symmetric systems with matter in the form of an ideal fluid and for two models of running of the Newton coupling and the cosmological term. For a static spherically symmetric system with the matter obeying the polytropic equation of state the running scale-setting is performed analytically. The obtained result for the running scale matches the Ansatz introduced in a recent paper by Rodrigues, Letelier and Shapiro which provides an excellent explanation of rotation curves for a number of galaxies. A systematic explanation of the galaxy rotation curves using the scale-setting procedure introduced in this Letter is identified as an important future goal.

AdS/CFT and local renormalization group with gauge fields

NASA Astrophysics Data System (ADS)

Kikuchi, Ken; Sakai, Tadakatsu

2016-03-01

We revisit a study of local renormalization group (RG) with background gauge fields incorporated using the AdS/CFT correspondence. Starting with a (d+1)-dimensional bulk gravity coupled to scalars and gauge fields, we derive a local RG equation from a flow equation by working in the Hamilton-Jacobi formulation of the bulk theory. The Gauss's law constraint associated with gauge symmetry plays an important role. RG flows of the background gauge fields are governed by vector β-functions, and some of their interesting properties are known to follow. We give a systematic rederivation of them on the basis of the flow equation. Fixing an ambiguity of local counterterms in such a manner that is natural from the viewpoint of the flow equation, we determine all the coefficients uniquely appearing in the trace of the stress tensor for d=4. A relation between a choice of schemes and a virial current is discussed. As a consistency check, these are found to satisfy the integrability conditions of local RG transformations. From these results, we are led to a proof of a holographic c-theorem by determining a full family of schemes where a trace anomaly coefficient is related with a holographic c-function.

Remarks on the renormalization group in statistical fluid dynamics

NASA Astrophysics Data System (ADS)

Fournier, J.-D.; Frisch, U.

1983-08-01

A variant of the renormalization group is applied to the problem of randomly forced fluids studied by Forster, Nelson, and Stephen

Fickian dispersion is anomalous

DOE PAGES

Cushman, John H.; O’Malley, Dan

2015-06-22

The thesis put forward here is that the occurrence of Fickian dispersion in geophysical settings is a rare event and consequently should be labeled as anomalous. What people classically call anomalous is really the norm. In a Lagrangian setting, a process with mean square displacement which is proportional to time is generally labeled as Fickian dispersion. With a number of counter examples we show why this definition is fraught with difficulty. In a related discussion, we show an infinite second moment does not necessarily imply the process is super dispersive. By employing a rigorous mathematical definition of Fickian dispersion wemore » illustrate why it is so hard to find a Fickian process. We go on to employ a number of renormalization group approaches to classify non-Fickian dispersive behavior. Scaling laws for the probability density function for a dispersive process, the distribution for the first passage times, the mean first passage time, and the finite-size Lyapunov exponent are presented for fixed points of both deterministic and stochastic renormalization group operators. The fixed points of the renormalization group operators are p-self-similar processes. A generalized renormalization group operator is introduced whose fixed points form a set of generalized self-similar processes. Finally, power-law clocks are introduced to examine multi-scaling behavior. Several examples of these ideas are presented and discussed.« less

Fixing the fixed-point system—Applying Dynamic Renormalization Group to systems with long-range interactions

NASA Astrophysics Data System (ADS)

Katzav, Eytan

2013-04-01

In this paper, a mode of using the Dynamic Renormalization Group (DRG) method is suggested in order to cope with inconsistent results obtained when applying it to a continuous family of one-dimensional nonlocal models. The key observation is that the correct fixed-point dynamical system has to be identified during the analysis in order to account for all the relevant terms that are generated under renormalization. This is well established for static problems, however poorly implemented in dynamical ones. An application of this approach to a nonlocal extension of the Kardar-Parisi-Zhang equation resolves certain problems in one-dimension. Namely, obviously problematic predictions are eliminated and the existing exact analytic results are recovered.

Loop optimization for tensor network renormalization

NASA Astrophysics Data System (ADS)

Yang, Shuo; Gu, Zheng-Cheng; Wen, Xiao-Gang

We introduce a tensor renormalization group scheme for coarse-graining a two-dimensional tensor network, which can be successfully applied to both classical and quantum systems on and off criticality. The key idea of our scheme is to deform a 2D tensor network into small loops and then optimize tensors on each loop. In this way we remove short-range entanglement at each iteration step, and significantly improve the accuracy and stability of the renormalization flow. We demonstrate our algorithm in the classical Ising model and a frustrated 2D quantum model. NSF Grant No. DMR-1005541 and NSFC 11274192, BMO Financial Group, John Templeton Foundation, Government of Canada through Industry Canada, Province of Ontario through the Ministry of Economic Development & Innovation.

A functional renormalization method for wave propagation in random media

NASA Astrophysics Data System (ADS)

Lamagna, Federico; Calzetta, Esteban

2017-08-01

We develop the exact renormalization group approach as a way to evaluate the effective speed of the propagation of a scalar wave in a medium with random inhomogeneities. We use the Martin-Siggia-Rose formalism to translate the problem into a non equilibrium field theory one, and then consider a sequence of models with a progressively lower infrared cutoff; in the limit where the cutoff is removed we recover the problem of interest. As a test of the formalism, we compute the effective dielectric constant of an homogeneous medium interspersed with randomly located, interpenetrating bubbles. A simple approximation to the renormalization group equations turns out to be equivalent to a self-consistent two-loops evaluation of the effective dielectric constant.

Singlet vs Nonsinglet Perturbative Renormalization factors of Staggered Fermion Bilinears

NASA Astrophysics Data System (ADS)

Panagopoulos, Haralambos; Spanoudes, Gregoris

2018-03-01

In this paper we present the perturbative computation of the difference between the renormalization factors of flavor singlet (Σfψ¯fΓψf', f : flavor index) and nonsinglet (ψ¯f1Γψf2,f1 ≠ f2) bilinear quark operators (where Γ = 𝟙, γ5, γ µ, γ5 γ µ, γ5 σµv on the lattice. The computation is performed to two loops and to lowest order in the lattice spacing, using Symanzik improved gluons and staggered fermions with twice stout-smeared links. The stout smearing procedure is also applied to the definition of bilinear operators. A significant part of this work is the development of a method for treating some new peculiar divergent integrals stemming from the staggered formalism. Our results can be combined with precise simulation results for the renormalization factors of the nonsinglet operators, in order to obtain an estimate of the renormalization factors for the singlet operators. The results have been published in Physical Review D [1].

Renormalization of the fragmentation equation: Exact self-similar solutions and turbulent cascades

NASA Astrophysics Data System (ADS)

Saveliev, V. L.; Gorokhovski, M. A.

2012-12-01

Using an approach developed earlier for renormalization of the Boltzmann collision integral [Saveliev and Nanbu, Phys. Rev. E1539-375510.1103/PhysRevE.65.051205 65, 051205 (2002)], we derive an exact divergence form for the fragmentation operator. Then we reduce the fragmentation equation to the continuity equation in size space, with the flux given explicitly. This allows us to obtain self-similar solutions and to find the integral of motion for these solutions (we call it the bare flux). We show how these solutions can be applied as a description of cascade processes in three- and two-dimensional turbulence. We also suggested an empirical cascade model of impact fragmentation of brittle materials.

Renormalization in Quantum Field Theory and the Riemann-Hilbert Problem I: The Hopf Algebra Structure of Graphs and the Main Theorem

NASA Astrophysics Data System (ADS)

Connes, Alain; Kreimer, Dirk

This paper gives a complete selfcontained proof of our result announced in [6] showing that renormalization in quantum field theory is a special instance of a general mathematical procedure of extraction of finite values based on the Riemann-Hilbert problem. We shall first show that for any quantum field theory, the combinatorics of Feynman graphs gives rise to a Hopf algebra which is commutative as an algebra. It is the dual Hopf algebra of the enveloping algebra of a Lie algebra whose basis is labelled by the one particle irreducible Feynman graphs. The Lie bracket of two such graphs is computed from insertions of one graph in the other and vice versa. The corresponding Lie group G is the group of characters of . We shall then show that, using dimensional regularization, the bare (unrenormalized) theory gives rise to a loop where C is a small circle of complex dimensions around the integer dimension D of space-time. Our main result is that the renormalized theory is just the evaluation at z=D of the holomorphic part γ+ of the Birkhoff decomposition of γ. We begin to analyse the group G and show that it is a semi-direct product of an easily understood abelian group by a highly non-trivial group closely tied up with groups of diffeomorphisms. The analysis of this latter group as well as the interpretation of the renormalization group and of anomalous dimensions are the content of our second paper with the same overall title.

Complexity theory, time series analysis and Tsallis q-entropy principle part one: theoretical aspects

NASA Astrophysics Data System (ADS)

Pavlos, George P.

2017-12-01

In this study, we present the highlights of complexity theory (Part I) and significant experimental verifications (Part II) and we try to give a synoptic description of complexity theory both at the microscopic and at the macroscopic level of the physical reality. Also, we propose that the self-organization observed macroscopically is a phenomenon that reveals the strong unifying character of the complex dynamics which includes thermodynamical and dynamical characteristics in all levels of the physical reality. From this point of view, macroscopical deterministic and stochastic processes are closely related to the microscopical chaos and self-organization. The scientific work of scientists such as Wilson, Nicolis, Prigogine, Hooft, Nottale, El Naschie, Castro, Tsallis, Chang and others is used for the development of a unified physical comprehension of complex dynamics from the microscopic to the macroscopic level. Finally, we provide a comprehensive description of the novel concepts included in the complexity theory from microscopic to macroscopic level. Some of the modern concepts that can be used for a unified description of complex systems and for the understanding of modern complexity theory, as it is manifested at the macroscopic and the microscopic level, are the fractal geometry and fractal space-time, scale invariance and scale relativity, phase transition and self-organization, path integral amplitudes, renormalization group theory, stochastic and chaotic quantization and E-infinite theory, etc.

Mrst '96: Current Ideas in Theoretical Physics - Proceedings of the Eighteenth Annual Montréal-Rochester-Syracuse-Toronto Meeting

NASA Astrophysics Data System (ADS)

O'Donnell, Patrick J.; Smith, Brian Hendee

1996-11-01

The Table of Contents for the full book PDF is as follows: * Preface * Roberto Mendel, An Appreciaton * The Infamous Coulomb Gauge * Renormalized Path Integral in Quantum Mechanics * New Analysis of the Divergence of Perturbation Theory * The Last of the Soluble Two Dimensional Field Theories? * Rb and Heavy Quark Mixing * Rb Problem: Loop Contributions and Supersymmetry * QCD Radiative Effects in Inclusive Hadronic B Decays * CP-Violating Dipole Moments of Quarks in the Kobayashi-Maskawa Model * Hints of Dynamical Symmetry Breaking? * Pi Pi Scattering in an Effective Chiral Lagrangian * Pion-Resonance Parameters from QCD Sum Rules * Higgs Theorem, Effective Action, and its Gauge Invariance * SUSY and the Decay H_2^0 to gg * Effective Higgs-to-Light Quark Coupling Induced by Heavy Quark Loops * Heavy Charged Lepton Production in Superstring Inspired E6 Models * The Elastic Properties of a Flat Crystalline Membrane * Gauge Dependence of Topological Observables in Chern-Simons Theory * Entanglement Entropy From Edge States * A Simple General Treatment of Flavor Oscillations * From Schrödinger to Maupertuis: Least Action Principles from Quantum Mechanics * The Matrix Method for Multi-Loop Feynman Integrals * Simplification in QCD and Electroweak Calculations * Programme * List of Participants

The density-matrix renormalization group: a short introduction.

PubMed

Schollwöck, Ulrich

2011-07-13

The density-matrix renormalization group (DMRG) method has established itself over the last decade as the leading method for the simulation of the statics and dynamics of one-dimensional strongly correlated quantum lattice systems. The DMRG is a method that shares features of a renormalization group procedure (which here generates a flow in the space of reduced density operators) and of a variational method that operates on a highly interesting class of quantum states, so-called matrix product states (MPSs). The DMRG method is presented here entirely in the MPS language. While the DMRG generally fails in larger two-dimensional systems, the MPS picture suggests a straightforward generalization to higher dimensions in the framework of tensor network states. The resulting algorithms, however, suffer from difficulties absent in one dimension, apart from a much more unfavourable efficiency, such that their ultimate success remains far from clear at the moment.

Multireference quantum chemistry through a joint density matrix renormalization group and canonical transformation theory.

PubMed

Yanai, Takeshi; Kurashige, Yuki; Neuscamman, Eric; Chan, Garnet Kin-Lic

2010-01-14

We describe the joint application of the density matrix renormalization group and canonical transformation theory to multireference quantum chemistry. The density matrix renormalization group provides the ability to describe static correlation in large active spaces, while the canonical transformation theory provides a high-order description of the dynamic correlation effects. We demonstrate the joint theory in two benchmark systems designed to test the dynamic and static correlation capabilities of the methods, namely, (i) total correlation energies in long polyenes and (ii) the isomerization curve of the [Cu(2)O(2)](2+) core. The largest complete active spaces and atomic orbital basis sets treated by the joint DMRG-CT theory in these systems correspond to a (24e,24o) active space and 268 atomic orbitals in the polyenes and a (28e,32o) active space and 278 atomic orbitals in [Cu(2)O(2)](2+).

Entanglement Holographic Mapping of Many-Body Localized System by Spectrum Bifurcation Renormalization Group

NASA Astrophysics Data System (ADS)

You, Yi-Zhuang; Qi, Xiao-Liang; Xu, Cenke

We introduce the spectrum bifurcation renormalization group (SBRG) as a generalization of the real-space renormalization group for the many-body localized (MBL) system without truncating the Hilbert space. Starting from a disordered many-body Hamiltonian in the full MBL phase, the SBRG flows to the MBL fixed-point Hamiltonian, and generates the local conserved quantities and the matrix product state representations for all eigenstates. The method is applicable to both spin and fermion models with arbitrary interaction strength on any lattice in all dimensions, as long as the models are in the MBL phase. In particular, we focus on the 1 d interacting Majorana chain with strong disorder, and map out its phase diagram using the entanglement entropy. The SBRG flow also generates an entanglement holographic mapping, which duals the MBL state to a fragmented holographic space decorated with small blackholes.

Leading temperature dependence of the conductance in Kondo-correlated quantum dots.

PubMed

Aligia, A A

2018-04-18

Using renormalized perturbation theory in the Coulomb repulsion, we derive an analytical expression for the leading term in the temperature dependence of the conductance through a quantum dot described by the impurity Anderson model, in terms of the renormalized parameters of the model. Taking these parameters from the literature, we compare the results with published ones calculated using the numerical renormalization group obtaining a very good agreement. The approach is superior to alternative perturbative treatments. We compare in particular to the results of a simple interpolative perturbation approach.

Density-matrix renormalization group method for the conductance of one-dimensional correlated systems using the Kubo formula

NASA Astrophysics Data System (ADS)

Bischoff, Jan-Moritz; Jeckelmann, Eric

2017-11-01

We improve the density-matrix renormalization group (DMRG) evaluation of the Kubo formula for the zero-temperature linear conductance of one-dimensional correlated systems. The dynamical DMRG is used to compute the linear response of a finite system to an applied ac source-drain voltage; then the low-frequency finite-system response is extrapolated to the thermodynamic limit to obtain the dc conductance of an infinite system. The method is demonstrated on the one-dimensional spinless fermion model at half filling. Our method is able to replicate several predictions of the Luttinger liquid theory such as the renormalization of the conductance in a homogeneous conductor, the universal effects of a single barrier, and the resonant tunneling through a double barrier.

Renormalization group procedure for potential -g/r2

NASA Astrophysics Data System (ADS)

Dawid, S. M.; Gonsior, R.; Kwapisz, J.; Serafin, K.; Tobolski, M.; Głazek, S. D.

2018-02-01

Schrödinger equation with potential - g /r2 exhibits a limit cycle, described in the literature in a broad range of contexts using various regularizations of the singularity at r = 0. Instead, we use the renormalization group transformation based on Gaussian elimination, from the Hamiltonian eigenvalue problem, of high momentum modes above a finite, floating cutoff scale. The procedure identifies a richer structure than the one we found in the literature. Namely, it directly yields an equation that determines the renormalized Hamiltonians as functions of the floating cutoff: solutions to this equation exhibit, in addition to the limit-cycle, also the asymptotic-freedom, triviality, and fixed-point behaviors, the latter in vicinity of infinitely many separate pairs of fixed points in different partial waves for different values of g.

Small-cluster renormalization group in Ising and Blume-Emery-Griffiths models with ferromagnetic, antiferromagnetic, and quenched disordered magnetic interactions

NASA Astrophysics Data System (ADS)

Antenucci, F.; Crisanti, A.; Leuzzi, L.

2014-07-01

The Ising and Blume-Emery-Griffiths (BEG) models' critical behavior is analyzed in two dimensions and three dimensions by means of a renormalization group scheme on small clusters made of a few lattice cells. Different kinds of cells are proposed for both ordered and disordered model cases. In particular, cells preserving a possible antiferromagnetic ordering under renormalization allow for the determination of the Néel critical point and its scaling indices. These also provide more reliable estimates of the Curie fixed point than those obtained using cells preserving only the ferromagnetic ordering. In all studied dimensions, the present procedure does not yield a strong-disorder critical point corresponding to the transition to the spin-glass phase. This limitation is thoroughly analyzed and motivated.

Exploration of quantum phases transition in the XXZ model with Dzyaloshinskii-Moriya interaction using trance distance discord

NASA Astrophysics Data System (ADS)

Zhang, Ren-jie; Xu, Shuai; Shi, Jia-dong; Ma, Wen-chao; Ye, Liu

2015-11-01

In the paper, we researched the quantum phase transition (QPT) in the anisotropic spin XXZ model by exploiting the quantum renormalization group (QRG) method. The innovation point is that we adopt a new approach called trace distance discord to indicate the quantum correlation of the system. QPT after several iterations of renormalization in current system has been observed. Consequently, it opened the possibility of investigation of QPR in the geometric discord territory. While the anisotropy suppresses the correlation due to favoring of the alignment of spins, the DM interaction restores the spoiled correlation via creation of the quantum fluctuations. We also apply quantum renormalization group method to probe the thermodynamic limit of the model and emerging of nonanalytic behavior of the correlation.

Critical behavior of a chiral superfluid in a bipartite square lattice

NASA Astrophysics Data System (ADS)

Okamoto, Junichi; Huang, Wen-Min; Höppner, Robert; Mathey, Ludwig

2018-01-01

We study the critical behavior of Bose-Einstein condensation in the second band of a bipartite optical square lattice in a renormalization group framework at one-loop order. Within our field theoretical representation of the system, we approximate the system as a two-component Bose gas in three dimensions. We demonstrate that the system is in a different universality class than the previously studied condensation in a frustrated triangular lattice due to an additional Umklapp scattering term, which stabilizes the chiral superfluid order at low temperatures. We derive the renormalization group flow of the system and show that this order persists in the low energy limit. Furthermore, the renormalization flow suggests that the phase transition from the thermal phase to the chiral superfluid state is first order.

Development of a Renormalization Group Approach to Multi-Scale Plasma Physics Computation

DTIC Science & Technology

2012-03-28

with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 1...NUMBER(S) 12. DISTRIBUTION/AVAILABILITY STATEMENT 13. SUPPLEMENTARY NOTES 14. ABSTRACT 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: a . REPORT...code) 29-12-2008 Final Technical Report From 29-12-2008 To 16-95-2011 (STTR PHASE II) DEVELOPMENT OF A RENORMALIZATION GROUP APPROACH TO MULTI-SCALE

New applications of renormalization group methods in nuclear physics.

PubMed

Furnstahl, R J; Hebeler, K

2013-12-01

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

Renormalization Group Theory for the Imbalanced Fermi Gas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gubbels, K. B.; Stoof, H. T. C.

2008-04-11

We formulate a Wilsonian renormalization group theory for the imbalanced Fermi gas. The theory is able to recover quantitatively well-established results in both the weak-coupling and the strong-coupling (unitarity) limits. We determine for the latter case the line of second-order phase transitions of the imbalanced Fermi gas and, in particular, the location of the tricritical point. We obtain good agreement with the recent experiments of Y. Shin et al. [Nature (London) 451, 689 (2008)].

Application of renormalization group theory to the large-eddy simulation of transitional boundary layers

NASA Technical Reports Server (NTRS)

Piomelli, Ugo; Zang, Thomas A.; Speziale, Charles G.; Lund, Thomas S.

1990-01-01

An eddy viscosity model based on the renormalization group theory of Yakhot and Orszag (1986) is applied to the large-eddy simulation of transition in a flat-plate boundary layer. The simulation predicts with satisfactory accuracy the mean velocity and Reynolds stress profiles, as well as the development of the important scales of motion. The evolution of the structures characteristic of the nonlinear stages of transition is also predicted reasonably well.

Functional renormalization group approach to SU(N ) Heisenberg models: Real-space renormalization group at arbitrary N

NASA Astrophysics Data System (ADS)

Buessen, Finn Lasse; Roscher, Dietrich; Diehl, Sebastian; Trebst, Simon

2018-02-01

The pseudofermion functional renormalization group (pf-FRG) is one of the few numerical approaches that has been demonstrated to quantitatively determine the ordering tendencies of frustrated quantum magnets in two and three spatial dimensions. The approach, however, relies on a number of presumptions and approximations, in particular the choice of pseudofermion decomposition and the truncation of an infinite number of flow equations to a finite set. Here we generalize the pf-FRG approach to SU (N )-spin systems with arbitrary N and demonstrate that the scheme becomes exact in the large-N limit. Numerically solving the generalized real-space renormalization group equations for arbitrary N , we can make a stringent connection between the physically most significant case of SU(2) spins and more accessible SU (N ) models. In a case study of the square-lattice SU (N ) Heisenberg antiferromagnet, we explicitly demonstrate that the generalized pf-FRG approach is capable of identifying the instability indicating the transition into a staggered flux spin liquid ground state in these models for large, but finite, values of N . In a companion paper [Roscher et al., Phys. Rev. B 97, 064416 (2018), 10.1103/PhysRevB.97.064416] we formulate a momentum-space pf-FRG approach for SU (N ) spin models that allows us to explicitly study the large-N limit and access the low-temperature spin liquid phase.

The long flow to freedom

DOE PAGES

Aharony, Ofer; Razamat, Shlomo S.; Seiberg, Nathan; ...

2017-02-10

Two-dimensional field theories do not have a moduli space of vacua. Instead, it is common that their low-energy behavior is a sigma model with a target space. When this target space is compact its renormalization group flow is standard. When it is non-compact the continuous spectrum of operators can change the qualitative behavior. Here we discuss two-dimensional gauge theories with N = (2,2) supersymmetry. We focus on two specific theories, for which we argue that they flow to free chiral multiplets at low energies: the U(1) gauge theory with one flavor (two chiral superfields with charges plus and minus one)more » and a non-zero Fayet-Iliopoulos term, and pure SU( N) gauge theories. We argue that the renormalization group flow of these theories has an interesting order of limits issue. Holding the position on the target space fixed, the space flattens out under the renormalization group. On the other hand, if we first go to infinity on the target space and then perform the renormalization group, we always have a non-trivial space, e.g. a cone with a deficit angle. We explain how to interpret low-energy dualities between theories with non-compact target spaces. As a result, we expect a similar qualitative behavior also for other non-compact sigma models, even when they do not flow to free theories.« less

Kenneth Wilson and Renormalization

Science.gov Websites

of the Renormalization Group (RG) into a central tool in physics. ... He received a doctorate from one of the most amazing experiences of my life," says Peskin. "He was saying, 'I see the big actually the data you need to move from one scale to another. ... RG theory implies that, with enough

Renormalizable group field theory beyond melonic diagrams: An example in rank four

NASA Astrophysics Data System (ADS)

Carrozza, Sylvain; Lahoche, Vincent; Oriti, Daniele

2017-09-01

We prove the renormalizability of a gauge-invariant, four-dimensional group field theory (GFT) model on SU(2), whose defining interactions correspond to necklace bubbles (found also in the context of new large-N expansions of tensor models), rather than melonic ones, which are not renormalizable in this case. The respective scaling of different interactions in the vicinity of the Gaussian fixed point is determined by the renormalization group itself. This is possible because the appropriate notion of canonical dimension of the GFT coupling constants takes into account the detailed combinatorial structure of the individual interaction terms. This is one more instance of the peculiarity (and greater mathematical richness) of GFTs with respect to ordinary local quantum field theories. We also explore the renormalization group flow of the model at the nonperturbative level, using functional renormalization group methods, and identify a nontrivial fixed point in various truncations. This model is expected to have a similar structure of divergences as the GFT models of 4D quantum gravity, thus paving the way to more detailed investigations on them.

Enriching Group Counseling through Integrating Yoga Concepts and Practices

ERIC Educational Resources Information Center

Rybak, Christopher; Deuskar, Megha

2010-01-01

Integrating practices from yoga with group counseling offers many creative paths of therapeutic learning. While yoga emphasizes the increased sense of connection with the self, group counseling emphasizes the increased sense of authenticity in relationship with oneself and with others. Common aims of both yoga and counseling are liberation from…

Monte Carlo renormalization-group study of the Baxter-Wu model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Novotny, M.A.; Landau, D.P.; Swendsen, R.H.

1982-07-01

The effectiveness of a Monte Carlo renormalization-group method is studied by applying it to the Baxter-Wu model (Ising spins on a triangular lattice with three-spin interactions). The calculations yield three relevent eigenvalues in good agreement with exact or conjectured results. We demonstrate that the method is capable of distinguishing between models expected to be in the same universality class, when one of them (four-state Potts) exhibits logarithmic corrections to the usual power-law singularities and the other (Baxter-Wu) does not.

New applications of the renormalization group method in physics: a brief introduction.

PubMed

Meurice, Y; Perry, R; Tsai, S-W

2011-07-13

The renormalization group (RG) method developed by Ken Wilson more than four decades ago has revolutionized the way we think about problems involving a broad range of energy scales such as phase transitions, turbulence, continuum limits and bifurcations in dynamical systems. The Theme Issue provides articles reviewing recent progress made using the RG method in atomic, condensed matter, nuclear and particle physics. In the following, we introduce these articles in a way that emphasizes common themes and the universal aspects of the method.

Multiloop Functional Renormalization Group That Sums Up All Parquet Diagrams

NASA Astrophysics Data System (ADS)

Kugler, Fabian B.; von Delft, Jan

2018-02-01

We present a multiloop flow equation for the four-point vertex in the functional renormalization group (FRG) framework. The multiloop flow consists of successive one-loop calculations and sums up all parquet diagrams to arbitrary order. This provides substantial improvement of FRG computations for the four-point vertex and, consequently, the self-energy. Using the x-ray-edge singularity as an example, we show that solving the multiloop FRG flow is equivalent to solving the (first-order) parquet equations and illustrate this with numerical results.

Renormalizing a viscous fluid model for large scale structure formation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Führer, Florian; Rigopoulos, Gerasimos, E-mail: fuhrer@thphys.uni-heidelberg.de, E-mail: gerasimos.rigopoulos@ncl.ac.uk

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 ordermore » 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.« less

Two-loop renormalization of gaugino masses in general supersymmetric gauge models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yamada, Y.

1994-01-03

We calculate the two-loop renormalization group equations for the running gaugino masses in general supersymmetry (SUSY) gauge models, improving our previous result. We also study its consequences on the unification of the gaugino masses in the SUSY SU(5) model. The two-loop correction to the one-loop relation [ital m][sub [ital i

Critical Exponents, Scaling Law, Universality and Renormalization Group Flow in Strong Coupling QED

NASA Astrophysics Data System (ADS)

Kondo, Kei-Ichi

The critical behavior of strongly coupled QED with a chiral-invariant four-fermion interaction (gauged Nambu-Jona-Lasinio model) is investigated through the unquenched Schwinger-Dyson equation including the fermion loop effect at the one-loop level. It is shown that the critical exponents satisfy the (hyper)scaling relations as in the quenched case. However, the respective critical exponent takes the classical mean-field value, and consequently unquenched QED belongs to the same universality class as the zero-charge model. On the other hand, it is pointed out that quenched QED violates not only universality but also weak universality, due to continuously varying critical exponents. Furthermore, the renormalization group flow of constant renormalized charge is given. All the results are consistent with triviality of QED and the gauged Nambu-Jona-Lasinio model in the unquenched case.

Interplay between Magnetism, Superconductivity, and Orbital Order in 5-Pocket Model for Iron-Based Superconductors: Parquet Renormalization Group Study.

PubMed

Classen, Laura; Xing, Rui-Qi; Khodas, Maxim; Chubukov, Andrey V

2017-01-20

We report the results of the parquet renormalization group (RG) analysis of the phase diagram of the most general 5-pocket model for Fe-based superconductors. We use as an input the orbital structure of excitations near the five pockets made out of d_{xz}, d_{yz}, and d_{xy} orbitals and argue that there are 40 different interactions between low-energy fermions in the orbital basis. All interactions flow under the RG, as one progressively integrates out fermions with higher energies. We find that the low-energy behavior is amazingly simple, despite the large number of interactions. Namely, at low energies the full 5-pocket model effectively reduces either to a 3-pocket model made of one d_{xy} hole pocket and two electron pockets or a 4-pocket model made of two d_{xz}/d_{yz} hole pockets and two electron pockets. The leading instability in the effective 4-pocket model is a spontaneous orbital (nematic) order, followed by s^{+-} superconductivity. In the effective 3-pocket model, orbital fluctuations are weaker, and the system develops either s^{+-} superconductivity or a stripe spin-density wave. In the latter case, nematicity is induced by composite spin fluctuations.

Driven similarity renormalization group: Third-order multireference perturbation theory.

PubMed

Li, Chenyang; Evangelista, Francesco A

2017-03-28

A third-order multireference perturbation theory based on the driven similarity renormalization group (DSRG-MRPT3) approach is presented. The DSRG-MRPT3 method has several appealing features: (a) it is intruder free, (b) it is size consistent, (c) it leads to a non-iterative algorithm with O(N 6 ) scaling, and (d) it includes reference relaxation effects. The DSRG-MRPT3 scheme is benchmarked on the potential energy curves of F 2 , H 2 O 2 , C 2 H 6 , and N 2 along the F-F, O-O, C-C, and N-N bond dissociation coordinates, respectively. The nonparallelism errors of DSRG-MRPT3 are consistent with those of complete active space third-order perturbation theory and multireference configuration interaction with singles and doubles and show significant improvements over those obtained from DSRG second-order multireference perturbation theory. Our efficient implementation of the DSRG-MRPT3 based on factorized electron repulsion integrals enables studies of medium-sized open-shell organic compounds. This point is demonstrated with computations of the singlet-triplet splitting (Δ ST =E T -E S ) of 9,10-anthracyne. At the DSRG-MRPT3 level of theory, our best estimate of the adiabatic Δ ST is 3.9 kcal mol -1 , a value that is within 0.1 kcal mol -1 from multireference coupled cluster results.

Functional renormalization-group approaches, one-particle (irreducible) reducible with respect to local Green’s functions, with dynamical mean-field theory as a starting point

DOE Office of Scientific and Technical Information (OSTI.GOV)

Katanin, A. A., E-mail: katanin@mail.ru

We consider formulations of the functional renormalization-group (fRG) flow for correlated electronic systems with the dynamical mean-field theory as a starting point. We classify the corresponding renormalization-group schemes into those neglecting one-particle irreducible six-point vertices (with respect to the local Green’s functions) and neglecting one-particle reducible six-point vertices. The former class is represented by the recently introduced DMF{sup 2}RG approach [31], but also by the scale-dependent generalization of the one-particle irreducible representation (with respect to local Green’s functions, 1PI-LGF) of the generating functional [20]. The second class is represented by the fRG flow within the dual fermion approach [16, 32].more » We compare formulations of the fRG approach in each of these cases and suggest their further application to study 2D systems within the Hubbard model.« less

Impact of topology in foliated quantum Einstein gravity.

PubMed

Houthoff, W B; Kurov, A; Saueressig, F

2017-01-01

We use a functional renormalization group equation tailored to the Arnowitt-Deser-Misner formulation of gravity to study the scale dependence of Newton's coupling and the cosmological constant on a background spacetime with topology [Formula: see text]. The resulting beta functions possess a non-trivial renormalization group fixed point, which may provide the high-energy completion of the theory through the asymptotic safety mechanism. The fixed point is robust with respect to changing the parametrization of the metric fluctuations and regulator scheme. The phase diagrams show that this fixed point is connected to a classical regime through a crossover. In addition the flow may exhibit a regime of "gravitational instability", modifying the theory in the deep infrared. Our work complements earlier studies of the gravitational renormalization group flow on a background topology [Formula: see text] (Biemans et al. Phys Rev D 95:086013, 2017, Biemans et al. arXiv:1702.06539, 2017) and establishes that the flow is essentially independent of the background topology.

Phase structure of NJL model with weak renormalization group

NASA Astrophysics Data System (ADS)

Aoki, Ken-Ichi; Kumamoto, Shin-Ichiro; Yamada, Masatoshi

2018-06-01

We analyze the chiral phase structure of the Nambu-Jona-Lasinio model at finite temperature and density by using the functional renormalization group (FRG). The renormalization group (RG) equation for the fermionic effective potential V (σ ; t) is given as a partial differential equation, where σ : = ψ bar ψ and t is a dimensionless RG scale. When the dynamical chiral symmetry breaking (DχSB) occurs at a certain scale tc, V (σ ; t) has singularities originated from the phase transitions, and then one cannot follow RG flows after tc. In this study, we introduce the weak solution method to the RG equation in order to follow the RG flows after the DχSB and to evaluate the dynamical mass and the chiral condensate in low energy scales. It is shown that the weak solution of the RG equation correctly captures vacuum structures and critical phenomena within the pure fermionic system. We show the chiral phase diagram on temperature, chemical potential and the four-Fermi coupling constant.

Effective field renormalization group approach for Ising lattice spin systems

NASA Astrophysics Data System (ADS)

Fittipaldi, Ivon P.

1994-03-01

A new applicable real-space renormalization group framework (EFRG) for computing the critical properties of Ising lattice spin systems is presented. The method, which follows up the same strategy of the mean-field renormalization group scheme (MFRG), is based on rigorous Ising spin identities and utilizes a convenient differential operator expansion technique. Within this scheme, in contrast with the usual mean-field type of equation of state, all the relevant self-spin correlations are taken exactly into account. The results for the critical coupling and the critical exponent v, for the correlation length, are very satisfactory and it is shown that this technique leads to rather accurate results which represent a remarkable improvement on those obtained from the standard MFRG method. In particular, it is shown that the present EFRG approach correctly distinguishes the geometry of the lattice structure even when employing its simplest size-cluster version. Owing to its simplicity we also comment on the wide applicability of the present method to problems in crystalline and disordered Ising spin systems.

Asymptotic safety of quantum gravity beyond Ricci scalars

NASA Astrophysics Data System (ADS)

Falls, Kevin; King, Callum R.; Litim, Daniel F.; Nikolakopoulos, Kostas; Rahmede, Christoph

2018-04-01

We investigate the asymptotic safety conjecture for quantum gravity including curvature invariants beyond Ricci scalars. Our strategy is put to work for families of gravitational actions which depend on functions of the Ricci scalar, the Ricci tensor, and products thereof. Combining functional renormalization with high order polynomial approximations and full numerical integration we derive the renormalization group flow for all couplings and analyse their fixed points, scaling exponents, and the fixed point effective action as a function of the background Ricci curvature. The theory is characterized by three relevant couplings. Higher-dimensional couplings show near-Gaussian scaling with increasing canonical mass dimension. We find that Ricci tensor invariants stabilize the UV fixed point and lead to a rapid convergence of polynomial approximations. We apply our results to models for cosmology and establish that the gravitational fixed point admits inflationary solutions. We also compare findings with those from f (R ) -type theories in the same approximation and pin-point the key new effects due to Ricci tensor interactions. Implications for the asymptotic safety conjecture of gravity are indicated.

Restoration of dimensional reduction in the random-field Ising model at five dimensions

NASA Astrophysics Data System (ADS)

Fytas, Nikolaos G.; Martín-Mayor, Víctor; Picco, Marco; Sourlas, Nicolas

2017-04-01

The random-field Ising model is one of the few disordered systems where the perturbative renormalization group can be carried out to all orders of perturbation theory. This analysis predicts dimensional reduction, i.e., that the critical properties of the random-field Ising model in D dimensions are identical to those of the pure Ising ferromagnet in D -2 dimensions. It is well known that dimensional reduction is not true in three dimensions, thus invalidating the perturbative renormalization group prediction. Here, we report high-precision numerical simulations of the 5D random-field Ising model at zero temperature. We illustrate universality by comparing different probability distributions for the random fields. We compute all the relevant critical exponents (including the critical slowing down exponent for the ground-state finding algorithm), as well as several other renormalization-group invariants. The estimated values of the critical exponents of the 5D random-field Ising model are statistically compatible to those of the pure 3D Ising ferromagnet. These results support the restoration of dimensional reduction at D =5 . We thus conclude that the failure of the perturbative renormalization group is a low-dimensional phenomenon. We close our contribution by comparing universal quantities for the random-field problem at dimensions 3 ≤D <6 to their values in the pure Ising model at D -2 dimensions, and we provide a clear verification of the Rushbrooke equality at all studied dimensions.

Restoration of dimensional reduction in the random-field Ising model at five dimensions.

PubMed

Fytas, Nikolaos G; Martín-Mayor, Víctor; Picco, Marco; Sourlas, Nicolas

2017-04-01

The random-field Ising model is one of the few disordered systems where the perturbative renormalization group can be carried out to all orders of perturbation theory. This analysis predicts dimensional reduction, i.e., that the critical properties of the random-field Ising model in D dimensions are identical to those of the pure Ising ferromagnet in D-2 dimensions. It is well known that dimensional reduction is not true in three dimensions, thus invalidating the perturbative renormalization group prediction. Here, we report high-precision numerical simulations of the 5D random-field Ising model at zero temperature. We illustrate universality by comparing different probability distributions for the random fields. We compute all the relevant critical exponents (including the critical slowing down exponent for the ground-state finding algorithm), as well as several other renormalization-group invariants. The estimated values of the critical exponents of the 5D random-field Ising model are statistically compatible to those of the pure 3D Ising ferromagnet. These results support the restoration of dimensional reduction at D=5. We thus conclude that the failure of the perturbative renormalization group is a low-dimensional phenomenon. We close our contribution by comparing universal quantities for the random-field problem at dimensions 3≤D<6 to their values in the pure Ising model at D-2 dimensions, and we provide a clear verification of the Rushbrooke equality at all studied dimensions.

Functional renormalization group approach to electronic structure calculations for systems without translational symmetry

NASA Astrophysics Data System (ADS)

Seiler, Christian; Evers, Ferdinand

2016-10-01

A formalism for electronic-structure calculations is presented that is based on the functional renormalization group (FRG). The traditional FRG has been formulated for systems that exhibit a translational symmetry with an associated Fermi surface, which can provide the organization principle for the renormalization group (RG) procedure. We here advance an alternative formulation, where the RG flow is organized in the energy-domain rather than in k space. This has the advantage that it can also be applied to inhomogeneous matter lacking a band structure, such as disordered metals or molecules. The energy-domain FRG (ɛ FRG) presented here accounts for Fermi-liquid corrections to quasiparticle energies and particle-hole excitations. It goes beyond the state of the art G W -BSE , because in ɛ FRG the Bethe-Salpeter equation (BSE) is solved in a self-consistent manner. An efficient implementation of the approach that has been tested against exact diagonalization calculations and calculations based on the density matrix renormalization group is presented. Similar to the conventional FRG, also the ɛ FRG is able to signalize the vicinity of an instability of the Fermi-liquid fixed point via runaway flow of the corresponding interaction vertex. Embarking upon this fact, in an application of ɛ FRG to the spinless disordered Hubbard model we calculate its phase boundary in the plane spanned by the interaction and disorder strength. Finally, an extension of the approach to finite temperatures and spin S =1 /2 is also given.

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

PubMed

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

2015-12-01

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

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 the choice of initial scale is highly suppressed even for low-order predictions. Thus the PMC, based on the standard RGI, has a rigorous foundation; it eliminates an unnecessary systematic error for high precision pQCD predictions and can be widely applied to virtually all high-energy hadronic processes, including multi-scale problems.

Magnetic moments induce strong phonon renormalization in FeSi.

PubMed

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

2015-11-27

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.

Running with rugby balls: bulk renormalization of codimension-2 branes

NASA Astrophysics Data System (ADS)

Williams, M.; Burgess, C. P.; van Nierop, L.; Salvio, A.

2013-01-01

We compute how one-loop bulk effects renormalize both bulk and brane effective interactions for geometries sourced by codimension-two branes. We do so by explicitly integrating out spin-zero, -half and -one particles in 6-dimensional Einstein-Maxwell-Scalar theories compactified to 4 dimensions on a flux-stabilized 2D geometry. (Our methods apply equally well for D dimensions compactified to D - 2 dimensions, although our explicit formulae do not capture all divergences when D > 6.) The renormalization of bulk interactions are independent of the boundary conditions assumed at the brane locations, and reproduce standard heat-kernel calculations. Boundary conditions at any particular brane do affect how bulk loops renormalize this brane's effective action, but not the renormalization of other distant branes. Although we explicitly compute our loops using a rugby ball geometry, because we follow only UV effects our results apply more generally to any geometry containing codimension-two sources with conical singularities. Our results have a variety of uses, including calculating the UV sensitivity of one-loop vacuum energy seen by observers localized on the brane. We show how these one-loop effects combine in a surprising way with bulk back-reaction to give the complete low-energy effective cosmological constant, and comment on the relevance of this calculation to proposed applications of codimension-two 6D models to solutions of the hierarchy and cosmological constant problems.

A key heterogeneous structure of fractal networks based on inverse renormalization scheme

NASA Astrophysics Data System (ADS)

Bai, Yanan; Huang, Ning; Sun, Lina

2018-06-01

Self-similarity property of complex networks was found by the application of renormalization group theory. Based on this theory, network topologies can be classified into universality classes in the space of configurations. In return, through inverse renormalization scheme, a given primitive structure can grow into a pure fractal network, then adding different types of shortcuts, it exhibits different characteristics of complex networks. However, the effect of primitive structure on networks structural property has received less attention. In this paper, we introduce a degree variance index to measure the dispersion of nodes degree in the primitive structure, and investigate the effect of the primitive structure on network structural property quantified by network efficiency. Numerical simulations and theoretical analysis show a primitive structure is a key heterogeneous structure of generated networks based on inverse renormalization scheme, whether or not adding shortcuts, and the network efficiency is positively correlated with degree variance of the primitive structure.

Going the distance: spatial scale of athletic experience affects the accuracy of path integration.

PubMed

Smith, Alastair D; Howard, Christina J; Alcock, Niall; Cater, Kirsten

2010-09-01

Evidence suggests that athletically trained individuals are more accurate than untrained individuals in updating their spatial position through idiothetic cues. We assessed whether training at different spatial scales affects the accuracy of path integration. Groups of rugby players (large-scale training) and martial artists (small-scale training) participated in a triangle-completion task: they were led (blindfolded) along two sides of a right-angled triangle and were required to complete the hypotenuse by returning to the origin. The groups did not differ in their assessment of the distance to the origin, but rugby players were more accurate than martial artists in assessing the correct angle to turn (heading), and landed significantly closer to the origin. These data support evidence that distance and heading components can be dissociated. Furthermore, they suggest that the spatial scale at which an individual is trained may affect the accuracy of one component of path integration but not the other.

One-dimensional continuum electronic structure with the density-matrix renormalization group and its implications for density-functional theory.

PubMed

Stoudenmire, E M; Wagner, Lucas O; White, Steven R; Burke, Kieron

2012-08-03

We extend the density matrix renormalization group to compute exact ground states of continuum many-electron systems in one dimension with long-range interactions. We find the exact ground state of a chain of 100 strongly correlated artificial hydrogen atoms. The method can be used to simulate 1D cold atom systems and to study density-functional theory in an exact setting. To illustrate, we find an interacting, extended system which is an insulator but whose Kohn-Sham system is metallic.

2PI effective theory at next-to-leading order using the functional renormalization group

NASA Astrophysics Data System (ADS)

Carrington, M. E.; Friesen, S. A.; Meggison, B. A.; Phillips, C. D.; Pickering, D.; Sohrabi, K.

2018-02-01

We consider a symmetric scalar theory with quartic coupling in four dimensions. We show that the four-loop 2PI calculation can be done using a renormalization group method. The calculation involves one bare coupling constant which is introduced at the level of the Lagrangian and is therefore conceptually simpler than a standard 2PI calculation, which requires multiple counterterms. We explain how our method can be used to do the corresponding calculation at the 4PI level, which cannot be done using any known method by introducing counterterms.

Topological Luttinger liquids from decorated domain walls

NASA Astrophysics Data System (ADS)

Parker, Daniel E.; Scaffidi, Thomas; Vasseur, Romain

2018-04-01

We introduce a systematic construction of a gapless symmetry-protected topological phase in one dimension by "decorating" the domain walls of Luttinger liquids. The resulting strongly interacting phases provide a concrete example of a gapless symmetry-protected topological (gSPT) phase with robust symmetry-protected edge modes. Using boundary conformal field theory arguments, we show that while the bulks of such gSPT phases are identical to conventional Luttinger liquids, their boundary critical behavior is controlled by a different, strongly coupled renormalization group fixed point. Our results are checked against extensive density matrix renormalization group calculations.

Exploring excited eigenstates of many-body systems using the functional renormalization group

NASA Astrophysics Data System (ADS)

Klöckner, Christian; Kennes, Dante Marvin; Karrasch, Christoph

2018-05-01

We introduce approximate, functional renormalization group based schemes to obtain correlation functions in pure excited eigenstates of large fermionic many-body systems at arbitrary energies. The algorithms are thoroughly benchmarked and their strengths and shortcomings are documented using a one-dimensional interacting tight-binding chain as a prototypical testbed. We study two "toy applications" from the world of Luttinger liquid physics: the survival of power laws in lowly excited states as well as the spectral function of high-energy "block" excitations, which feature several single-particle Fermi edges.

Application of the principle of maximum conformality to the hadroproduction of the Higgs boson at the LHC

DOE Office of Scientific and Technical Information (OSTI.GOV)

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

We present improved perturbative QCD (pQCD) predictions for Higgs boson hadroproduction at the LHC by applying the principle of maximum conformality (PMC), a procedure which resums the pQCD series using the renormalization group (RG), thereby eliminating the dependence of the predictions on the choice of the renormalization scheme while minimizing sensitivity to the initial choice of the renormalization scale. In previous pQCD predictions for Higgs boson hadroproduction, it has been conventional to assume that the renormalization scale μ r of the QCD coupling α s ( μ r ) is the Higgs mass and then to vary this choice overmore » the range 1 / 2 m H < μ r < 2 m H in order to estimate the theory uncertainty. However, this error estimate is only sensitive to the nonconformal β terms in the pQCD series, and thus it fails to correctly estimate the theory uncertainty in cases where a pQCD series has large higher-order contributions, as is the case for Higgs boson hadroproduction. Furthermore, this ad hoc choice of scale and range gives pQCD predictions which depend on the renormalization scheme being used, in contradiction to basic RG principles. In contrast, after applying the PMC, we obtain next-to-next-to-leading-order RG resummed pQCD predictions for Higgs boson hadroproduction which are renormalization-scheme independent and have minimal sensitivity to the choice of the initial renormalization scale. Taking m H = 125 GeV , the PMC predictions for the p p → H X Higgs inclusive hadroproduction cross sections for various LHC center-of-mass energies are σ Incl | 7 TeV = 21.2 1 + 1.36 - 1.32 pb , σ Incl | 8 TeV = 27.3 7 + 1.65 - 1.59 pb , and σ Incl | 13 TeV = 65.7 2 + 3.46 - 3.0 pb . We also predict the fiducial cross section σ fid ( p p → H → γ γ ) : σ fid | 7 TeV = 30.1 + 2.3 - 2.2 fb , σ fid | 8 TeV = 38.3 + 2.9 - 2.8 fb , and σ fid | 13 TeV = 85.8 + 5.7 - 5.3 fb . The error limits in these predictions include the small residual high-order renormalization-scale dependence plus the uncertainty from the factorization scale. The PMC predictions show better agreement with the ATLAS measurements than the LHC Higgs Cross Section Working Group predictions which are based on conventional renormalization-scale setting.« less

A global solution to the Schrödinger equation: From Henstock to Feynman

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nathanson, Ekaterina S., E-mail: enathanson@ggc.edu; Jørgensen, Palle E. T., E-mail: palle-jorgensen@uiowa.edu

2015-09-15

One of the key elements of Feynman’s formulation of non-relativistic quantum mechanics is a so-called Feynman path integral. It plays an important role in the theory, but it appears as a postulate based on intuition, rather than a well-defined object. All previous attempts to supply Feynman’s theory with rigorous mathematics underpinning, based on the physical requirements, have not been satisfactory. The difficulty comes from the need to define a measure on the infinite dimensional space of paths and to create an integral that would possess all of the properties requested by Feynman. In the present paper, we consider a newmore » approach to defining the Feynman path integral, based on the theory developed by Muldowney [A Modern Theory of Random Variable: With Applications in Stochastic Calcolus, Financial Mathematics, and Feynman Integration (John Wiley & Sons, Inc., New Jersey, 2012)]. Muldowney uses the Henstock integration technique and deals with non-absolute integrability of the Fresnel integrals, in order to obtain a representation of the Feynman path integral as a functional. This approach offers a mathematically rigorous definition supporting Feynman’s intuitive derivations. But in his work, Muldowney gives only local in space-time solutions. A physical solution to the non-relativistic Schrödinger equation must be global, and it must be given in the form of a unitary one-parameter group in L{sup 2}(ℝ{sup n}). The purpose of this paper is to show that a system of one-dimensional local Muldowney’s solutions may be extended to yield a global solution. Moreover, the global extension can be represented by a unitary one-parameter group acting in L{sup 2}(ℝ{sup n})« less

Quantization of Simple Parametrized Systems

NASA Astrophysics Data System (ADS)

Ruffini, Giulio

1995-01-01

I study the canonical formulation and quantization of some simple parametrized systems using Dirac's formalism and the Becchi-Rouet-Stora-Tyutin (BRST) extended phase space method. These systems include the parametrized particle and minisuperspace. Using Dirac's formalism I first analyze for each case the construction of the classical reduced phase space. There are two separate features of these systems that may make this construction difficult: (a) Because of the boundary conditions used, the actions are not gauge invariant at the boundaries. (b) The constraints may have a disconnected solution space. The relativistic particle and minisuperspace have such complicated constraints, while the non-relativistic particle displays only the first feature. I first show that a change of gauge fixing is equivalent to a canonical transformation in the reduced phase space, thus resolving the problems associated with the first feature above. Then I consider the quantization of these systems using several approaches: Dirac's method, Dirac-Fock quantization, and the BRST formalism. In the cases of the relativistic particle and minisuperspace I consider first the quantization of one branch of the constraint at the time and then discuss the backgrounds in which it is possible to quantize simultaneously both branches. I motivate and define the inner product, and obtain, for example, the Klein-Gordon inner product for the relativistic case. Then I show how to construct phase space path integral representations for amplitudes in these approaches--the Batalin-Fradkin-Vilkovisky (BFV) and the Faddeev path integrals --from which one can then derive the path integrals in coordinate space--the Faddeev-Popov path integral and the geometric path integral. In particular I establish the connection between the Hilbert space representation and the range of the lapse in the path integrals. I also examine the class of paths that contribute in the path integrals and how they affect space-time covariance, concluding that it is consistent to take paths that move forward in time only when there is no electric field. The key elements in this analysis are the space-like paths and the behavior of the action under the non-trivial ( Z_2) element of the reparametrization group.

FAST-PT: a novel algorithm to calculate convolution integrals in cosmological perturbation theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

McEwen, Joseph E.; Fang, Xiao; Hirata, Christopher M.

2016-09-01

We present a novel algorithm, FAST-PT, for performing convolution or mode-coupling integrals that appear in nonlinear cosmological perturbation theory. The algorithm uses several properties of gravitational structure formation—the locality of the dark matter equations and the scale invariance of the problem—as well as Fast Fourier Transforms to describe the input power spectrum as a superposition of power laws. This yields extremely fast performance, enabling mode-coupling integral computations fast enough to embed in Monte Carlo Markov Chain parameter estimation. We describe the algorithm and demonstrate its application to calculating nonlinear corrections to the matter power spectrum, including one-loop standard perturbation theorymore » and the renormalization group approach. We also describe our public code (in Python) to implement this algorithm. The code, along with a user manual and example implementations, is available at https://github.com/JoeMcEwen/FAST-PT.« less

MS overline -on-shell quark mass relation up to four loops in QCD and a general SU (N ) gauge group

NASA Astrophysics Data System (ADS)

Marquard, Peter; Smirnov, Alexander V.; Smirnov, Vladimir A.; Steinhauser, Matthias; Wellmann, David

2016-10-01

We compute the relation between heavy quark masses defined in the modified minimal subtraction and the on-shell schemes. Detailed results are presented for all coefficients of the SU (Nc) color factors. The reduction of the four-loop on-shell integrals is performed for a general QCD gauge parameter. Altogether there are about 380 master integrals. Some of them are computed analytically, others with high numerical precision using Mellin-Barnes representations, and the rest numerically with the help of FIESTA. We discuss in detail the precise numerical evaluation of the four-loop master integrals. Updated relations between various short-distance masses and the MS ¯ quark mass to next-to-next-to-next-to-leading order accuracy are provided for the charm, bottom and top quarks. We discuss the dependence on the renormalization and factorization scale.

Covariant path integrals on hyperbolic surfaces

NASA Astrophysics Data System (ADS)

Schaefer, Joe

1997-11-01

DeWitt's covariant formulation of path integration [B. De Witt, "Dynamical theory in curved spaces. I. A review of the classical and quantum action principles," Rev. Mod. Phys. 29, 377-397 (1957)] has two practical advantages over the traditional methods of "lattice approximations;" there is no ordering problem, and classical symmetries are manifestly preserved at the quantum level. Applying the spectral theorem for unbounded self-adjoint operators, we provide a rigorous proof of the convergence of certain path integrals on Riemann surfaces of constant curvature -1. The Pauli-DeWitt curvature correction term arises, as in DeWitt's work. Introducing a Fuchsian group Γ of the first kind, and a continuous, bounded, Γ-automorphic potential V, we obtain a Feynman-Kac formula for the automorphic Schrödinger equation on the Riemann surface ΓH. We analyze the Wick rotation and prove the strong convergence of the so-called Feynman maps [K. D. Elworthy, Path Integration on Manifolds, Mathematical Aspects of Superspace, edited by Seifert, Clarke, and Rosenblum (Reidel, Boston, 1983), pp. 47-90] on a dense set of states. Finally, we give a new proof of some results in C. Grosche and F. Steiner, "The path integral on the Poincare upper half plane and for Liouville quantum mechanics," Phys. Lett. A 123, 319-328 (1987).

Solvable Hydrodynamics of Quantum Integrable Systems

NASA Astrophysics Data System (ADS)

Bulchandani, Vir B.; Vasseur, Romain; Karrasch, Christoph; Moore, Joel E.

2017-12-01

The conventional theory of hydrodynamics describes the evolution in time of chaotic many-particle systems from local to global equilibrium. In a quantum integrable system, local equilibrium is characterized by a local generalized Gibbs ensemble or equivalently a local distribution of pseudomomenta. We study time evolution from local equilibria in such models by solving a certain kinetic equation, the "Bethe-Boltzmann" equation satisfied by the local pseudomomentum density. Explicit comparison with density matrix renormalization group time evolution of a thermal expansion in the XXZ model shows that hydrodynamical predictions from smooth initial conditions can be remarkably accurate, even for small system sizes. Solutions are also obtained in the Lieb-Liniger model for free expansion into vacuum and collisions between clouds of particles, which model experiments on ultracold one-dimensional Bose gases.

Apker Award Recipient: Renormalization-Group Study of Helium Mixtures Immersed in a Porous Medium

NASA Astrophysics Data System (ADS)

Lopatnikova, Anna

1998-03-01

Superfluidity and phase separation in ^3He-^4He mixtures immersed in aerogel are studied by renormalization-group theory. Firstly, the theory is applied to jungle-gym (non-random) aerogel.(A. Lopatnikova and A.N. Berker, Phys. Rev. B 55, 3798 (1997).) This calculation is conducted via the coupled renormalization-group mappings of interactions near and away from aerogel. Superfluidity at very low ^4He concentrations and a depressed tricritical temperature are found at the onset of superfludity. A superfluid-superfluid phase separation, terminating at an isolated critical point, is found entirely within the superfluid phase. Secondly, the theory is applied to true aerogel, which has quenched disorder at both atomic and geometric levels.(A. Lopatnikova and A.N. Berker, Phys. Rev. B 56, 11865 (1997).) This calculation is conducted via the coupled renormalization-group mappings, near and away from aerogel, of quenched probability distributions of random interactions. Random-bond effects on superfluidity onset and random-field effects on superfluid phase separation are seen. The quenched randomness causes the λ line of second-order phase transitions of superfluidity onset to reach zero temperature, in agreement with general prediction and experiments. Based on these studies, the experimentally observed(S.B. Kim, J. Ma, and M.H.W. Chan, Phys. Rev. Lett. 71, 2268 (1993); N. Mulders and M.H.W. Chan, Phys. Rev. Lett. 75, 3705 (1995).) distinctive characteristics of ^3He-^4He mixtures in aerogel are related to the aerogel properties of connectivity, tenuousness, and atomic and geometric randomness.

Setting the renormalization scale in pQCD: Comparisons of the principle of maximum conformality with the sequential extended Brodsky-Lepage-Mackenzie approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ma, Hong -Hao; Wu, Xing -Gang; Ma, Yang

A key problem in making precise perturbative QCD (pQCD) predictions is how to set the renormalization scale of the running coupling unambiguously at each finite order. The elimination of the uncertainty in setting the renormalization scale in pQCD will greatly increase the precision of collider tests of the Standard Model and the sensitivity to new phenomena. Renormalization group invariance requires that predictions for observables must also be independent on the choice of the renormalization scheme. The well-known Brodsky-Lepage-Mackenzie (BLM) approach cannot be easily extended beyond next-to-next-to-leading order of pQCD. Several suggestions have been proposed to extend the BLM approach tomore » all orders. In this paper we discuss two distinct methods. One is based on the “Principle of Maximum Conformality” (PMC), which provides a systematic all-orders method to eliminate the scale and scheme ambiguities of pQCD. The PMC extends the BLM procedure to all orders using renormalization group methods; as an outcome, it significantly improves the pQCD convergence by eliminating renormalon divergences. An alternative method is the “sequential extended BLM” (seBLM) approach, which has been primarily designed to improve the convergence of pQCD series. The seBLM, as originally proposed, introduces auxiliary fields and follows the pattern of the β0-expansion to fix the renormalization scale. However, the seBLM requires a recomputation of pQCD amplitudes including the auxiliary fields; due to the limited availability of calculations using these auxiliary fields, the seBLM has only been applied to a few processes at low orders. In order to avoid the complications of adding extra fields, we propose a modified version of seBLM which allows us to apply this method to higher orders. As a result, we then perform detailed numerical comparisons of the two alternative scale-setting approaches by investigating their predictions for the annihilation cross section ratio R e+e– at four-loop order in pQCD.« less

Multigranular integrated services optical network

NASA Astrophysics Data System (ADS)

Yu, Oliver; Yin, Leping; Xu, Huan; Liao, Ming

2006-12-01

Based on all-optical switches without requiring fiber delay lines and optical-electrical-optical interfaces, the multigranular optical switching (MGOS) network integrates three transport services via unified core control to efficiently support bursty and stream traffic of subwavelength to multiwavelength bandwidth. Adaptive robust optical burst switching (AR-OBS) aggregates subwavelength burst traffic into asynchronous light-rate bursts, transported via slotted-time light paths established by fast two-way reservation with robust blocking recovery control. Multiwavelength optical switching (MW-OS) decomposes multiwavelength stream traffic into a group of timing-related light-rate streams, transported via a light-path group to meet end-to-end delay-variation requirements. Optical circuit switching (OCS) simply converts wavelength stream traffic from an electrical-rate into a light-rate stream. The MGOS network employs decoupled routing, wavelength, and time-slot assignment (RWTA) and novel group routing and wavelength assignment (GRWA) to select slotted-time light paths and light-path groups, respectively. The selected resources are reserved by the unified multigranular robust fast optical reservation protocol (MG-RFORP). Simulation results show that elastic traffic is efficiently supported via AR-OBS in terms of loss rate and wavelength utilization, while connection-oriented wavelength traffic is efficiently supported via wavelength-routed OCS in terms of connection blocking and wavelength utilization. The GRWA-tuning result for MW-OS is also shown.

Calculational Schemes in GUTs

NASA Astrophysics Data System (ADS)

Kounnas, Costas

The following sections are included: * Introduction * Mass Spectrum in a Spontaneously Broken-Theory SU(5) - Minimal Model * Renormalization and Renormalization Group Equation (R.G.E.) * Step Approximation and Decoupling Theorem * Notion of the Effective Coupling Constant * First Estimation of MX, α(MX) and sin2θ(MW) * Renormalization Properties and Photon-Z Mixing * β-Function Definitions * Threshold Functions and Decoupling Theorem * MX-Determination * Proton Lifetime * sin2θ(μ)-Determination * Quark-Lepton Mass Relations (mb/mτ) * Overview of the Conventional GUTs - Hierarchy Problem * Stability of Hierarchy - Supersymmetric GUTS * Cosmologically Acceptable SUSY GUT Models * Radiative Breaking of SU(2) × U(1) — MW/MX Hierarchy Generation * No Scale Supergravity Models^{56,57} Dynamical Determination of M_{B}-M_{F} * Conclusion * References

3,4-Methylenedioxymethamphetamine in Adult Rats Produces Deficits in Path Integration and Spatial Reference Memory

PubMed Central

Able, Jessica A.; Gudelsky, Gary A.; Vorhees, Charles V.; Williams, Michael T.

2010-01-01

Background ±3,4-Methylenedioxymethamphetamine (MDMA) is a recreational drug that causes cognitive deficits in humans. A rat model for learning and memory deficits has not been established, although some cognitive deficits have been reported. Methods Male Sprague-Dawley rats were treated with MDMA (15 mg/kg × 4 doses) or saline (SAL) (n = 20/treatment group) and tested in different learning paradigms: 1) path integration in the Cincinnati water maze (CWM), 2) spatial learning in the Morris water maze (MWM), and 3) novel object recognition (NOR). One week after drug administration, testing began in the CWM, then four phases of MWM, and finally NOR. Following behavioral testing, monoamine levels were assessed. Results ±3,4-Methylenedioxymethamphetamine-treated rats committed more CWM errors than did SAL-treated rats. ±3,4-Methylenedioxymethamphetamine-treated animals were further from the former platform position during each 30-second MWM probe trial but showed no differences during learning trials with the platform present. There were no group differences in NOR. ± 3,4-Methylenedioxymethamphetamine depleted serotonin in all brain regions and dopamine in the striatum. Conclusions ±3,4-Methylenedioxymethamphetamine produced MWM reference memory deficits even after complex learning in the CWM, where deficits in path integration learning occurred. Assessment of path integration may provide a sensitive index of MDMA-induced learning deficits. PMID:16324685

[Application of clinical nursing path integrated with holistic nursing in advanced schistosomiasis patients with ascites].

PubMed

Mei-Zhi, Yuan; Jing-Ru, Sun; Tao, Chen; Xiao-Yu, Zhang; Liang-Cai, He; Jia-Song, Wang

2016-05-12

To evaluate the effect of the clinical nursing path integrated with the holistic nursing on advanced schistosomiasis patients with ascites. A total of 226 advanced schistosomiasis patients with ascites were randomly divided into a control group and an experimental group (113 cases each group). The subjects in the experimental group were nursed by the clinical nursing path integrated with the holistic nursing, while those in the control group were nursed only by the holistic nursing. Then the clinical relevant indexes of the two groups were observed, and the quality of life of the patients before and after hospital discharge was assessed. The improvement rate, satisfaction degree, and awareness rate of health knowledge of the patients in the experiment group were 93.8%, 100% and 97.4%, respectively, which were significantly higher than those of the control group (all P < 0.05). The mortality rate and the complication rate of the patients in the experimental group were 0 and 2.7%, respectively, which were significantly lower than those of the control group (both P < 0.05). In addition, the average hospitalization days and the hospitalization cost of the experiment group were (12.2 ± 0.7) d and (4 725.0 ± 310.1) Yuan respectively, which were less than those of the control group (both P < 0.01). When 6 months after the discharge from hospital, the quality of life of the patients in the experimental group in various fields was significantly better than that of the control group (all P < 0.05). The clinical nursing pathway integrated with holistic nursing can effectively improve the improvement rate and decrease the mortality of the advanced schistosomiasis patients with ascites; meanwhile, it can shorten the hospitalization time and save the hospitalization cost. Therefore, this nursing model is suitable for popularization and application in the treatment and nursing work of the advanced schistosomiasis assistance.

A unified effective-field renormalization-group framework approach for the quenched diluted Ising models

NASA Astrophysics Data System (ADS)

de Albuquerque, Douglas F.; Fittipaldi, I. P.

1994-05-01

A unified effective-field renormalization-group framework (EFRG) for both quenched bond- and site-diluted Ising models is herein developed by extending recent works. The method, as in the previous works, follows up the same strategy of the mean-field renormalization-group scheme (MFRG), and is achieved by introducing an alternative way for constructing classical effective-field equations of state, based on rigorous Ising spin identities. The concentration dependence of the critical temperature, Tc(p), and the critical concentrations of magnetic atoms, pc, at which the transition temperature goes to zero, are evaluated for several two- and three-dimensional lattice structures. The obtained values of Tc and pc and the resulting phase diagrams for both bond and site cases are much more accurate than those estimated by the standard MFRG approach. Although preserving the same level of simplicity as the MFRG, it is shown that the present EFRG method, even by considering its simplest size-cluster version, provides results that correctly distinguishes those lattices that have the same coordination number, but differ in dimensionality or geometry.

Asymmetric Top Rotors in Superfluid Para-Hydrogen Nano-Clusters

NASA Astrophysics Data System (ADS)

Zeng, Tao; Li, Hui; Roy, Pierre-Nicholas

2012-06-01

We present the first simulation study of bosonic clusters doped with an asymmetric top molecule. A variation of the path-integral Monte Carlo method is developed to study a para-water (pH_2O) impurity in para-hydrogen (pH_2) clusters. The growth pattern of the doped clusters is similar in nature to that of the pure clusters. The pH_2O molecule appears to rotate freely in the cluster due to its large rotational constants and the lack of adiabatic following. The presence of pH_2O substantially quenches the superfluid response of pH_2 with respect to the space fixed frame. We also study the behaviour of a sulphur dioxide (32S16O_2) dopant in the pH_2 clusters. For such a heavy rotor, the adiabatic following of the pH_2 molecules is established and the superfluid renormalization of the rotational constants is observed. The rotational structure of the SO_2-p(H_2)_N clusters' ro-vibrational spectra is predicted. The connection between the superfluid response respect to the external boundary rotation and the dopant rotation is discussed.

Higher-order quantum-chromodynamic corrections to the longitudinal coefficient function in deep-inelastic scattering

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sowell, G.A.

1982-01-01

A calculation of nonsinglet longitudinal coefficient function of deep-inelastic scattering through order-g/sup 4/ is presented, using the operator-product expansion and the renormalization group. Both ultraviolet and infrared divergences are regulated with dimensional regularization. The renormalization scheme dependence of the result is discussed along with its phenomenological application in the determination of R = sigma/sub L//sigma/sub T/.

Efficient tree tensor network states (TTNS) for quantum chemistry: Generalizations of the density matrix renormalization group algorithm

NASA Astrophysics Data System (ADS)

Nakatani, Naoki; Chan, Garnet Kin-Lic

2013-04-01

We investigate tree tensor network states for quantum chemistry. Tree tensor network states represent one of the simplest generalizations of matrix product states and the density matrix renormalization group. While matrix product states encode a one-dimensional entanglement structure, tree tensor network states encode a tree entanglement structure, allowing for a more flexible description of general molecules. We describe an optimal tree tensor network state algorithm for quantum chemistry. We introduce the concept of half-renormalization which greatly improves the efficiency of the calculations. Using our efficient formulation we demonstrate the strengths and weaknesses of tree tensor network states versus matrix product states. We carry out benchmark calculations both on tree systems (hydrogen trees and π-conjugated dendrimers) as well as non-tree molecules (hydrogen chains, nitrogen dimer, and chromium dimer). In general, tree tensor network states require much fewer renormalized states to achieve the same accuracy as matrix product states. In non-tree molecules, whether this translates into a computational savings is system dependent, due to the higher prefactor and computational scaling associated with tree algorithms. In tree like molecules, tree network states are easily superior to matrix product states. As an illustration, our largest dendrimer calculation with tree tensor network states correlates 110 electrons in 110 active orbitals.

Driven similarity renormalization group: Third-order multireference perturbation theory

DOE PAGES

Li, Chenyang; Evangelista, Francesco A.

2017-03-28

Here, a third-order multireference perturbation theory based on the driven similarity renormalization group (DSRG-MRPT3) approach is presented. The DSRG-MRPT3 method has several appealing features: (a) it is intruder free, (b) it is size consistent, (c) it leads to a non-iterative algorithm with O(N 6) scaling, and (d) it includes reference relaxation effects. The DSRG-MRPT3 scheme is benchmarked on the potential energy curves of F 2, H 2O 2, C 2H 6, and N 2 along the F–F, O–O, C–C, and N–N bond dissociation coordinates, respectively. The nonparallelism errors of DSRG-MRPT3 are consistent with those of complete active space third-order perturbationmore » theory and multireference configuration interaction with singles and doubles and show significant improvements over those obtained from DSRG second-order multireference perturbation theory. Our efficient implementation of the DSRG-MRPT3 based on factorized electron repulsion integrals enables studies of medium-sized open-shell organic compounds. This point is demonstrated with computations of the singlet-triplet splitting (Δ ST = E T–E S) of 9,10-anthracyne. At the DSRG-MRPT3 level of theory, our best estimate of the adiabatic Δ ST is 3.9 kcal mol –1, a value that is within 0.1 kcal mol –1 from multireference coupled cluster results.« less

Driven similarity renormalization group: Third-order multireference perturbation theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Chenyang; Evangelista, Francesco A.

Here, a third-order multireference perturbation theory based on the driven similarity renormalization group (DSRG-MRPT3) approach is presented. The DSRG-MRPT3 method has several appealing features: (a) it is intruder free, (b) it is size consistent, (c) it leads to a non-iterative algorithm with O(N 6) scaling, and (d) it includes reference relaxation effects. The DSRG-MRPT3 scheme is benchmarked on the potential energy curves of F 2, H 2O 2, C 2H 6, and N 2 along the F–F, O–O, C–C, and N–N bond dissociation coordinates, respectively. The nonparallelism errors of DSRG-MRPT3 are consistent with those of complete active space third-order perturbationmore » theory and multireference configuration interaction with singles and doubles and show significant improvements over those obtained from DSRG second-order multireference perturbation theory. Our efficient implementation of the DSRG-MRPT3 based on factorized electron repulsion integrals enables studies of medium-sized open-shell organic compounds. This point is demonstrated with computations of the singlet-triplet splitting (Δ ST = E T–E S) of 9,10-anthracyne. At the DSRG-MRPT3 level of theory, our best estimate of the adiabatic Δ ST is 3.9 kcal mol –1, a value that is within 0.1 kcal mol –1 from multireference coupled cluster results.« less

The Renormalization-Group Method in the Problem on Calculation of the Spectral Energy Density of Fluid Turbulence

NASA Astrophysics Data System (ADS)

Teodorovich, E. V.

2018-03-01

In order to find the shape of energy spectrum within the framework of the model of stationary homogeneous isotropic turbulence, the renormalization-group equations, which reflect the Markovian nature of the mechanism of energy transfer along the wavenumber spectrum, are used in addition to the dimensional considerations and the energy balance equation. For the spectrum, the formula depends on three parameters, namely, the wavenumber, which determines the upper boundary of the range of the turbulent energy production, the spectral flux through this boundary, and the fluid kinematic viscosity.

Electron paramagnetic resonance g-tensors from state interaction spin-orbit coupling density matrix renormalization group

NASA Astrophysics Data System (ADS)

Sayfutyarova, Elvira R.; Chan, Garnet Kin-Lic

2018-05-01

We present a state interaction spin-orbit coupling method to calculate electron paramagnetic resonance g-tensors from density matrix renormalization group wavefunctions. We apply the technique to compute g-tensors for the TiF3 and CuCl42 - complexes, a [2Fe-2S] model of the active center of ferredoxins, and a Mn4CaO5 model of the S2 state of the oxygen evolving complex. These calculations raise the prospects of determining g-tensors in multireference calculations with a large number of open shells.

Improving the In-Medium Similarity Renormalization Group via approximate inclusion of three-body effects

NASA Astrophysics Data System (ADS)

Morris, Titus; Bogner, Scott

2015-10-01

The In-Medium Similarity Renormalization Group (IM-SRG) has been applied successfully not only to several closed shell finite nuclei, but has recently been used to produce effective shell model interactions that are competitive with phenomenological interactions in the SD shell. A recent alternative method for solving of the IM-SRG equations, called the Magnus expansion, not only provides a computationally feasible route to producing observables, but also allows for approximate handling of induced three-body forces. Promising results for several systems, including finite nuclei, will be presented and discussed.

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.

Renormalization-group study of superfluidity and phase separation of helium mixtures immersed in a nonrandom aerogel

NASA Astrophysics Data System (ADS)

Lopatnikova, Anna; Nihat Berker, A.

1997-02-01

Superfluidity and phase separation in 3-4He mixtures immersed in a jungle-gym (nonrandom) aerogel are studied by renormalization-group theory. Phase diagrams are calculated for a variety of aerogel concentrations. Superfluidity at very low 4He concentrations and a depressed tricritical temperature are found at the onset of superfluidity. A superfluid-superfluid phase separation, terminating at an isolated critical point, is found entirely within the superfluid phase. These phenomena and trends with respect to aerogel concentration are explained by the connectivity and tenuousness of a jungle-gym aerogel.

Density matrix renormalization group for a highly degenerate quantum system: Sliding environment block approach

NASA Astrophysics Data System (ADS)

Schmitteckert, Peter

2018-04-01

We present an infinite lattice density matrix renormalization group sweeping procedure which can be used as a replacement for the standard infinite lattice blocking schemes. Although the scheme is generally applicable to any system, its main advantages are the correct representation of commensurability issues and the treatment of degenerate systems. As an example we apply the method to a spin chain featuring a highly degenerate ground-state space where the new sweeping scheme provides an increase in performance as well as accuracy by many orders of magnitude compared to a recently published work.

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

DOE PAGES

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

2015-12-22

A primary problem affecting perturbative quantum chromodynamic (pQCD) analyses is the lack of a method for setting the QCD running-coupling renormalization scale such that maximally precise fixed-order predictions for physical observables are obtained. The Principle of Maximum Conformality (PMC) eliminates the ambiguities associated with the conventional renormalization scale-setting procedure, yielding predictions that are independent of the choice of renormalization scheme. The QCD coupling scales and the effective number of quark flavors are set order-by-order in the pQCD series. The PMC has a solid theoretical foundation, satisfying the standard renormalization group invariance condition and all of the self-consistency conditions derived frommore » the renormalization group. The PMC scales at each order are obtained by shifting the arguments of the strong force coupling constant αs to eliminate all non-conformal {βi} terms in the pQCD series. The {βi} terms are determined from renormalization group equations without ambiguity. The correct behavior of the running coupling at each order and at each phase-space point can then be obtained. The PMC reduces in the 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 energies, the angular distributions of heavy quarks can be used to obtain a direct determination of the heavy quark potential. A discussion of the angular distributions of massive quarks and leptons is also presented, including the fermionic component of the two-loop corrections to the electromagnetic form factors. Furthermore, these results demonstrate that the application of the PMC systematically eliminates a major theoretical uncertainty for pQCD predictions, thus increasing collider sensitivity to possible new physics beyond the Standard Model.« less

Measurement of J-integral in CAD/CAM dental ceramics and composite resin by digital image correlation.

PubMed

Jiang, Yanxia; Akkus, Anna; Roperto, Renato; Akkus, Ozan; Li, Bo; Lang, Lisa; Teich, Sorin

2016-09-01

Ceramic and composite resin blocks for CAD/CAM machining of dental restorations are becoming more common. The sample sizes affordable by these blocks are smaller than ideal for stress intensity factor (SIF) based tests. The J-integral measurement calls for full field strain measurement, making it challenging to conduct. Accordingly, the J-integral values of dental restoration materials used in CAD/CAM restorations have not been reported to date. Digital image correlation (DIC) provides full field strain maps, making it possible to calculate the J-integral value. The aim of this study was to measure the J-integral value for CAD/CAM restorative materials. Four types of materials (sintered IPS E-MAX CAD, non-sintered IPS E-MAX CAD, Vita Mark II and Paradigm MZ100) were used to prepare beam samples for three-point bending tests. J-integrals were calculated for different integral path size and locations with respect to the crack tip. J-integral at path 1 for each material was 1.26±0.31×10(-4)MPam for MZ 100, 0.59±0.28×10(-4)MPam for sintered E-MAX, 0.19±0.07×10(-4)MPam for VM II, and 0.21±0.05×10(-4)MPam for non-sintered E-MAX. There were no significant differences between different integral path size, except for the non-sintered E-MAX group. J-integral paths of non-sintered E-MAX located within 42% of the height of the sample provided consistent values whereas outside this range resulted in lower J-integral values. Moreover, no significant difference was found among different integral path locations. The critical SIF was calculated from J-integral (KJ) along with geometry derived SIF values (KI). KI values were comparable with KJ and geometry based SIF values obtained from literature. Therefore, DIC derived J-integral is a reliable way to assess the fracture toughness of small sized specimens for dental CAD/CAM restorative materials; however, with caution applied to the selection of J-integral path. Copyright © 2016 Elsevier Ltd. All rights reserved.

Charged plate in asymmetric electrolytes: One-loop renormalization of surface charge density and Debye length due to ionic correlations.

PubMed

Ding, Mingnan; Lu, Bing-Sui; Xing, Xiangjun

2016-10-01

Self-consistent field theory (SCFT) is used to study the mean potential near a charged plate inside a m:-n electrolyte. A perturbation series is developed in terms of g=4πκb, where band1/κ are Bjerrum length and bare Debye length, respectively. To the zeroth order, we obtain the nonlinear Poisson-Boltzmann theory. For asymmetric electrolytes (m≠n), the first order (one-loop) correction to mean potential contains a secular term, which indicates the breakdown of the regular perturbation method. Using a renormalizaton group transformation, we remove the secular term and obtain a globally well-behaved one-loop approximation with a renormalized Debye length and a renormalized surface charge density. Furthermore, we find that if the counterions are multivalent, the surface charge density is renormalized substantially downwards and may undergo a change of sign, if the bare surface charge density is sufficiently large. Our results agrees with large MC simulation even when the density of electrolytes is relatively high.

Nonlinear Gyro-Landau-Fluid Equations

NASA Astrophysics Data System (ADS)

Raskolnikov, I.; Mattor, Nathan; Parker, Scott E.

1996-11-01

We present fluid equations which describe the effects of both linear and nonlinear Landau damping (wave-particle-wave effects). These are derived using a recently developed analytical method similar to renormalization group theory. (Scott E. Parker and Daniele Carati, Phys. Rev. Lett. 75), 441 (1995). In this technique, the phase space structure inherent in Landau damping is treated analytically by building a ``renormalized collisionality'' onto a bare collisionality (which may be taken as vanishingly small). Here we apply this technique to the nonlinear ion gyrokinetic equation in slab geometry, obtaining nonlinear fluid equations for density, parallel momentum and heat. Wave-particle resonances are described by two functions appearing in the heat equation: a renormalized ``collisionality'' and a renormalized nonlinear coupling coeffient. It will be shown that these new equations may correct a deficiency in existing gyrofluid equations, (G. W. Hammett and F. W. Perkins, Phys. Rev. Lett. 64,) 3019 (1990). which can severely underestimate the strength of nonlinear interaction in regimes where linear resonance is strong. (N. Mattor, Phys. Fluids B 4,) 3952 (1992).

Surprises in low-dimensional correlated systems

NASA Astrophysics Data System (ADS)

Lin, Hsiu-Hau

In this thesis, correlation effects in low-dimensional systems were studied. In particular, we focus on two systems: a point-contact in the quantum-Hall regime under the influence of ac drive and quasi-one-dimensional ladder materials with generic interactions in weak coupling. Powerful techniques, including renormalization group, quantum field theory, operator product expansions, bosonization,...etc., were employed to extract surprising physics out of these strongly fluctuating systems. We first study the effect of an ac drive on the current-voltage (I-V) characteristics of a tunnel junction between two fractional Quantum Hall fluids at filling nu-1 an odd integer. In a semi-classical limit, the tunneling current exhibits mode-locking, which corresponds to plateaus in the I-V curve at integer multiples of I = ef , with f the ac drive frequency. However, the full quantum model exhibits rounded plateaus centered around the quantized current values due to quantum fluctuations. The locations of these plateaus can serve as an indirect hint of fractional charges. Switching attentions to quasi-one-dimensional coupled-chain systems, we present a systematic weak-coupling renormalization group (RG) technique and find that generally broad regions of the phase space of the ladder materials are unstable to pairing, usually with approximate d-wave symmetry. The dimensional crossovers from 1D to 2D were also discussed. Carbon nanotubes as possible candidates that display such unconventional pairing and interesting physics in weak coupling were discussed. Quite surprisingly, a hidden symmetry was found in the weakly-coupled two-leg ladder. A perturbative renormalization group analysis reveals that at half-filling the model scales onto an exactly soluble SO(8) symmetric Gross-Neveu model. Integrability of the Gross-Neveu model is employed to extract the exact energies, degeneracies and quantum numbers of all the low energy excited states, which fall into degenerate SO(8) multiplets. For generic physical interactions, there are four robust phases which have different SO(8) symmetries but share a common SO(5) symmetry. The effects of marginal chiral interactions were discussed at the end. Finally, we summarize our main results and discuss related open questions for future study.

On the soft supersymmetry-breaking parameters in gauge-mediated models

NASA Astrophysics Data System (ADS)

Wagner, C. E. M.

1998-09-01

Gauge mediation of supersymmetry breaking in the observable sector is an attractive idea, which naturally alleviates the flavor changing neutral current problem of supersymmetric theories. Quite generally, however, the number and quantum number of the messengers are not known; nor is their characteristic mass scale determined by the theory. Using the recently proposed method to extract supersymmetry-breaking parameters from wave-function renormalization, we derived general formulae for the soft supersymmetry-breaking parameters in the observable sector, valid in the small and moderate tan β regimes, for the case of split messengers. The full leading-order effects of top Yukawa and gauge couplings on the soft supersymmetry-breaking parameters are included. We give a simple interpretation of the general formulae in terms of the renormalization group evolution of the soft supersymmetry-breaking parameters. As a by-product of this analysis, the one-loop renormalization group evolution of the soft supersymmetry-breaking parameters is obtained for arbitrary boundary conditions of the scalar and gaugino mass parameters at high energies.

Renormalization group study of the melting of a two-dimensional system of collapsing hard disks

NASA Astrophysics Data System (ADS)

Ryzhov, V. N.; Tareyeva, E. E.; Fomin, Yu. D.; Tsiok, E. N.; Chumakov, E. S.

2017-06-01

We consider the melting of a two-dimensional system of collapsing hard disks (a system with a hard-disk potential to which a repulsive step is added) for different values of the repulsive-step width. We calculate the system phase diagram by the method of the density functional in crystallization theory using equations of the Berezinskii-Kosterlitz-Thouless-Halperin-Nelson-Young theory to determine the lines of stability with respect to the dissociation of dislocation pairs, which corresponds to the continuous transition from the solid to the hexatic phase. We show that the crystal phase can melt via a continuous transition at low densities (the transition to the hexatic phase) with a subsequent transition from the hexatic phase to the isotropic liquid and via a first-order transition. Using the solution of renormalization group equations with the presence of singular defects (dislocations) in the system taken into account, we consider the influence of the renormalization of the elastic moduli on the form of the phase diagram.

Renormalization group method based on the ionization energy theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arulsamy, Andrew Das, E-mail: sadwerdna@gmail.com; School of Physics, University of Sydney, Sydney, New South Wales 2006

2011-03-15

Proofs are developed to explicitly show that the ionization energy theory is a renormalized theory, which mathematically exactly satisfies the renormalization group formalisms developed by Gell-Mann-Low, Shankar and Zinn-Justin. However, the cutoff parameter for the ionization energy theory relies on the energy-level spacing, instead of lattice point spacing in k-space. Subsequently, we apply the earlier proofs to prove that the mathematical structure of the ionization-energy dressed electron-electron screened Coulomb potential is exactly the same as the ionization-energy dressed electron-phonon interaction potential. The latter proof is proven by means of the second-order time-independent perturbation theory with the heavier effective mass condition,more » as required by the electron-electron screened Coulomb potential. The outcome of this proof is that we can derive the heat capacity and the Debye frequency as a function of ionization energy, which can be applied in strongly correlated matter and nanostructures.« less

Integral transforms of the quantum mechanical path integral: Hit function and path-averaged potential.

PubMed

Edwards, James P; Gerber, Urs; Schubert, Christian; Trejo, Maria Anabel; Weber, Axel

2018-04-01

We introduce two integral transforms of the quantum mechanical transition kernel that represent physical information about the path integral. These transforms can be interpreted as probability distributions on particle trajectories measuring respectively the relative contribution to the path integral from paths crossing a given spatial point (the hit function) and the likelihood of values of the line integral of the potential along a path in the ensemble (the path-averaged potential).

Integral transforms of the quantum mechanical path integral: Hit function and path-averaged potential

NASA Astrophysics Data System (ADS)

Edwards, James P.; Gerber, Urs; Schubert, Christian; Trejo, Maria Anabel; Weber, Axel

2018-04-01

We introduce two integral transforms of the quantum mechanical transition kernel that represent physical information about the path integral. These transforms can be interpreted as probability distributions on particle trajectories measuring respectively the relative contribution to the path integral from paths crossing a given spatial point (the hit function) and the likelihood of values of the line integral of the potential along a path in the ensemble (the path-averaged potential).

E-cigarette marketing and older smokers: road to renormalization.

PubMed

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

2015-05-01

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. 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. 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. 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.

Anomalous dimension in a two-species reaction-diffusion system

NASA Astrophysics Data System (ADS)

Vollmayr-Lee, Benjamin; Hanson, Jack; McIsaac, R. Scott; Hellerick, Joshua D.

2018-01-01

We study a two-species reaction-diffusion system with the reactions A+A\\to (0, A) and A+B\\to A , with general diffusion constants D A and D B . Previous studies showed that for dimensions d≤slant 2 the B particle density decays with a nontrivial, universal exponent that includes an anomalous dimension resulting from field renormalization. We demonstrate via renormalization group methods that the scaled B particle correlation function has a distinct anomalous dimension resulting in the asymptotic scaling \\tilde CBB(r, t) ˜ tφf(r/\\sqrt{t}) , where the exponent ϕ results from the renormalization of the square of the field associated with the B particles. We compute this exponent to first order in \

Homing by path integration when a locomotion trajectory crosses itself.

PubMed

Yamamoto, Naohide; Meléndez, Jayleen A; Menzies, Derek T

2014-01-01

Path integration is a process with which navigators derive their current position and orientation by integrating self-motion signals along a locomotion trajectory. It has been suggested that path integration becomes disproportionately erroneous when the trajectory crosses itself. However, there is a possibility that this previous finding was confounded by effects of the length of a traveled path and the amount of turns experienced along the path, two factors that are known to affect path integration performance. The present study was designed to investigate whether the crossover of a locomotion trajectory truly increases errors of path integration. In an experiment, blindfolded human navigators were guided along four paths that varied in their lengths and turns, and attempted to walk directly back to the beginning of the paths. Only one of the four paths contained a crossover. Results showed that errors yielded from the path containing the crossover were not always larger than those observed in other paths, and the errors were attributed solely to the effects of longer path lengths or greater degrees of turns. These results demonstrated that path crossover does not always cause significant disruption in path integration processes. Implications of the present findings for models of path integration are discussed.

Spectroscopic accuracy directly from quantum chemistry: application to ground and excited states of beryllium dimer.

PubMed

Sharma, Sandeep; Yanai, Takeshi; Booth, George H; Umrigar, C J; Chan, Garnet Kin-Lic

2014-03-14

We combine explicit correlation via the canonical transcorrelation approach with the density matrix renormalization group and initiator full configuration interaction quantum Monte Carlo methods to compute a near-exact beryllium dimer curve, without the use of composite methods. In particular, our direct density matrix renormalization group calculations produce a well-depth of D(e) = 931.2 cm(-1) which agrees very well with recent experimentally derived estimates D(e) = 929.7±2 cm(-1) [J. M. Merritt, V. E. Bondybey, and M. C. Heaven, Science 324, 1548 (2009)] and D(e) = 934.6 cm(-1) [K. Patkowski, V. Špirko, and K. Szalewicz, Science 326, 1382 (2009)], as well the best composite theoretical estimates, D(e) = 938±15 cm(-1) [K. Patkowski, R. Podeszwa, and K. Szalewicz, J. Phys. Chem. A 111, 12822 (2007)] and D(e) = 935.1±10 cm(-1) [J. Koput, Phys. Chem. Chem. Phys. 13, 20311 (2011)]. Our results suggest possible inaccuracies in the functional form of the potential used at shorter bond lengths to fit the experimental data [J. M. Merritt, V. E. Bondybey, and M. C. Heaven, Science 324, 1548 (2009)]. With the density matrix renormalization group we also compute near-exact vertical excitation energies at the equilibrium geometry. These provide non-trivial benchmarks for quantum chemical methods for excited states, and illustrate the surprisingly large error that remains for 1 ¹Σ(g)⁻ state with approximate multi-reference configuration interaction and equation-of-motion coupled cluster methods. Overall, we demonstrate that explicitly correlated density matrix renormalization group and initiator full configuration interaction quantum Monte Carlo methods allow us to fully converge to the basis set and correlation limit of the non-relativistic Schrödinger equation in small molecules.

Renormalization Group Studies and Monte Carlo Simulation for Quantum Spin Systems.

NASA Astrophysics Data System (ADS)

Pan, Ching-Yan

We have discussed the extended application of various real space renormalization group methods to the quantum spin systems. At finite temperature, we extended both the reliability and range of application of the decimation renormalization group method (DRG) for calculating the thermal and magnetic properties of low-dimensional quantum spin chains, in which we have proposed general models of the three-state Potts model and the general Heisenberg model. Some interesting finite-temperature behavior of the models has been obtained. We also proposed a general formula for the critical properties of the n-dimensional q-state Potts model by using a modified migdal-Kadanoff approach which is in very good agreement with all available results for general q and d. For high-spin systems, we have investigated the famous Haldane's prediction by using a modified block renormalization group approach in spin -1over2, spin-1 and spin-3 over2 cases. Our result supports Haldane's prediction and a novel property of the spin-1 Heisenberg antiferromagnet has been predicted. A modified quantum monte Carlo simulation approach has been developed in this study which we use to treat quantum interacting problems (we only work on quantum spin systems in this study) without the "negative sign problem". We also obtain with the Monte Carlo approach the numerical derivative directly. Furthermore, using this approach we have obtained the energy spectrum and the thermodynamic properties of the antiferromagnetic q-state Potts model, and have studied the q-color problem with the result which supports Mattis' recent conjecture of entropy for the n -dimensional q-state Potts antiferromagnet. We also find a general solution for the q-color problem in d dimensions.

Strong disorder real-space renormalization for the many-body-localized phase of random Majorana models

NASA Astrophysics Data System (ADS)

Monthus, Cécile

2018-03-01

For the many-body-localized phase of random Majorana models, a general strong disorder real-space renormalization procedure known as RSRG-X (Pekker et al 2014 Phys. Rev. X 4 011052) is described to produce the whole set of excited states, via the iterative construction of the local integrals of motion (LIOMs). The RG rules are then explicitly derived for arbitrary quadratic Hamiltonians (free-fermions models) and for the Kitaev chain with local interactions involving even numbers of consecutive Majorana fermions. The emphasis is put on the advantages of the Majorana language over the usual quantum spin language to formulate unified RSRG-X rules.

Pseudo-time algorithms for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Turkel, E.

1986-01-01

A pseudo-time method is introduced to integrate the compressible Navier-Stokes equations to a steady state. This method is a generalization of a method used by Crocco and also by Allen and Cheng. We show that for a simple heat equation that this is just a renormalization of the time. For a convection-diffusion equation the renormalization is dependent only on the viscous terms. We implement the method for the Navier-Stokes equations using a Runge-Kutta type algorithm. This permits the time step to be chosen based on the inviscid model only. We also discuss the use of residual smoothing when viscous terms are present.

Bethe-Boltzmann hydrodynamics and spin transport in the XXZ chain

NASA Astrophysics Data System (ADS)

Bulchandani, Vir B.; Vasseur, Romain; Karrasch, Christoph; Moore, Joel E.

2018-01-01

Quantum integrable systems, such as the interacting Bose gas in one dimension and the XXZ quantum spin chain, have an extensive number of local conserved quantities that endow them with exotic thermalization and transport properties. We discuss recently introduced hydrodynamic approaches for such integrable systems from the viewpoint of kinetic theory and extend the previous works by proposing a numerical scheme to solve the hydrodynamic equations for finite times and arbitrary locally equilibrated initial conditions. We then discuss how such methods can be applied to describe nonequilibrium steady states involving ballistic heat and spin currents. In particular, we show that the spin Drude weight in the XXZ chain, previously accessible only by rigorous techniques of limited scope or controversial thermodynamic Bethe ansatz arguments, may be evaluated from hydrodynamics in very good agreement with density-matrix renormalization group calculations.

Topological superconductivity in monolayer transition metal dichalcogenides.

PubMed

Hsu, Yi-Ting; Vaezi, Abolhassan; Fischer, Mark H; Kim, Eun-Ah

2017-04-11

Theoretically, it has been known that breaking spin degeneracy and effectively realizing spinless fermions is a promising path to topological superconductors. Yet, topological superconductors are rare to date. Here we propose to realize spinless fermions by splitting the spin degeneracy in momentum space. Specifically, we identify monolayer hole-doped transition metal dichalcogenide (TMD)s as candidates for topological superconductors out of such momentum-space-split spinless fermions. Although electron-doped TMDs have recently been found superconducting, the observed superconductivity is unlikely topological because of the near spin degeneracy. Meanwhile, hole-doped TMDs with momentum-space-split spinless fermions remain unexplored. Employing a renormalization group analysis, we propose that the unusual spin-valley locking in hole-doped TMDs together with repulsive interactions selectively favours two topological superconducting states: interpocket paired state with Chern number 2 and intrapocket paired state with finite pair momentum. A confirmation of our predictions will open up possibilities for manipulating topological superconductors on the device-friendly platform of monolayer TMDs.

Generalized recursive solutions to Ornstein-Zernike integral equations

NASA Astrophysics Data System (ADS)

Rossky, Peter J.; Dale, William D. T.

1980-09-01

Recursive procedures for the solution of a class of integral equations based on the Ornstein-Zernike equation are developed; the hypernetted chain and Percus-Yevick equations are two special cases of the class considered. It is shown that certain variants of the new procedures developed here are formally equivalent to those recently developed by Dale and Friedman, if the new recursive expressions are initialized in the same way as theirs. However, the computational solution of the new equations is significantly more efficient. Further, the present analysis leads to the identification of various graphical quantities arising in the earlier study with more familiar quantities related to pair correlation functions. The analysis is greatly facilitated by the use of several identities relating simple chain sums whose graphical elements can be written as a sum of two or more parts. In particular, the use of these identities permits renormalization of the equivalent series solution to the integral equation to be directly incorporated into the recursive solution in a straightforward manner. Formulas appropriate to renormalization with respect to long and short range parts of the pair potential, as well as more general components of the direct correlation function, are obtained. To further illustrate the utility of this approach, we show that a simple generalization of the hypernetted chain closure relation for the direct correlation function leads directly to the reference hypernetted chain (RHNC) equation due to Lado. The form of the correlation function used in the exponential approximation of Andersen and Chandler is then seen to be equivalent to the first estimate obtained from a renormalized RHNC equation.

L'enseignement de la musique et de la langue seconde: pistes d'integration et consequences sur les apprentissages (The Teaching of Music and Second Language: Paths for Integration and Consequences for Instruction).

ERIC Educational Resources Information Center

Lowe, Anne S.

1998-01-01

An experiment in a grade 2 French immersion program compared performance of a group-taught music lessons totally integrated into classroom instruction and a group not given music instruction. Pre- and post-tests of tonal-rhythmic patterns and form that have commonalities with pronunciation, oral grammar, vocabulary, and reading comprehension found…

Renormalization of Supersymmetric QCD on the Lattice

NASA Astrophysics Data System (ADS)

Costa, Marios; Panagopoulos, Haralambos

2018-03-01

We perform a pilot study of the perturbative renormalization of a Supersymmetric gauge theory with matter fields on the lattice. As a specific example, we consider Supersymmetric N=1 QCD (SQCD). We study the self-energies of all particles which appear in this theory, as well as the renormalization of the coupling constant. To this end we compute, perturbatively to one-loop, the relevant two-point and three-point Green's functions using both dimensional and lattice regularizations. Our lattice formulation involves theWilson discretization for the gluino and quark fields; for gluons we employ the Wilson gauge action; for scalar fields (squarks) we use naive discretization. The gauge group that we consider is SU(Nc), while the number of colors, Nc, the number of flavors, Nf, and the gauge parameter, α, are left unspecified. We obtain analytic expressions for the renormalization factors of the coupling constant (Zg) and of the quark (ZΨ), gluon (Zu), gluino (Zλ), squark (ZA±), and ghost (Zc) fields on the lattice. We also compute the critical values of the gluino, quark and squark masses. Finally, we address the mixing which occurs among squark degrees of freedom beyond tree level: we calculate the corresponding mixing matrix which is necessary in order to disentangle the components of the squark field via an additional finite renormalization.

F4 symmetric ϕ3 theory at four loops

NASA Astrophysics Data System (ADS)

Gracey, J. A.

2017-03-01

The renormalization group functions for six dimensional scalar ϕ3 theory with an F4 symmetry are provided at four loops in the modified minimal subtraction (MS ¯ ) scheme. Aside from the anomalous dimension of ϕ and the β -function this includes the mass operator and a ϕ2-type operator. The anomalous dimension of the latter is computed explicitly at four loops for the 26 and 324 representations of F4. The ɛ expansion of all the related critical exponents are determined to O (ɛ4). For instance the value for Δϕ agrees with recent conformal bootstrap estimates in 5 and 5.95 dimensions. The renormalization group functions are also provided at four loops for the group E6.

Variational optimization algorithms for uniform matrix product states

NASA Astrophysics Data System (ADS)

Zauner-Stauber, V.; Vanderstraeten, L.; Fishman, M. T.; Verstraete, F.; Haegeman, J.

2018-01-01

We combine the density matrix renormalization group (DMRG) with matrix product state tangent space concepts to construct a variational algorithm for finding ground states of one-dimensional quantum lattices in the thermodynamic limit. A careful comparison of this variational uniform matrix product state algorithm (VUMPS) with infinite density matrix renormalization group (IDMRG) and with infinite time evolving block decimation (ITEBD) reveals substantial gains in convergence speed and precision. We also demonstrate that VUMPS works very efficiently for Hamiltonians with long-range interactions and also for the simulation of two-dimensional models on infinite cylinders. The new algorithm can be conveniently implemented as an extension of an already existing DMRG implementation.

Improving the In-Medium Similarity Renormalization Group via approximate inclusion of three-body effects

NASA Astrophysics Data System (ADS)

Morris, Titus; Bogner, Scott

2016-09-01

The In-Medium Similarity Renormalization Group (IM-SRG) has been applied successfully to the ground state of closed shell finite nuclei. Recent work has extended its ability to target excited states of these closed shell systems via equation of motion methods, and also complete spectra of the whole SD shell via effective shell model interactions. A recent alternative method for solving of the IM-SRG equations, based on the Magnus expansion, not only provides a computationally feasible route to producing observables, but also allows for approximate handling of induced three-body forces. Promising results for several systems, including finite nuclei, will be presented and discussed.

Multicritical points for spin-glass models on hierarchical lattices.

PubMed

Ohzeki, Masayuki; Nishimori, Hidetoshi; Berker, A Nihat

2008-06-01

The locations of multicritical points on many hierarchical lattices are numerically investigated by the renormalization group analysis. The results are compared with an analytical conjecture derived by using the duality, the gauge symmetry, and the replica method. We find that the conjecture does not give the exact answer but leads to locations slightly away from the numerically reliable data. We propose an improved conjecture to give more precise predictions of the multicritical points than the conventional one. This improvement is inspired by a different point of view coming from the renormalization group and succeeds in deriving very consistent answers with many numerical data.

Renormalization group analysis of turbulence

NASA Technical Reports Server (NTRS)

Smith, Leslie M.

1989-01-01

The objective is to understand and extend a recent theory of turbulence based on dynamic renormalization group (RNG) techniques. The application of RNG methods to hydrodynamic turbulence was explored most extensively by Yakhot and Orszag (1986). An eddy viscosity was calculated which was consistent with the Kolmogorov inertial range by systematic elimination of the small scales in the flow. Further, assumed smallness of the nonlinear terms in the redefined equations for the large scales results in predictions for important flow constants such as the Kolmogorov constant. It is emphasized that no adjustable parameters are needed. The parameterization of the small scales in a self-consistent manner has important implications for sub-grid modeling.

Deviation pattern approach for optimizing perturbative terms of QCD renormalization group invariant observables

NASA Astrophysics Data System (ADS)

Khellat, M. R.; Mirjalili, A.

2017-03-01

We first consider the idea of renormalization group-induced estimates, in the context of optimization procedures, for the Brodsky-Lepage-Mackenzie approach to generate higher-order contributions to QCD perturbative series. Secondly, we develop the deviation pattern approach (DPA) in which through a series of comparisons between lowerorder RG-induced estimates and the corresponding analytical calculations, one could modify higher-order RG-induced estimates. Finally, using the normal estimation procedure and DPA, we get estimates of αs4 corrections for the Bjorken sum rule of polarized deep-inelastic scattering and for the non-singlet contribution to the Adler function.

Renormalization-Group Theory Study of Superfluidity and Phase Separation of Helium Mixtures Immersed in Jungle-Gym Aerogel

NASA Astrophysics Data System (ADS)

Lopatnikova, Anna; Berker, A. Nihat

1997-03-01

Superfluidity and phase separation in ^3He-^4He mixtures immersed in jungle-gym (non-random) aerogel are studied by renormalization-group theory.(Phys. Rev. B, in press (1996)) Phase diagrams are calculated for a variety of aerogel concentrations. Superfluidity at very low ^4He concentrations and a depressed tricritical temperature are found at the onset of superfluidity. A superfluid-superfluid phase separation, terminating at an isolated critical point, is found entirely within the superfluid phase. These phenomena, and trends with respect to aerogel concentration, are explained by the connectivity and tenuousness of jungle-gym aerogel.

Renormalization-group study of superfluidity and phase separation of helium mixtures immersed in a nonrandom aerogel

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lopatnikova, A.; Berker, A.N.

1997-02-01

Superfluidity and phase separation in {sup 3}He-{sup 4}He mixtures immersed in a jungle-gym (nonrandom) aerogel are studied by renormalization-group theory. Phase diagrams are calculated for a variety of aerogel concentrations. Superfluidity at very low {sup 4}He concentrations and a depressed tricritical temperature are found at the onset of superfluidity. A superfluid-superfluid phase separation, terminating at an isolated critical point, is found entirely within the superfluid phase. These phenomena and trends with respect to aerogel concentration are explained by the connectivity and tenuousness of a jungle-gym aerogel. {copyright} {ital 1997} {ital The American Physical Society}

Experience with turbulence interaction and turbulence-chemistry models at Fluent Inc.

NASA Technical Reports Server (NTRS)

Choudhury, D.; Kim, S. E.; Tselepidakis, D. P.; Missaghi, M.

1995-01-01

This viewgraph presentation discusses (1) turbulence modeling: challenges in turbulence modeling, desirable attributes of turbulence models, turbulence models in FLUENT, and examples using FLUENT; and (2) combustion modeling: turbulence-chemistry interaction and FLUENT equilibrium model. As of now, three turbulence models are provided: the conventional k-epsilon model, the renormalization group model, and the Reynolds-stress model. The renormalization group k-epsilon model has broadened the range of applicability of two-equation turbulence models. The Reynolds-stress model has proved useful for strongly anisotropic flows such as those encountered in cyclones, swirlers, and combustors. Issues remain, such as near-wall closure, with all classes of models.

Renormalization-group study of the Nagel-Schreckenberg model

NASA Astrophysics Data System (ADS)

Teoh, Han Kheng; Yong, Ee Hou

2018-03-01

We study the phase transition from free flow to congested phases in the Nagel-Schreckenberg (NS) model by using the dynamically driven renormalization group (DDRG). The breaking probability p that governs the driving strategy is investigated. For the deterministic case p =0 , the dynamics remain invariant in each renormalization-group (RG) transformation. Two fully attractive fixed points, ρc*=0 and 1, and one unstable fixed point, ρc*=1 /(vmax+1 ) , are obtained. The critical exponent ν which is related to the correlation length is calculated for various vmax. The critical exponent appears to decrease weakly with vmax from ν =1.62 to the asymptotical value of 1.00. For the random case p >0 , the transition rules in the coarse-grained scale are found to be different from the NS specification. To have a qualitative understanding of the effect of stochasticity, the case p →0 is studied with simulation, and the RG flow in the ρ -p plane is obtained. The fixed points p =0 and 1 that govern the driving strategy of the NS model are found. A short discussion on the extension of the DDRG method to the NS model with the open-boundary condition is outlined.

Stepwise positional-orientational order and the multicritical-multistructural global phase diagram of the s=3/2 Ising model from renormalization-group theory.

PubMed

Yunus, Çağın; Renklioğlu, Başak; Keskin, Mustafa; Berker, A Nihat

2016-06-01

The spin-3/2 Ising model, with nearest-neighbor interactions only, is the prototypical system with two different ordering species, with concentrations regulated by a chemical potential. Its global phase diagram, obtained in d=3 by renormalization-group theory in the Migdal-Kadanoff approximation or equivalently as an exact solution of a d=3 hierarchical lattice, with flows subtended by 40 different fixed points, presents a very rich structure containing eight different ordered and disordered phases, with more than 14 different types of phase diagrams in temperature and chemical potential. It exhibits phases with orientational and/or positional order. It also exhibits quintuple phase transition reentrances. Universality of critical exponents is conserved across different renormalization-group flow basins via redundant fixed points. One of the phase diagrams contains a plastic crystal sequence, with positional and orientational ordering encountered consecutively as temperature is lowered. The global phase diagram also contains double critical points, first-order and critical lines between two ordered phases, critical end points, usual and unusual (inverted) bicritical points, tricritical points, multiple tetracritical points, and zero-temperature criticality and bicriticality. The four-state Potts permutation-symmetric subspace is contained in this model.

Implementation of rigorous renormalization group method for ground space and low-energy states of local Hamiltonians

NASA Astrophysics Data System (ADS)

Roberts, Brenden; Vidick, Thomas; Motrunich, Olexei I.

2017-12-01

The success of polynomial-time tensor network methods for computing ground states of certain quantum local Hamiltonians has recently been given a sound theoretical basis by Arad et al. [Math. Phys. 356, 65 (2017), 10.1007/s00220-017-2973-z]. The convergence proof, however, relies on "rigorous renormalization group" (RRG) techniques which differ fundamentally from existing algorithms. We introduce a practical adaptation of the RRG procedure which, while no longer theoretically guaranteed to converge, finds matrix product state ansatz approximations to the ground spaces and low-lying excited spectra of local Hamiltonians in realistic situations. In contrast to other schemes, RRG does not utilize variational methods on tensor networks. Rather, it operates on subsets of the system Hilbert space by constructing approximations to the global ground space in a treelike manner. We evaluate the algorithm numerically, finding similar performance to density matrix renormalization group (DMRG) in the case of a gapped nondegenerate Hamiltonian. Even in challenging situations of criticality, large ground-state degeneracy, or long-range entanglement, RRG remains able to identify candidate states having large overlap with ground and low-energy eigenstates, outperforming DMRG in some cases.

E-cigarette Marketing and Older Smokers: Road to Renormalization

PubMed Central

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

2015-01-01

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

Qualitative Evaluation of Project P.A.T.H.S.: An Integration of Findings Based on Program Participants

PubMed Central

Shek, Daniel T. L.; Sun, Rachel C. F.

2012-01-01

An integration of the qualitative evaluation findings collected in different cohorts of students who participated in Project P.A.T.H.S. (Positive Adolescent Training through Holistic Social Programmes) (n = 252 students in 29 focus groups) was carried out. With specific focus on how the informants described the program, results showed that the descriptions were mainly positive in nature, suggesting that the program was well received by the program participants. When the informants were invited to name three metaphors that could stand for the program, positive metaphors were commonly used. Beneficial effects of the program in different psychosocial domains were also voiced by the program participants. The qualitative findings integrated in this paper provide further support for the effectiveness of the Tier 1 Program of Project P.A.T.H.S. in promoting holistic development in Chinese adolescents in Hong Kong. PMID:22666134

Combining path integration and remembered landmarks when navigating without vision.

PubMed

Kalia, Amy A; Schrater, Paul R; Legge, Gordon E

2013-01-01

This study investigated the interaction between remembered landmark and path integration strategies for estimating current location when walking in an environment without vision. We asked whether observers navigating without vision only rely on path integration information to judge their location, or whether remembered landmarks also influence judgments. Participants estimated their location in a hallway after viewing a target (remembered landmark cue) and then walking blindfolded to the same or a conflicting location (path integration cue). We found that participants averaged remembered landmark and path integration information when they judged that both sources provided congruent information about location, which resulted in more precise estimates compared to estimates made with only path integration. In conclusion, humans integrate remembered landmarks and path integration in a gated fashion, dependent on the congruency of the information. Humans can flexibly combine information about remembered landmarks with path integration cues while navigating without visual information.

Combining Path Integration and Remembered Landmarks When Navigating without Vision

PubMed Central

Kalia, Amy A.; Schrater, Paul R.; Legge, Gordon E.

2013-01-01

This study investigated the interaction between remembered landmark and path integration strategies for estimating current location when walking in an environment without vision. We asked whether observers navigating without vision only rely on path integration information to judge their location, or whether remembered landmarks also influence judgments. Participants estimated their location in a hallway after viewing a target (remembered landmark cue) and then walking blindfolded to the same or a conflicting location (path integration cue). We found that participants averaged remembered landmark and path integration information when they judged that both sources provided congruent information about location, which resulted in more precise estimates compared to estimates made with only path integration. In conclusion, humans integrate remembered landmarks and path integration in a gated fashion, dependent on the congruency of the information. Humans can flexibly combine information about remembered landmarks with path integration cues while navigating without visual information. PMID:24039742

Precise MS light-quark masses from lattice QCD in the regularization invariant symmetric momentum-subtraction scheme

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gorbahn, Martin; Jaeger, Sebastian; Department of Physics and Astronomy, University of Sussex, Falmer, Brighton BN1 9QH

2010-12-01

We compute the conversion factors needed to obtain the MS and renormalization-group-invariant (RGI) up, down, and strange quark masses at next-to-next-to-leading order from the corresponding parameters renormalized in the recently proposed RI/SMOM and RI/SMOM{sub {gamma}{sub {mu}} }renormalization schemes. This is important for obtaining the MS masses with the best possible precision from numerical lattice QCD simulations, because the customary RI{sup (')}/MOM scheme is afflicted with large irreducible uncertainties both on the lattice and in perturbation theory. We find that the smallness of the known one-loop matching coefficients is accompanied by even smaller two-loop contributions. From a study of residual scalemore » dependences, we estimate the resulting perturbative uncertainty on the light-quark masses to be about 2% in the RI/SMOM scheme and about 3% in the RI/SMOM{sub {gamma}{sub {mu}} }scheme. Our conversion factors are given in fully analytic form, for general covariant gauge and renormalization point. We provide expressions for the associated anomalous dimensions.« less

Chiral algebras in Landau-Ginzburg models

NASA Astrophysics Data System (ADS)

Dedushenko, Mykola

2018-03-01

Chiral algebras in the cohomology of the {\\overline{Q}}+ supercharge of two-dimensional N=(0,2) theories on flat spacetime are discussed. Using the supercurrent multiplet, we show that the answer is renormalization group invariant for theories with an R-symmetry. For N=(0,2) Landau-Ginzburg models, the chiral algebra is determined by the operator equations of motion, which preserve their classical form, and quantum renormalization of composite operators. We study these theories and then specialize to the N=(2,2) models and consider some examples.

Polymer diffusion in quenched disorder: A renormalization group approach

NASA Astrophysics Data System (ADS)

Ebert, Ute

1996-01-01

We study the diffusion of polymers through quenched short-range correlated random media by renormalization group (RG) methods, which allow us to derive universal predictions in the limit of long chains and weak disorder. We take local quenched random potentials with second moment v and the excluded-volume interaction u of the chain segments into account. We show that our model contains the relevant features of polymer diffusion in random media in the RG sense if we focus on the local entropic effects rather than on the topological constraints of a quenched random medium. The dynamic generating functional and the general structure of its perturbation expansion in u and v are derived. The distribution functions for the center-of-mass motion and the internal modes of one chain and for the correlation of the center of mass motions of two chains are calculated to one-loop order. The results allow for sufficient cross-checks to have trust in the one-loop renormalizability of the model. The general structure as well as the one-loop results of the integrated RG flow of the parameters are discussed. Universal results can be found for the effective static interaction w≔u-v≥0 and for small effective disorder couplingbar v(l) on the intermediate length scale l. As a first physical prediction from our analysis, we determine the general nonlinear scaling form of the chain diffusion constant and evaluate it explicitly as[Figure not available: see fulltext.] forbar v(l) ≪ 1.

Off-shell hydrodynamics from holography

DOE PAGES

Crossley, Michael; Glorioso, Paolo; Liu, Hong; ...

2016-02-18

In this article, we outline a program for obtaining an action principle for dissipative fluid dynamics by considering the holographic Wilsonian renormalization group applied to systems with a gravity dual. As a first step, in this paper we restrict to systems with a non-dissipative horizon. By integrating out gapped degrees of freedom in the bulk gravitational system between an asymptotic boundary and a horizon, we are led to a formulation of hydrodynamics where the dynamical variables are not standard velocity and temperature fields, but the relative embedding of the boundary and horizon hypersurfaces. At zeroth order, this action reduces tomore » that proposed by Dubovsky et al. as an off-shell formulation of ideal fluid dynamics.« less

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Myoung-Jae; Jung, Young-Dae, E-mail: ydjung@hanyang.ac.kr; Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590

2016-01-15

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

Functional renormalization group approach to the Yang-Lee edge singularity

DOE PAGES

An, X.; Mesterházy, D.; Stephanov, M. A.

2016-07-08

Here, we determine the scaling properties of the Yang-Lee edge singularity as described by a one-component scalar field theory with imaginary cubic coupling, using the nonperturbative functional renormalization group in 3 ≤ d ≤ 6 Euclidean dimensions. We find very good agreement with high-temperature series data in d = 3 dimensions and compare our results to recent estimates of critical exponents obtained with the four-loop ϵ = 6 - d expansion and the conformal bootstrap. The relevance of operator insertions at the corresponding fixed point of the RG β functions is discussed and we estimate the error associated with O(∂more » 4) truncations of the scale-dependent effective action.« less

Functional renormalization group approach to the Yang-Lee edge singularity

DOE Office of Scientific and Technical Information (OSTI.GOV)

An, X.; Mesterházy, D.; Stephanov, M. A.

Here, we determine the scaling properties of the Yang-Lee edge singularity as described by a one-component scalar field theory with imaginary cubic coupling, using the nonperturbative functional renormalization group in 3 ≤ d ≤ 6 Euclidean dimensions. We find very good agreement with high-temperature series data in d = 3 dimensions and compare our results to recent estimates of critical exponents obtained with the four-loop ϵ = 6 - d expansion and the conformal bootstrap. The relevance of operator insertions at the corresponding fixed point of the RG β functions is discussed and we estimate the error associated with O(∂more » 4) truncations of the scale-dependent effective action.« less

Finite-size scaling study of the two-dimensional Blume-Capel model

NASA Astrophysics Data System (ADS)

Beale, Paul D.

1986-02-01

The phase diagram of the two-dimensional Blume-Capel model is investigated by using the technique of phenomenological finite-size scaling. The location of the tricritical point and the values of the critical and tricritical exponents are determined. The location of the tricritical point (Tt=0.610+/-0.005, Dt=1.9655+/-0.0010) is well outside the error bars for the value quoted in previous Monte Carlo simulations but in excellent agreement with more recent Monte Carlo renormalization-group results. The values of the critical and tricritical exponents, with the exception of the leading thermal tricritical exponent, are in excellent agreement with previous calculations, conjectured values, and Monte Carlo renormalization-group studies.

Scaling properties of the two-dimensional randomly stirred Navier-Stokes equation.

PubMed

Mazzino, Andrea; Muratore-Ginanneschi, Paolo; Musacchio, Stefano

2007-10-05

We inquire into the scaling properties of the 2D Navier-Stokes equation sustained by a force field with Gaussian statistics, white noise in time, and with a power-law correlation in momentum space of degree 2 - 2 epsilon. This is at variance with the setting usually assumed to derive Kraichnan's classical theory. We contrast accurate numerical experiments with the different predictions provided for the small epsilon regime by Kraichnan's double cascade theory and by renormalization group analysis. We give clear evidence that for all epsilon, Kraichnan's theory is consistent with the observed phenomenology. Our results call for a revision in the renormalization group analysis of (2D) fully developed turbulence.

Universal renormalization-group dynamics at the onset of chaos in logistic maps and nonextensive statistical mechanics

NASA Astrophysics Data System (ADS)

Baldovin, F.; Robledo, A.

2002-10-01

We uncover the dynamics at the chaos threshold μ∞ of the logistic map and find that it consists of trajectories made of intertwined power laws that reproduce the entire period-doubling cascade that occurs for μ<μ∞. We corroborate this structure analytically via the Feigenbaum renormalization-group (RG) transformation and find that the sensitivity to initial conditions has precisely the form of a q exponential, of which we determine the q index and the q-generalized Lyapunov coefficient λq. Our results are an unequivocal validation of the applicability of the nonextensive generalization of Boltzmann-Gibbs statistical mechanics to critical points of nonlinear maps.

Functional renormalization group and variational Monte Carlo studies of the electronic instabilities in graphene near (1)/(4) doping

NASA Astrophysics Data System (ADS)

Wang, Wan-Sheng; Xiang, Yuan-Yuan; Wang, Qiang-Hua; Wang, Fa; Yang, Fan; Lee, Dung-Hai

2012-01-01

We study the electronic instabilities of near 1/4 electron doped graphene using the singular-mode functional renormalization group, with a self-adaptive k mesh to improve the treatment of the van Hove singularities, and variational Monte Carlo method. At 1/4 doping the system is a chiral spin-density wave state exhibiting the anomalous quantized Hall effect. When the doping deviates from 1/4, the dx2-y2+idxy Cooper pairing becomes the leading instability. Our results suggest that near 1/4 electron or hole doping (away from the neutral point) the graphene is either a Chern insulator or a topoligical superconductor.

Stochastic quantization and holographic Wilsonian renormalization group of free massive fermion

NASA Astrophysics Data System (ADS)

Moon, Sung Pil

2018-06-01

We examine a suggested relation between stochastic quantization and the holographic Wilsonian renormalization group in the massive fermion case on Euclidean AdS space. The original suggestion about the general relation between the two theories is posted in arXiv:1209.2242. In the previous researches, it is already verified that scalar fields, U(1) gauge fields, and massless fermions are consistent with the relation. In this paper, we examine the relation in the massive fermion case. Contrary to the other case, in the massive fermion case, the action needs particular boundary terms to satisfy boundary conditions. We finally confirm that the proposed suggestion is also valid in the massive fermion case.

On the Yakhot-Orszag renormalization group method for deriving turbulence statistics and models

NASA Technical Reports Server (NTRS)

Smith, L. M.; Reynolds, W. C.

1992-01-01

An independent, comprehensive, critical review of the 'renormalization group' (RNG) theory of turbulence developed by Yakhot and Orszag (1986) is provided. Their basic theory for the Navier-Stokes equations is confirmed, and approximations in the scale removal procedure are discussed. The YO derivations of the velocity-derivative skewness and the transport equation for the energy dissipation rate are examined. An algebraic error in the derivation of the skewness is corrected. The corrected RNG skewness value of -0.59 is in agreement with experiments at moderate Reynolds numbers. Several problems are identified in the derivation of the energy dissipation rate equations which suggest that the derivation should be reformulated.

Development of renormalization group analysis of turbulence

NASA Technical Reports Server (NTRS)

Smith, L. M.

1990-01-01

The renormalization group (RG) procedure for nonlinear, dissipative systems is now quite standard, and its applications to the problem of hydrodynamic turbulence are becoming well known. In summary, the RG method isolates self similar behavior and provides a systematic procedure to describe scale invariant dynamics in terms of large scale variables only. The parameterization of the small scales in a self consistent manner has important implications for sub-grid modeling. This paper develops the homogeneous, isotropic turbulence and addresses the meaning and consequence of epsilon-expansion. The theory is then extended to include a weak mean flow and application of the RG method to a sequence of models is shown to converge to the Navier-Stokes equations.

Loop Variables in String Theory

NASA Astrophysics Data System (ADS)

Sathiapalan, B.

The loop variable approach is a proposal for a gauge-invariant generalization of the sigma-model renormalization group method of obtaining equations of motion in string theory. The basic guiding principle is space-time gauge invariance rather than world sheet properties. In essence it is a version of Wilson's exact renormalization group equation for the world sheet theory. It involves all the massive modes and is defined with a finite world sheet cutoff, which allows one to go off the mass-shell. On shell the tree amplitudes of string theory are reproduced. The equations are gauge-invariant off shell also. This paper is a self-contained discussion of the loop variable approach as well as its connection with the Wilsonian RG.

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.

Quantum multicriticality in disordered Weyl semimetals

NASA Astrophysics Data System (ADS)

Luo, Xunlong; Xu, Baolong; Ohtsuki, Tomi; Shindou, Ryuichi

2018-01-01

In electronic band structure of solid-state material, two band-touching points with linear dispersion appear in pairs in the momentum space. When they annihilate each other, the system undergoes a quantum phase transition from a three-dimensional (3D) Weyl semimetal (WSM) phase to a band insulator phase such as a Chern band insulator (CI) phase. The phase transition is described by a new critical theory with a "magnetic dipole"-like object in the momentum space. In this paper, we reveal that the critical theory hosts a novel disorder-driven quantum multicritical point, which is encompassed by three quantum phases: a renormalized WSM phase, a CI phase, and a diffusive metal (DM) phase. Based on the renormalization group argument, we first clarify scaling properties around the band-touching points at the quantum multicritical point as well as all phase boundaries among these three phases. Based on numerical calculations of localization length, density of states, and critical conductance distribution, we next prove that a localization-delocalization transition between the CI phase with a finite zero-energy density of states (zDOS) and DM phase belongs to an ordinary 3D unitary class. Meanwhile, a localization-delocalization transition between the Chern insulator phase with zero zDOS and a renormalized WSM phase turns out to be a direct phase transition whose critical exponent ν =0.80 ±0.01 . We interpret these numerical results by a renormalization group analysis on the critical theory.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Csaki, Csaba; Erlich, Joshua; Hollowood, Timothy J.

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 Minkowskimore » 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.« less

Statistical symmetry restoration in fully developed turbulence: Renormalization group analysis of two models.

PubMed

Antonov, N V; Gulitskiy, N M; Kostenko, M M; Malyshev, A V

2018-03-01

In this paper we consider the model of incompressible fluid described by the stochastic Navier-Stokes equation with finite correlation time of a random force. Inertial-range asymptotic behavior of fully developed turbulence is studied by means of the field theoretic renormalization group within the one-loop approximation. It is corroborated that regardless of the values of model parameters and initial data the inertial-range behavior of the model is described by the limiting case of vanishing correlation time. This indicates that the Galilean symmetry of the model violated by the "colored" random force is restored in the inertial range. This regime corresponds to the only nontrivial fixed point of the renormalization group equation. The stability of this point depends on the relation between the exponents in the energy spectrum E∝k^{1-y} and the dispersion law ω∝k^{2-η}. The second analyzed problem is the passive advection of a scalar field by this velocity ensemble. Correlation functions of the scalar field exhibit anomalous scaling behavior in the inertial-convective range. We demonstrate that in accordance with Kolmogorov's hypothesis of the local symmetry restoration the main contribution to the operator product expansion is given by the isotropic operator, while anisotropic terms should be considered only as corrections.

Statistical symmetry restoration in fully developed turbulence: Renormalization group analysis of two models

NASA Astrophysics Data System (ADS)

Antonov, N. V.; Gulitskiy, N. M.; Kostenko, M. M.; Malyshev, A. V.

2018-03-01

In this paper we consider the model of incompressible fluid described by the stochastic Navier-Stokes equation with finite correlation time of a random force. Inertial-range asymptotic behavior of fully developed turbulence is studied by means of the field theoretic renormalization group within the one-loop approximation. It is corroborated that regardless of the values of model parameters and initial data the inertial-range behavior of the model is described by the limiting case of vanishing correlation time. This indicates that the Galilean symmetry of the model violated by the "colored" random force is restored in the inertial range. This regime corresponds to the only nontrivial fixed point of the renormalization group equation. The stability of this point depends on the relation between the exponents in the energy spectrum E ∝k1 -y and the dispersion law ω ∝k2 -η . The second analyzed problem is the passive advection of a scalar field by this velocity ensemble. Correlation functions of the scalar field exhibit anomalous scaling behavior in the inertial-convective range. We demonstrate that in accordance with Kolmogorov's hypothesis of the local symmetry restoration the main contribution to the operator product expansion is given by the isotropic operator, while anisotropic terms should be considered only as corrections.

Exact renormalization group in Batalin-Vilkovisky theory

NASA Astrophysics Data System (ADS)

Zucchini, Roberto

2018-03-01

In this paper, inspired by the Costello's seminal work [11], we present a general formulation of exact renormalization group (RG) within the Batalin-Vilkovisky (BV) quantization scheme. In the spirit of effective field theory, the BV bracket and Laplacian structure as well as the BV effective action (EA) depend on an effective energy scale. The BV EA at a certain scale satisfies the BV quantum master equation at that scale. The RG flow of the EA is implemented by BV canonical maps intertwining the BV structures at different scales. Infinitesimally, this generates the BV exact renormalization group equation (RGE). We show that BV RG theory can be extended by augmenting the scale parameter space R to its shifted tangent bundle T [1]ℝ. The extra odd direction in scale space allows for a BV RG supersymmetry that constrains the structure of the BV RGE bringing it to Polchinski's form [6]. We investigate the implications of BV RG supersymmetry in perturbation theory. Finally, we illustrate our findings by constructing free models of BV RG flow and EA exhibiting RG supersymmetry in the degree -1 symplectic framework and studying the perturbation theory thereof. We find in particular that the odd partner of effective action describes perturbatively the deviation of the interacting RG flow from its free counterpart.

Critical behavior of the anisotropic Heisenberg model by effective-field renormalization group

NASA Astrophysics Data System (ADS)

de Sousa, J. Ricardo; Fittipaldi, I. P.

1994-05-01

A real-space effective-field renormalization-group method (ERFG) recently derived for computing critical properties of Ising spins is extended to treat the quantum spin-1/2 anisotropic Heisenberg model. The formalism is based on a generalized but approximate Callen-Suzuki spin relation and utilizes a convenient differential operator expansion technique. The method is illustrated in several lattice structures by employing its simplest approximation version in which clusters with one (N'=1) and two (N=2) spins are used. The results are compared with those obtained from the standard mean-field (MFRG) and Migdal-Kadanoff (MKRG) renormalization-group treatments and it is shown that this technique leads to rather accurate results. It is shown that, in contrast with the MFRG and MKRG predictions, the EFRG, besides correctly distinguishing the geometries of different lattice structures, also provides a vanishing critical temperature for all two-dimensional lattices in the isotropic Heisenberg limit. For the simple cubic lattice, the dependence of the transition temperature Tc with the exchange anisotropy parameter Δ [i.e., Tc(Δ)], and the resulting value for the critical thermal crossover exponent φ [i.e., Tc≂Tc(0)+AΔ1/φ ] are in quite good agreement with results available in the literature in which more sophisticated treatments are used.

Solar System constraints on renormalization group extended general relativity: The PPN and Laplace-Runge-Lenz analyses with the external potential effect

NASA Astrophysics Data System (ADS)

Rodrigues, Davi C.; Mauro, Sebastião; de Almeida, Álefe O. F.

2016-10-01

General relativity extensions based on renormalization group effects are motivated by a known physical principle and constitute a class of extended gravity theories that have some unexplored unique aspects. In this work we develop in detail the Newtonian and post-Newtonian limits of a realization called renormalization group extended general relativity (RGGR). Special attention is given to the external potential effect, which constitutes a type of screening mechanism typical of RGGR. In the Solar System, RGGR depends on a single dimensionless parameter ν¯⊙, and this parameter is such that for ν¯⊙=0 one fully recovers GR in the Solar System. Previously this parameter was constrained to be |ν¯ ⊙|≲10-21 , without considering the external potential effect. Here we show that under a certain approximation RGGR can be cast in a form compatible with the parametrized post-Newtonian (PPN) formalism, and we use both the PPN formalism and the Laplace-Runge-Lenz technique to put new bounds on ν¯⊙, either considering or not the external potential effect. With the external potential effect the new bound reads |ν¯ ⊙|≲10-16 . We discuss the possible consequences of this bound on the dark matter abundance in galaxies.

Coarse-Graining of Polymer Dynamics via Energy Renormalization

NASA Astrophysics Data System (ADS)

Xia, Wenjie; Song, Jake; Phelan, Frederick; Douglas, Jack; Keten, Sinan

The computational prediction of the properties of polymeric materials to serve the needs of materials design and prediction of their performance is a grand challenge due to the prohibitive computational times of all-atomistic (AA) simulations. Coarse-grained (CG) modeling is an essential strategy for making progress on this problem. While there has been intense activity in this area, effective methods of coarse-graining have been slow to develop. Our approach to this fundamental problem starts from the observation that integrating out degrees of freedom of the AA model leads to a strong modification of the configurational entropy and cohesive interaction. Based on this observation, we propose a temperature-dependent systematic renormalization of the cohesive interaction in the CG modeling to recover the thermodynamic modifications in the system and the dynamics of the AA model. Here, we show that this energy renormalization approach to CG can faithfully estimate the diffusive, segmental and glassy dynamics of the AA model over a large temperature range spanning from the Arrhenius melt to the non-equilibrium glassy states. Our proposed CG strategy offers a promising strategy for developing thermodynamically consistent CG models with temperature transferability.

From individual spiking neurons to population behavior: Systematic elimination of short-wavelength spatial modes

NASA Astrophysics Data System (ADS)

Steyn-Ross, Moira L.; Steyn-Ross, D. A.

2016-02-01

Mean-field models of the brain approximate spiking dynamics by assuming that each neuron responds to its neighbors via a naive spatial average that neglects local fluctuations and correlations in firing activity. In this paper we address this issue by introducing a rigorous formalism to enable spatial coarse-graining of spiking dynamics, scaling from the microscopic level of a single type 1 (integrator) neuron to a macroscopic assembly of spiking neurons that are interconnected by chemical synapses and nearest-neighbor gap junctions. Spiking behavior at the single-neuron scale ℓ ≈10 μ m is described by Wilson's two-variable conductance-based equations [H. R. Wilson, J. Theor. Biol. 200, 375 (1999), 10.1006/jtbi.1999.1002], driven by fields of incoming neural activity from neighboring neurons. We map these equations to a coarser spatial resolution of grid length B ℓ , with B ≫1 being the blocking ratio linking micro and macro scales. Our method systematically eliminates high-frequency (short-wavelength) spatial modes q ⃗ in favor of low-frequency spatial modes Q ⃗ using an adiabatic elimination procedure that has been shown to be equivalent to the path-integral coarse graining applied to renormalization group theory of critical phenomena. This bottom-up neural regridding allows us to track the percolation of synaptic and ion-channel noise from the single neuron up to the scale of macroscopic population-average variables. Anticipated applications of neural regridding include extraction of the current-to-firing-rate transfer function, investigation of fluctuation criticality near phase-transition tipping points, determination of spatial scaling laws for avalanche events, and prediction of the spatial extent of self-organized macrocolumnar structures. As a first-order exemplar of the method, we recover nonlinear corrections for a coarse-grained Wilson spiking neuron embedded in a network of identical diffusively coupled neurons whose chemical synapses have been disabled. Intriguingly, we find that reblocking transforms the original type 1 Wilson integrator into a type 2 resonator whose spike-rate transfer function exhibits abrupt spiking onset with near-vertical takeoff and chaotic dynamics just above threshold.

Exact phase boundaries and topological phase transitions of the X Y Z spin chain

NASA Astrophysics Data System (ADS)

Jafari, S. A.

2017-07-01

Within the block spin renormalization group, we give a very simple derivation of the exact phase boundaries of the X Y Z spin chain. First, we identify the Ising order along x ̂ or y ̂ as attractive renormalization group fixed points of the Kitaev chain. Then, in a global phase space composed of the anisotropy λ of the X Y interaction and the coupling Δ of the Δ σzσz interaction, we find that the above fixed points remain attractive in the two-dimesional parameter space. We therefore classify the gapped phases of the X Y Z spin chain as: (1) either attracted to the Ising limit of the Kitaev-chain, which in turn is characterized by winding number ±1 , depending on whether the Ising order parameter is along x ̂ or y ̂ directions; or (2) attracted to the charge density wave (CDW) phases of the underlying Jordan-Wigner fermions, which is characterized by zero winding number. We therefore establish that the exact phase boundaries of the X Y Z model in Baxter's solution indeed correspond to topological phase transitions. The topological nature of the phase transitions of the X Y Z model justifies why our analytical solution of the three-site problem that is at the core of the present renormalization group treatment is able to produce the exact phase boundaries of Baxter's solution. We argue that the distribution of the winding numbers between the three Ising phases is a matter of choice of the coordinate system, and therefore the CDW-Ising phase is entitled to host appropriate form of zero modes. We further observe that in the Kitaev-chain the renormalization group flow can be cast into a geometric progression of a properly identified parameter. We show that this new parameter is actually the size of the (Majorana) zero modes.

Horizon as critical phenomenon

NASA Astrophysics Data System (ADS)

Lee, Sung-Sik

2016-09-01

We show that renormalization group flow can be viewed as a gradual wave function collapse, where a quantum state associated with the action of field theory evolves toward a final state that describes an IR fixed point. The process of collapse is described by the radial evolution in the dual holographic theory. If the theory is in the same phase as the assumed IR fixed point, the initial state is smoothly projected to the final state. If in a different phase, the initial state undergoes a phase transition which in turn gives rise to a horizon in the bulk geometry. We demonstrate the connection between critical behavior and horizon in an example, by deriving the bulk metrics that emerge in various phases of the U( N ) vector model in the large N limit based on the holographic dual constructed from quantum renormalization group. The gapped phase exhibits a geometry that smoothly ends at a finite proper distance in the radial direction. The geometric distance in the radial direction measures a complexity: the depth of renormalization group transformation that is needed to project the generally entangled UV state to a direct product state in the IR. For gapless states, entanglement persistently spreads out to larger length scales, and the initial state can not be projected to the direct product state. The obstruction to smooth projection at charge neutral point manifests itself as the long throat in the anti-de Sitter space. The Poincare horizon at infinity marks the critical point which exhibits a divergent length scale in the spread of entanglement. For the gapless states with non-zero chemical potential, the bulk space becomes the Lifshitz geometry with the dynamical critical exponent two. The identification of horizon as critical point may provide an explanation for the universality of horizon. We also discuss the structure of the bulk tensor network that emerges from the quantum renormalization group.

Line Interference Effects Using a Refined Robert-Bonamy Formalism: the Test Case of the Isotropic Raman Spectra of Autoperturbed N2

NASA Technical Reports Server (NTRS)

Boulet, Christian; Ma, Qiancheng; Thibault, Franck

2014-01-01

A symmetrized version of the recently developed refined Robert-Bonamy formalism [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] is proposed. This model takes into account line coupling effects and hence allows the calculation of the off-diagonal elements of the relaxation matrix, without neglecting the rotational structure of the perturbing molecule. The formalism is applied to the isotropic Raman spectra of autoperturbed N2 for which a benchmark quantum relaxation matrix has recently been proposed. The consequences of the classical path approximation are carefully analyzed. Methods correcting for effects of inelasticity are considered. While in the right direction, these corrections appear to be too crude to provide off diagonal elements which would yield, via the sum rule, diagonal elements in good agreement with the quantum results. In order to overcome this difficulty, a re-normalization procedure is applied, which ensures that the off-diagonal elements do lead to the exact quantum diagonal elements. The agreement between the (re-normalized) semi-classical and quantum relaxation matrices is excellent, at least for the Raman spectra of N2, opening the way to the analysis of more complex molecular systems.

Weyl consistency conditions in non-relativistic quantum field theory

DOE PAGES

Pal, Sridip; Grinstein, Benjamín

2016-12-05

Weyl consistency conditions have been used in unitary relativistic quantum field theory to impose constraints on the renormalization group flow of certain quantities. We classify the Weyl anomalies and their renormalization scheme ambiguities for generic non-relativistic theories in 2 + 1 dimensions with anisotropic scaling exponent z = 2; the extension to other values of z are discussed as well. We give the consistency conditions among these anomalies. As an application we find several candidates for a C-theorem. Here, we comment on possible candidates for a C-theorem in higher dimensions.

Exact renormalization group equation for the Lifshitz critical point

NASA Astrophysics Data System (ADS)

Bervillier, C.

2004-10-01

An exact renormalization equation (ERGE) accounting for an anisotropic scaling is derived. The critical and tricritical Lifshitz points are then studied at leading order of the derivative expansion which is shown to involve two differential equations. The resulting estimates of the Lifshitz critical exponents compare well with the O(ε) calculations. In the case of the Lifshitz tricritical point, it is shown that a marginally relevant coupling defies the perturbative approach since it actually makes the fixed point referred to in the previous perturbative calculations O(ε) finally unstable.

Renormalization of Extended QCD2

NASA Astrophysics Data System (ADS)

Fukaya, Hidenori; Yamamura, Ryo

2015-10-01

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

Quantization of the nonlinear sigma model revisited

NASA Astrophysics Data System (ADS)

Nguyen, Timothy

2016-08-01

We revisit the subject of perturbatively quantizing the nonlinear sigma model in two dimensions from a rigorous, mathematical point of view. Our main contribution is to make precise the cohomological problem of eliminating potential anomalies that may arise when trying to preserve symmetries under quantization. The symmetries we consider are twofold: (i) diffeomorphism covariance for a general target manifold; (ii) a transitive group of isometries when the target manifold is a homogeneous space. We show that there are no anomalies in case (i) and that (ii) is also anomaly-free under additional assumptions on the target homogeneous space, in agreement with the work of Friedan. We carry out some explicit computations for the O(N)-model. Finally, we show how a suitable notion of the renormalization group establishes the Ricci flow as the one loop renormalization group flow of the nonlinear sigma model.

Spatial variation of vessel grouping in the xylem of Betula platyphylla Roth.

PubMed

Zhao, Xiping

2016-01-01

Vessel grouping in angiosperms may improve hydraulic integration and increase the spread of cavitations through redundancy pathways. Although disputed, it is increasingly attracting research interest as a potentially significant hydraulic trait. However, the variation of vessel grouping in a tree is poorly understood. I measured the number of solitary and grouped vessels in the xylem of Betula platyphylla Roth. from the pith to the bark along the water flow path. The vessel grouping parameters included the mean number of vessels per vessel group (VG), percentage of solitary vessels (SVP), percentage of radial multiple vessels (MVP), and percentage of cluster vessels (CVP). The effects of cambial age (CA) and flow path-length (PL) on the vessel grouping were analyzed using a linear mixed model.VG and CVP increased nonlinearly, SVP decreased nonlinearly with PL. In trunks and branches, VG and CVP decreased nonlinearly, and SVP increased nonlinearly with CA. In roots, the parameters had no change with CA. MVP was almost constant with PL or CA. The results suggest that vessel grouping has a nonrandom variation pattern, which is affected deeply by cambial age and water flow path.

How nonperturbative is the infrared regime of Landau gauge Yang-Mills correlators?

NASA Astrophysics Data System (ADS)

Reinosa, U.; Serreau, J.; Tissier, M.; Wschebor, N.

2017-07-01

We study the Landau gauge correlators of Yang-Mills fields for infrared Euclidean momenta in the context of a massive extension of the Faddeev-Popov Lagrangian which, we argue, underlies a variety of continuum approaches. Standard (perturbative) renormalization group techniques with a specific, infrared-safe renormalization scheme produce so-called decoupling and scaling solutions for the ghost and gluon propagators, which correspond to nontrivial infrared fixed points. The decoupling fixed point is infrared stable and weakly coupled, while the scaling fixed point is unstable and generically strongly coupled except for low dimensions d →2 . Under the assumption that such a scaling fixed point exists beyond one-loop order, we find that the corresponding ghost and gluon scaling exponents are, respectively, 2 αF=2 -d and 2 αG=d at all orders of perturbation theory in the present renormalization scheme. We discuss the relation between the ghost wave function renormalization, the gluon screening mass, the scale of spectral positivity violation, and the gluon mass parameter. We also show that this scaling solution does not realize the standard Becchi-Rouet-Stora-Tyutin symmetry of the Faddeev-Popov Lagrangian. Finally, we discuss our findings in relation to the results of nonperturbative continuum methods.

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.

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.

The Integration of Geographical Information System and Remotely Sensed Data to Track and Predict the Migration Path of the Africanized Honey Bee

NASA Technical Reports Server (NTRS)

Ward, Charles; Bravo, Jessica; De Luna, Rosalia; Lopez, Gerardo; Pichardo, Itza; Trejo, Danny; Vargas, Gabriel

1997-01-01

One of the research groups at the Pan American Center for Earth and Environmental Studies (PACES) is researching the northward migration path of Africanized Honey Bees or often referred to in the popular press as killer bees. The goal of the Killer Bee Research Group (KBRG) is to set up a database in the form of a geographical information system, which will be used to track and predict the bees future migration path. Included in this paper is background information on geographical information systems, the SPANS Explorer software package which was used to implement the database, and Advanced Very High Resolution Radiometer data and how each of these is being incorporated in the research. With an accurate means of predicting future migration paths, the negative effects of the Africanized honey bees maybe reduced.

Observation of an anisotropic Dirac cone reshaping and ferrimagnetic spin polarization in an organic conductor

PubMed Central

Hirata, Michihiro; Ishikawa, Kyohei; Miyagawa, Kazuya; Tamura, Masafumi; Berthier, Claude; Basko, Denis; Kobayashi, Akito; Matsuno, Genki; Kanoda, Kazushi

2016-01-01

The Coulomb interaction among massless Dirac fermions in graphene is unscreened around the isotropic Dirac points, causing a logarithmic velocity renormalization and a cone reshaping. In less symmetric Dirac materials possessing anisotropic cones with tilted axes, the Coulomb interaction can provide still more exotic phenomena, which have not been experimentally unveiled yet. Here, using site-selective nuclear magnetic resonance, we find a non-uniform cone reshaping accompanied by a bandwidth reduction and an emergent ferrimagnetism in tilted Dirac cones that appear on the verge of charge ordering in an organic compound. Our theoretical analyses based on the renormalization-group approach and the Hubbard model show that these observations are the direct consequences of the long-range and short-range parts of the Coulomb interaction, respectively. The cone reshaping and the bandwidth renormalization, as well as the magnetic behaviour revealed here, can be ubiquitous and vital for many Dirac materials. PMID:27578363

Mass deformations of 5d SCFTs via holography

NASA Astrophysics Data System (ADS)

Gutperle, Michael; Kaidi, Justin; Raj, Himanshu

2018-02-01

Using six-dimensional Euclidean F (4) gauged supergravity we construct a holographic renormalization group flow for a CFT on S 5. Numerical solutions to the BPS equations are obtained and the free energy of the theory on S 5 is determined holographically by calculation of the renormalized on-shell supergravity action. In the process, we deal with subtle issues such as holographic renormalization and addition of finite counterterms. We then propose a candidate field theory dual to these solutions. This tentative dual is a supersymmetry-preserving deformation of the strongly-coupled non-Lagrangian SCFT derived from the D4-D8 system in string theory. In the IR, this theory is a mass deformation of a USp(2 N ) gauge theory. A localization calculation of the free energy is performed for this IR theory, which for reasonably small values of the deformation parameter is found to have the same qualitative behaviour as the holographic free energy.

Baryon chiral perturbation theory extended beyond the low-energy region.

PubMed

Epelbaum, E; Gegelia, J; Meißner, Ulf-G; Yao, De-Liang

We consider an extension of the one-nucleon sector of baryon chiral perturbation theory beyond the low-energy region. The applicability of this approach for higher energies is restricted to small scattering angles, i.e. the kinematical region, where the quark structure of hadrons cannot be resolved. The main idea is to re-arrange the low-energy effective Lagrangian according to a new power counting and to exploit the freedom of the choice of the renormalization condition for loop diagrams. We generalize the extended on-mass-shell scheme for the one-nucleon sector of baryon chiral perturbation theory by choosing a sliding scale, that is, we expand the physical amplitudes around kinematical points beyond the threshold. This requires the introduction of complex-valued renormalized coupling constants, which can be either extracted from experimental data, or calculated using the renormalization group evolution of coupling constants fixed in threshold region.

Evidence for equivalence of diffusion processes of passive scalar and magnetic fields in anisotropic Navier-Stokes turbulence.

PubMed

Jurčišinová, E; Jurčišin, M

2017-05-01

The influence of the uniaxial small-scale anisotropy on the kinematic magnetohydrodynamic turbulence is investigated by using the field theoretic renormalization group technique in the one-loop approximation of a perturbation theory. The infrared stable fixed point of the renormalization group equations, which drives the scaling properties of the model in the inertial range, is investigated as the function of the anisotropy parameters and it is shown that, at least at the one-loop level of approximation, the diffusion processes of the weak passive magnetic field in the anisotropically driven kinematic magnetohydrodynamic turbulence are completely equivalent to the corresponding diffusion processes of passively advected scalar fields in the anisotropic Navier-Stokes turbulent environments.

Estimate of the critical exponents from the field-theoretical renormalization group: mathematical meaning of the 'Standard Values'

DOE Office of Scientific and Technical Information (OSTI.GOV)

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

2008-06-15

New estimates of the critical exponents have been obtained from the field-theoretical renormalization group using a new method for summing divergent series. The results almost coincide with the central values obtained by Le Guillou and Zinn-Justin (the so-called standard values), but have lower uncertainty. It has been shown that usual field-theoretical estimates implicitly imply the smoothness of the coefficient functions. The last assumption is open for discussion in view of the existence of the oscillating contribution to the coefficient functions. The appropriate interpretation of the last contribution is necessary both for the estimation of the systematic errors of the standardmore » values and for a further increase in accuracy.« less

Renormalization Group Theory, the Epsilon Expansion and Ken Wilson as I knew Him

NASA Astrophysics Data System (ADS)

Fisher, Michael E.

The tasks posed for renormalization group theory (RGT) within statistical physics by critical phenomena theory in the 1960's are set out briefly in contradistinction to quantum field theory (QFT), which was the origin for Ken Wilson's concerns. Kadanoff's 1966 block spin scaling picture and its difficulties are presented;Wilson's early vision of flows is described from the author's perspective. How Wilson's subsequent breakthrough ideas, published in 1971, led to the epsilon expansion and the resulting clarity is related. Concluding sections complete the general picture of flows in a space of Hamiltonians, universality and scaling. The article represents a 40% condensation (but with added items) of an earlier account: Rev. Mod. Phys. 70, 653-681 (1998).

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.

Non-local geometry inside Lifshitz horizon

NASA Astrophysics Data System (ADS)

Hu, Qi; Lee, Sung-Sik

2017-07-01

Based on the quantum renormalization group, we derive the bulk geometry that emerges in the holographic dual of the fermionic U( N ) vector model at a nonzero charge density. The obstruction that prohibits the metallic state from being smoothly deformable to the direct product state under the renormalization group flow gives rise to a horizon at a finite radial coordinate in the bulk. The region outside the horizon is described by the Lifshitz geometry with a higher-spin hair determined by microscopic details of the boundary theory. On the other hand, the interior of the horizon is not described by any Riemannian manifold, as it exhibits an algebraic non-locality. The non-local structure inside the horizon carries the information on the shape of the filled Fermi sea.

The renormalization scale-setting problem in QCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu, Xing-Gang; Brodsky, Stanley J.; Mojaza, Matin

2013-09-01

A key problem in making precise perturbative QCD predictions is to set the proper renormalization scale of the running coupling. The conventional scale-setting procedure assigns an arbitrary range and an arbitrary systematic error to fixed-order pQCD predictions. In fact, this ad hoc procedure gives results which depend on the choice of the renormalization scheme, and it is in conflict with the standard scale-setting procedure used in QED. Predictions for physical results should be independent of the choice of the scheme or other theoretical conventions. We review current ideas and points of view on how to deal with the renormalization scalemore » ambiguity and show how to obtain renormalization scheme- and scale-independent estimates. We begin by introducing the renormalization group (RG) equation and an extended version, which expresses the invariance of physical observables under both the renormalization scheme and scale-parameter transformations. The RG equation provides a convenient way for estimating the scheme- and scale-dependence of a physical process. We then discuss self-consistency requirements of the RG equations, such as reflexivity, symmetry, and transitivity, which must be satisfied by a scale-setting method. Four typical scale setting methods suggested in the literature, i.e., the Fastest Apparent Convergence (FAC) criterion, the Principle of Minimum Sensitivity (PMS), the Brodsky–Lepage–Mackenzie method (BLM), and the Principle of Maximum Conformality (PMC), are introduced. Basic properties and their applications are discussed. We pay particular attention to the PMC, which satisfies all of the requirements of RG invariance. Using the PMC, all non-conformal terms associated with the β-function in the perturbative series are summed into the running coupling, and one obtains a unique, scale-fixed, scheme-independent prediction at any finite order. The PMC provides the principle underlying the BLM method, since it gives the general rule for extending BLM up to any perturbative order; in fact, they are equivalent to each other through the PMC–BLM correspondence principle. Thus, all the features previously observed in the BLM literature are also adaptable to the PMC. The PMC scales and the resulting finite-order PMC predictions are to high accuracy independent of the choice of the initial renormalization scale, and thus consistent with RG invariance. The PMC is also consistent with the renormalization scale-setting procedure for QED in the zero-color limit. The use of the PMC thus eliminates a serious systematic scale error in perturbative QCD predictions, greatly improving the precision of empirical tests of the Standard Model and their sensitivity to new physics.« less

Path Integration on the Upper Half-Plane

NASA Astrophysics Data System (ADS)

Kubo, R.

1987-10-01

Feynman's path integral is considered on the Poincaré upper half-plane. It is shown that the fundermental solution to the heat equation partial f/partial t=Delta_{H}f can be expressed in terms of a path integral. A simple relation between the path integral and the Selberg trace formula is discussed briefly.

Path integration of head direction: updating a packet of neural activity at the correct speed using axonal conduction delays.

PubMed

Walters, Daniel; Stringer, Simon; Rolls, Edmund

2013-01-01

The head direction cell system is capable of accurately updating its current representation of head direction in the absence of visual input. This is known as the path integration of head direction. An important question is how the head direction cell system learns to perform accurate path integration of head direction. In this paper we propose a model of velocity path integration of head direction in which the natural time delay of axonal transmission between a linked continuous attractor network and competitive network acts as a timing mechanism to facilitate the correct speed of path integration. The model effectively learns a "look-up" table for the correct speed of path integration. In simulation, we show that the model is able to successfully learn two different speeds of path integration across two different axonal conduction delays, and without the need to alter any other model parameters. An implication of this model is that, by learning look-up tables for each speed of path integration, the model should exhibit a degree of robustness to damage. In simulations, we show that the speed of path integration is not significantly affected by degrading the network through removing a proportion of the cells that signal rotational velocity.

Path Integration of Head Direction: Updating a Packet of Neural Activity at the Correct Speed Using Axonal Conduction Delays

PubMed Central

Walters, Daniel; Stringer, Simon; Rolls, Edmund

2013-01-01

The head direction cell system is capable of accurately updating its current representation of head direction in the absence of visual input. This is known as the path integration of head direction. An important question is how the head direction cell system learns to perform accurate path integration of head direction. In this paper we propose a model of velocity path integration of head direction in which the natural time delay of axonal transmission between a linked continuous attractor network and competitive network acts as a timing mechanism to facilitate the correct speed of path integration. The model effectively learns a “look-up” table for the correct speed of path integration. In simulation, we show that the model is able to successfully learn two different speeds of path integration across two different axonal conduction delays, and without the need to alter any other model parameters. An implication of this model is that, by learning look-up tables for each speed of path integration, the model should exhibit a degree of robustness to damage. In simulations, we show that the speed of path integration is not significantly affected by degrading the network through removing a proportion of the cells that signal rotational velocity. PMID:23526976

Testing the renormalisation group theory of cooperative transitions at the lambda point of helium

NASA Technical Reports Server (NTRS)

Lipa, J. A.; Li, Q.; Chui, T. C. P.; Marek, D.

1988-01-01

The status of high resolution tests of the renormalization group theory of cooperative phase transitions performed near the lambda point of helium is described. The prospects for performing improved tests in space are discussed.

Maximally random discrete-spin systems with symmetric and asymmetric interactions and maximally degenerate ordering

NASA Astrophysics Data System (ADS)

Atalay, Bora; Berker, A. Nihat

2018-05-01

Discrete-spin systems with maximally random nearest-neighbor interactions that can be symmetric or asymmetric, ferromagnetic or antiferromagnetic, including off-diagonal disorder, are studied, for the number of states q =3 ,4 in d dimensions. We use renormalization-group theory that is exact for hierarchical lattices and approximate (Migdal-Kadanoff) for hypercubic lattices. For all d >1 and all noninfinite temperatures, the system eventually renormalizes to a random single state, thus signaling q ×q degenerate ordering. Note that this is the maximally degenerate ordering. For high-temperature initial conditions, the system crosses over to this highly degenerate ordering only after spending many renormalization-group iterations near the disordered (infinite-temperature) fixed point. Thus, a temperature range of short-range disorder in the presence of long-range order is identified, as previously seen in underfrustrated Ising spin-glass systems. The entropy is calculated for all temperatures, behaves similarly for ferromagnetic and antiferromagnetic interactions, and shows a derivative maximum at the short-range disordering temperature. With a sharp immediate contrast of infinitesimally higher dimension 1 +ɛ , the system is as expected disordered at all temperatures for d =1 .

Turbulent mixing of a critical fluid: The non-perturbative renormalization

NASA Astrophysics Data System (ADS)

Hnatič, M.; Kalagov, G.; Nalimov, M.

2018-01-01

Non-perturbative Renormalization Group (NPRG) technique is applied to a stochastical model of a non-conserved scalar order parameter near its critical point, subject to turbulent advection. The compressible advecting flow is modeled by a random Gaussian velocity field with zero mean and correlation function 〈υjυi 〉 ∼ (Pji⊥ + αPji∥) /k d + ζ. Depending on the relations between the parameters ζ, α and the space dimensionality d, the model reveals several types of scaling regimes. Some of them are well known (model A of equilibrium critical dynamics and linear passive scalar field advected by a random turbulent flow), but there is a new nonequilibrium regime (universality class) associated with new nontrivial fixed points of the renormalization group equations. We have obtained the phase diagram (d, ζ) of possible scaling regimes in the system. The physical point d = 3, ζ = 4 / 3 corresponding to three-dimensional fully developed Kolmogorov's turbulence, where critical fluctuations are irrelevant, is stable for α ≲ 2.26. Otherwise, in the case of "strong compressibility" α ≳ 2.26, the critical fluctuations of the order parameter become relevant for three-dimensional turbulence. Estimations of critical exponents for each scaling regime are presented.

String Theory: exact solutions, marginal deformations and hyperbolic spaces

NASA Astrophysics Data System (ADS)

Orlando, Domenico

2006-10-01

This thesis is almost entirely devoted to studying string theory backgrounds characterized by simple geometrical and integrability properties. The archetype of this type of system is given by Wess-Zumino-Witten models, describing string propagation in a group manifold or, equivalently, a class of conformal field theories with current algebras. We study the moduli space of such models by using truly marginal deformations. Particular emphasis is placed on asymmetric deformations that, together with the CFT description, enjoy a very nice spacetime interpretation in terms of the underlying Lie algebra. Then we take a slight detour so to deal with off-shell systems. Using a renormalization-group approach we describe the relaxation towards the symmetrical equilibrium situation. In he final chapter we consider backgrounds with Ramond-Ramond field and in particular we analyze direct products of constant-curvature spaces and find solutions with hyperbolic spaces.

Phases of unstable conifolds

DOE Office of Scientific and Technical Information (OSTI.GOV)

Narayan, K.

2007-03-15

We explore the phase structure induced by closed string tachyon condensation of toric nonsupersymmetric conifold-like singularities described by an integral charge matrix Q=(n{sub 1}n{sub 2}-n{sub 3}-n{sub 4}), n{sub i}>0, iQ{sub i}{ne}0, initiated by Narayan [J. High Energy Phys. 03 (2006) 036]. Using gauged linear sigma model renormalization group flows and toric geometry techniques, we see a cascadelike phase structure containing decays to lower order conifold-like singularities, including, in particular, the supersymmetric conifold and the Y{sup pq} spaces. This structure is consistent with the Type II GSO projection obtained previously for these singularities. Transitions between the various phases of these geometriesmore » include flips and flops.« less

Threshold and flavor effects in the renormalization group equations of the MSSM. II. Dimensionful couplings

NASA Astrophysics Data System (ADS)

Box, Andrew D.; Tata, Xerxes

2009-02-01

We reexamine the one-loop renormalization group equations (RGEs) for the dimensionful parameters of the minimal supersymmetric standard model (MSSM) with broken supersymmetry, allowing for arbitrary flavor structure of the soft SUSY-breaking parameters. We include threshold effects by evaluating the β-functions in a sequence of (nonsupersymmetric) effective theories with heavy particles decoupled at the scale of their mass. We present the most general form for high-scale, soft SUSY-breaking parameters that obtains if we assume that the supersymmetry-breaking mechanism does not introduce new intergenerational couplings. This form, possibly amended to allow additional sources of flavor-violation, serves as a boundary condition for solving the RGEs for the dimensionful MSSM parameters. We then present illustrative examples of numerical solutions to the RGEs. We find that in a SUSY grand unified theory with the scale of SUSY scalars split from that of gauginos and higgsinos, the gaugino mass unification condition may be violated by O(10%). As another illustration, we show that in mSUGRA, the rate for the flavor-violating ttilde 1→c Ztilde 1 decay obtained using the complete RGE solution is smaller than that obtained using the commonly used “single-step” integration of the RGEs by a factor 10-25, and so may qualitatively change expectations for topologies from top-squark pair production at colliders. Together with the RGEs for dimensionless couplings presented in a companion paper, the RGEs in Appendix 2 of this paper form a complete set of one-loop MSSM RGEs that include threshold and flavor-effects necessary for two-loop accuracy.

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

PubMed

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 et al., Nature (London) 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/N(0) → 0 in the limit of large systems (where N(0) is the initial size of the graph and N its size at a given RSR step). In contrast, it happens at finite N/N(0) in sparse ER graphs and in the annealed model, while it happens for N/N(0) → 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 et al. [Phys. Rev. Lett. 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 percolation, allowing us to obtain very high statistics.

Breaking of scale invariance in the time dependence of correlation functions in isotropic and homogeneous turbulence

NASA Astrophysics Data System (ADS)

Tarpin, Malo; Canet, Léonie; Wschebor, Nicolás

2018-05-01

In this paper, we present theoretical results on the statistical properties of stationary, homogeneous, and isotropic turbulence in incompressible flows in three dimensions. Within the framework of the non-perturbative renormalization group, we derive a closed renormalization flow equation for a generic n-point correlation (and response) function for large wave-numbers with respect to the inverse integral scale. The closure is obtained from a controlled expansion and relies on extended symmetries of the Navier-Stokes field theory. It yields the exact leading behavior of the flow equation at large wave-numbers |p→ i| and for arbitrary time differences ti in the stationary state. Furthermore, we obtain the form of the general solution of the corresponding fixed point equation, which yields the analytical form of the leading wave-number and time dependence of n-point correlation functions, for large wave-numbers and both for small ti and in the limit ti → ∞. At small ti, the leading contribution at large wave-numbers is logarithmically equivalent to -α (ɛL ) 2 /3|∑tip→ i|2, where α is a non-universal constant, L is the integral scale, and ɛ is the mean energy injection rate. For the 2-point function, the (tp)2 dependence is known to originate from the sweeping effect. The derived formula embodies the generalization of the effect of sweeping to n-point correlation functions. At large wave-numbers and large ti, we show that the ti2 dependence in the leading order contribution crosses over to a |ti| dependence. The expression of the correlation functions in this regime was not derived before, even for the 2-point function. Both predictions can be tested in direct numerical simulations and in experiments.

An open-chain imaginary-time path-integral sampling approach to the calculation of approximate symmetrized quantum time correlation functions.

PubMed

Cendagorta, Joseph R; Bačić, Zlatko; Tuckerman, Mark E

2018-03-14

We introduce a scheme for approximating quantum time correlation functions numerically within the Feynman path integral formulation. Starting with the symmetrized version of the correlation function expressed as a discretized path integral, we introduce a change of integration variables often used in the derivation of trajectory-based semiclassical methods. In particular, we transform to sum and difference variables between forward and backward complex-time propagation paths. Once the transformation is performed, the potential energy is expanded in powers of the difference variables, which allows us to perform the integrals over these variables analytically. The manner in which this procedure is carried out results in an open-chain path integral (in the remaining sum variables) with a modified potential that is evaluated using imaginary-time path-integral sampling rather than requiring the generation of a large ensemble of trajectories. Consequently, any number of path integral sampling schemes can be employed to compute the remaining path integral, including Monte Carlo, path-integral molecular dynamics, or enhanced path-integral molecular dynamics. We believe that this approach constitutes a different perspective in semiclassical-type approximations to quantum time correlation functions. Importantly, we argue that our approximation can be systematically improved within a cumulant expansion formalism. We test this approximation on a set of one-dimensional problems that are commonly used to benchmark approximate quantum dynamical schemes. We show that the method is at least as accurate as the popular ring-polymer molecular dynamics technique and linearized semiclassical initial value representation for correlation functions of linear operators in most of these examples and improves the accuracy of correlation functions of nonlinear operators.

An open-chain imaginary-time path-integral sampling approach to the calculation of approximate symmetrized quantum time correlation functions

NASA Astrophysics Data System (ADS)

Cendagorta, Joseph R.; Bačić, Zlatko; Tuckerman, Mark E.

2018-03-01

We introduce a scheme for approximating quantum time correlation functions numerically within the Feynman path integral formulation. Starting with the symmetrized version of the correlation function expressed as a discretized path integral, we introduce a change of integration variables often used in the derivation of trajectory-based semiclassical methods. In particular, we transform to sum and difference variables between forward and backward complex-time propagation paths. Once the transformation is performed, the potential energy is expanded in powers of the difference variables, which allows us to perform the integrals over these variables analytically. The manner in which this procedure is carried out results in an open-chain path integral (in the remaining sum variables) with a modified potential that is evaluated using imaginary-time path-integral sampling rather than requiring the generation of a large ensemble of trajectories. Consequently, any number of path integral sampling schemes can be employed to compute the remaining path integral, including Monte Carlo, path-integral molecular dynamics, or enhanced path-integral molecular dynamics. We believe that this approach constitutes a different perspective in semiclassical-type approximations to quantum time correlation functions. Importantly, we argue that our approximation can be systematically improved within a cumulant expansion formalism. We test this approximation on a set of one-dimensional problems that are commonly used to benchmark approximate quantum dynamical schemes. We show that the method is at least as accurate as the popular ring-polymer molecular dynamics technique and linearized semiclassical initial value representation for correlation functions of linear operators in most of these examples and improves the accuracy of correlation functions of nonlinear operators.

Estimating the boundaries of a limit cycle in a 2D dynamical system using renormalization group

NASA Astrophysics Data System (ADS)

Dutta, Ayan; Das, Debapriya; Banerjee, Dhruba; Bhattacharjee, Jayanta K.

2018-04-01

While the plausibility of formation of limit cycle has been a well studied topic in context of the Poincare-Bendixson theorem, studies on estimates in regard to the possible size and shape of the limit cycle seem to be scanty in the literature. In this paper we present a pedagogical study of some aspects of the size of this limit cycle using perturbative renormalization group by doing detailed and explicit calculations upto second order for the Selkov model for glycolytic oscillations. This famous model is well known to lead to a limit cycle for certain ranges of values of the parameters involved in the problem. Within the tenets of the approximations made, reasonable agreement with the numerical plots can be achieved.

Dissipative exciton transfer in donor-bridge-acceptor systems: numerical renormalization group calculation of equilibrium properties.

PubMed

Tornow, Sabine; Tong, Ning-Hua; Bulla, Ralf

2006-07-05

We present a detailed model study of exciton transfer processes in donor-bridge-acceptor (DBA) systems. Using a model which includes the intermolecular Coulomb interaction and the coupling to a dissipative environment we calculate the phase diagram, the absorption spectrum as well as dynamic equilibrium properties with the numerical renormalization group. This method is non-perturbative and therefore allows one to cover the full parameter space, especially the case when the intermolecular Coulomb interaction is of the same order as the coupling to the environment and perturbation theory cannot be applied. For DBA systems with up to six sites we found a transition to the localized phase (self-trapping) depending on the coupling to the dissipative environment. We discuss various criteria which favour delocalized exciton transfer.

Deriving amplitude equations for weakly-nonlinear oscillators and their generalizations

NASA Astrophysics Data System (ADS)

O'Malley, Robert E., Jr.; Williams, David B.

2006-06-01

Results by physicists on renormalization group techniques have recently sparked interest in the singular perturbations community of applied mathematicians. The survey paper, [Phys. Rev. E 54(1) (1996) 376-394], by Chen et al. demonstrated that many problems which applied mathematicians solve using disparate methods can be solved using a single approach. Analysis of that renormalization group method by Mudavanhu and O'Malley [Stud. Appl. Math. 107(1) (2001) 63-79; SIAM J. Appl. Math. 63(2) (2002) 373-397], among others, indicates that the technique can be streamlined. This paper carries that analysis several steps further to present an amplitude equation technique which is both well adapted for use with a computer algebra system and easy to relate to the classical methods of averaging and multiple scales.

Symmetry-conserving purification of quantum states within the density matrix renormalization group

DOE PAGES

Nocera, Alberto; Alvarez, Gonzalo

2016-01-28

The density matrix renormalization group (DMRG) algorithm was originally designed to efficiently compute the zero-temperature or ground-state properties of one-dimensional strongly correlated quantum systems. The development of the algorithm at finite temperature has been a topic of much interest, because of the usefulness of thermodynamics quantities in understanding the physics of condensed matter systems, and because of the increased complexity associated with efficiently computing temperature-dependent properties. The ancilla method is a DMRG technique that enables the computation of these thermodynamic quantities. In this paper, we review the ancilla method, and improve its performance by working on reduced Hilbert spaces andmore » using canonical approaches. Furthermore we explore its applicability beyond spins systems to t-J and Hubbard models.« less

Hybrid Defect Phase Transition: Renormalization Group and Monte Carlo Analysis

NASA Astrophysics Data System (ADS)

Kaufman, Miron; Diep, H. T.

2010-03-01

For the q-state Potts model with 2 < q <= 4 on the square lattice with a defect line, the order parameter on the defect line jumps discontinuously from zero to a nonzero value while the defect energy varies continuously with the temperature at the critical temperature. Monte-Carlo simulations (H. T. Diep, M. Kaufman, Phys Rev E 2009) of the q-state Potts model on a square lattice with a line of defects verify the renormalization group prediction (M. Kaufman, R. B. Griffiths, Phys Rev B 1982) on the occurrence of the hybrid transition on the defect line. This is interesting since for those q values the bulk transition is continuous. This hybrid (continuous - discontinuous) defect transition is induced by the infinite range correlations at the bulk critical point.

Multiloop functional renormalization group for general models

NASA Astrophysics Data System (ADS)

Kugler, Fabian B.; von Delft, Jan

2018-02-01

We present multiloop flow equations in the functional renormalization group (fRG) framework for the four-point vertex and self-energy, formulated for a general fermionic many-body problem. This generalizes the previously introduced vertex flow [F. B. Kugler and J. von Delft, Phys. Rev. Lett. 120, 057403 (2018), 10.1103/PhysRevLett.120.057403] and provides the necessary corrections to the self-energy flow in order to complete the derivative of all diagrams involved in the truncated fRG flow. Due to its iterative one-loop structure, the multiloop flow is well suited for numerical algorithms, enabling improvement of many fRG computations. We demonstrate its equivalence to a solution of the (first-order) parquet equations in conjunction with the Schwinger-Dyson equation for the self-energy.

Toward a Model of Social Influence that Explains Minority Student Integration into the Scientific Community

ERIC Educational Resources Information Center

Estrada, Mica; Woodcock, Anna; Hernandez, Paul R.; Schultz, P. Wesley

2011-01-01

Students from several ethnic minority groups are underrepresented in the sciences, indicating that minority students more frequently drop out of the scientific career path than nonminority students. Viewed from a perspective of social influence, this pattern suggests that minority students do not integrate into the scientific community at the same…

Thermalization and light cones in a model with weak integrability breaking

DOE PAGES

Bertini, Bruno; Essler, Fabian H. L.; Groha, Stefan; ...

2016-12-09

Here, we employ equation-of-motion techniques to study the nonequilibrium dynamics in a lattice model of weakly interacting spinless fermions. Our model provides a simple setting for analyzing the effects of weak integrability-breaking perturbations on the time evolution after a quantum quench. We establish the accuracy of the method by comparing results at short and intermediate times to time-dependent density matrix renormalization group computations. For sufficiently weak integrability-breaking interactions we always observe prethermalization plateaus, where local observables relax to nonthermal values at intermediate time scales. At later times a crossover towards thermal behavior sets in. We determine the associated time scale,more » which depends on the initial state, the band structure of the noninteracting theory, and the strength of the integrability-breaking perturbation. Our method allows us to analyze in some detail the spreading of correlations and in particular the structure of the associated light cones in our model. We find that the interior and exterior of the light cone are separated by an intermediate region, the temporal width of which appears to scale with a universal power law t 1/3.« less

Supersymmetric QCD on the lattice: An exploratory study

NASA Astrophysics Data System (ADS)

Costa, M.; Panagopoulos, H.

2017-08-01

We perform a pilot study of the perturbative renormalization of a supersymmetric gauge theory with matter fields on the lattice. As a specific example, we consider supersymmetric N =1 QCD (SQCD). We study the self-energies of all particles which appear in this theory, as well as the renormalization of the coupling constant. To this end we compute, perturbatively to one-loop, the relevant two-point and three-point Green's functions using both dimensional and lattice regularizations. Our lattice formulation involves the Wilson discretization for the gluino and quark fields; for gluons we employ the Wilson gauge action; for scalar fields (squarks) we use naïve discretization. The gauge group that we consider is S U (Nc), while the number of colors, Nc, the number of flavors, Nf, and the gauge parameter, α , are left unspecified. We obtain analytic expressions for the renormalization factors of the coupling constant (Zg) and of the quark (Zψ), gluon (Zu), gluino (Zλ), squark (ZA ±), and ghost (Zc) fields on the lattice. We also compute the critical values of the gluino, quark and squark masses. Finally, we address the mixing which occurs among squark degrees of freedom beyond tree level: we calculate the corresponding mixing matrix which is necessary in order to disentangle the components of the squark field via an additional finite renormalization.

Flux Renormalization in Constant Power Burnup Calculations

DOE PAGES

Isotalo, Aarno E.; Aalto Univ., Otaniemi; Davidson, Gregory G.; ...

2016-06-15

To more accurately represent the desired power in a constant power burnup calculation, the depletion steps of the calculation can be divided into substeps and the neutron flux renormalized on each substep to match the desired power. Here, this paper explores how such renormalization should be performed, how large a difference it makes, and whether using renormalization affects results regarding the relative performance of different neutronics–depletion coupling schemes. When used with older coupling schemes, renormalization can provide a considerable improvement in overall accuracy. With previously published higher order coupling schemes, which are more accurate to begin with, renormalization has amore » much smaller effect. Finally, while renormalization narrows the differences in the accuracies of different coupling schemes, their order of accuracy is not affected.« less

Sensorimotor-Conceptual Integration in Free Walking Enhances Divergent Thinking for Young and Older Adults

PubMed Central

Kuo, Chun-Yu; Yeh, Yei-Yu

2016-01-01

Prior research has shown that free walking can enhance creative thinking. Nevertheless, it remains unclear whether bidirectional body-mind links are essential for the positive effect of free walking on creative thinking. Moreover, it is unknown whether the positive effect can be generalized to older adults. In Experiment 1, we replicated previous findings with two additional groups of young participants. Participants in the rectangular-walking condition walked along a rectangular path while generating unusual uses for chopsticks. Participants in the free-walking group walked freely as they wished, and participants in the free-generation condition generated unconstrained free paths while the participants in the random-experienced condition walked those paths. Only the free-walking group showed better performance in fluency, flexibility, and originality. In Experiment 2, two groups of older adults were randomly assigned to the free-walking and rectangular-walking conditions. The free-walking group showed better performance than the rectangular-walking group. Moreover, older adults in the free-walking group outperformed young adults in the rectangular-walking group in originality and performed comparably in fluency and flexibility. Bidirectional links between proprioceptive-motor kinematics and metaphorical abstract concepts can enhance divergent thinking for both young and older adults. PMID:27790178

Group field theory with noncommutative metric variables.

PubMed

Baratin, Aristide; Oriti, Daniele

2010-11-26

We introduce a dual formulation of group field theories as a type of noncommutative field theories, making their simplicial geometry manifest. For Ooguri-type models, the Feynman amplitudes are simplicial path integrals for BF theories. We give a new definition of the Barrett-Crane model for gravity by imposing the simplicity constraints directly at the level of the group field theory action.

Geometry, Heat Equation and Path Integrals on the Poincaré Upper Half-Plane

NASA Astrophysics Data System (ADS)

Kubo, R.

1988-01-01

Geometry, heat equation and Feynman's path integrals are studied on the Poincaré upper half-plane. The fundamental solution to the heat equation partial f/partial t = Delta_{H} f is expressed in terms of a path integral defined on the upper half-plane. It is shown that Kac's statement that Feynman's path integral satisfies the Schrödinger equation is also valid for our case.

On coherent states for the simplest quantum groups

NASA Astrophysics Data System (ADS)

Jurčo, Branislav

1991-01-01

The coherent states for the simplest quantum groups ( q-Heisenberg-Weyl, SU q (2) and the discrete series of representations of SU q (1, 1)) are introduced and their properties investigated. The corresponding analytic representations, path integrals, and q-deformation of Berezin's quantization on ℂ, a sphere, and the Lobatchevsky plane are discussed.

Book Review:

NASA Astrophysics Data System (ADS)

Louko, Jorma

2007-04-01

Bastianelli and van Nieuwenhuizen's monograph `Path Integrals and Anomalies in Curved Space' collects in one volume the results of the authors' 15-year research programme on anomalies that arise in Feynman diagrams of quantum field theories on curved manifolds. The programme was spurred by the path-integral techniques introduced in Alvarez-Gaumé and Witten's renowned 1983 paper on gravitational anomalies which, together with the anomaly cancellation paper by Green and Schwarz, led to the string theory explosion of the 1980s. The authors have produced a tour de force, giving a comprehensive and pedagogical exposition of material that is central to current research. The first part of the book develops from scratch a formalism for defining and evaluating quantum mechanical path integrals in nonlinear sigma models, using time slicing regularization, mode regularization and dimensional regularization. The second part applies this formalism to quantum fields of spin 0, 1/2, 1 and 3/2 and to self-dual antisymmetric tensor fields. The book concludes with a discussion of gravitational anomalies in 10-dimensional supergravities, for both classical and exceptional gauge groups. The target audience is researchers and graduate students in curved spacetime quantum field theory and string theory, and the aims, style and pedagogical level have been chosen with this audience in mind. Path integrals are treated as calculational tools, and the notation and terminology are throughout tailored to calculational convenience, rather than to mathematical rigour. The style is closer to that of an exceedingly thorough and self-contained review article than to that of a textbook. As the authors mention, the first part of the book can be used as an introduction to path integrals in quantum mechanics, although in a classroom setting perhaps more likely as supplementary reading than a primary class text. Readers outside the core audience, including this reviewer, will gain from the book a heightened appreciation of the central role of regularization as a defining ingredient of a quantum field theory and will be impressed by the agreement of results arising from different regularization schemes. The readers may in particular enjoy the authors' `brief history of anomalies' in quantum field theory, as well as a similar historical discussion of path integrals in quantum mechanics.

Non-Perturbative Renormalization of the Lattice Heavy Quark Classical Velocity

NASA Astrophysics Data System (ADS)

Mandula, Jeffrey E.; Ogilvie, Michael C.

1997-02-01

We discuss the renormalization of the lattice formulation of the Heavy Quark Effective Theory (LHQET). In addition to wave function and composite operator renormalizations, on the lattice the classical velocity is also renormalized. The origin of this renormalization is the reduction of Lorentz (or O(4)) invariance to (hyper)cubic invariance. We present results of a new, direct lattice simulation of this finite renormalization, and compare the results to the perturbative (one loop) result. The simulation results are obtained with the use of a variationally optimized heavy-light meson operator, using an ensemble of lattices provided by the Fermilab ACP-MAPS collaboration.

Aspects of Higher-Spin Conformal Field Theories and Their Renormalization Group Flows

NASA Astrophysics Data System (ADS)

Diab, Kenan S.

In this thesis, we study conformal field theories (CFTs) with higher-spin symmetry and the renormalization group flows of some models with interactions that weakly break the higher-spin symmetry. When the higher-spin symmetry is exact, we will present CFT analogues of two classic results in quantum field theory: the Coleman-Mandula theorem, which is the subject of chapter 2, and the Weinberg-Witten theorem, which is the subject of chapter 3. Schematically, our Coleman-Mandula analogue states that a CFT that contains a symmetric conserved current of spin s > 2 in any dimension d > 3 is effectively free, and our Weinberg-Witten analogue states that the presence of certain short, higher-spin, "sufficiently asymmetric" representations of the conformal group is either inconsistent with conformal symmetry or leads to free theories in d = 4 dimensions. In both chapters, the basic strategy is to solve certain Ward identities in convenient kinematical limits and thereby show that the number of solutions is very limited. In the latter chapter, Hofman-Maldacena bounds, which constrain one-point functions of the stress tensor in general states, play a key role. Then, in chapter 4, we will focus on the particular examples of the O(N) and Gross-Neveu model in continuous dimensions. Using diagrammatic techniques, we explicitly calculate how the coefficients of the two-point function of a U(1) current and the two-point function of the stress tensor (CJ and CT, respectively) are renormalized in the 1/N and epsilon expansions. From the higher-spin perspective, these models are interesting since they are related via the AdS/CFT correspondence to Vasiliev gravity. In addition to checking and extending a number of previously-known results about CT and CJ in these theories, we find that in certain dimensions, CJ and CT are not monotonic along the renormalization group flow. Although it was already known that certain supersymmetric models do not satisfy a "CJ"- or " CT"-theorem, this shows that such a theorem is unlikely to hold even under more restrictive assumptions.

Molecular dynamics at low time resolution.

PubMed

Faccioli, P

2010-10-28

The internal dynamics of macromolecular systems is characterized by widely separated time scales, ranging from fraction of picoseconds to nanoseconds. In ordinary molecular dynamics simulations, the elementary time step Δt used to integrate the equation of motion needs to be chosen much smaller of the shortest time scale in order not to cut-off physical effects. We show that in systems obeying the overdamped Langevin equation, it is possible to systematically correct for such discretization errors. This is done by analytically averaging out the fast molecular dynamics which occurs at time scales smaller than Δt, using a renormalization group based technique. Such a procedure gives raise to a time-dependent calculable correction to the diffusion coefficient. The resulting effective Langevin equation describes by construction the same long-time dynamics, but has a lower time resolution power, hence it can be integrated using larger time steps Δt. We illustrate and validate this method by studying the diffusion of a point-particle in a one-dimensional toy model and the denaturation of a protein.

Generalized hydrodynamics and non-equilibrium steady states in integrable many-body quantum systems

NASA Astrophysics Data System (ADS)

Vasseur, Romain; Bulchandani, Vir; Karrasch, Christoph; Moore, Joel

The long-time dynamics of thermalizing many-body quantum systems can typically be described in terms of a conventional hydrodynamics picture that results from the decay of all but a few slow modes associated with standard conservation laws (such as particle number, energy, or momentum). However, hydrodynamics is expected to fail for integrable systems that are characterized by an infinite number of conservation laws, leading to unconventional transport properties and to complex non-equilibrium states beyond the traditional dogma of statistical mechanics. In this talk, I will describe recent attempts to understand such stationary states far from equilibrium using a generalized hydrodynamics picture. I will discuss the consistency of ``Bethe-Boltzmann'' kinetic equations with linear response Drude weights and with density-matrix renormalization group calculations. This work was supported by the Department of Energy through the Quantum Materials program (R. V.), NSF DMR-1206515, AFOSR MURI and a Simons Investigatorship (J. E. M.), DFG through the Emmy Noether program KA 3360/2-1 (C. K.).

Thermodynamics in the vicinity of a relativistic quantum critical point in 2+1 dimensions.

PubMed

Rançon, A; Kodio, O; Dupuis, N; Lecheminant, P

2013-07-01

We study the thermodynamics of the relativistic quantum O(N) model in two space dimensions. In the vicinity of the zero-temperature quantum critical point (QCP), the pressure can be written in the scaling form P(T)=P(0)+N(T(3)/c(2))F(N)(Δ/T), where c is the velocity of the excitations at the QCP and |Δ| a characteristic zero-temperature energy scale. Using both a large-N approach to leading order and the nonperturbative renormalization group, we compute the universal scaling function F(N). For small values of N (N/~1) regimes, but fails to describe the nonmonotonic behavior of F(N) in the quantum critical regime. We discuss the renormalization-group flows in the various regimes near the QCP and make the connection with the quantum nonlinear sigma model in the renormalized classical regime. We compute the Berezinskii-Kosterlitz-Thouless transition temperature in the quantum O(2) model and find that in the vicinity of the QCP the universal ratio T(BKT)/ρ(s)(0) is very close to π/2, implying that the stiffness ρ(s)(T(BKT)(-)) at the transition is only slightly reduced with respect to the zero-temperature stiffness ρ(s)(0). Finally, we briefly discuss the experimental determination of the universal function F(2) from the pressure of a Bose gas in an optical lattice near the superfluid-Mott-insulator transition.

Strong-coupling Bose polarons out of equilibrium: Dynamical renormalization-group approach

NASA Astrophysics Data System (ADS)

Grusdt, Fabian; Seetharam, Kushal; Shchadilova, Yulia; Demler, Eugene

2018-03-01

When a mobile impurity interacts with a surrounding bath of bosons, it forms a polaron. Numerous methods have been developed to calculate how the energy and the effective mass of the polaron are renormalized by the medium for equilibrium situations. Here, we address the much less studied nonequilibrium regime and investigate how polarons form dynamically in time. To this end, we develop a time-dependent renormalization-group approach which allows calculations of all dynamical properties of the system and takes into account the effects of quantum fluctuations in the polaron cloud. We apply this method to calculate trajectories of polarons following a sudden quench of the impurity-boson interaction strength, revealing how the polaronic cloud around the impurity forms in time. Such trajectories provide additional information about the polaron's properties which are challenging to extract directly from the spectral function measured experimentally using ultracold atoms. At strong couplings, our calculations predict the appearance of trajectories where the impurity wavers back at intermediate times as a result of quantum fluctuations. Our method is applicable to a broader class of nonequilibrium problems. As a check, we also apply it to calculate the spectral function and find good agreement with experimental results. At very strong couplings, we predict that quantum fluctuations lead to the appearance of a dark continuum with strongly suppressed spectral weight at low energies. While our calculations start from an effective Fröhlich Hamiltonian describing impurities in a three-dimensional Bose-Einstein condensate, we also calculate the effects of additional terms in the Hamiltonian beyond the Fröhlich paradigm. We demonstrate that the main effect of these additional terms on the attractive side of a Feshbach resonance is to renormalize the coupling strength of the effective Fröhlich model.

PathVisio 3: an extendable pathway analysis toolbox.

PubMed

Kutmon, Martina; van Iersel, Martijn P; Bohler, Anwesha; Kelder, Thomas; Nunes, Nuno; Pico, Alexander R; Evelo, Chris T

2015-02-01

PathVisio is a commonly used pathway editor, visualization and analysis software. Biological pathways have been used by biologists for many years to describe the detailed steps in biological processes. Those powerful, visual representations help researchers to better understand, share and discuss knowledge. Since the first publication of PathVisio in 2008, the original paper was cited more than 170 times and PathVisio was used in many different biological studies. As an online editor PathVisio is also integrated in the community curated pathway database WikiPathways. Here we present the third version of PathVisio with the newest additions and improvements of the application. The core features of PathVisio are pathway drawing, advanced data visualization and pathway statistics. Additionally, PathVisio 3 introduces a new powerful extension systems that allows other developers to contribute additional functionality in form of plugins without changing the core application. PathVisio can be downloaded from http://www.pathvisio.org and in 2014 PathVisio 3 has been downloaded over 5,500 times. There are already more than 15 plugins available in the central plugin repository. PathVisio is a freely available, open-source tool published under the Apache 2.0 license (http://www.apache.org/licenses/LICENSE-2.0). It is implemented in Java and thus runs on all major operating systems. The code repository is available at http://svn.bigcat.unimaas.nl/pathvisio. The support mailing list for users is available on https://groups.google.com/forum/#!forum/wikipathways-discuss and for developers on https://groups.google.com/forum/#!forum/wikipathways-devel.

Path integration on the hyperbolic plane with a magnetic field

NASA Astrophysics Data System (ADS)

Grosche, Christian

1990-08-01

In this paper I discuss the path integrals on three formulations of hyperbolic geometry, where a constant magnetic field B is included. These are: the pseudosphere Λ2, the Poincaré disc D, and the hyperbolic strip S. The corresponding path integrals can be reformulated in terms of the path integral for the modified Pöschl-Teller potential. The wave-functions and the energy spectrum for the discrete and continuous part of the spectrum are explicitly calculated in each case. First the results are compared for the limit B → 0 with previous calculations and second with the path integration on the Poincaré upper half-plane U. This work is a continuation of the path integral calculations for the free motion on the various formulations on the hyperbolic plane and for the case of constant magnetic field on the Poincaré upper half-plane U.

Dissociable cognitive mechanisms underlying human path integration.

PubMed

Wiener, Jan M; Berthoz, Alain; Wolbers, Thomas

2011-01-01

Path integration is a fundamental mechanism of spatial navigation. In non-human species, it is assumed to be an online process in which a homing vector is updated continuously during an outward journey. In contrast, human path integration has been conceptualized as a configural process in which travelers store working memory representations of path segments, with the computation of a homing vector only occurring when required. To resolve this apparent discrepancy, we tested whether humans can employ different path integration strategies in the same task. Using a triangle completion paradigm, participants were instructed either to continuously update the start position during locomotion (continuous strategy) or to remember the shape of the outbound path and to calculate home vectors on basis of this representation (configural strategy). While overall homing accuracy was superior in the configural condition, participants were quicker to respond during continuous updating, strongly suggesting that homing vectors were computed online. Corroborating these findings, we observed reliable differences in head orientation during the outbound path: when participants applied the continuous updating strategy, the head deviated significantly from straight ahead in direction of the start place, which can be interpreted as a continuous motor expression of the homing vector. Head orientation-a novel online measure for path integration-can thus inform about the underlying updating mechanism already during locomotion. In addition to demonstrating that humans can employ different cognitive strategies during path integration, our two-systems view helps to resolve recent controversies regarding the role of the medial temporal lobe in human path integration.

Line interference effects using a refined Robert-Bonamy formalism: The test case of the isotropic Raman spectra of autoperturbed N{sub 2}

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boulet, Christian, E-mail: Christian.boulet@u-psud.fr; Ma, Qiancheng; Thibault, Franck

A symmetrized version of the recently developed refined Robert-Bonamy formalism [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] is proposed. This model takes into account line coupling effects and hence allows the calculation of the off-diagonal elements of the relaxation matrix, without neglecting the rotational structure of the perturbing molecule. The formalism is applied to the isotropic Raman spectra of autoperturbed N{sub 2} for which a benchmark quantum relaxation matrix has recently been proposed. The consequences of the classical path approximation are carefully analyzed. Methods correcting for effects of inelasticity are considered. While inmore » the right direction, these corrections appear to be too crude to provide off diagonal elements which would yield, via the sum rule, diagonal elements in good agreement with the quantum results. In order to overcome this difficulty, a re-normalization procedure is applied, which ensures that the off-diagonal elements do lead to the exact quantum diagonal elements. The agreement between the (re-normalized) semi-classical and quantum relaxation matrices is excellent, at least for the Raman spectra of N{sub 2}, opening the way to the analysis of more complex molecular systems.« less

Entanglement Entropy of Black Holes.

PubMed

Solodukhin, Sergey N

2011-01-01

The entanglement entropy is a fundamental quantity, which characterizes the correlations between sub-systems in a larger quantum-mechanical system. For two sub-systems separated by a surface the entanglement entropy is proportional to the area of the surface and depends on the UV cutoff, which regulates the short-distance correlations. The geometrical nature of entanglement-entropy calculation is particularly intriguing when applied to black holes when the entangling surface is the black-hole horizon. I review a variety of aspects of this calculation: the useful mathematical tools such as the geometry of spaces with conical singularities and the heat kernel method, the UV divergences in the entropy and their renormalization, the logarithmic terms in the entanglement entropy in four and six dimensions and their relation to the conformal anomalies. The focus in the review is on the systematic use of the conical singularity method. The relations to other known approaches such as 't Hooft's brick-wall model and the Euclidean path integral in the optical metric are discussed in detail. The puzzling behavior of the entanglement entropy due to fields, which non-minimally couple to gravity, is emphasized. The holographic description of the entanglement entropy of the blackhole horizon is illustrated on the two- and four-dimensional examples. Finally, I examine the possibility to interpret the Bekenstein-Hawking entropy entirely as the entanglement entropy.

Entanglement Entropy of Black Holes

NASA Astrophysics Data System (ADS)

Solodukhin, Sergey N.

2011-10-01

The entanglement entropy is a fundamental quantity, which characterizes the correlations between sub-systems in a larger quantum-mechanical system. For two sub-systems separated by a surface the entanglement entropy is proportional to the area of the surface and depends on the UV cutoff, which regulates the short-distance correlations. The geometrical nature of entanglement-entropy calculation is particularly intriguing when applied to black holes when the entangling surface is the black-hole horizon. I review a variety of aspects of this calculation: the useful mathematical tools such as the geometry of spaces with conical singularities and the heat kernel method, the UV divergences in the entropy and their renormalization, the logarithmic terms in the entanglement entropy in four and six dimensions and their relation to the conformal anomalies. The focus in the review is on the systematic use of the conical singularity method. The relations to other known approaches such as 't Hooft's brick-wall model and the Euclidean path integral in the optical metric are discussed in detail. The puzzling behavior of the entanglement entropy due to fields, which non-minimally couple to gravity, is emphasized. The holographic description of the entanglement entropy of the blackhole horizon is illustrated on the two- and four-dimensional examples. Finally, I examine the possibility to interpret the Bekenstein-Hawking entropy entirely as the entanglement entropy.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Song, Mi-Young; Yoon, Jung-Sik; Jung, Young-Dae, E-mail: ydjung@hanyang.ac.kr

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 ismore » 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.« less

Structure of p-shell nuclei using three-nucleon interactions evolved with the similarity renormalization group

DOE PAGES

Jurgenson, E. D.; Maris, P.; Furnstahl, R. J.; ...

2013-05-13

The similarity renormalization group (SRG) is used to soften interactions for ab initio nuclear structure calculations by decoupling low- and high-energy Hamiltonian matrix elements. The substantial contribution of both initial and SRG-induced three-nucleon forces requires their consistent evolution in a three-particle basis space before applying them to larger nuclei. While, in principle, the evolved Hamiltonians are unitarily equivalent, in practice the need for basis truncation introduces deviations, which must be monitored. Here we present benchmark no-core full configuration calculations with SRG-evolved interactions in p-shell nuclei over a wide range of softening. As a result, these calculations are used to assessmore » convergence properties, extrapolation techniques, and the dependence of energies, including four-body contributions, on the SRG resolution scale.« less

Cosmological attractor inflation from the RG-improved Higgs sector of finite gauge theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Elizalde, Emilio; Odintsov, Sergei D.; Pozdeeva, Ekaterina O.

2016-02-01

The possibility to construct an inflationary scenario for renormalization-group improved potentials corresponding to the Higgs sector of finite gauge models is investigated. Taking into account quantum corrections to the renormalization-group potential which sums all leading logs of perturbation theory is essential for a successful realization of the inflationary scenario, with very reasonable parameter values. The inflationary models thus obtained are seen to be in good agreement with the most recent and accurate observational data. More specifically, the values of the relevant inflationary parameters, n{sub s} and r, are close to the corresponding ones in the R{sup 2} and Higgs-driven inflationmore » scenarios. It is shown that the model here constructed and Higgs-driven inflation belong to the same class of cosmological attractors.« less

In-Medium Similarity Renormalization Group Approach to the Nuclear Many-Body Problem

NASA Astrophysics Data System (ADS)

Hergert, Heiko; Bogner, Scott K.; Lietz, Justin G.; Morris, Titus D.; Novario, Samuel J.; Parzuchowski, Nathan M.; Yuan, Fei

We present a pedagogical discussion of Similarity Renormalization Group (SRG) methods, in particular the In-Medium SRG (IMSRG) approach for solving the nuclear many-body problem. These methods use continuous unitary transformations to evolve the nuclear Hamiltonian to a desired shape. The IMSRG, in particular, is used to decouple the ground state from all excitations and solve the many-body Schrödinger equation. We discuss the IMSRG formalism as well as its numerical implementation, and use the method to study the pairing model and infinite neutron matter. We compare our results with those of Coupled cluster theory (Chap. 8), Configuration-Interaction Monte Carlo (Chap. 9), and the Self-Consistent Green's Function approach discussed in Chap. 11 The chapter concludes with an expanded overview of current research directions, and a look ahead at upcoming developments.

Fermi-edge singularity and the functional renormalization group

NASA Astrophysics Data System (ADS)

Kugler, Fabian B.; von Delft, Jan

2018-05-01

We study the Fermi-edge singularity, describing the response of a degenerate electron system to optical excitation, in the framework of the functional renormalization group (fRG). Results for the (interband) particle-hole susceptibility from various implementations of fRG (one- and two-particle-irreducible, multi-channel Hubbard–Stratonovich, flowing susceptibility) are compared to the summation of all leading logarithmic (log) diagrams, achieved by a (first-order) solution of the parquet equations. For the (zero-dimensional) special case of the x-ray-edge singularity, we show that the leading log formula can be analytically reproduced in a consistent way from a truncated, one-loop fRG flow. However, reviewing the underlying diagrammatic structure, we show that this derivation relies on fortuitous partial cancellations special to the form of and accuracy applied to the x-ray-edge singularity and does not generalize.

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.

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.

Stability of Dirac Liquids with Strong Coulomb Interaction.

PubMed

Tupitsyn, Igor S; Prokof'ev, Nikolay V

2017-01-13

We develop and apply the diagrammatic Monte Carlo technique to address the problem of the stability of the Dirac liquid state (in a graphene-type system) against the strong long-range part of the Coulomb interaction. So far, all attempts to deal with this problem in the field-theoretical framework were limited either to perturbative or random phase approximation and functional renormalization group treatments, with diametrically opposite conclusions. Our calculations aim at the approximation-free solution with controlled accuracy by computing vertex corrections from higher-order skeleton diagrams and establishing the renormalization group flow of the effective Coulomb coupling constant. We unambiguously show that with increasing the system size L (up to ln(L)∼40), the coupling constant always flows towards zero; i.e., the two-dimensional Dirac liquid is an asymptotically free T=0 state with divergent Fermi velocity.

Critical properties of the classical XY and classical Heisenberg models: A renormalization group study

NASA Astrophysics Data System (ADS)

de Sousa, J. Ricardo; de Albuquerque, Douglas F.

1997-02-01

By using two approaches of renormalization group (RG), mean field RG (MFRG) and effective field RG (EFRG), we study the critical properties of the simple cubic lattice classical XY and classical Heisenberg models. The methods are illustrated by employing its simplest approximation version in which small clusters with one ( N‧ = 1) and two ( N = 2) spins are used. The thermal and magnetic critical exponents, Yt and Yh, and the critical parameter Kc are numerically obtained and are compared with more accurate methods (Monte Carlo, series expansion and ε-expansion). The results presented in this work are in excellent agreement with these sophisticated methods. We have also shown that the exponent Yh does not depend on the symmetry n of the Hamiltonian, hence the criteria of universality for this exponent is only a function of the dimension d.

Renormalization Group for nonlinear oscillators in the absence of linear restoring force

NASA Astrophysics Data System (ADS)

Sarkar, A.; Bhattacharjee, J. K.

2010-09-01

Perturbative Renormalization Group (RG) has been very useful in probing periodic orbits in two-dimensional dynamical systems (Sarkar A., Bhattacharjee J. K., Chakraborty S. and Banerjee D., arXiv:1005.2858v1 (2010)). The method relies on finding a linear center, around which perturbation analysis is done. However it is not obvious as to how systems devoid of any linear terms may be approached using this method. We propose here how RG can be done even in the absence of linear terms. We successfully apply the method to extract correct results for a variant of the second-order Riccati equation. In this variant the periodic orbit disappears as a parameter is varied. Our RG captures this disappearance correctly. We have also applied the technique successfully on the force-free Van der Pol-Duffing oscillator.

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.

Turbulent compressible fluid: Renormalization group analysis, scaling regimes, and anomalous scaling of advected scalar fields

NASA Astrophysics Data System (ADS)

Antonov, N. V.; Gulitskiy, N. M.; Kostenko, M. M.; Lučivjanský, T.

2017-03-01

We study a model of fully developed turbulence of a compressible fluid, based on the stochastic Navier-Stokes equation, by means of the field-theoretic renormalization group. In this approach, scaling properties are related to the fixed points of the renormalization group equations. Previous analysis of this model near the real-world space dimension 3 identified a scaling regime [N. V. Antonov et al., Theor. Math. Phys. 110, 305 (1997), 10.1007/BF02630456]. The aim of the present paper is to explore the existence of additional regimes, which could not be found using the direct perturbative approach of the previous work, and to analyze the crossover between different regimes. It seems possible to determine them near the special value of space dimension 4 in the framework of double y and ɛ expansion, where y is the exponent associated with the random force and ɛ =4 -d is the deviation from the space dimension 4. Our calculations show that there exists an additional fixed point that governs scaling behavior. Turbulent advection of a passive scalar (density) field by this velocity ensemble is considered as well. We demonstrate that various correlation functions of the scalar field exhibit anomalous scaling behavior in the inertial-convective range. The corresponding anomalous exponents, identified as scaling dimensions of certain composite fields, can be systematically calculated as a series in y and ɛ . All calculations are performed in the leading one-loop approximation.

High-precision calculations in strongly coupled quantum field theory with next-to-leading-order renormalized Hamiltonian Truncation

NASA Astrophysics Data System (ADS)

Elias-Miró, Joan; Rychkov, Slava; Vitale, Lorenzo G.

2017-10-01

Hamiltonian Truncation (a.k.a. Truncated Spectrum Approach) is an efficient numerical technique to solve strongly coupled QFTs in d = 2 spacetime dimensions. Further theoretical developments are needed to increase its accuracy and the range of applicability. With this goal in mind, here we present a new variant of Hamiltonian Truncation which exhibits smaller dependence on the UV cutoff than other existing implementations, and yields more accurate spectra. The key idea for achieving this consists in integrating out exactly a certain class of high energy states, which corresponds to performing renormalization at the cubic order in the interaction strength. We test the new method on the strongly coupled two-dimensional quartic scalar theory. Our work will also be useful for the future goal of extending Hamiltonian Truncation to higher dimensions d ≥ 3.

Computation of parton distributions from the quasi-PDF approach at the physical point

NASA Astrophysics Data System (ADS)

Alexandrou, Constantia; Bacchio, Simone; Cichy, Krzysztof; Constantinou, Martha; Hadjiyiannakou, Kyriakos; Jansen, Karl; Koutsou, Giannis; Scapellato, Aurora; Steffens, Fernanda

2018-03-01

We show the first results for parton distribution functions within the proton at the physical pion mass, employing the method of quasi-distributions. In particular, we present the matrix elements for the iso-vector combination of the unpolarized, helicity and transversity quasi-distributions, obtained with Nf = 2 twisted mass cloverimproved fermions and a proton boosted with momentum |p→| = 0.83 GeV. The momentum smearing technique has been applied to improve the overlap with the proton boosted state. Moreover, we present the renormalized helicity matrix elements in the RI' scheme, following the non-perturbative renormalization prescription recently developed by our group.

On the effective field theory of intersecting D3-branes

NASA Astrophysics Data System (ADS)

Abbaspur, Reza

2018-05-01

We study the effective field theory of two intersecting D3-branes with one common dimension along the lines recently proposed in ref. [1]. We introduce a systematic way of deriving the classical effective action to arbitrary orders in perturbation theory. Using a proper renormalization prescription to handle logarithmic divergencies arising at all orders in the perturbation series, we recover the first order renormalization group equation of ref. [1] plus an infinite set of higher order equations. We show the consistency of the higher order equations with the first order one and hence interpret the first order result as an exact RG flow equation in the classical theory.

Emergence of criticality in the transportation passenger flow: scaling and renormalization in the Seoul bus system.

PubMed

Goh, Segun; Lee, Keumsook; Choi, Moo Young; Fortin, Jean-Yves

2014-01-01

Social systems have recently attracted much attention, with attempts to understand social behavior with the aid of statistical mechanics applied to complex systems. Collective properties of such systems emerge from couplings between components, for example, individual persons, transportation nodes such as airports or subway stations, and administrative districts. Among various collective properties, criticality is known as a characteristic property of a complex system, which helps the systems to respond flexibly to external perturbations. This work considers the criticality of the urban transportation system entailed in the massive smart card data on the Seoul transportation network. Analyzing the passenger flow on the Seoul bus system during one week, we find explicit power-law correlations in the system, that is, power-law behavior of the strength correlation function of bus stops and verify scale invariance of the strength fluctuations. Such criticality is probed by means of the scaling and renormalization analysis of the modified gravity model applied to the system. Here a group of nearby (bare) bus stops are transformed into a (renormalized) "block stop" and the scaling relations of the network density turn out to be closely related to the fractal dimensions of the system, revealing the underlying structure. Specifically, the resulting renormalized values of the gravity exponent and of the Hill coefficient give a good description of the Seoul bus system: The former measures the characteristic dimensionality of the network whereas the latter reflects the coupling between distinct transportation modes. It is thus demonstrated that such ideas of physics as scaling and renormalization can be applied successfully to social phenomena exemplified by the passenger flow.

Emergence of Criticality in the Transportation Passenger Flow: Scaling and Renormalization in the Seoul Bus System

PubMed Central

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

Effects of renormalizing the chiral SU(2) quark-meson model

NASA Astrophysics Data System (ADS)

Zacchi, Andreas; Schaffner-Bielich, Jürgen

2018-04-01

We investigate the restoration of chiral symmetry at finite temperature in the SU(2) quark-meson model, where the mean field approximation is compared to the renormalized version for quarks and mesons. In a combined approach at finite temperature, all the renormalized versions show a crossover transition. The inclusion of different renormalization scales leave the order parameter and the mass spectra nearly untouched but strongly influence the thermodynamics at low temperatures and around the phase transition. We find unphysical results for the renormalized version of mesons and the combined one.

A Dynamic Bayesian Observer Model Reveals Origins of Bias in Visual Path Integration.

PubMed

Lakshminarasimhan, Kaushik J; Petsalis, Marina; Park, Hyeshin; DeAngelis, Gregory C; Pitkow, Xaq; Angelaki, Dora E

2018-06-20

Path integration is a strategy by which animals track their position by integrating their self-motion velocity. To identify the computational origins of bias in visual path integration, we asked human subjects to navigate in a virtual environment using optic flow and found that they generally traveled beyond the goal location. Such a behavior could stem from leaky integration of unbiased self-motion velocity estimates or from a prior expectation favoring slower speeds that causes velocity underestimation. Testing both alternatives using a probabilistic framework that maximizes expected reward, we found that subjects' biases were better explained by a slow-speed prior than imperfect integration. When subjects integrate paths over long periods, this framework intriguingly predicts a distance-dependent bias reversal due to buildup of uncertainty, which we also confirmed experimentally. These results suggest that visual path integration in noisy environments is limited largely by biases in processing optic flow rather than by leaky integration. Copyright © 2018 Elsevier Inc. All rights reserved.

Which way and how far? Tracking of translation and rotation information for human path integration.

PubMed

Chrastil, Elizabeth R; Sherrill, Katherine R; Hasselmo, Michael E; Stern, Chantal E

2016-10-01

Path integration, the constant updating of the navigator's knowledge of position and orientation during movement, requires both visuospatial knowledge and memory. This study aimed to develop a systems-level understanding of human path integration by examining the basic building blocks of path integration in humans. To achieve this goal, we used functional imaging to examine the neural mechanisms that support the tracking and memory of translational and rotational components of human path integration. Critically, and in contrast to previous studies, we examined movement in translation and rotation tasks with no defined end-point or goal. Navigators accumulated translational and rotational information during virtual self-motion. Activity in hippocampus, retrosplenial cortex (RSC), and parahippocampal cortex (PHC) increased during both translation and rotation encoding, suggesting that these regions track self-motion information during path integration. These results address current questions regarding distance coding in the human brain. By implementing a modified delayed match to sample paradigm, we also examined the encoding and maintenance of path integration signals in working memory. Hippocampus, PHC, and RSC were recruited during successful encoding and maintenance of path integration information, with RSC selective for tasks that required processing heading rotation changes. These data indicate distinct working memory mechanisms for translation and rotation, which are essential for updating neural representations of current location. The results provide evidence that hippocampus, PHC, and RSC flexibly track task-relevant translation and rotation signals for path integration and could form the hub of a more distributed network supporting spatial navigation. Hum Brain Mapp 37:3636-3655, 2016. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Renormalized Hamiltonian for a peptide chain: Digitalizing the protein folding problem

NASA Astrophysics Data System (ADS)

Fernández, Ariel; Colubri, Andrés

2000-05-01

A renormalized Hamiltonian for a flexible peptide chain is derived to generate the long-time limit dynamics compatible with a coarsening of torsional conformation space. The renormalization procedure is tailored taking into account the coarse graining imposed by the backbone torsional constraints due to the local steric hindrance and the local backbone-side-group interactions. Thus, the torsional degrees of freedom for each residue are resolved modulo basins of attraction in its so-called Ramachandran map. This Ramachandran renormalization (RR) procedure is implemented so that the chain is energetically driven to form contact patterns as their respective collective topological constraints are fulfilled within the coarse description. In this way, the torsional dynamics are digitalized and become codified as an evolving pattern in a binary matrix. Each accepted Monte Carlo step in a canonical ensemble simulation is correlated with the real mean first passage time it takes to reach the destination coarse topological state. This real-time correlation enables us to test the RR dynamics by comparison with experimentally probed kinetic bottlenecks along the dominant folding pathway. Such intermediates are scarcely populated at any given time, but they determine the kinetic funnel leading to the active structure. This landscape region is reached through kinetically controlled steps needed to overcome the conformational entropy of the random coil. The results are specialized for the bovine pancreatic trypsin inhibitor, corroborating the validity of our method.

Perfect discretization of reparametrization invariant path integrals

NASA Astrophysics Data System (ADS)

Bahr, Benjamin; Dittrich, Bianca; Steinhaus, Sebastian

2011-05-01

To obtain a well-defined path integral one often employs discretizations. In the case of gravity and reparametrization-invariant systems, the latter of which we consider here as a toy example, discretizations generically break diffeomorphism and reparametrization symmetry, respectively. This has severe implications, as these symmetries determine the dynamics of the corresponding system. Indeed we will show that a discretized path integral with reparametrization-invariance is necessarily also discretization independent and therefore uniquely determined by the corresponding continuum quantum mechanical propagator. We use this insight to develop an iterative method for constructing such a discretized path integral, akin to a Wilsonian RG flow. This allows us to address the problem of discretization ambiguities and of an anomaly-free path integral measure for such systems. The latter is needed to obtain a path integral, that can act as a projector onto the physical states, satisfying the quantum constraints. We will comment on implications for discrete quantum gravity models, such as spin foams.

Assessing notions of denormalization and renormalization of smoking in light of e-cigarette regulation.

PubMed

Sæbø, Gunnar; Scheffels, Janne

2017-11-01

The rationale for 'denormalization' of smoking in tobacco policies has been challenged by the emergence of e-cigarettes and the need to regulate e-cigarette use and promotion. Our aim is to assess the research status on e-cigarettes' contribution to 'renormalization' of smoking and to clarify how renormalization of smoking can be appraised at the conceptual and empirical level. Combining conceptual analysis and narrative review, the paper brings out three dimensions of denormalization/renormalization of smoking ('unacceptability/acceptability'; 'invisibility/visibility'; 'phasing out behaviour/maintaining behaviour') and an inherent duality of the e-cigarette as a smoking-like device and a smoking alternative. These analytical dimensions are applied qualitatively to consider the literature identified by searching the Web of Science database for 'e-cigarettes AND renormalization' (and variants thereof). Theoretically, normative changes in smoking acceptability, increased visibility of e-cigarettes and use, and observations of actual use (prevalence, dual use, gateway) can all be applied to illustrate processes of renormalization. However, only acceptability measures and user measures can be said to be empirical tests of renormalization effects. Visibility measures are only based on logical assumptions of a possible renormalization; they are not in themselves indicative of any "real" renormalization effects and can just as well be understood as possible consequences of normalization of e-cigarettes. Just as a downward trend in smoking prevalence is the litmus test of whether denormalization policy works, stagnating or rising smoking prevalence should be the main empirical indicator of renormalization. Copyright © 2017 Elsevier B.V. All rights reserved.

Distinct roles of hippocampus and medial prefrontal cortex in spatial and nonspatial memory.

PubMed

Sapiurka, Maya; Squire, Larry R; Clark, Robert E

2016-12-01

In earlier work, patients with hippocampal damage successfully path integrated, apparently by maintaining spatial information in working memory. In contrast, rats with hippocampal damage were unable to path integrate, even when the paths were simple and working memory might have been expected to support performance. We considered possible ways to understand these findings. We tested rats with either hippocampal lesions or lesions of medial prefrontal cortex (mPFC) on three tasks of spatial or nonspatial memory: path integration, spatial alternation, and a nonspatial alternation task. Rats with mPFC lesions were impaired on both spatial and nonspatial alternation but performed normally on path integration. By contrast, rats with hippocampal lesions were impaired on path integration and spatial alternation but performed normally on nonspatial alternation. We propose that rodent neocortex is limited in its ability to construct a coherent spatial working memory of complex environments. Accordingly, in tasks such as path integration and spatial alternation, working memory cannot depend on neocortex alone. Rats may accomplish many spatial memory tasks by relying on long-term memory. Alternatively, they may accomplish these tasks within working memory through sustained coordination between hippocampus and other cortical brain regions such as mPFC, in the case of spatial alternation, or parietal cortex in the case of path integration. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Argo, P.E.; DeLapp, D.; Sutherland, C.D.

TRACKER is an extension of a three-dimensional Hamiltonian raytrace code developed some thirty years ago by R. Michael Jones. Subsequent modifications to this code, which is commonly called the {open_quotes}Jones Code,{close_quotes} were documented by Jones and Stephensen (1975). TRACKER incorporates an interactive user`s interface, modern differential equation integrators, graphical outputs, homing algorithms, and the Ionospheric Conductivity and Electron Density (ICED) ionosphere. TRACKER predicts the three-dimensional paths of radio waves through model ionospheres by numerically integrating Hamilton`s equations, which are a differential expression of Fermat`s principle of least time. By using continuous models, the Hamiltonian method avoids false caustics and discontinuousmore » raypath properties often encountered in other raytracing methods. In addition to computing the raypath, TRACKER also calculates the group path (or pulse travel time), the phase path, the geometrical (or {open_quotes}real{close_quotes}) pathlength, and the Doppler shift (if the time variation of the ionosphere is explicitly included). Computational speed can be traded for accuracy by specifying the maximum allowable integration error per step in the integration. Only geometrical optics are included in the main raytrace code; no partial reflections or diffraction effects are taken into account. In addition, TRACKER does not lend itself to statistical descriptions of propagation -- it requires a deterministic model of the ionosphere.« less

Simple Approach to Renormalize the Cabibbo-Kobayashi-Maskawa Matrix

DOE Office of Scientific and Technical Information (OSTI.GOV)

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.

Path integrals and the WKB approximation in loop quantum cosmology

NASA Astrophysics Data System (ADS)

Ashtekar, Abhay; Campiglia, Miguel; Henderson, Adam

2010-12-01

We follow the Feynman procedure to obtain a path integral formulation of loop quantum cosmology starting from the Hilbert space framework. Quantum geometry effects modify the weight associated with each path so that the effective measure on the space of paths is different from that used in the Wheeler-DeWitt theory. These differences introduce some conceptual subtleties in arriving at the WKB approximation. But the approximation is well defined and provides intuition for the differences between loop quantum cosmology and the Wheeler-DeWitt theory from a path integral perspective.

Perfect discretization of path integrals

NASA Astrophysics Data System (ADS)

Steinhaus, Sebastian

2012-05-01

In order to obtain a well-defined path integral one often employs discretizations. In the case of General Relativity these generically break diffeomorphism symmetry, which has severe consequences since these symmetries determine the dynamics of the corresponding system. In this article we consider the path integral of reparametrization invariant systems as a toy example and present an improvement procedure for the discretized propagator. Fixed points and convergence of the procedure are discussed. Furthermore we show that a reparametrization invariant path integral implies discretization independence and acts as a projector onto physical states.

Master equations and the theory of stochastic path integrals

NASA Astrophysics Data System (ADS)

Weber, Markus F.; Frey, Erwin

2017-04-01

This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations. We focus on numerical and analytical methods going beyond the low-noise limit and provide a unified framework for the study of master equations. After deriving the forward and backward master equations from the Chapman-Kolmogorov equation, we show how the two master equations can be cast into either of four linear partial differential equations (PDEs). Three of these PDEs are discussed in detail. The first PDE governs the time evolution of a generalized probability generating function whose basis depends on the stochastic process under consideration. Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE. The second PDE is novel and is obeyed by a distribution that is marginalized over an initial state. It proves useful for the computation of mean extinction times. The third PDE describes the time evolution of a ‘generating functional’, which generalizes the so-called Poisson representation. Subsequently, the solutions of the PDEs are expressed in terms of two path integrals: a ‘forward’ and a ‘backward’ path integral. Combined with inverse transformations, one obtains two distinct path integral representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Moreover, we show how a well-known path integral representation of averaged observables can be recovered from them. Upon expanding the forward and the backward path integrals around stationary paths, we then discuss and extend a recent method for the computation of rare event probabilities. Besides, we also derive path integral representations for processes with continuous state spaces whose forward and backward master equations admit Kramers-Moyal expansions. A truncation of the backward expansion at the level of a diffusion approximation recovers a classic path integral representation of the (backward) Fokker-Planck equation. One can rewrite this path integral in terms of an Onsager-Machlup function and, for purely diffusive Brownian motion, it simplifies to the path integral of Wiener. To make this review accessible to a broad community, we have used the language of probability theory rather than quantum (field) theory and do not assume any knowledge of the latter. The probabilistic structures underpinning various technical concepts, such as coherent states, the Doi-shift, and normal-ordered observables, are thereby made explicit.

Master equations and the theory of stochastic path integrals.

PubMed

Weber, Markus F; Frey, Erwin

2017-04-01

This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations. We focus on numerical and analytical methods going beyond the low-noise limit and provide a unified framework for the study of master equations. After deriving the forward and backward master equations from the Chapman-Kolmogorov equation, we show how the two master equations can be cast into either of four linear partial differential equations (PDEs). Three of these PDEs are discussed in detail. The first PDE governs the time evolution of a generalized probability generating function whose basis depends on the stochastic process under consideration. Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE. The second PDE is novel and is obeyed by a distribution that is marginalized over an initial state. It proves useful for the computation of mean extinction times. The third PDE describes the time evolution of a 'generating functional', which generalizes the so-called Poisson representation. Subsequently, the solutions of the PDEs are expressed in terms of two path integrals: a 'forward' and a 'backward' path integral. Combined with inverse transformations, one obtains two distinct path integral representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Moreover, we show how a well-known path integral representation of averaged observables can be recovered from them. Upon expanding the forward and the backward path integrals around stationary paths, we then discuss and extend a recent method for the computation of rare event probabilities. Besides, we also derive path integral representations for processes with continuous state spaces whose forward and backward master equations admit Kramers-Moyal expansions. A truncation of the backward expansion at the level of a diffusion approximation recovers a classic path integral representation of the (backward) Fokker-Planck equation. One can rewrite this path integral in terms of an Onsager-Machlup function and, for purely diffusive Brownian motion, it simplifies to the path integral of Wiener. To make this review accessible to a broad community, we have used the language of probability theory rather than quantum (field) theory and do not assume any knowledge of the latter. The probabilistic structures underpinning various technical concepts, such as coherent states, the Doi-shift, and normal-ordered observables, are thereby made explicit.

Criticality of the random field Ising model in and out of equilibrium: A nonperturbative functional renormalization group description

NASA Astrophysics Data System (ADS)

Balog, Ivan; Tarjus, Gilles; Tissier, Matthieu

2018-03-01

We show that, contrary to previous suggestions based on computer simulations or erroneous theoretical treatments, the critical points of the random-field Ising model out of equilibrium, when quasistatically changing the applied source at zero temperature, and in equilibrium are not in the same universality class below some critical dimension dD R≈5.1 . We demonstrate this by implementing a nonperturbative functional renormalization group for the associated dynamical field theory. Above dD R, the avalanches, which characterize the evolution of the system at zero temperature, become irrelevant at large distance, and hysteresis and equilibrium critical points are then controlled by the same fixed point. We explain how to use computer simulation and finite-size scaling to check the correspondence between in and out of equilibrium criticality in a far less ambiguous way than done so far.

Nonlinear relativistic plasma resonance: Renormalization group approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Metelskii, I. I., E-mail: metelski@lebedev.ru; Kovalev, V. F., E-mail: vfkvvfkv@gmail.com; Bychenkov, V. Yu., E-mail: bychenk@lebedev.ru

An analytical solution to the nonlinear set of equations describing the electron dynamics and electric field structure in the vicinity of the critical density in a nonuniform plasma is constructed using the renormalization group approach with allowance for relativistic effects of electron motion. It is demonstrated that the obtained solution describes two regimes of plasma oscillations in the vicinity of the plasma resonance— stationary and nonstationary. For the stationary regime, the spatiotemporal and spectral characteristics of the resonantly enhanced electric field are investigated in detail and the effect of the relativistic nonlinearity on the spatial localization of the energy ofmore » the plasma relativistic field is considered. The applicability limits of the obtained solution, which are determined by the conditions of plasma wave breaking in the vicinity of the resonance, are established and analyzed in detail for typical laser and plasma parameters. The applicability limits of the earlier developed nonrelativistic theories are refined.« less

Non-Fermi-liquid superconductivity: Eliashberg approach versus the renormalization group

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Huajia; Raghu, Srinivas; Torroba, Gonzalo

Here, we address the problem of superconductivity for non-Fermi liquids using two commonly adopted, yet apparently distinct, methods: (1) the renormalization group (RG) and (2) Eliashberg theory. The extent to which both methods yield consistent solutions for the low-energy behavior of quantum metals has remained unclear. We show that the perturbative RG beta function for the 4-Fermi coupling can be explicitly derived from the linearized Eliashberg equations, under the assumption that quantum corrections are approximately local across energy scales. We apply our analysis to the test case of phonon-mediated superconductivity and show the consistency of both the Eliashberg and RGmore » treatments. We next study superconductivity near a class of quantum critical points and find a transition between superconductivity and a “naked” metallic quantum critical point with finite, critical BCS couplings. We speculate on the applications of our theory to the phenomenology of unconventional metals.« less

Non-Fermi-liquid superconductivity: Eliashberg approach versus the renormalization group

DOE PAGES

Wang, Huajia; Raghu, Srinivas; Torroba, Gonzalo

2017-04-15

Here, we address the problem of superconductivity for non-Fermi liquids using two commonly adopted, yet apparently distinct, methods: (1) the renormalization group (RG) and (2) Eliashberg theory. The extent to which both methods yield consistent solutions for the low-energy behavior of quantum metals has remained unclear. We show that the perturbative RG beta function for the 4-Fermi coupling can be explicitly derived from the linearized Eliashberg equations, under the assumption that quantum corrections are approximately local across energy scales. We apply our analysis to the test case of phonon-mediated superconductivity and show the consistency of both the Eliashberg and RGmore » treatments. We next study superconductivity near a class of quantum critical points and find a transition between superconductivity and a “naked” metallic quantum critical point with finite, critical BCS couplings. We speculate on the applications of our theory to the phenomenology of unconventional metals.« less

Ground states of linear rotor chains via the density matrix renormalization group

NASA Astrophysics Data System (ADS)

Iouchtchenko, Dmitri; Roy, Pierre-Nicholas

2018-04-01

In recent years, experimental techniques have enabled the creation of ultracold optical lattices of molecules and endofullerene peapod nanomolecular assemblies. It was previously suggested that the rotor model resulting from the placement of dipolar linear rotors in one-dimensional lattices at low temperature has a transition between ordered and disordered phases. We use the density matrix renormalization group (DMRG) to compute ground states of chains of up to 100 rotors and provide further evidence of the phase transition in the form of a diverging entanglement entropy. We also propose two methods and present some first steps toward rotational spectra of such molecular assemblies using DMRG. The present work showcases the power of DMRG in this new context of interacting molecular rotors and opens the door to the study of fundamental questions regarding criticality in systems with continuous degrees of freedom.

A state interaction spin-orbit coupling density matrix renormalization group method

NASA Astrophysics Data System (ADS)

Sayfutyarova, Elvira R.; Chan, Garnet Kin-Lic

2016-06-01

We describe a state interaction spin-orbit (SISO) coupling method using density matrix renormalization group (DMRG) wavefunctions and the spin-orbit mean-field (SOMF) operator. We implement our DMRG-SISO scheme using a spin-adapted algorithm that computes transition density matrices between arbitrary matrix product states. To demonstrate the potential of the DMRG-SISO scheme we present accurate benchmark calculations for the zero-field splitting of the copper and gold atoms, comparing to earlier complete active space self-consistent-field and second-order complete active space perturbation theory results in the same basis. We also compute the effects of spin-orbit coupling on the spin-ladder of the iron-sulfur dimer complex [Fe2S2(SCH3)4]3-, determining the splitting of the lowest quartet and sextet states. We find that the magnitude of the zero-field splitting for the higher quartet and sextet states approaches a significant fraction of the Heisenberg exchange parameter.

Oscillators: Old and new perspectives

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bhattacharjee, Jayanta K.; Roy, Jyotirmoy

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

Numerical renormalization group method for entanglement negativity at finite temperature

NASA Astrophysics Data System (ADS)

Shim, Jeongmin; Sim, H.-S.; Lee, Seung-Sup B.

2018-04-01

We develop a numerical method to compute the negativity, an entanglement measure for mixed states, between the impurity and the bath in quantum impurity systems at finite temperature. We construct a thermal density matrix by using the numerical renormalization group (NRG), and evaluate the negativity by implementing the NRG approximation that reduces computational cost exponentially. We apply the method to the single-impurity Kondo model and the single-impurity Anderson model. In the Kondo model, the negativity exhibits a power-law scaling at temperature much lower than the Kondo temperature and a sudden death at high temperature. In the Anderson model, the charge fluctuation of the impurity contributes to the negativity even at zero temperature when the on-site Coulomb repulsion of the impurity is finite, while at low temperature the negativity between the impurity spin and the bath exhibits the same power-law scaling behavior as in the Kondo model.

Influence of phonon-assisted tunneling on the linear thermoelectric transport through molecular quantum dots

NASA Astrophysics Data System (ADS)

Khedri, A.; Meden, V.; Costi, T. A.

2017-11-01

We investigate the effect of vibrational degrees of freedom on the linear thermoelectric transport through a single-level quantum dot described by the spinless Anderson-Holstein impurity model. To study the effects of strong electron-phonon coupling, we use the nonperturbative numerical renormalization group approach. We also compare our results, at weak to intermediate coupling, with those obtained by employing the functional renormalization group method, finding good agreement in this parameter regime. When applying a gate voltage at finite temperatures, the inelastic scattering processes, induced by phonon-assisted tunneling, result in an interesting interplay between electrical and thermal transport. We explore different parameter regimes and identify situations for which the thermoelectric power as well as the dimensionless figure of merit are significantly enhanced via a Mahan-Sofo type of mechanism. We show, in particular, that this occurs at strong electron-phonon coupling and in the antiadiabatic regime.

Multistage electronic nematic transitions in cuprate superconductors: A functional-renormalization-group analysis

NASA Astrophysics Data System (ADS)

Tsuchiizu, Masahisa; Kawaguchi, Kouki; Yamakawa, Youichi; Kontani, Hiroshi

2018-04-01

Recently, complex rotational symmetry-breaking phenomena have been discovered experimentally in cuprate superconductors. To find the realized order parameters, we study various unconventional charge susceptibilities in an unbiased way by applying the functional-renormalization-group method to the d -p Hubbard model. Without assuming the wave vector of the order parameter, we reveal that the most dominant instability is the uniform (q =0 ) charge modulation on the px and py orbitals, which possesses d symmetry. This uniform nematic order triggers another nematic p -orbital density wave along the axial (Cu-Cu) direction at Qa≈(π /2 ,0 ) . It is predicted that uniform nematic order is driven by the spin fluctuations in the pseudogap region, and another nematic density-wave order at q =Qa is triggered by the uniform order. The predicted multistage nematic transitions are caused by Aslamazov-Larkin-type fluctuation-exchange processes.

Tau hadronic spectral function moments: perturbative expansion and αs extractions

NASA Astrophysics Data System (ADS)

Boito, D.

2016-04-01

In the extraction of αs from hadronic τ decays different moments of the spectral functions have been used. Furthermore, the two mainstream renormalization group improvement (RGI) frameworks, namely Fixed Order Perturbation Theory (FOPT) and Contour Improved Perturbation Theory (CIPT), lead to conflicting values of αs. In order to improve the strategy used in αs determinations, we have performed a systematic study of the perturbative behaviour of these spectral moments in the context of FOPT and CIPT. Higher order coefficients of the perturbative series, yet unknown, were modelled using available knowledge of the renormalon content of the QCD Adler function. We conclude that within these RGI frameworks some of the moments often employed in αs extractions should be avoided due to their poor perturbative behaviour. Finally, under reasonable assumptions about higher orders, we conclude that FOPT is the preferred method to perform the renormalization group improvement of the perturbative series.

τ hadronic spectral function moments in a nonpower QCD perturbation theory

NASA Astrophysics Data System (ADS)

Abbas, Gauhar; Ananthanarayan, B.; Caprini, I.; Fischer, J.

2016-04-01

The moments of the hadronic spectral functions are of interest for the extraction of the strong coupling and other QCD parameters from the hadronic decays of the τ lepton. We consider the perturbative behavior of these moments in the framework of a QCD nonpower perturbation theory, defined by the technique of series acceleration by conformal mappings, which simultaneously implements renormalization-group summation and has a tame large-order behavior. Two recently proposed models of the Adler function are employed to generate the higher order coefficients of the perturbation series and to predict the exact values of the moments, required for testing the properties of the perturbative expansions. We show that the contour-improved nonpower perturbation theories and the renormalization-group-summed nonpower perturbation theories have very good convergence properties for a large class of moments of the so-called ;reference model;, including moments that are poorly described by the standard expansions.

Development of a recursion RNG-based turbulence model

NASA Technical Reports Server (NTRS)

Zhou, YE; Vahala, George; Thangam, S.

1993-01-01

Reynolds stress closure models based on the recursion renormalization group theory are developed for the prediction of turbulent separated flows. The proposed model uses a finite wavenumber truncation scheme to account for the spectral distribution of energy. In particular, the model incorporates effects of both local and nonlocal interactions. The nonlocal interactions are shown to yield a contribution identical to that from the epsilon-renormalization group (RNG), while the local interactions introduce higher order dispersive effects. A formal analysis of the model is presented and its ability to accurately predict separated flows is analyzed from a combined theoretical and computational stand point. Turbulent flow past a backward facing step is chosen as a test case and the results obtained based on detailed computations demonstrate that the proposed recursion -RNG model with finite cut-off wavenumber can yield very good predictions for the backstep problem.

Renormalization group equation analysis of a pseudoscalar portal dark matter model

NASA Astrophysics Data System (ADS)

Ghorbani, Karim

2017-10-01

We investigate the vacuum stability and perturbativity of a pseudoscalar portal dark matter (DM) model with a Dirac DM candidate, through the renormalization group equation analysis at one-loop order. The model has a particular feature which can evade the direct detection upper bounds measured by XENON100 and even that from planned experiment XENON1T. We first find the viable regions in the parameter space which will give rise to correct DM relic density and comply with the constraints from Higgs physics. We show that for a given mass of the pseudoscalar, the mixing angle plays no significant role in the running of the couplings. Then we study the running of the couplings for various pseudoscalar masses at mixing angle θ =6^\\circ , and find the scale of validity in terms of the dark coupling, {λ }d. Depending on our choice of the cutoff scale, the resulting viable parameter space will be determined.

Mixed Spin-1/2 and Spin-5/2 Model by Renormalization Group Theory: Recursion Equations and Thermodynamic Study

NASA Astrophysics Data System (ADS)

Antari, A. El; Zahir, H.; Hasnaoui, A.; Hachem, N.; Alrajhi, A.; Madani, M.; Bouziani, M. El

2018-04-01

Using the renormalization group approximation, specifically the Migdal-Kadanoff technique, we investigate the Blume-Capel model with mixed spins S = 1/2 and S = 5/2 on d-dimensional hypercubic lattice. The flow in the parameter space of the Hamiltonian and the thermodynamic functions are determined. The phase diagram of this model is plotted in the (anisotropy, temperature) plane for both cases d = 2 and d = 3 in which the system exhibits the first and second order phase transitions and critical end-points. The associated fixed points are drawn up in a table, and by linearizing the transformation at the vicinity of these points, we determine the critical exponents for d = 2 and d = 3. We have also presented a variation of the free energy derivative at the vicinity of the first and second order transitions. Finally, this work is completed by a discussion and comparison with other approximation.

Staggered Orbital Currents in the Half-Filled Two-Leg Ladder

NASA Astrophysics Data System (ADS)

Fjaerestad, J. O.; Marston, Brad; Sudbo, A.

2002-03-01

We present strong analytical and numerical evidence for the existence of a staggered flux (SF) phase in the half-filled two-leg ladder, with true long-range order in the counter-circulating currents. Using abelian bosonization with a careful treatment of the Klein factors, we show that a certain phase of the half-filled ladder, previously identified as having spin-Peierls order, instead exhibits staggered orbital currents with no dimerization.(J. O. Fjærestad and J. B. Marston, cond- mat/0107094.) This result, combined with a weak-coupling renormalization-group analysis, implies that the SF phase exists in a region of the phase diagram of the half-filled t-U-V-J ladder. Using the density-matrix renormalization-group (DMRG) approach generalized to complex-valued wavefunctions, we demonstrate that the SF phase exhibits robust currents at intermediate values of the interaction strengths.

Stiffening of fluid membranes due to thermal undulations: density-matrix renormalization-group study.

PubMed

Nishiyama, Yoshihiro

2002-12-01

It has been considered that the effective bending rigidity of fluid membranes should be reduced by thermal undulations. However, recent thorough investigation by Pinnow and Helfrich revealed the significance of measure factors for the partition sum. Accepting the local curvature as a statistical measure, they found that fluid membranes are stiffened macroscopically. In order to examine this remarkable idea, we performed extensive ab initio simulations for a fluid membrane. We set up a transfer matrix that is diagonalized by means of the density-matrix renormalization group. Our method has an advantage, in that it allows us to survey various statistical measures. As a consequence, we found that the effective bending rigidity flows toward strong coupling under the choice of local curvature as a statistical measure. On the contrary, for other measures such as normal displacement and tilt angle, we found a clear tendency toward softening.

Prediction of global vapor-liquid equilibria for mixtures containing polar and associating components with improved renormalization group theory.

PubMed

Mi, Jianguo; Tang, Yiping; Zhong, Chongli; Li, Yi-Gui

2005-11-03

Our recently improved renormalization group (RG) theory is further reformulated within the context of density functional theory. To improve the theory for polar and associating fluids, an explicit and complete expression of the theory is derived in which the density fluctuation is expanded up to the third-order term instead of the original second-order term. A new predictive equation of state based on the first-order mean spherical approximation statistical associating fluid theory (FMSA-SAFT) and the newly improved RG theory is proposed for systems containing polar and associating fluids. The calculated results for both pure fluids and mixtures are in good agreement with experimental data both inside and outside the critical region. This work demonstrates that the RG theory incorporated with the solution of FMSA is a promising route for accurately describing the global phase behavior of complex fluids and mixtures.

PathCase-SB architecture and database design

PubMed Central

2011-01-01

Background Integration of metabolic pathways resources and regulatory metabolic network models, and deploying new tools on the integrated platform can help perform more effective and more efficient systems biology research on understanding the regulation in metabolic networks. Therefore, the tasks of (a) integrating under a single database environment regulatory metabolic networks and existing models, and (b) building tools to help with modeling and analysis are desirable and intellectually challenging computational tasks. Description PathCase Systems Biology (PathCase-SB) is built and released. The PathCase-SB database provides data and API for multiple user interfaces and software tools. The current PathCase-SB system provides a database-enabled framework and web-based computational tools towards facilitating the development of kinetic models for biological systems. PathCase-SB aims to integrate data of selected biological data sources on the web (currently, BioModels database and KEGG), and to provide more powerful and/or new capabilities via the new web-based integrative framework. This paper describes architecture and database design issues encountered in PathCase-SB's design and implementation, and presents the current design of PathCase-SB's architecture and database. Conclusions PathCase-SB architecture and database provide a highly extensible and scalable environment with easy and fast (real-time) access to the data in the database. PathCase-SB itself is already being used by researchers across the world. PMID:22070889

Non-duplicate polarization-diversity 8 × 8 Si-wire PILOSS switch integrated with polarization splitter-rotators.

PubMed

Tanizawa, Ken; Suzuki, Keijiro; Ikeda, Kazuhiro; Namiki, Shu; Kawashima, Hitoshi

2017-05-15

We demonstrate a fully integrated polarization-diversity 8 × 8 thermo-optic Si-wire switch that uses only a single path-independent insertion loss (PILOSS) switch matrix. All input/output ports of the PILOSS switch matrix are uniquely assigned for polarization diversity without switch duplication. To integrate polarization splitter-rotators on a chip, we propose a compact path-length-equalized polarization-diversity switch configuration. Polarization-dependent loss (PDL) and differential group delay (DGD) are minimized. The 8 × 8 switch is fabricated by the CMOS-compatible fabrication process on 300-mm diameter wafer and additional etching of upper cladding after dicing. The chip size is 7 × 10.5 mm 2 . A PDL of 2 dB and a DGD of 1.5 ps are achieved. The crosstalk in the worst-case scenario is -20 dB in the full C-band.

Second-order perturbation theory with a density matrix renormalization group self-consistent field reference function: theory and application to the study of chromium dimer.

PubMed

Kurashige, Yuki; Yanai, Takeshi

2011-09-07

We present a second-order perturbation theory based on a density matrix renormalization group self-consistent field (DMRG-SCF) reference function. The method reproduces the solution of the complete active space with second-order perturbation theory (CASPT2) when the DMRG reference function is represented by a sufficiently large number of renormalized many-body basis, thereby being named DMRG-CASPT2 method. The DMRG-SCF is able to describe non-dynamical correlation with large active space that is insurmountable to the conventional CASSCF method, while the second-order perturbation theory provides an efficient description of dynamical correlation effects. The capability of our implementation is demonstrated for an application to the potential energy curve of the chromium dimer, which is one of the most demanding multireference systems that require best electronic structure treatment for non-dynamical and dynamical correlation as well as large basis sets. The DMRG-CASPT2/cc-pwCV5Z calculations were performed with a large (3d double-shell) active space consisting of 28 orbitals. Our approach using large-size DMRG reference addressed the problems of why the dissociation energy is largely overestimated by CASPT2 with the small active space consisting of 12 orbitals (3d4s), and also is oversensitive to the choice of the zeroth-order Hamiltonian. © 2011 American Institute of Physics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Gyeong Won; Shim, Jaewon; Jung, Young-Dae, E-mail: ydjung@hanyang.ac.kr

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 themore » 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.« less

Metal-insulator transition in AlxGa1-xAs/GaAs heterostructures with large spacer width

NASA Astrophysics Data System (ADS)

Gold, A.

1991-10-01

Analytical results are presented for the mobility of a two-dimensional electron gas in a heterostructure with a thick spacer layer α. Due to multiple-scattering effects a metal-insulator transition occurs at a critical electron density Nc=N1/2i/(4π1/2α) (Ni is the impurity density). The transport mean free path l(t) (calculated in Born approximation) at the metal-insulator transition is l(t)c=2α. A localization criterion in terms of the renormalized single-particle mean free path l(sr) is presented: kFcl(sr)c=(1/2)1/2 (kFc is the Fermi wave number at the critical density). I compare the theoretical results with recent experimental results found in AlxGa1-xAs/GaAs heterostructures with large spacer width: 1200<α<2800 Å. Remote impurity doping and homogeneous background doping are considered. The only fitting parameter used for the theoretical results is the background doping density NB=6×1013 cm-3. My theory is in fair agreement with the experimental results.

The path dependency theory: analytical framework to study institutional integration. The case of France.

PubMed

Trouvé, Hélène; Couturier, Yves; Etheridge, Francis; Saint-Jean, Olivier; Somme, Dominique

2010-06-30

The literature on integration indicates the need for an enhanced theorization of institutional integration. This article proposes path dependence as an analytical framework to study the systems in which integration takes place. PRISMA proposes a model for integrating health and social care services for older adults. This model was initially tested in Quebec. The PRISMA France study gave us an opportunity to analyze institutional integration in France. A qualitative approach was used. Analyses were based on semi-structured interviews with actors of all levels of decision-making, observations of advisory board meetings, and administrative documents. Our analyses revealed the complexity and fragmentation of institutional integration. The path dependency theory, which analyzes the change capacity of institutions by taking into account their historic structures, allows analysis of this situation. The path dependency to the Bismarckian system and the incomplete reforms of gerontological policies generate the coexistence and juxtaposition of institutional systems. In such a context, no institution has sufficient ability to determine gerontology policy and build institutional integration by itself. Using path dependence as an analytical framework helps to understand the reasons why institutional integration is critical to organizational and clinical integration, and the complex construction of institutional integration in France.

Electric Dipole Moment Results from lattice QCD

NASA Astrophysics Data System (ADS)

Dragos, Jack; Luu, Thomas; Shindler, Andrea; de Vries, Jordy

2018-03-01

We utilize the gradient flow to define and calculate electric dipole moments induced by the strong QCD θ-term and the dimension-6 Weinberg operator. The gradient flow is a promising tool to simplify the renormalization pattern of local operators. The results of the nucleon electric dipole moments are calculated on PACS-CS gauge fields (available from the ILDG) using Nf = 2+1, of discrete size 323×64 and spacing a ≃ 0.09 fm. These gauge fields use a renormalization-group improved gauge action and a nonperturbatively O(a) improved clover quark action at β = 1.90, with cSW = 1.715. The calculation is performed at pion masses of mπ ≃ 411, 701 MeV.

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.

Effects of two-loop contributions in the pseudofermion functional renormalization group method for quantum spin systems

NASA Astrophysics Data System (ADS)

Rück, Marlon; Reuther, Johannes

2018-04-01

We implement an extension of the pseudofermion functional renormalization group method for quantum spin systems that takes into account two-loop diagrammatic contributions. An efficient numerical treatment of the additional terms is achieved within a nested graph construction which recombines different one-loop interaction channels. In order to be fully self-consistent with respect to self-energy corrections, we also include certain three-loop terms of Katanin type. We first apply this formalism to the antiferromagnetic J1-J2 Heisenberg model on the square lattice and benchmark our results against the previous one-loop plus Katanin approach. Even though the renormalization group (RG) equations undergo significant modifications when including the two-loop terms, the magnetic phase diagram, comprising Néel ordered and collinear ordered phases separated by a magnetically disordered regime, remains remarkably unchanged. Only the boundary position between the disordered and the collinear phases is found to be moderately affected by two-loop terms. On the other hand, critical RG scales, which we associate with critical temperatures Tc, are reduced by a factor of ˜2 indicating that the two-loop diagrams play a significant role in enforcing the Mermin-Wagner theorem. Improved estimates for critical temperatures are also obtained for the Heisenberg ferromagnet on the three-dimensional simple cubic lattice where errors in Tc are reduced by ˜34 % . These findings have important implications for the quantum phase diagrams calculated within the previous one-loop plus Katanin approach which turn out to be already well converged.

Renormalization of the Lattice Heavy Quark Classical Velocity

NASA Astrophysics Data System (ADS)

Mandula, Jeffrey E.; Ogilvie, Michael C.

1996-03-01

In the lattice formulation of the Heavy Quark Effective Theory (LHQET), the "classical velocity" v becomes renormalized. The origin of this renormalization is the reduction of Lorentz (or O(4)) invariance to (hyper)cubic invariance. The renormalization is finite and depends on the form of the decretization of the reduced heavy quark Dirac equation. For the Forward Time — Centered Space discretization, the renormalization is computed both perturbatively, to one loop, and non-perturbatively using two ensembles of lattices, one at β = 5.7 and the other at β = 6.1 The estimates agree, and indicate that for small classical velocities, ν→ is reduced by about 25-30%.

Two-nucleon S10 amplitude zero in chiral effective field theory

NASA Astrophysics Data System (ADS)

Sánchez, M. Sánchez; Yang, C.-J.; Long, Bingwei; van Kolck, U.

2018-02-01

We present a new rearrangement of short-range interactions in the S10 nucleon-nucleon channel within chiral effective field theory. This is intended to address the slow convergence of Weinberg's scheme, which we attribute to its failure to reproduce the amplitude zero (scattering momentum ≃340 MeV) at leading order. After the power counting scheme is modified to accommodate the zero at leading order, it includes subleading corrections perturbatively in a way that is consistent with renormalization-group invariance. Systematic improvement is shown at next-to-leading order, and we obtain results that fit empirical phase shifts remarkably well all the way up to the pion-production threshold. An approach in which pions have been integrated out is included, which allows us to derive analytic results that also fit phenomenology surprisingly well.

Ward identities and combinatorics of rainbow tensor models

NASA Astrophysics Data System (ADS)

Itoyama, H.; Mironov, A.; Morozov, A.

2017-06-01

We discuss the notion of renormalization group (RG) completion of non-Gaussian Lagrangians and its treatment within the framework of Bogoliubov-Zimmermann theory in application to the matrix and tensor models. With the example of the simplest non-trivial RGB tensor theory (Aristotelian rainbow), we introduce a few methods, which allow one to connect calculations in the tensor models to those in the matrix models. As a byproduct, we obtain some new factorization formulas and sum rules for the Gaussian correlators in the Hermitian and complex matrix theories, square and rectangular. These sum rules describe correlators as solutions to finite linear systems, which are much simpler than the bilinear Hirota equations and the infinite Virasoro recursion. Search for such relations can be a way to solving the tensor models, where an explicit integrability is still obscure.

Two-path plasmonic interferometer with integrated detector

DOEpatents

Dyer, Gregory Conrad; Shaner, Eric A.; Aizin, Gregory

2016-03-29

An electrically tunable terahertz two-path plasmonic interferometer with an integrated detection element can down convert a terahertz field to a rectified DC signal. The integrated detector utilizes a resonant plasmonic homodyne mixing mechanism that measures the component of the plasma waves in-phase with an excitation field that functions as the local oscillator in the mixer. The plasmonic interferometer comprises two independently tuned electrical paths. The plasmonic interferometer enables a spectrometer-on-a-chip where the tuning of electrical path length plays an analogous role to that of physical path length in macroscopic Fourier transform interferometers.

The path integral on the pseudosphere

NASA Astrophysics Data System (ADS)

Grosche, C.; Steiner, F.

1988-02-01

A rigorous path integral treatment for the d-dimensional pseudosphere Λd-1 , a Riemannian manifold of constant negative curvature, is presented. The path integral formulation is based on a canonical approach using Weyl-ordering and the Hamiltonian path integral defined on midpoints. The time-dependent and energy-dependent Feynman kernels obtain different expressions in the even- and odd-dimensional cases, respectively. The special case of the three-dimensional pseudosphere, which is analytically equivalent to the Poincaré upper half plane, the Poincaré disc, and the hyperbolic strip, is discussed in detail including the energy spectrum and the normalised wave-functions.

Renormalization of entanglement entropy from topological terms

NASA Astrophysics Data System (ADS)

Anastasiou, Giorgos; Araya, Ignacio J.; Olea, Rodrigo

2018-05-01

We propose a renormalization scheme for entanglement entropy of three-dimensional CFTs with a four-dimensional asymptotically AdS gravity dual in the context of the gauge/gravity correspondence. The procedure consists in adding the Chern form as a boundary term to the area functional of the Ryu-Takayanagi minimal surface. We provide an explicit prescription for the renormalized entanglement entropy, which is derived via the replica trick. This is achieved by considering a Euclidean gravitational action renormalized by the addition of the Chern form at the spacetime boundary, evaluated in the conically-singular replica manifold. We show that the addition of this boundary term cancels the divergent part of the entanglement entropy, recovering the results obtained by Taylor and Woodhead. We comment on how this prescription for renormalizing the entanglement entropy is in line with the general program of topological renormalization in asymptotically AdS gravity.

Formulation of D-brane Dynamics

NASA Astrophysics Data System (ADS)

Evans, Thomas

2012-03-01

It is the purpose of this paper (within the context of STS rules & guidelines ``research report'') to formulate a statistical-mechanical form of D-brane dynamics. We consider first the path integral formulation of quantum mechanics, and extend this to a path-integral formulation of D-brane mechanics, summing over all the possible path integral sectors of R-R, NS charged states. We then investigate this generalization utilizing a path-integral formulation summing over all the possible path integral sectors of R-R charged states, calculated from the mean probability tree-level amplitude of type I, IIA, and IIB strings, serving as a generalization of all strings described by D-branes. We utilize this generalization to study black holes in regimes where the initial D-brane system is legitimate, and further this generalization to look at information loss near regions of nonlocality on a non-ordinary event horizon. We see here that in these specific regimes, we can calculate a path integral formulation, as describing D0-brane mechanics, tracing the dissipation of entropy throughout the event horizon. This is used to study the information paradox, and to propose a resolution between the phenomena and the correct and expected quantum mechanical description. This is done as our path integral throughout entropy entering the event horizon effectively and correctly encodes the initial state in subtle correlations in the Hawking radiation.

All-Optical Wavelength-Path Service With Quality Assurance by Multilayer Integration System

NASA Astrophysics Data System (ADS)

Yagi, Mikio; Tanaka, Shinya; Satomi, Shuichi; Ryu, Shiro; Asano, Shoichiro

2006-09-01

In the future all-optical network controlled by generalized multiprotocol label switching (GMPLS), the wavelength path between end nodes will change dynamically. This inevitably means that the fiber parameters along the wavelength path will also vary. This variation in fiber parameters influences the signal quality of high-speed-transmission system (bit rates over 40 Gb/s). Therefore, at a path setup, the fiber-parameter effect should be adequately compensated. Moreover, the path setup must be completed fast enough to meet the network-application demands. To realize the rapid setup of adequate paths, a multilayer integration system for all-optical wavelength-path quality assurance is proposed. This multilayer integration system is evaluated in a field trial. In the trial, the GMPLS control plane, measurement plane, and data plane coordinated to maintain the quality of a 40-Gb/s wavelength path that would otherwise be degraded by the influence of chromatic dispersion. It is also demonstrated that the multilayer integration system can assure the signal quality in the face of not only chromatic dispersion but also degradation in the optical signal-to-noise ratio by the use of a 2R regeneration system. Our experiments confirm that the proposed multilayer integration system is an essential part of future all-optical networks.

Two-channel Kondo effect and renormalization flow with macroscopic quantum charge states.

PubMed

Iftikhar, Z; Jezouin, S; Anthore, A; Gennser, U; Parmentier, F D; Cavanna, A; Pierre, F

2015-10-08

Many-body correlations and macroscopic quantum behaviours are fascinating condensed matter problems. A powerful test-bed for the many-body concepts and methods is the Kondo effect, which entails the coupling of a quantum impurity to a continuum of states. It is central in highly correlated systems and can be explored with tunable nanostructures. Although Kondo physics is usually associated with the hybridization of itinerant electrons with microscopic magnetic moments, theory predicts that it can arise whenever degenerate quantum states are coupled to a continuum. Here we demonstrate the previously elusive 'charge' Kondo effect in a hybrid metal-semiconductor implementation of a single-electron transistor, with a quantum pseudospin of 1/2 constituted by two degenerate macroscopic charge states of a metallic island. In contrast to other Kondo nanostructures, each conduction channel connecting the island to an electrode constitutes a distinct and fully tunable Kondo channel, thereby providing unprecedented access to the two-channel Kondo effect and a clear path to multi-channel Kondo physics. Using a weakly coupled probe, we find the renormalization flow, as temperature is reduced, of two Kondo channels competing to screen the charge pseudospin. This provides a direct view of how the predicted quantum phase transition develops across the symmetric quantum critical point. Detuning the pseudospin away from degeneracy, we demonstrate, on a fully characterized device, quantitative agreement with the predictions for the finite-temperature crossover from quantum criticality.

A formalism for the systematic treatment of rapidity logarithms in Quantum Field Theory

NASA Astrophysics Data System (ADS)

Chiu, Jui-Yu; Jain, Ambar; Neill, Duff; Rothstein, Ira Z.

2012-05-01

Many observables in QCD rely upon the resummation of perturbation theory to retain predictive power. Resummation follows after one factorizes the cross section into the relevant modes. The class of observables which are sensitive to soft recoil effects are particularly challenging to factorize and resum since they involve rapidity logarithms. Such observables include: transverse momentum distributions at p T much less then the high energy scattering scale, jet broadening, exclusive hadroproduction and decay, as well as the Sudakov form factor. In this paper we will present a formalism which allows one to factorize and resum the perturbative series for such observables in a systematic fashion through the notion of a "rapidity renormalization group". That is, a Collin-Soper like equation is realized as a renormalization group equation, but has a more universal applicability to observables beyond the traditional transverse momentum dependent parton distribution functions (TMDPDFs) and the Sudakov form factor. This formalism has the feature that it allows one to track the (non-standard) scheme dependence which is inherent in any sce- nario where one performs a resummation of rapidity divergences. We present a pedagogical introduction to the formalism by applying it to the well-known massive Sudakov form fac- tor. The formalism is then used to study observables of current interest. A factorization theorem for the transverse momentum distribution of Higgs production is presented along with the result for the resummed cross section at NLL. Our formalism allows one to define gauge invariant TMDPDFs which are independent of both the hard scattering amplitude and the soft function, i.e. they are universal. We present details of the factorization and re- summation of the jet broadening cross section including a renormalization in p ⊥ space. We furthermore show how to regulate and renormalize exclusive processes which are plagued by endpoint singularities in such a way as to allow for a consistent resummation.

Path Integral Computation of Quantum Free Energy Differences Due to Alchemical Transformations Involving Mass and Potential.

PubMed

Pérez, Alejandro; von Lilienfeld, O Anatole

2011-08-09

Thermodynamic integration, perturbation theory, and λ-dynamics methods were applied to path integral molecular dynamics calculations to investigate free energy differences due to "alchemical" transformations. Several estimators were formulated to compute free energy differences in solvable model systems undergoing changes in mass and/or potential. Linear and nonlinear alchemical interpolations were used for the thermodynamic integration. We find improved convergence for the virial estimators, as well as for the thermodynamic integration over nonlinear interpolation paths. Numerical results for the perturbative treatment of changes in mass and electric field strength in model systems are presented. We used thermodynamic integration in ab initio path integral molecular dynamics to compute the quantum free energy difference of the isotope transformation in the Zundel cation. The performance of different free energy methods is discussed.

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.

Tensor hypercontraction. II. Least-squares renormalization.

PubMed

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

2012-12-14

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

Path integrals, supersymmetric quantum mechanics, and the Atiyah-Singer index theorem for twisted Dirac

NASA Astrophysics Data System (ADS)

Fine, Dana S.; Sawin, Stephen

2017-01-01

Feynman's time-slicing construction approximates the path integral by a product, determined by a partition of a finite time interval, of approximate propagators. This paper formulates general conditions to impose on a short-time approximation to the propagator in a general class of imaginary-time quantum mechanics on a Riemannian manifold which ensure that these products converge. The limit defines a path integral which agrees pointwise with the heat kernel for a generalized Laplacian. The result is a rigorous construction of the propagator for supersymmetric quantum mechanics, with potential, as a path integral. Further, the class of Laplacians includes the square of the twisted Dirac operator, which corresponds to an extension of N = 1/2 supersymmetric quantum mechanics. General results on the rate of convergence of the approximate path integrals suffice in this case to derive the local version of the Atiyah-Singer index theorem.

The path integral on the Poincaré upper half-plane with a magnetic field and for the Morse potential

NASA Astrophysics Data System (ADS)

Grosche, Christian

1988-10-01

Rigorous path integral treatments on the Poincaré upper half-plane with a magnetic field and for the Morse potential are presented. The calculation starts with the path integral on the Poincaré upper half-plane with a magnetic field. By a Fourier expansion and a non-linear transformation this problem is reformulated in terms of the path integral for the Morse potential. This latter problem can be reduced by an appropriate space-time transformation to the path integral for the harmonic oscillator with generalised angular momentum, a technique which has been developed in recent years. The well-known solution for the last problem enables one to give explicit expressions for the Feynman kernels for the Morse potential and for the Poincaré upper half-plane with magnetic field, respectively. The wavefunctions and the energy spectrum for the bound and scattering states are given, respectively.

The path dependency theory: analytical framework to study institutional integration. The case of France

PubMed Central

Trouvé, Hélène; Couturier, Yves; Etheridge, Francis; Saint-Jean, Olivier; Somme, Dominique

2010-01-01

Background The literature on integration indicates the need for an enhanced theorization of institutional integration. This article proposes path dependence as an analytical framework to study the systems in which integration takes place. Purpose PRISMA proposes a model for integrating health and social care services for older adults. This model was initially tested in Quebec. The PRISMA France study gave us an opportunity to analyze institutional integration in France. Methods A qualitative approach was used. Analyses were based on semi-structured interviews with actors of all levels of decision-making, observations of advisory board meetings, and administrative documents. Results Our analyses revealed the complexity and fragmentation of institutional integration. The path dependency theory, which analyzes the change capacity of institutions by taking into account their historic structures, allows analysis of this situation. The path dependency to the Bismarckian system and the incomplete reforms of gerontological policies generate the coexistence and juxtaposition of institutional systems. In such a context, no institution has sufficient ability to determine gerontology policy and build institutional integration by itself. Conclusion Using path dependence as an analytical framework helps to understand the reasons why institutional integration is critical to organizational and clinical integration, and the complex construction of institutional integration in France. PMID:20689740

Structural impact on the eigenenergy renormalization for carbon and silicon allotropes and boron nitride polymorphs

NASA Astrophysics Data System (ADS)

Tutchton, Roxanne; Marchbanks, Christopher; Wu, Zhigang

2018-05-01

The phonon-induced renormalization of electronic band structures is investigated through first-principles calculations based on the density functional perturbation theory for nine materials with various crystal symmetries. Our results demonstrate that the magnitude of the zero-point renormalization (ZPR) of the electronic band structure is dependent on both crystal structure and material composition. We have performed analysis of the electron-phonon-coupling-induced renormalization for two silicon (Si) allotropes, three carbon (C) allotropes, and four boron nitride (BN) polymorphs. Phonon dispersions of each material were computed, and our analysis indicates that materials with optical phonons at higher maximum frequencies, such as graphite and hexagonal BN, have larger absolute ZPRs, with the exception of graphene, which has a considerably smaller ZPR despite having phonon frequencies in the same range as graphite. Depending on the structure and material, renormalizations can be comparable to the GW many-body corrections to Kohn-Sham eigenenergies and, thus, need to be considered in electronic structure calculations. The temperature dependence of the renormalizations is also considered, and in all materials, the eigenenergy renormalization at the band gap and around the Fermi level increases with increasing temperature.

Mnemonic discrimination relates to perforant path integrity: An ultra-high resolution diffusion tensor imaging study.

PubMed

Bennett, Ilana J; Stark, Craig E L

2016-03-01

Pattern separation describes the orthogonalization of similar inputs into unique, non-overlapping representations. This computational process is thought to serve memory by reducing interference and to be mediated by the dentate gyrus of the hippocampus. Using ultra-high in-plane resolution diffusion tensor imaging (hrDTI) in older adults, we previously demonstrated that integrity of the perforant path, which provides input to the dentate gyrus from entorhinal cortex, was associated with mnemonic discrimination, a behavioral outcome designed to load on pattern separation. The current hrDTI study assessed the specificity of this perforant path integrity-mnemonic discrimination relationship relative to other cognitive constructs (identified using a factor analysis) and white matter tracts (hippocampal cingulum, fornix, corpus callosum) in 112 healthy adults (20-87 years). Results revealed age-related declines in integrity of the perforant path and other medial temporal lobe (MTL) tracts (hippocampal cingulum, fornix). Controlling for global effects of brain aging, perforant path integrity related only to the factor that captured mnemonic discrimination performance. Comparable integrity-mnemonic discrimination relationships were also observed for the hippocampal cingulum and fornix. Thus, whereas perforant path integrity specifically relates to mnemonic discrimination, mnemonic discrimination may be mediated by a broader MTL network. Copyright © 2015 Elsevier Inc. All rights reserved.

Aspects of Galileon non-renormalization

DOE PAGES

Goon, Garrett; Hinterbichler, Kurt; Joyce, Austin; ...

2016-11-18

We discuss non-renormalization theorems applying to galileon field theories and their generalizations. Galileon theories are similar in many respects to other derivatively coupled effective field theories, including general relativity and P ( X) theories. In particular, these other theories also enjoy versions of non-renormalization theorems that protect certain operators against corrections from self-loops. Furthermore, we argue that the galileons are distinguished by the fact that they are not renormalized even by loops of other heavy fields whose couplings respect the galileon symmetry.

Composite operator and condensate in the S U (N ) Yang-Mills theory with U (N -1 ) stability group

NASA Astrophysics Data System (ADS)

Warschinke, Matthias; Matsudo, Ryutaro; Nishino, Shogo; Shinohara, Toru; Kondo, Kei-Ichi

2018-02-01

Recently, some reformulations of the Yang-Mills theory inspired by the Cho-Faddeev-Niemi decomposition have been developed in order to understand confinement from the viewpoint of the dual superconductivity. In this paper we focus on the reformulated S U (N ) Yang-Mills theory in the minimal option with U (N -1 ) stability group. Despite existing numerical simulations on the lattice we perform the perturbative analysis to one-loop level as a first step towards the nonperturbative analytical treatment. First, we give the Feynman rules and calculate all renormalization factors to obtain the standard renormalization group functions to one-loop level in light of the renormalizability of this theory. Then we introduce a mixed gluon-ghost composite operator of mass dimension 2 and show the Bechi-Rouet-Stora-Tyutin invariance and the multiplicative renormalizability. Armed with these results, we argue the existence of the mixed gluon-ghost condensate by means of the so-called local composite operator formalism, which leads to various interesting implications for confinement as shown in preceding works.

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.

The generalized scheme-independent Crewther relation in QCD

NASA Astrophysics Data System (ADS)

Shen, Jian-Ming; Wu, Xing-Gang; Ma, Yang; Brodsky, Stanley J.

2017-07-01

The Principle of Maximal Conformality (PMC) provides a systematic way to set the renormalization scales order-by-order for any perturbative QCD calculable processes. The resulting predictions are independent of the choice of renormalization scheme, a requirement of renormalization group invariance. The Crewther relation, which was originally derived as a consequence of conformally invariant field theory, provides a remarkable connection between two observables when the β function vanishes: one can show that the product of the Bjorken sum rule for spin-dependent deep inelastic lepton-nucleon scattering times the Adler function, defined from the cross section for electron-positron annihilation into hadrons, has no pQCD radiative corrections. The ;Generalized Crewther Relation; relates these two observables for physical QCD with nonzero β function; specifically, it connects the non-singlet Adler function (Dns) to the Bjorken sum rule coefficient for polarized deep-inelastic electron scattering (CBjp) at leading twist. A scheme-dependent ΔCSB-term appears in the analysis in order to compensate for the conformal symmetry breaking (CSB) terms from perturbative QCD. In conventional analyses, this normally leads to unphysical dependence in both the choice of the renormalization scheme and the choice of the initial scale at any finite order. However, by applying PMC scale-setting, we can fix the scales of the QCD coupling unambiguously at every order of pQCD. The result is that both Dns and the inverse coefficient CBjp-1 have identical pQCD coefficients, which also exactly match the coefficients of the corresponding conformal theory. Thus one obtains a new generalized Crewther relation for QCD which connects two effective charges, αˆd (Q) =∑i≥1 αˆg1 i (Qi), at their respective physical scales. This identity is independent of the choice of the renormalization scheme at any finite order, and the dependence on the choice of the initial scale is negligible. Similar scale-fixed commensurate scale relations also connect other physical observables at their physical momentum scales, thus providing convention-independent, fundamental precision tests of QCD.

Sensory feedback in a bump attractor model of path integration.

PubMed

Poll, Daniel B; Nguyen, Khanh; Kilpatrick, Zachary P

2016-04-01

Mammalian spatial navigation systems utilize several different sensory information channels. This information is converted into a neural code that represents the animal's current position in space by engaging place cell, grid cell, and head direction cell networks. In particular, sensory landmark (allothetic) cues can be utilized in concert with an animal's knowledge of its own velocity (idiothetic) cues to generate a more accurate representation of position than path integration provides on its own (Battaglia et al. The Journal of Neuroscience 24(19):4541-4550 (2004)). We develop a computational model that merges path integration with feedback from external sensory cues that provide a reliable representation of spatial position along an annular track. Starting with a continuous bump attractor model, we explore the impact of synaptic spatial asymmetry and heterogeneity, which disrupt the position code of the path integration process. We use asymptotic analysis to reduce the bump attractor model to a single scalar equation whose potential represents the impact of asymmetry and heterogeneity. Such imperfections cause errors to build up when the network performs path integration, but these errors can be corrected by an external control signal representing the effects of sensory cues. We demonstrate that there is an optimal strength and decay rate of the control signal when cues appear either periodically or randomly. A similar analysis is performed when errors in path integration arise from dynamic noise fluctuations. Again, there is an optimal strength and decay of discrete control that minimizes the path integration error.

Effect of friction on electron transfer: The two reaction coordinate case

NASA Astrophysics Data System (ADS)

Onuchic, José Nelson

1987-04-01

Electron transfer is a very important reaction in many biological processes such as photosynthesis and oxidative phosphorylation. In many of these reactions, most of the interesting dynamics can be included by using two reaction coordinates: one fast (local high frequency vibration modes) and one slow (outersphere modes such as solvent polarization). We report a model to describe this problem, which uses path integral techniques to calculate electron transfer rates, and also to obtain the Fokker-Planck equations associated with this model. Different limiting cases lead to qualitatively different results such as exponential or nonexponential time decay for the donor survival probability. Conditions for the validity of the adiabatic or the nonadiabatic limits will be discussed. Application of this model to real systems is proposed, in particular for a porphyrin rigidly linked to a quinone, which is a very interesting model compound for primary events of photosynthesis. This model can also be used for other multicoordinate biological reactions such as ligand binding to heme proteins. Also, in the concluding part of Sec. III, we discuss the important limit where the fast vibronic mode is much faster than all the other nuclear modes coupled to the problem. In this limit the fast mode ``renormalizes'' the electronic matrix element, and this considerably simplifies the treatment of the problem, reducing it to coupling only to the slow modes.

Fractional Stochastic Field Theory

NASA Astrophysics Data System (ADS)

Honkonen, Juha

2018-02-01

Models describing evolution of physical, chemical, biological, social and financial processes are often formulated as differential equations with the understanding that they are large-scale equations for averages of quantities describing intrinsically random processes. Explicit account of randomness may lead to significant changes in the asymptotic behaviour (anomalous scaling) in such models especially in low spatial dimensions, which in many cases may be captured with the use of the renormalization group. Anomalous scaling and memory effects may also be introduced with the use of fractional derivatives and fractional noise. Construction of renormalized stochastic field theory with fractional derivatives and fractional noise in the underlying stochastic differential equations and master equations and the interplay between fluctuation-induced and built-in anomalous scaling behaviour is reviewed and discussed.

On the robustness of the primordial power spectrum in renormalized Higgs inflation

NASA Astrophysics Data System (ADS)

Bezrukov, Fedor; Pauly, Martin; Rubio, Javier

2018-02-01

We study the cosmological consequences of higher-dimensional operators respecting the asymptotic symmetries of the tree-level Higgs inflation action. The main contribution of these operators to the renormalization group enhanced potential is localized in a compact field range, whose upper limit is close to the end of inflation. The spectrum of primordial fluctuations in the so-called universal regime turns out to be almost insensitive to radiative corrections and in excellent agreement with the present cosmological data. However, higher-dimensional operators can play an important role in critical Higgs inflation scenarios containing a quasi-inflection point along the inflationary trajectory. The interplay of radiative corrections with this quasi-inflection point may translate into a sizable modification of the inflationary observables.

A Note on Feynman Path Integral for Electromagnetic External Fields

NASA Astrophysics Data System (ADS)

Botelho, Luiz C. L.

2017-08-01

We propose a Fresnel stochastic white noise framework to analyze the nature of the Feynman paths entering on the Feynman Path Integral expression for the Feynman Propagator of a particle quantum mechanically moving under an external electromagnetic time-independent potential.

An Anatomically Constrained Model for Path Integration in the Bee Brain.

PubMed

Stone, Thomas; Webb, Barbara; Adden, Andrea; Weddig, Nicolai Ben; Honkanen, Anna; Templin, Rachel; Wcislo, William; Scimeca, Luca; Warrant, Eric; Heinze, Stanley

2017-10-23

Path integration is a widespread navigational strategy in which directional changes and distance covered are continuously integrated on an outward journey, enabling a straight-line return to home. Bees use vision for this task-a celestial-cue-based visual compass and an optic-flow-based visual odometer-but the underlying neural integration mechanisms are unknown. Using intracellular electrophysiology, we show that polarized-light-based compass neurons and optic-flow-based speed-encoding neurons converge in the central complex of the bee brain, and through block-face electron microscopy, we identify potential integrator cells. Based on plausible output targets for these cells, we propose a complete circuit for path integration and steering in the central complex, with anatomically identified neurons suggested for each processing step. The resulting model circuit is thus fully constrained biologically and provides a functional interpretation for many previously unexplained architectural features of the central complex. Moreover, we show that the receptive fields of the newly discovered speed neurons can support path integration for the holonomic motion (i.e., a ground velocity that is not precisely aligned with body orientation) typical of bee flight, a feature not captured in any previously proposed model of path integration. In a broader context, the model circuit presented provides a general mechanism for producing steering signals by comparing current and desired headings-suggesting a more basic function for central complex connectivity, from which path integration may have evolved. Copyright © 2017 Elsevier Ltd. All rights reserved.

Spin coherent-state path integrals and the instanton calculus

NASA Astrophysics Data System (ADS)

Garg, Anupam; Kochetov, Evgueny; Park, Kee-Su; Stone, Michael

2003-01-01

We use an instanton approximation to the continuous-time spin coherent-state path integral to obtain the tunnel splitting of classically degenerate ground states. We show that provided the fluctuation determinant is carefully evaluated, the path integral expression is accurate to order O(1/j). We apply the method to the LMG model and to the molecular magnet Fe8 in a transverse field.

Critical behavior of two- and three-dimensional ferromagnetic and antiferromagnetic spin-ice systems using the effective-field renormalization group technique

NASA Astrophysics Data System (ADS)

Garcia-Adeva, Angel J.; Huber, David L.

2001-07-01

In this work we generalize and subsequently apply the effective-field renormalization-group (EFRG) technique to the problem of ferro- and antiferromagnetically coupled Ising spins with local anisotropy axes in geometrically frustrated geometries (kagomé and pyrochlore lattices). In this framework, we calculate the various ground states of these systems and the corresponding critical points. Excellent agreement is found with exact and Monte Carlo results. The effects of frustration are discussed. As pointed out by other authors, it turns out that the spin-ice model can be exactly mapped to the standard Ising model, but with effective interactions of the opposite sign to those in the original Hamiltonian. Therefore, the ferromagnetic spin ice is frustrated and does not order. Antiferromagnetic spin ice (in both two and three dimensions) is found to undergo a transition to a long-range-ordered state. The thermal and magnetic critical exponents for this transition are calculated. It is found that the thermal exponent is that of the Ising universality class, whereas the magnetic critical exponent is different, as expected from the fact that the Zeeman term has a different symmetry in these systems. In addition, the recently introduced generalized constant coupling method is also applied to the calculation of the critical points and ground-state configurations. Again, a very good agreement is found with exact, Monte Carlo, and renormalization-group calculations for the critical points. Incidentally, we show that the generalized constant coupling approach can be regarded as the lowest-order limit of the EFRG technique, in which correlations outside a frustrated unit are neglected, and scaling is substituted by strict equality of the thermodynamic quantities.

Variational nature, integration, and properties of Newton reaction path

NASA Astrophysics Data System (ADS)

Bofill, Josep Maria; Quapp, Wolfgang

2011-02-01

The distinguished coordinate path and the reduced gradient following path or its equivalent formulation, the Newton trajectory, are analyzed and unified using the theory of calculus of variations. It is shown that their minimum character is related to the fact that the curve is located in a valley region. In this case, we say that the Newton trajectory is a reaction path with the category of minimum energy path. In addition to these findings a Runge-Kutta-Fehlberg algorithm to integrate these curves is also proposed.

Variational nature, integration, and properties of Newton reaction path.

PubMed

Bofill, Josep Maria; Quapp, Wolfgang

2011-02-21

The distinguished coordinate path and the reduced gradient following path or its equivalent formulation, the Newton trajectory, are analyzed and unified using the theory of calculus of variations. It is shown that their minimum character is related to the fact that the curve is located in a valley region. In this case, we say that the Newton trajectory is a reaction path with the category of minimum energy path. In addition to these findings a Runge-Kutta-Fehlberg algorithm to integrate these curves is also proposed.

Monotonic entropy growth for a nonlinear model of random exchanges.

PubMed

Apenko, S M

2013-02-01

We present a proof of the monotonic entropy growth for a nonlinear discrete-time model of a random market. This model, based on binary collisions, also may be viewed as a particular case of Ulam's redistribution of energy problem. We represent each step of this dynamics as a combination of two processes. The first one is a linear energy-conserving evolution of the two-particle distribution, for which the entropy growth can be easily verified. The original nonlinear process is actually a result of a specific "coarse graining" of this linear evolution, when after the collision one variable is integrated away. This coarse graining is of the same type as the real space renormalization group transformation and leads to an additional entropy growth. The combination of these two factors produces the required result which is obtained only by means of information theory inequalities.

Scaling theory of topological phase transitions

NASA Astrophysics Data System (ADS)

Chen, Wei

2016-02-01

Topologically ordered systems are characterized by topological invariants that are often calculated from the momentum space integration of a certain function that represents the curvature of the many-body state. The curvature function may be Berry curvature, Berry connection, or other quantities depending on the system. Akin to stretching a messy string to reveal the number of knots it contains, a scaling procedure is proposed for the curvature function in inversion symmetric systems, from which the topological phase transition can be identified from the flow of the driving energy parameters that control the topology (hopping, chemical potential, etc) under scaling. At an infinitesimal operation, one obtains the renormalization group (RG) equations for the driving energy parameters. A length scale defined from the curvature function near the gap-closing momentum is suggested to characterize the scale invariance at critical points and fixed points, and displays a universal critical behavior in a variety of systems examined.

Monotonic entropy growth for a nonlinear model of random exchanges

NASA Astrophysics Data System (ADS)

Apenko, S. M.

2013-02-01

We present a proof of the monotonic entropy growth for a nonlinear discrete-time model of a random market. This model, based on binary collisions, also may be viewed as a particular case of Ulam's redistribution of energy problem. We represent each step of this dynamics as a combination of two processes. The first one is a linear energy-conserving evolution of the two-particle distribution, for which the entropy growth can be easily verified. The original nonlinear process is actually a result of a specific “coarse graining” of this linear evolution, when after the collision one variable is integrated away. This coarse graining is of the same type as the real space renormalization group transformation and leads to an additional entropy growth. The combination of these two factors produces the required result which is obtained only by means of information theory inequalities.

Two-nucleon S 0 1 amplitude zero in chiral effective field theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sanchez, M. Sanchez; Yang, C. -J.; Long, Bingwei

We present a new rearrangement of short-range interactions in the 1S 0 nucleon-nucleon channel within chiral effective field theory. This is intended to address the slow convergence of Weinberg’s scheme, which we attribute to its failure to reproduce the amplitude zero (scattering momentum ≃340 MeV) at leading order. After the power counting scheme is modified to accommodate the zero at leading order, it includes subleading corrections perturbatively in a way that is consistent with renormalization-group invariance. Systematic improvement is shown at next-to-leading order, and we obtain results that fit empirical phase shifts remarkably well all the way up to themore » pion-production threshold. As a result, an approach in which pions have been integrated out is included, which allows us to derive analytic results that also fit phenomenology surprisingly well.« less

Two-nucleon S 0 1 amplitude zero in chiral effective field theory

DOE PAGES

Sanchez, M. Sanchez; Yang, C. -J.; Long, Bingwei; ...

2018-02-05

We present a new rearrangement of short-range interactions in the 1S 0 nucleon-nucleon channel within chiral effective field theory. This is intended to address the slow convergence of Weinberg’s scheme, which we attribute to its failure to reproduce the amplitude zero (scattering momentum ≃340 MeV) at leading order. After the power counting scheme is modified to accommodate the zero at leading order, it includes subleading corrections perturbatively in a way that is consistent with renormalization-group invariance. Systematic improvement is shown at next-to-leading order, and we obtain results that fit empirical phase shifts remarkably well all the way up to themore » pion-production threshold. As a result, an approach in which pions have been integrated out is included, which allows us to derive analytic results that also fit phenomenology surprisingly well.« less

Path integration of head direction: updating a packet of neural activity at the correct speed using neuronal time constants.

PubMed

Walters, D M; Stringer, S M

2010-07-01

A key question in understanding the neural basis of path integration is how individual, spatially responsive, neurons may self-organize into networks that can, through learning, integrate velocity signals to update a continuous representation of location within an environment. It is of vital importance that this internal representation of position is updated at the correct speed, and in real time, to accurately reflect the motion of the animal. In this article, we present a biologically plausible model of velocity path integration of head direction that can solve this problem using neuronal time constants to effect natural time delays, over which associations can be learned through associative Hebbian learning rules. The model comprises a linked continuous attractor network and competitive network. In simulation, we show that the same model is able to learn two different speeds of rotation when implemented with two different values for the time constant, and without the need to alter any other model parameters. The proposed model could be extended to path integration of place in the environment, and path integration of spatial view.

From classical to quantum and back: Hamiltonian adaptive resolution path integral, ring polymer, and centroid molecular dynamics

NASA Astrophysics Data System (ADS)

Kreis, Karsten; Kremer, Kurt; Potestio, Raffaello; Tuckerman, Mark E.

2017-12-01

Path integral-based methodologies play a crucial role for the investigation of nuclear quantum effects by means of computer simulations. However, these techniques are significantly more demanding than corresponding classical simulations. To reduce this numerical effort, we recently proposed a method, based on a rigorous Hamiltonian formulation, which restricts the quantum modeling to a small but relevant spatial region within a larger reservoir where particles are treated classically. In this work, we extend this idea and show how it can be implemented along with state-of-the-art path integral simulation techniques, including path-integral molecular dynamics, which allows for the calculation of quantum statistical properties, and ring-polymer and centroid molecular dynamics, which allow the calculation of approximate quantum dynamical properties. To this end, we derive a new integration algorithm that also makes use of multiple time-stepping. The scheme is validated via adaptive classical-path-integral simulations of liquid water. Potential applications of the proposed multiresolution method are diverse and include efficient quantum simulations of interfaces as well as complex biomolecular systems such as membranes and proteins.

Enzymatic Kinetic Isotope Effects from Path-Integral Free Energy Perturbation Theory.

PubMed

Gao, J

2016-01-01

Path-integral free energy perturbation (PI-FEP) theory is presented to directly determine the ratio of quantum mechanical partition functions of different isotopologs in a single simulation. Furthermore, a double averaging strategy is used to carry out the practical simulation, separating the quantum mechanical path integral exactly into two separate calculations, one corresponding to a classical molecular dynamics simulation of the centroid coordinates, and another involving free-particle path-integral sampling over the classical, centroid positions. An integrated centroid path-integral free energy perturbation and umbrella sampling (PI-FEP/UM, or simply, PI-FEP) method along with bisection sampling was summarized, which provides an accurate and fast convergent method for computing kinetic isotope effects for chemical reactions in solution and in enzymes. The PI-FEP method is illustrated by a number of applications, to highlight the computational precision and accuracy, the rule of geometrical mean in kinetic isotope effects, enhanced nuclear quantum effects in enzyme catalysis, and protein dynamics on temperature dependence of kinetic isotope effects. © 2016 Elsevier Inc. All rights reserved.

Repeated Structural Imaging Reveals Nonlinear Progression of Experience-Dependent Volume Changes in Human Motor Cortex.

PubMed

Wenger, Elisabeth; Kühn, Simone; Verrel, Julius; Mårtensson, Johan; Bodammer, Nils Christian; Lindenberger, Ulman; Lövdén, Martin

2017-05-01

Evidence for experience-dependent structural brain change in adult humans is accumulating. However, its time course is not well understood, as intervention studies typically consist of only 2 imaging sessions (before vs. after training). We acquired up to 18 structural magnetic resonance images over a 7-week period while 15 right-handed participants practiced left-hand writing and drawing. After 4 weeks, we observed increases in gray matter of both left and right primary motor cortices relative to a control group; 3 weeks later, these differences were no longer reliable. Time-series analyses revealed that gray matter in the primary motor cortices expanded during the first 4 weeks and then partially renormalized, in particular in the right hemisphere, despite continued practice and increasing task proficiency. Similar patterns of expansion followed by partial renormalization are also found in synaptogenesis, cortical map plasticity, and maturation, and may qualify as a general principle of structural plasticity. Research on human brain plasticity needs to encompass more than 2 measurement occasions to capture expansion and potential renormalization processes over time. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Normal state of metallic hydrogen sulfide

NASA Astrophysics Data System (ADS)

Kudryashov, N. A.; Kutukov, A. A.; Mazur, E. A.

2017-02-01

A generalized theory of the normal properties of metals in the case of electron-phonon (EP) systems with a nonconstant density of electron states has been used to study the normal state of the SH3 and SH2 phases of hydrogen sulfide at different pressures. The frequency dependence of the real Re Σ (ω) and imaginary ImΣ (ω) parts of the self-energy Σ (ω) part (SEP) of the Green's function of the electron Σ (ω), real part Re Z (ω), and imaginary part Im Z (ω) of the complex renormalization of the mass of the electron; the real part Re χ (ω) and the imaginary part Imχ (ω) of the complex renormalization of the chemical potential; and the density of electron states N (ɛ) renormalized by strong electron-phonon interaction have been calculated. Calculations have been carried out for the stable orthorhombic structure (space group Im3¯ m) of the hydrogen sulfide SH3 for three values of the pressure P = 170, 180, and 225 GPa; and for an SH2 structure with a symmetry of I4/ mmm ( D4 h1¯7) for three values of pressure P = 150, 180, and 225 GP at temperature T = 200 K.

Renormalization scheme dependence of the two-loop QCD corrections to the neutral Higgs-boson masses in the MSSM.

PubMed

Borowka, S; Hahn, T; Heinemeyer, S; Heinrich, G; Hollik, W

Reaching a theoretical accuracy in the prediction of the lightest MSSM Higgs-boson mass, [Formula: see text], 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 [Formula: see text] (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-[Formula: see text] 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 [Formula: see text] obtained with the top-quark mass renormalized on-shell and [Formula: see text]. 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.

Many-body effects and ultraviolet renormalization in three-dimensional Dirac materials

NASA Astrophysics Data System (ADS)

Throckmorton, Robert; Hofmann, Johannes; Barnes, Edwin

We develop a theory for electron-electron interaction-induced many-body effects in three dimensional (3D) Weyl or Dirac semimetals, including interaction corrections to the polarizability, electron self-energy, and vertex function, up to second order in the effective fine structure constant of the Dirac material. These results are used to derive the higher-order ultraviolet renormalization of the Fermi velocity, effective coupling, and quasiparticle residue, revealing that the corrections to the renormalization group (RG) flows of both the velocity and coupling counteract the leading-order tendencies of velocity enhancement and coupling suppression at low energies. This in turn leads to the emergence of a critical coupling above which the interaction strength grows with decreasing energy scale. In addition, we identify a range of coupling strengths below the critical point in which the Fermi velocity varies non-monotonically as the low-energy, non-interacting fixed point is approached. Furthermore, we find that while the higher-order correction to the flow of the coupling is generally small compared to the leading order, the corresponding correction to the velocity flow carries an additional factor of the Dirac cone flavor number relative to the leading-order result. Supported by LPS-MPO-CMTC.

Scale-invariant feature extraction of neural network and renormalization group flow

NASA Astrophysics Data System (ADS)

Iso, Satoshi; Shiba, Shotaro; Yokoo, Sumito

2018-05-01

Theoretical understanding of how a deep neural network (DNN) extracts features from input images is still unclear, but it is widely believed that the extraction is performed hierarchically through a process of coarse graining. It reminds us of the basic renormalization group (RG) concept in statistical physics. In order to explore possible relations between DNN and RG, we use the restricted Boltzmann machine (RBM) applied to an Ising model and construct a flow of model parameters (in particular, temperature) generated by the RBM. We show that the unsupervised RBM trained by spin configurations at various temperatures from T =0 to T =6 generates a flow along which the temperature approaches the critical value Tc=2.2 7 . This behavior is the opposite of the typical RG flow of the Ising model. By analyzing various properties of the weight matrices of the trained RBM, we discuss why it flows towards Tc and how the RBM learns to extract features of spin configurations.

The density matrix renormalization group algorithm on kilo-processor architectures: Implementation and trade-offs

NASA Astrophysics Data System (ADS)

Nemes, Csaba; Barcza, Gergely; Nagy, Zoltán; Legeza, Örs; Szolgay, Péter

2014-06-01

In the numerical analysis of strongly correlated quantum lattice models one of the leading algorithms developed to balance the size of the effective Hilbert space and the accuracy of the simulation is the density matrix renormalization group (DMRG) algorithm, in which the run-time is dominated by the iterative diagonalization of the Hamilton operator. As the most time-dominant step of the diagonalization can be expressed as a list of dense matrix operations, the DMRG is an appealing candidate to fully utilize the computing power residing in novel kilo-processor architectures. In the paper a smart hybrid CPU-GPU implementation is presented, which exploits the power of both CPU and GPU and tolerates problems exceeding the GPU memory size. Furthermore, a new CUDA kernel has been designed for asymmetric matrix-vector multiplication to accelerate the rest of the diagonalization. Besides the evaluation of the GPU implementation, the practical limits of an FPGA implementation are also discussed.

Asymptotically free theory with scale invariant thermodynamics

NASA Astrophysics Data System (ADS)

Ferrari, Gabriel N.; Kneur, Jean-Loïc; Pinto, Marcus Benghi; Ramos, Rudnei O.

2017-12-01

A recently developed variational resummation technique, incorporating renormalization group properties consistently, has been shown to solve the scale dependence problem that plagues the evaluation of thermodynamical quantities, e.g., within the framework of approximations such as in the hard-thermal-loop resummed perturbation theory. This method is used in the present work to evaluate thermodynamical quantities within the two-dimensional nonlinear sigma model, which, apart from providing a technically simpler testing ground, shares some common features with Yang-Mills theories, like asymptotic freedom, trace anomaly and the nonperturbative generation of a mass gap. The present application confirms that nonperturbative results can be readily generated solely by considering the lowest-order (quasiparticle) contribution to the thermodynamic effective potential, when this quantity is required to be renormalization group invariant. We also show that when the next-to-leading correction from the method is accounted for, the results indicate convergence, apart from optimally preserving, within the approximations here considered, the sought-after scale invariance.

A low-cost approach to electronic excitation energies based on the driven similarity renormalization group

NASA Astrophysics Data System (ADS)

Li, Chenyang; Verma, Prakash; Hannon, Kevin P.; Evangelista, Francesco A.

2017-08-01

We propose an economical state-specific approach to evaluate electronic excitation energies based on the driven similarity renormalization group truncated to second order (DSRG-PT2). Starting from a closed-shell Hartree-Fock wave function, a model space is constructed that includes all single or single and double excitations within a given set of active orbitals. The resulting VCIS-DSRG-PT2 and VCISD-DSRG-PT2 methods are introduced and benchmarked on a set of 28 organic molecules [M. Schreiber et al., J. Chem. Phys. 128, 134110 (2008)]. Taking CC3 results as reference values, mean absolute deviations of 0.32 and 0.22 eV are observed for VCIS-DSRG-PT2 and VCISD-DSRG-PT2 excitation energies, respectively. Overall, VCIS-DSRG-PT2 yields results with accuracy comparable to those from time-dependent density functional theory using the B3LYP functional, while VCISD-DSRG-PT2 gives excitation energies comparable to those from equation-of-motion coupled cluster with singles and doubles.

Full Quantum Dynamics Simulation of a Realistic Molecular System Using the Adaptive Time-Dependent Density Matrix Renormalization Group Method.

PubMed

Yao, Yao; Sun, Ke-Wei; Luo, Zhen; Ma, Haibo

2018-01-18

The accurate theoretical interpretation of ultrafast time-resolved spectroscopy experiments relies on full quantum dynamics simulations for the investigated system, which is nevertheless computationally prohibitive for realistic molecular systems with a large number of electronic and/or vibrational degrees of freedom. In this work, we propose a unitary transformation approach for realistic vibronic Hamiltonians, which can be coped with using the adaptive time-dependent density matrix renormalization group (t-DMRG) method to efficiently evolve the nonadiabatic dynamics of a large molecular system. We demonstrate the accuracy and efficiency of this approach with an example of simulating the exciton dissociation process within an oligothiophene/fullerene heterojunction, indicating that t-DMRG can be a promising method for full quantum dynamics simulation in large chemical systems. Moreover, it is also shown that the proper vibronic features in the ultrafast electronic process can be obtained by simulating the two-dimensional (2D) electronic spectrum by virtue of the high computational efficiency of the t-DMRG method.

Wilsonian Renormalization Group and the Lippmann-Schwinger Equation with a Multitude of Cutoff Parameters

NASA Astrophysics Data System (ADS)

Epelbaum, E.; Gegelia, J.; Meißner, Ulf-G.

2018-03-01

The Wilsonian renormalization group approach to the Lippmann-Schwinger equation with a multitude of cutoff parameters is introduced. A system of integro-differential equations for the cutoff-dependent potential is obtained. As an illustration, a perturbative solution of these equations with two cutoff parameters for a simple case of an S-wave low-energy potential in the form of a Taylor series in momenta is obtained. The relevance of the obtained results for the effective field theory approach to nucleon-nucleon scattering is discussed. Supported in part by BMBF under Grant No. 05P2015 - NUSTAR R&D), DFG and NSFC through Funds Provided to the Sino- German CRC 110 “Symmetries and the Emergence of Structure in QCD”, National Natural Science Foundation of China under Grant No. 11621131001, DFG Grant No. TRR110, the Georgian Shota Rustaveli National Science Foundation (grant FR/417/6-100/14) and the CAS President’s International Fellowship Initiative (PIFI) under Grant No. 2017VMA0025

Nonequilibrium Kondo effect in a magnetic field: auxiliary master equation approach

NASA Astrophysics Data System (ADS)

Fugger, Delia M.; Dorda, Antonius; Schwarz, Frauke; von Delft, Jan; Arrigoni, Enrico

2018-01-01

We study the single-impurity Anderson model out of equilibrium under the influence of a bias voltage ϕ and a magnetic field B. We investigate the interplay between the shift ({ω }B) of the Kondo peak in the spin-resolved density of states (DOS) and the one ({φ }B) of the conductance anomaly. In agreement with experiments and previous theoretical calculations we find that, while the latter displays a rather linear behavior with an almost constant slope as a function of B down to the Kondo scale, the DOS shift first features a slower increase reaching the same behavior as {φ }B only for | g| {μ }BB\\gg {k}B{T}K. Our auxiliary master equation approach yields highly accurate nonequilibrium results for the DOS and for the conductance all the way from within the Kondo up to the charge fluctuation regime, showing excellent agreement with a recently introduced scheme based on a combination of numerical renormalization group with time-dependent density matrix renormalization group.

Renormalization-group theory for finite-size scaling in extreme statistics

NASA Astrophysics Data System (ADS)

Györgyi, G.; Moloney, N. R.; Ozogány, K.; Rácz, Z.; Droz, M.

2010-04-01

We present a renormalization-group (RG) approach to explain universal features of extreme statistics applied here to independent identically distributed variables. The outlines of the theory have been described in a previous paper, the main result being that finite-size shape corrections to the limit distribution can be obtained from a linearization of the RG transformation near a fixed point, leading to the computation of stable perturbations as eigenfunctions. Here we show details of the RG theory which exhibit remarkable similarities to the RG known in statistical physics. Besides the fixed points explaining universality, and the least stable eigendirections accounting for convergence rates and shape corrections, the similarities include marginally stable perturbations which turn out to be generic for the Fisher-Tippett-Gumbel class. Distribution functions containing unstable perturbations are also considered. We find that, after a transitory divergence, they return to the universal fixed line at the same or at a different point depending on the type of perturbation.

A state interaction spin-orbit coupling density matrix renormalization group method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sayfutyarova, Elvira R.; Chan, Garnet Kin-Lic

We describe a state interaction spin-orbit (SISO) coupling method using density matrix renormalization group (DMRG) wavefunctions and the spin-orbit mean-field (SOMF) operator. We implement our DMRG-SISO scheme using a spin-adapted algorithm that computes transition density matrices between arbitrary matrix product states. To demonstrate the potential of the DMRG-SISO scheme we present accurate benchmark calculations for the zero-field splitting of the copper and gold atoms, comparing to earlier complete active space self-consistent-field and second-order complete active space perturbation theory results in the same basis. We also compute the effects of spin-orbit coupling on the spin-ladder of the iron-sulfur dimer complex [Fe{submore » 2}S{sub 2}(SCH{sub 3}){sub 4}]{sup 3−}, determining the splitting of the lowest quartet and sextet states. We find that the magnitude of the zero-field splitting for the higher quartet and sextet states approaches a significant fraction of the Heisenberg exchange parameter.« less

Algorithmic-Reducibility = Renormalization-Group Fixed-Points; ``Noise''-Induced Phase-Transitions (NITs) to Accelerate Algorithmics (``NIT-Picking'') Replacing CRUTCHES!!!: Gauss Modular/Clock-Arithmetic Congruences = Signal X Noise PRODUCTS..

NASA Astrophysics Data System (ADS)

Siegel, J.; Siegel, Edward Carl-Ludwig

2011-03-01

Cook-Levin computational-"complexity"(C-C) algorithmic-equivalence reduction-theorem reducibility equivalence to renormalization-(semi)-group phase-transitions critical-phenomena statistical-physics universality-classes fixed-points, is exploited with Gauss modular/clock-arithmetic/model congruences = signal X noise PRODUCT reinterpretation. Siegel-Baez FUZZYICS=CATEGORYICS(SON of ``TRIZ''): Category-Semantics(C-S) tabular list-format truth-table matrix analytics predicts and implements "noise"-induced phase-transitions (NITs) to accelerate versus to decelerate Harel [Algorithmics(1987)]-Sipser[Intro. Theory Computation(1997) algorithmic C-C: "NIT-picking" to optimize optimization-problems optimally(OOPO). Versus iso-"noise" power-spectrum quantitative-only amplitude/magnitude-only variation stochastic-resonance, this "NIT-picking" is "noise" power-spectrum QUALitative-type variation via quantitative critical-exponents variation. Computer-"science" algorithmic C-C models: Turing-machine, finite-state-models/automata, are identified as early-days once-workable but NOW ONLY LIMITING CRUTCHES IMPEDING latter-days new-insights!!!

Functional renormalization group and bosonization as a solver for 2D fermionic Hubbard models

NASA Astrophysics Data System (ADS)

Schuetz, Florian; Marston, Brad

2007-03-01

The functional renormalization group (fRG) provides an unbiased framework to analyze competing instabilities in two-dimensional electron systems and has been used extensively over the past decade [1]. In order to obtain an equally unbiased tool to interprete the flow, we investigate the combination of a many-patch, one-loop calculation with higher dimensional bosonization [2] of the resulting low-energy action. Subsequently a semi-classical approximation [3] can be used to describe the resulting phases. The spinless Hubbard model on a square lattice with nearest neighbor repulsion is investigated as a test case. [1] M. Salmhofer and C. Honerkamp, Prog. Theor. Phys. 105, 1 (2001). [2] A. Houghton, H.-J. Kwon, J. B. Marston, Adv.Phys. 49, 141 (2000); P. Kopietz, Bosonization of interacting fermions in arbitrary dimensions, (Springer, Berlin, 1997). [3] H.-H. Lin, L. Balents, M. P. A. Fisher, Phys. Rev. B 56, 6569 6593 (1997); J. O. Fjaerestad, J. B. Marston, U. Schollwoeck, Ann. Phys. (N.Y.) 321, 894 (2006).

Renormalization group approach to symmetry protected topological phases

NASA Astrophysics Data System (ADS)

van Nieuwenburg, Evert P. L.; Schnyder, Andreas P.; Chen, Wei

2018-04-01

A defining feature of a symmetry protected topological phase (SPT) in one dimension is the degeneracy of the Schmidt values for any given bipartition. For the system to go through a topological phase transition separating two SPTs, the Schmidt values must either split or cross at the critical point in order to change their degeneracies. A renormalization group (RG) approach based on this splitting or crossing is proposed, through which we obtain an RG flow that identifies the topological phase transitions in the parameter space. Our approach can be implemented numerically in an efficient manner, for example, using the matrix product state formalism, since only the largest first few Schmidt values need to be calculated with sufficient accuracy. Using several concrete models, we demonstrate that the critical points and fixed points of the RG flow coincide with the maxima and minima of the entanglement entropy, respectively, and the method can serve as a numerically efficient tool to analyze interacting SPTs in the parameter space.

Asymptotic behavior of solutions of the renormalization group K-epsilon turbulence model

NASA Technical Reports Server (NTRS)

Yakhot, A.; Staroselsky, I.; Orszag, S. A.

1994-01-01

Presently, the only efficient way to calculate turbulent flows in complex geometries of engineering interest is to use Reynolds-average Navier-Stokes (RANS) equations. As compared to the original Navier-Stokes problem, these RANS equations posses much more complicated nonlinear structure and may exhibit far more complex nonlinear behavior. In certain cases, the asymptotic behavior of such models can be studied analytically which, aside from being an interesting fundamental problem, is important for better understanding of the internal structure of the models as well as to improve their performances. The renormalization group (RNG) K-epsilon turbulence model, derived directly from the incompresible Navier-Stokes equations, is analyzed. It has already been used to calculate a variety of turbulent and transitional flows in complex geometries. For large values of the RNG viscosity parameter, the model may exhibit singular behavior. In the form of the RNG K-epsilon model that avoids the use of explicit wall functions, a = 1, so the RNG viscosity parameter must be smaller than 23.62 to avoid singularities.

Global phase diagram of the spinless Falicov-Kimball model in d = 3 : renormalization-group theory

NASA Astrophysics Data System (ADS)

Sariyer, Ozan S.; Hinczewski, Michael; Berker, A. Nihat

2011-03-01

The global phase diagram of the spinless Falicov-Kimball model in d = 3 spatial dimensions is obtained by renormalization-group theory. This global phase diagram exhibits five distinct phases. Four of these phases are charge-ordered (CO) phases, in which the system forms two sublattices with different electron densities. The phase boundaries are second order, except for an intermediate interaction regime, where a first-order phase boundary between two CO phases occurs. The first-order phase boundary is delimited by special bicritical points. The cross-sections of the global phase diagram with respect to the chemical potentials of the localized and mobile electrons, at all representative interaction and hopping strengths, are calculated and exhibit three distinct topologies. The phase diagrams with respect to electron densities are also calculated. This research was supported by the Alexander von Humboldt Foundation, the Scientific and Technological Research Council of Turkey (TÜBITAK), and the Academy of Sciences of Turkey.

Renormalization group scale-setting from the action—a road to modified gravity theories

NASA Astrophysics Data System (ADS)

Domazet, Silvije; Štefančić, Hrvoje

2012-12-01

The renormalization group (RG) corrected gravitational action in Einstein-Hilbert and other truncations is considered. The running scale of the RG is treated as a scalar field at the level of the action and determined in a scale-setting procedure recently introduced by Koch and Ramirez for the Einstein-Hilbert truncation. The scale-setting procedure is elaborated for other truncations of the gravitational action and applied to several phenomenologically interesting cases. It is shown how the logarithmic dependence of the Newton's coupling on the RG scale leads to exponentially suppressed effective cosmological constant and how the scale-setting in particular RG-corrected gravitational theories yields the effective f(R) modified gravity theories with negative powers of the Ricci scalar R. The scale-setting at the level of the action at the non-Gaussian fixed point in Einstein-Hilbert and more general truncations is shown to lead to universal effective action quadratic in the Ricci tensor.

Architectural constraints are a major factor reducing path integration accuracy in the rat head direction cell system.

PubMed

Page, Hector J I; Walters, Daniel; Stringer, Simon M

2015-01-01

Head direction cells fire to signal the direction in which an animal's head is pointing. They are able to track head direction using only internally-derived information (path integration)In this simulation study we investigate the factors that affect path integration accuracy. Specifically, two major limiting factors are identified: rise time, the time after stimulation it takes for a neuron to start firing, and the presence of symmetric non-offset within-layer recurrent collateral connectivity. On the basis of the latter, the important prediction is made that head direction cell regions directly involved in path integration will not contain this type of connectivity; giving a theoretical explanation for architectural observations. Increased neuronal rise time is found to slow path integration, and the slowing effect for a given rise time is found to be more severe in the context of short conduction delays. Further work is suggested on the basis of our findings, which represent a valuable contribution to understanding of the head direction cell system.

Simplified path integral for supersymmetric quantum mechanics and type-A trace anomalies

NASA Astrophysics Data System (ADS)

Bastianelli, Fiorenzo; Corradini, Olindo; Iacconi, Laura

2018-05-01

Particles in a curved space are classically described by a nonlinear sigma model action that can be quantized through path integrals. The latter require a precise regularization to deal with the derivative interactions arising from the nonlinear kinetic term. Recently, for maximally symmetric spaces, simplified path integrals have been developed: they allow to trade the nonlinear kinetic term with a purely quadratic kinetic term (linear sigma model). This happens at the expense of introducing a suitable effective scalar potential, which contains the information on the curvature of the space. The simplified path integral provides a sensible gain in the efficiency of perturbative calculations. Here we extend the construction to models with N = 1 supersymmetry on the worldline, which are applicable to the first quantized description of a Dirac fermion. As an application we use the simplified worldline path integral to compute the type-A trace anomaly of a Dirac fermion in d dimensions up to d = 16.

Feynman path integral application on deriving black-scholes diffusion equation for european option pricing

NASA Astrophysics Data System (ADS)

Utama, Briandhika; Purqon, Acep

2016-08-01

Path Integral is a method to transform a function from its initial condition to final condition through multiplying its initial condition with the transition probability function, known as propagator. At the early development, several studies focused to apply this method for solving problems only in Quantum Mechanics. Nevertheless, Path Integral could also apply to other subjects with some modifications in the propagator function. In this study, we investigate the application of Path Integral method in financial derivatives, stock options. Black-Scholes Model (Nobel 1997) was a beginning anchor in Option Pricing study. Though this model did not successfully predict option price perfectly, especially because its sensitivity for the major changing on market, Black-Scholes Model still is a legitimate equation in pricing an option. The derivation of Black-Scholes has a high difficulty level because it is a stochastic partial differential equation. Black-Scholes equation has a similar principle with Path Integral, where in Black-Scholes the share's initial price is transformed to its final price. The Black-Scholes propagator function then derived by introducing a modified Lagrange based on Black-Scholes equation. Furthermore, we study the correlation between path integral analytical solution and Monte-Carlo numeric solution to find the similarity between this two methods.

On the interface between perturbative and nonperturbative QCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Deur, Alexandre; Brodsky, Stanley J.; de Teramond, Guy F.

2016-04-04

The QCD running couplingmore » $$\\alpha_s(Q^2)$$ sets the strength of the interactions of quarks and gluons as a function of the momentum transfer $Q$. The $Q^2$ dependence of the coupling is required to describe hadronic interactions at both large and short distances. In this article we adopt the light-front holographic approach to strongly-coupled QCD, a formalism which incorporates confinement, predicts the spectroscopy of hadrons composed of light quarks, and describes the low-$Q^2$ analytic behavior of the strong coupling $$\\alpha_s(Q^2)$$. The high-$Q^2$ dependence of the coupling $$\\alpha_s(Q^2)$$ is specified by perturbative QCD and its renormalization group equation. The matching of the high and low $Q^2$ regimes of $$\\alpha_s(Q^2)$$ then determines the scale $$Q_0$$ which sets the interface between perturbative and nonperturbative hadron dynamics. The value of $$Q_0$$ can be used to set the factorization scale for DGLAP evolution of hadronic structure functions and the ERBL evolution of distribution amplitudes. We discuss the scheme-dependence of the value of $$Q_0$$ and the infrared fixed-point of the QCD coupling. Our analysis is carried out for the $$\\bar{MS}$$, $$g_1$$, $MOM$ and $V$ renormalization schemes. Our results show that the discrepancies on the value of $$\\alpha_s$$ at large distance seen in the literature can be explained by different choices of renormalization schemes. Lastly, we also provide the formulae to compute $$\\alpha_s(Q^2)$$ over the entire range of space-like momentum transfer for the different renormalization schemes discussed in this article.« less

Diagrammatic analysis of correlations in polymer fluids: Cluster diagrams via Edwards' field theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Morse, David C.

2006-10-15

Edwards' functional integral approach to the statistical mechanics of polymer liquids is amenable to a diagrammatic analysis in which free energies and correlation functions are expanded as infinite sums of Feynman diagrams. This analysis is shown to lead naturally to a perturbative cluster expansion that is closely related to the Mayer cluster expansion developed for molecular liquids by Chandler and co-workers. Expansion of the functional integral representation of the grand-canonical partition function yields a perturbation theory in which all quantities of interest are expressed as functionals of a monomer-monomer pair potential, as functionals of intramolecular correlation functions of non-interacting molecules,more » and as functions of molecular activities. In different variants of the theory, the pair potential may be either a bare or a screened potential. A series of topological reductions yields a renormalized diagrammatic expansion in which collective correlation functions are instead expressed diagrammatically as functionals of the true single-molecule correlation functions in the interacting fluid, and as functions of molecular number density. Similar renormalized expansions are also obtained for a collective Ornstein-Zernicke direct correlation function, and for intramolecular correlation functions. A concise discussion is given of the corresponding Mayer cluster expansion, and of the relationship between the Mayer and perturbative cluster expansions for liquids of flexible molecules. The application of the perturbative cluster expansion to coarse-grained models of dense multi-component polymer liquids is discussed, and a justification is given for the use of a loop expansion. As an example, the formalism is used to derive a new expression for the wave-number dependent direct correlation function and recover known expressions for the intramolecular two-point correlation function to first-order in a renormalized loop expansion for coarse-grained models of binary homopolymer blends and diblock copolymer melts.« less

77 FR 74027 - Certain Integrated Circuit Packages Provided with Multiple Heat-Conducting Paths and Products...

Federal Register 2010, 2011, 2012, 2013, 2014

2012-12-12

... INTERNATIONAL TRADE COMMISSION [Investigation No. 337-TA-851] Certain Integrated Circuit Packages Provided with Multiple Heat- Conducting Paths and Products Containing Same; Commission Determination Not To... provided with multiple heat-conducting paths and products containing same by reason of infringement of...

FIELD EVALUATION OF A METHOD FOR ESTIMATING GASEOUS FLUXES FROM AREA SOURCES USING OPEN-PATH FTIR

EPA Science Inventory

The paper gives preliminary results from a field evaluation of a new approach for quantifying gaseous fugitive emissions of area air pollution sources. The approach combines path-integrated concentration data acquired with any path-integrated optical remote sensing (PI-ORS) ...

FIELD EVALUATION OF A METHOD FOR ESTIMATING GASEOUS FLUXES FROM AREA SOURCES USING OPEN-PATH FOURIER TRANSFORM INFRARED

EPA Science Inventory

The paper describes preliminary results from a field experiment designed to evaluate a new approach to quantifying gaseous fugitive emissions from area air pollution sources. The new approach combines path-integrated concentration data acquired with any path-integrated optical re...

Spatial Updating Strategy Affects the Reference Frame in Path Integration.

PubMed

He, Qiliang; McNamara, Timothy P

2018-06-01

This study investigated how spatial updating strategies affected the selection of reference frames in path integration. Participants walked an outbound path consisting of three successive waypoints in a featureless environment and then pointed to the first waypoint. We manipulated the alignment of participants' final heading at the end of the outbound path with their initial heading to examine the adopted reference frame. We assumed that the initial heading defined the principal reference direction in an allocentric reference frame. In Experiment 1, participants were instructed to use a configural updating strategy and to monitor the shape of the outbound path while they walked it. Pointing performance was best when the final heading was aligned with the initial heading, indicating the use of an allocentric reference frame. In Experiment 2, participants were instructed to use a continuous updating strategy and to keep track of the location of the first waypoint while walking the outbound path. Pointing performance was equivalent regardless of the alignment between the final and the initial headings, indicating the use of an egocentric reference frame. These results confirmed that people could employ different spatial updating strategies in path integration (Wiener, Berthoz, & Wolbers Experimental Brain Research 208(1) 61-71, 2011), and suggested that these strategies could affect the selection of the reference frame for path integration.

Topological terms, AdS2 n gravity, and renormalized entanglement entropy of holographic CFTs

NASA Astrophysics Data System (ADS)

Anastasiou, Giorgos; Araya, Ignacio J.; Olea, Rodrigo

2018-05-01

We extend our topological renormalization scheme for entanglement entropy to holographic CFTs of arbitrary odd dimensions in the context of the AdS /CFT correspondence. The procedure consists in adding the Chern form as a boundary term to the area functional of the Ryu-Takayanagi minimal surface. The renormalized entanglement entropy thus obtained can be rewritten in terms of the Euler characteristic and the AdS curvature of the minimal surface. This prescription considers the use of the replica trick to express the renormalized entanglement entropy in terms of the renormalized gravitational action evaluated on the conically singular replica manifold extended to the bulk. This renormalized action is obtained in turn by adding the Chern form as the counterterm at the boundary of the 2 n -dimensional asymptotically AdS bulk manifold. We explicitly show that, up to next-to-leading order in the holographic radial coordinate, the addition of this boundary term cancels the divergent part of the entanglement entropy. We discuss possible applications of the method for studying CFT parameters like central charges.

Classical closure theory and Lam's interpretation of epsilon-RNG

NASA Technical Reports Server (NTRS)

Zhou, YE

1995-01-01

Lam's phenomenological epsilon-renormalization group (RNG) model is quite different from the other members of that group. It does not make use of the correspondence principle and the epsilon-expansion procedure. We demonstrate that Lam's epsilon-RNG model is essentially the physical space version of the classical closure theory in spectral space and consider the corresponding treatment of the eddy viscosity and energy backscatter.

Solar System and stellar tests of a quantum-corrected gravity

NASA Astrophysics Data System (ADS)

Zhao, Shan-Shan; Xie, Yi

2015-09-01

The renormalization group running of the gravitational constant has a universal form and represents a possible extension of general relativity. These renormalization group effects on general relativity will cause the running of the gravitational constant, and there exists a scale of renormalization α ν , which depends on the mass of an astronomical system and needs to be determined by observations. We test renormalization group effects on general relativity and obtain the upper bounds of α ν in the low-mass scales: the Solar System and five systems of binary pulsars. Using the supplementary advances of the perihelia provided by INPOP10a (IMCCE, France) and EPM2011 (IAA RAS, Russia) ephemerides, we obtain new upper bounds on α ν in the Solar System when the Lense-Thirring effect due to the Sun's angular momentum and the uncertainty of the Sun's quadrupole moment are properly taken into account. These two factors were absent in the previous work. We find that INPOP10a yields the upper bound as α ν =(0.3 ±2.8 )×10-20 while EPM2011 gives α ν =(-2.5 ±8.3 )×10-21. Both of them are tighter than the previous result by 4 orders of magnitude. Furthermore, based on the observational data sets of five systems of binary pulsars: PSR J 0737 -3039 , PSR B 1534 +12 , PSR J 1756 -2251 , PSR B 1913 +16 , and PSR B 2127 +11 C , the upper bound is found as α ν =(-2.6 ±5.1 )×10-17. From the bounds of this work at a low-mass scale and the ones at the mass scale of galaxies, we might catch an updated glimpse of the mass dependence of α ν , and it is found that our improvement of the upper bounds in the Solar System can significantly change the possible pattern of the relation between log |α ν | and log m from a linear one to a power law, where m is the mass of an astronomical system. This suggests that |α ν | needs to be suppressed more rapidly with the decrease of the mass of low-mass systems. It also predicts that |α ν | might have an upper limit in high-mass astrophysical systems, which can be tested in the future.

Renormalization of the inflationary perturbations revisited

NASA Astrophysics Data System (ADS)

Markkanen, Tommi

2018-05-01

In this work we clarify aspects of renormalization on curved backgrounds focussing on the potential ramifications on the amplitude of inflationary perturbations. We provide an alternate view of the often used adiabatic prescription by deriving a correspondence between the adiabatic subtraction terms and traditional renormalization. Specifically, we show how adiabatic subtraction can be expressed as a set of counter terms that are introduced by redefining the bare parameters of the action. Our representation of adiabatic subtraction then allows us to easily find other renormalization prescriptions differing only in the finite parts of the counter terms. As our main result, we present for quadratic inflation how one may consistently express the renormalization of the spectrum of perturbations from inflation as a redefinition of the bare cosmological constant and Planck mass such that the observable predictions coincide with the unrenormalized result.

An automated integration-free path-integral method based on Kleinert's variational perturbation theory

NASA Astrophysics Data System (ADS)

Wong, Kin-Yiu; Gao, Jiali

2007-12-01

Based on Kleinert's variational perturbation (KP) theory [Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets, 3rd ed. (World Scientific, Singapore, 2004)], we present an analytic path-integral approach for computing the effective centroid potential. The approach enables the KP theory to be applied to any realistic systems beyond the first-order perturbation (i.e., the original Feynman-Kleinert [Phys. Rev. A 34, 5080 (1986)] variational method). Accurate values are obtained for several systems in which exact quantum results are known. Furthermore, the computed kinetic isotope effects for a series of proton transfer reactions, in which the potential energy surfaces are evaluated by density-functional theory, are in good accordance with experiments. We hope that our method could be used by non-path-integral experts or experimentalists as a "black box" for any given system.

Minimally doubled fermions at one loop

NASA Astrophysics Data System (ADS)

Capitani, Stefano; Weber, Johannes; Wittig, Hartmut

2009-10-01

Minimally doubled fermions have been proposed as a cost-effective realization of chiral symmetry at non-zero lattice spacing. Using lattice perturbation theory at one loop, we study their renormalization properties. Specifically, we investigate the consequences of the breaking of hyper-cubic symmetry, which is a typical feature of this class of fermionic discretizations. Our results for the quark self-energy indicate that the four-momentum undergoes a renormalization which is linearly divergent. We also compute renormalization factors for quark bilinears, construct the conserved vector and axial-vector currents and verify that at one loop the renormalization factors of the latter are equal to one.

Directional connectivity of resting state human fMRI data using cascaded ICA-PDC analysis.

PubMed

Silfverhuth, Minna J; Remes, Jukka; Starck, Tuomo; Nikkinen, Juha; Veijola, Juha; Tervonen, Osmo; Kiviniemi, Vesa

2011-11-01

Directional connectivity measures, such as partial directed coherence (PDC), give us means to explore effective connectivity in the human brain. By utilizing independent component analysis (ICA), the original data-set reduction was performed for further PDC analysis. To test this cascaded ICA-PDC approach in causality studies of human functional magnetic resonance imaging (fMRI) data. Resting state group data was imaged from 55 subjects using a 1.5 T scanner (TR 1800 ms, 250 volumes). Temporal concatenation group ICA in a probabilistic ICA and further repeatability runs (n = 200) were overtaken. The reduced data-set included the time series presentation of the following nine ICA components: secondary somatosensory cortex, inferior temporal gyrus, intracalcarine cortex, primary auditory cortex, amygdala, putamen and the frontal medial cortex, posterior cingulate cortex and precuneus, comprising the default mode network components. Re-normalized PDC (rPDC) values were computed to determine directional connectivity at the group level at each frequency. The integrative role was suggested for precuneus while the role of major divergence region may be proposed to primary auditory cortex and amygdala. This study demonstrates the potential of the cascaded ICA-PDC approach in directional connectivity studies of human fMRI.

Entanglement entropy in a boundary impurity model.

PubMed

Levine, G C

2004-12-31

Boundary impurities are known to dramatically alter certain bulk properties of (1+1)-dimensional strongly correlated systems. The entanglement entropy of a zero temperature Luttinger liquid bisected by a single impurity is computed using a novel finite size scaling or bosonization scheme. For a Luttinger liquid of length 2L and UV cutoff epsilon, the boundary impurity correction (deltaSimp) to the logarithmic entanglement entropy (Sent proportional, variant lnL/epsilon scales as deltaSimp approximately yrlnL/epsilon, where yr is the renormalized backscattering coupling constant. In this way, the entanglement entropy within a region is related to scattering through the region's boundary. In the repulsive case (g<1), deltaSimp diverges (negatively) suggesting that the entropy vanishes. Our results are consistent with the recent conjecture that entanglement entropy decreases irreversibly along renormalization group flow.

The metric on field space, functional renormalization, and metric–torsion quantum gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Reuter, Martin, E-mail: reuter@thep.physik.uni-mainz.de; Schollmeyer, Gregor M., E-mail: schollmeyer@thep.physik.uni-mainz.de

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 modifiedmore » FRGE is obtained if this metric is scale-dependent, as it happens in the metric–torsion system considered.« less

Gutzwiller renormalization group

DOE PAGES

Lanatà, Nicola; Yao, Yong -Xin; Deng, Xiaoyu; ...

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

Nonperturbative light-front Hamiltonian methods

NASA Astrophysics Data System (ADS)

Hiller, J. R.

2016-09-01

We examine the current state-of-the-art in nonperturbative calculations done with Hamiltonians constructed in light-front quantization of various field theories. The language of light-front quantization is introduced, and important (numerical) techniques, such as Pauli-Villars regularization, discrete light-cone quantization, basis light-front quantization, the light-front coupled-cluster method, the renormalization group procedure for effective particles, sector-dependent renormalization, and the Lanczos diagonalization method, are surveyed. Specific applications are discussed for quenched scalar Yukawa theory, ϕ4 theory, ordinary Yukawa theory, supersymmetric Yang-Mills theory, quantum electrodynamics, and quantum chromodynamics. The content should serve as an introduction to these methods for anyone interested in doing such calculations and as a rallying point for those who wish to solve quantum chromodynamics in terms of wave functions rather than random samplings of Euclidean field configurations.

Abnormalities in Structural Covariance of Cortical Gyrification in Parkinson's Disease.

PubMed

Xu, Jinping; Zhang, Jiuquan; Zhang, Jinlei; Wang, Yue; Zhang, Yanling; Wang, Jian; Li, Guanglin; Hu, Qingmao; Zhang, Yuanchao

2017-01-01

Although abnormal cortical morphology and connectivity between brain regions (structural covariance) have been reported in Parkinson's disease (PD), the topological organizations of large-scale structural brain networks are still poorly understood. In this study, we investigated large-scale structural brain networks in a sample of 37 PD patients and 34 healthy controls (HC) by assessing the structural covariance of cortical gyrification with local gyrification index (lGI). We demonstrated prominent small-world properties of the structural brain networks for both groups. Compared with the HC group, PD patients showed significantly increased integrated characteristic path length and integrated clustering coefficient, as well as decreased integrated global efficiency in structural brain networks. Distinct distributions of hub regions were identified between the two groups, showing more hub regions in the frontal cortex in PD patients. Moreover, the modular analyses revealed significantly decreased integrated regional efficiency in lateral Fronto-Insula-Temporal module, and increased integrated regional efficiency in Parieto-Temporal module in the PD group as compared to the HC group. In summary, our study demonstrated altered topological properties of structural networks at a global, regional and modular level in PD patients. These findings suggests that the structural networks of PD patients have a suboptimal topological organization, resulting in less effective integration of information between brain regions.

INNOVATIVE APPROACH FOR MEASURING AMMONIA AND METHANE FLUXES FROM A HOG FARM USING OPEN-PATH FOURIER TRANSFORM INFRARED SPECTROSCOPY

EPA Science Inventory

The paper describes a new approach to quantify emissions from area air pollution sources. The approach combines path-integrated concentration data acquired with any path-integrated optical remote sensing (PI-ORS) technique and computed tomography (CT) technique. In this study, an...

Complete one-loop renormalization of the Higgs-electroweak chiral Lagrangian

NASA Astrophysics Data System (ADS)

Buchalla, G.; Catà, O.; Celis, A.; Knecht, M.; Krause, C.

2018-03-01

Employing background-field method and super-heat-kernel expansion, we compute the complete one-loop renormalization of the electroweak chiral Lagrangian with a light Higgs boson. Earlier results from purely scalar fluctuations are confirmed as a special case. We also recover the one-loop renormalization of the conventional Standard Model in the appropriate limit.

Topological charge quantization via path integration: An application of the Kustaanheimo-Stiefel transformation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Inomata, A.; Junker, G.; Wilson, R.

1993-08-01

The unified treatment of the Dirac monopole, the Schwinger monopole, and the Aharonov-Bahn problem by Barut and Wilson is revisited via a path integral approach. The Kustaanheimo-Stiefel transformation of space and time is utilized to calculate the path integral for a charged particle in the singular vector potential. In the process of dimensional reduction, a topological charge quantization rule is derived, which contains Dirac's quantization condition as a special case. 32 refs.

Evaluation of the path integral for flow through random porous media

NASA Astrophysics Data System (ADS)

Westbroek, Marise J. E.; Coche, Gil-Arnaud; King, Peter R.; Vvedensky, Dimitri D.

2018-04-01

We present a path integral formulation of Darcy's equation in one dimension with random permeability described by a correlated multivariate lognormal distribution. This path integral is evaluated with the Markov chain Monte Carlo method to obtain pressure distributions, which are shown to agree with the solutions of the corresponding stochastic differential equation for Dirichlet and Neumann boundary conditions. The extension of our approach to flow through random media in two and three dimensions is discussed.

User's guide to Monte Carlo methods for evaluating path integrals

NASA Astrophysics Data System (ADS)

Westbroek, Marise J. E.; King, Peter R.; Vvedensky, Dimitri D.; Dürr, Stephan

2018-04-01

We give an introduction to the calculation of path integrals on a lattice, with the quantum harmonic oscillator as an example. In addition to providing an explicit computational setup and corresponding pseudocode, we pay particular attention to the existence of autocorrelations and the calculation of reliable errors. The over-relaxation technique is presented as a way to counter strong autocorrelations. The simulation methods can be extended to compute observables for path integrals in other settings.

Effect of electron-phonon coupling on energy and density of states renormalizations of dynamically screened graphene

NASA Astrophysics Data System (ADS)

Leblanc, J. P. F.; Carbotte, J. P.; Nicol, E. J.

2012-02-01

Motivated by recent tunneling and angle-resolved photoemission (ARPES) work [1,2], we explore the combined effect of electron-electron and electron-phonon couplings on the renormalized energy dispersion, the spectral function, and the density of states of doped graphene. We find that the plasmarons seen in ARPES are also observable in the density of states and appear as structures with quadratic dependence on energy about the minima. Further, we illustrate how knowledge of the slopes of both the density of states and the renormalized dispersion near the Fermi level can allow for the separation of momentum and frequency dependent renormalizations to the Fermi velocity. This analysis should allow for the isolation of the renormalization due to the electron-phonon interaction from that of the electron-electron interaction. [4pt] [1] Brar et al. Phys. Rev. Lett. 104, 036805 (2010) [2] Bostwick et al. Science 328, p.999 (2010)

Comment on ``Time-Dependent Density-Matrix Renormalization Group: A Systematic Method for the Study of Quantum Many-Body Out-of-Equilibrium Systems''

NASA Astrophysics Data System (ADS)

Luo, H. G.; Xiang, T.; Wang, X. Q.

2003-07-01

A Comment on the Letter by

Feynman formulae and phase space Feynman path integrals for tau-quantization of some Lévy-Khintchine type Hamilton functions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Butko, Yana A., E-mail: yanabutko@yandex.ru, E-mail: kinderknecht@math.uni-sb.de; Grothaus, Martin, E-mail: grothaus@mathematik.uni-kl.de; Smolyanov, Oleg G., E-mail: Smolyanov@yandex.ru

2016-02-15

Evolution semigroups generated by pseudo-differential operators are considered. These operators are obtained by different (parameterized by a number τ) procedures of quantization from a certain class of functions (or symbols) defined on the phase space. This class contains Hamilton functions of particles with variable mass in magnetic and potential fields and more general symbols given by the Lévy-Khintchine formula. The considered semigroups are represented as limits of n-fold iterated integrals when n tends to infinity. Such representations are called Feynman formulae. Some of these representations are constructed with the help of another pseudo-differential operator, obtained by the same procedure ofmore » quantization; such representations are called Hamiltonian Feynman formulae. Some representations are based on integral operators with elementary kernels; these are called Lagrangian Feynman formulae. Langrangian Feynman formulae provide approximations of evolution semigroups, suitable for direct computations and numerical modeling of the corresponding dynamics. Hamiltonian Feynman formulae allow to represent the considered semigroups by means of Feynman path integrals. In the article, a family of phase space Feynman pseudomeasures corresponding to different procedures of quantization is introduced. The considered evolution semigroups are represented as phase space Feynman path integrals with respect to these Feynman pseudomeasures, i.e., different quantizations correspond to Feynman path integrals with the same integrand but with respect to different pseudomeasures. This answers Berezin’s problem of distinguishing a procedure of quantization on the language of Feynman path integrals. Moreover, the obtained Lagrangian Feynman formulae allow also to calculate these phase space Feynman path integrals and to connect them with some functional integrals with respect to probability measures.« less

Vector navigation in desert ants, Cataglyphis fortis: celestial compass cues are essential for the proper use of distance information.

PubMed

Sommer, Stefan; Wehner, Rüdiger

2005-10-01

Foraging desert ants navigate primarily by path integration. They continually update homing direction and distance by employing a celestial compass and an odometer. Here we address the question of whether information about travel distance is correctly used in the absence of directional information. By using linear channels that were partly covered to exclude celestial compass cues, we were able to test the distance component of the path-integration process while suppressing the directional information. Our results suggest that the path integrator cannot process the distance information accumulated by the odometer while ants are deprived of celestial compass information. Hence, during path integration directional cues are a prerequisite for the proper use of travel-distance information by ants.

Asymptotically Free Gauge Theories. I

DOE R&D Accomplishments Database

Wilczek, Frank; Gross, David J.

1973-07-01

Asymptotically free gauge theories of the strong interactions are constructed and analyzed. The reasons for doing this are recounted, including a review of renormalization group techniques and their application to scaling phenomena. The renormalization group equations are derived for Yang-Mills theories. The parameters that enter into the equations are calculated to lowest order and it is shown that these theories are asymptotically free. More specifically the effective coupling constant, which determines the ultraviolet behavior of the theory, vanishes for large space-like momenta. Fermions are incorporated and the construction of realistic models is discussed. We propose that the strong interactions be mediated by a "color" gauge group which commutes with SU(3)xSU(3). The problem of symmetry breaking is discussed. It appears likely that this would have a dynamical origin. It is suggested that the gauge symmetry might not be broken, and that the severe infrared singularities prevent the occurrence of non-color singlet physical states. The deep inelastic structure functions, as well as the electron position total annihilation cross section are analyzed. Scaling obtains up to calculable logarithmic corrections, and the naive lightcone or parton model results follow. The problems of incorporating scalar mesons and breaking the symmetry by the Higgs mechanism are explained in detail.

Path optimization method for the sign problem

NASA Astrophysics Data System (ADS)

Ohnishi, Akira; Mori, Yuto; Kashiwa, Kouji

2018-03-01

We propose a path optimization method (POM) to evade the sign problem in the Monte-Carlo calculations for complex actions. Among many approaches to the sign problem, the Lefschetz-thimble path-integral method and the complex Langevin method are promising and extensively discussed. In these methods, real field variables are complexified and the integration manifold is determined by the flow equations or stochastically sampled. When we have singular points of the action or multiple critical points near the original integral surface, however, we have a risk to encounter the residual and global sign problems or the singular drift term problem. One of the ways to avoid the singular points is to optimize the integration path which is designed not to hit the singular points of the Boltzmann weight. By specifying the one-dimensional integration-path as z = t +if(t)(f ɛ R) and by optimizing f(t) to enhance the average phase factor, we demonstrate that we can avoid the sign problem in a one-variable toy model for which the complex Langevin method is found to fail. In this proceedings, we propose POM and discuss how we can avoid the sign problem in a toy model. We also discuss the possibility to utilize the neural network to optimize the path.

Data-driven Modeling of the Solar Corona by a New Three-dimensional Path-conservative Osher-Solomon MHD Model

NASA Astrophysics Data System (ADS)

Feng, Xueshang; Li, Caixia; Xiang, Changqing; Zhang, Man; Li, HuiChao; Wei, Fengsi

2017-11-01

A second-order path-conservative scheme with a Godunov-type finite-volume method has been implemented to advance the equations of single-fluid solar wind plasma magnetohydrodynamics (MHD) in time. This code operates on the six-component composite grid system in three-dimensional spherical coordinates with hexahedral cells of quadrilateral frustum type. The generalized Osher-Solomon Riemann solver is employed based on a numerical integration of the path-dependent dissipation matrix. For simplicity, the straight line segment path is used, and the path integral is evaluated in a fully numerical way by a high-order numerical Gauss-Legendre quadrature. Besides its very close similarity to Godunov type, the resulting scheme retains the attractive features of the original solver: it is nonlinear, free of entropy-fix, differentiable, and complete, in that each characteristic field results in a different numerical viscosity, due to the full use of the MHD eigenstructure. By using a minmod limiter for spatial oscillation control, the path-conservative scheme is realized for the generalized Lagrange multiplier and the extended generalized Lagrange multiplier formulation of solar wind MHD systems. This new model that is second order in space and time is written in the FORTRAN language with Message Passing Interface parallelization and validated in modeling the time-dependent large-scale structure of the solar corona, driven continuously by Global Oscillation Network Group data. To demonstrate the suitability of our code for the simulation of solar wind, we present selected results from 2009 October 9 to 2009 December 29 show its capability of producing a structured solar corona in agreement with solar coronal observations.

Life Strain, Social Control, Social Learning, and Delinquency: The Effects of Gender, Age, and Family SES Among Chinese Adolescents.

PubMed

Bao, Wan-Ning; Haas, Ain; Xie, Yunping

2016-09-01

Very few studies have examined the pathways to delinquency and causal factors for demographic subgroups of adolescents in a different culture. This article explores the effects of gender, age, and family socioeconomic status (SES) in an integrated model of strain, social control, social learning, and delinquency among a sample of Chinese adolescents. ANOVA is used to check for significant differences between categories of demographic groups on the variables in the integrated model, and the differential effects of causal factors in the theoretical path models are examined. Further tests of interaction effects are conducted to compare path coefficients between "high-risk" youths (i.e., male, mid-teen, and low family SES adolescents) and other subgroups. The findings identified similar pathways to delinquency across subgroups and clarified the salience of causal factors for male, mid-teen, and low SES adolescents in a different cultural context. © The Author(s) 2015.

Bose gases near resonance: Renormalized interactions in a condensate

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou, Fei, E-mail: feizhou@phas.ubc.ca; 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 effectivelymore » 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.« less

CCITT Study Group XVIII Work Program 1981-1984; (Integrated Services Digital Network)

DTIC Science & Technology

1981-06-01

ecitintwrste!D teaN he1B - 72 - COM VIII-No. 1-E The points lised below require particular attention in the studies, whereby acca -t should be taken of all...l I\\ I path> muldex f, fc c f3 fre’ue’o Z. -- frequency f F=ure 2 - ttput r a line .at.. a .a = ex Section (22) -79- COMl XVI-!O -E IA dB lie at...muldex fc f3 f, cf frequency -~frequency - Figure 3 -Jitter-transfer function of a line path and a muldex section Figure I4 shows the amplitude of

Renormalization scheme and gauge (in)dependence of the generalized Crewther relation: what are the real grounds of the β-factorization property?

NASA Astrophysics Data System (ADS)

Garkusha, A. V.; Kataev, A. L.; Molokoedov, V. S.

2018-02-01

The problem of scheme and gauge dependence of the factorization property of the renormalization group β-function in the SU( N c ) QCD generalized Crewther relation (GCR), which connects the flavor non-singlet contributions to the Adler and Bjorken polarized sum rule functions, is investigated at the O({a}_s^4) level of perturbation theory. It is known that in the gauge-invariant renormalization \\overline{MS} -scheme this property holds in the QCD GCR at least at this order. To study whether this factorization property is true in all gauge-invariant schemes, we consider the MS-like schemes in QCD and the QED-limit of the GCR in the \\overline{MS} -scheme and in two other gauge-independent subtraction schemes, namely in the momentum MOM and the on-shell OS schemes. In these schemes we confirm the existence of the β-function factorization in the QCD and QED variants of the GCR. The problem of the possible β-factorization in the gauge-dependent renormalization schemes in QCD is studied. To investigate this problem we consider the gauge non-invariant mMOM and MOMgggg-schemes. We demonstrate that in the mMOM scheme at the O({a}_s^3) level the β-factorization is valid for three values of the gauge parameter ξ only, namely for ξ = -3 , -1 and ξ = 0. In the O({a}_s^4) order of PT it remains valid only for case of the Landau gauge ξ = 0. The consideration of these two gauge-dependent schemes for the QCD GCR allows us to conclude that the factorization of RG β-function will always be implemented in any MOM-like renormalization schemes with linear covariant gauge at ξ = 0 and ξ = -3 at the O({a}_s^3) approximation. It is demonstrated that if factorization property for the MS-like schemes is true in all orders of PT, as theoretically indicated in the several works on the subject, then the factorization will also occur in the arbitrary MOM-like scheme in the Landau gauge in all orders of perturbation theory as well.

The generalized scheme-independent Crewther relation in QCD

DOE PAGES

Shen, Jian-Ming; Wu, Xing-Gang; Ma, Yang; ...

2017-05-10

The Principle of Maximal Conformality (PMC) provides a systematic way to set the renormalization scales order-by-order for any perturbative QCD calculable processes. The resulting predictions are independent of the choice of renormalization scheme, a requirement of renormalization group invariance. The Crewther relation, which was originally derived as a consequence of conformally invariant field theory, provides a remarkable connection between two observables when the β function vanishes: one can show that the product of the Bjorken sum rule for spin-dependent deep inelastic lepton–nucleon scattering times the Adler function, defined from the cross section for electron–positron annihilation into hadrons, has no pQCD radiative corrections. The “Generalized Crewther Relation” relates these two observables for physical QCD with nonzero β function; specifically, it connects the non-singlet Adler function (D ns) to the Bjorken sum rule coefficient for polarized deep-inelastic electron scattering (C Bjp) at leading twist. A scheme-dependent Δ CSB-term appears in the analysis in order to compensate for the conformal symmetry breaking (CSB) terms from perturbative QCD. In conventional analyses, this normally leads to unphysical dependence in both the choice of the renormalization scheme and the choice of the initial scale at any finite order. However, by applying PMC scale-setting, we can fix the scales of the QCD coupling unambiguously at every order of pQCD. The result is that both D ns and the inverse coefficient Cmore » $$-1\\atop{Bjp}$$ have identical pQCD coefficients, which also exactly match the coefficients of the corresponding conformal theory. Thus one obtains a new generalized Crewther relation for QCD which connects two effective charges, $$\\hat{α}$$ d(Q)=Σ i≥1$$\\hat{α}^i\\atop{g1}$$(Qi), at their respective physical scales. This identity is independent of the choice of the renormalization scheme at any finite order, and the dependence on the choice of the initial scale is negligible. Lastly, similar scale-fixed commensurate scale relations also connect other physical observables at their physical momentum scales, thus providing convention-independent, fundamental precision tests of QCD.« less

The generalized scheme-independent Crewther relation in QCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shen, Jian-Ming; Wu, Xing-Gang; Ma, Yang

The Principle of Maximal Conformality (PMC) provides a systematic way to set the renormalization scales order-by-order for any perturbative QCD calculable processes. The resulting predictions are independent of the choice of renormalization scheme, a requirement of renormalization group invariance. The Crewther relation, which was originally derived as a consequence of conformally invariant field theory, provides a remarkable connection between two observables when the β function vanishes: one can show that the product of the Bjorken sum rule for spin-dependent deep inelastic lepton–nucleon scattering times the Adler function, defined from the cross section for electron–positron annihilation into hadrons, has no pQCD radiative corrections. The “Generalized Crewther Relation” relates these two observables for physical QCD with nonzero β function; specifically, it connects the non-singlet Adler function (D ns) to the Bjorken sum rule coefficient for polarized deep-inelastic electron scattering (C Bjp) at leading twist. A scheme-dependent Δ CSB-term appears in the analysis in order to compensate for the conformal symmetry breaking (CSB) terms from perturbative QCD. In conventional analyses, this normally leads to unphysical dependence in both the choice of the renormalization scheme and the choice of the initial scale at any finite order. However, by applying PMC scale-setting, we can fix the scales of the QCD coupling unambiguously at every order of pQCD. The result is that both D ns and the inverse coefficient Cmore » $$-1\\atop{Bjp}$$ have identical pQCD coefficients, which also exactly match the coefficients of the corresponding conformal theory. Thus one obtains a new generalized Crewther relation for QCD which connects two effective charges, $$\\hat{α}$$ d(Q)=Σ i≥1$$\\hat{α}^i\\atop{g1}$$(Qi), at their respective physical scales. This identity is independent of the choice of the renormalization scheme at any finite order, and the dependence on the choice of the initial scale is negligible. Lastly, similar scale-fixed commensurate scale relations also connect other physical observables at their physical momentum scales, thus providing convention-independent, fundamental precision tests of QCD.« less

Time Reparametrization Group and the Long Time Behavior in Quantum Glassy Systems

NASA Astrophysics Data System (ADS)

Kennett, Malcolm P.; Chamon, Claudio

2001-02-01

We study the long time dynamics of a quantum version of the Sherrington-Kirkpatrick model. Time reparametrizations of the dynamical equations have a parallel with renormalization group transformations; in this language the long time behavior of this model is controlled by a reparametrization group ( RpG) fixed point of the classical dynamics. The irrelevance of quantum terms in the dynamical equations in the aging regime explains the classical nature of the out of equilibrium fluctuation-dissipation relation.

Asymptotic Analysis of the Ponzano-Regge Model with Non-Commutative Metric Boundary Data

NASA Astrophysics Data System (ADS)

Oriti, Daniele; Raasakka, Matti

2014-06-01

We apply the non-commutative Fourier transform for Lie groups to formulate the non-commutative metric representation of the Ponzano-Regge spin foam model for 3d quantum gravity. The non-commutative representation allows to express the amplitudes of the model as a first order phase space path integral, whose properties we consider. In particular, we study the asymptotic behavior of the path integral in the semi-classical limit. First, we compare the stationary phase equations in the classical limit for three different non-commutative structures corresponding to the symmetric, Duflo and Freidel-Livine-Majid quantization maps. We find that in order to unambiguously recover discrete geometric constraints for non-commutative metric boundary data through the stationary phase method, the deformation structure of the phase space must be accounted for in the variational calculus. When this is understood, our results demonstrate that the non-commutative metric representation facilitates a convenient semi-classical analysis of the Ponzano-Regge model, which yields as the dominant contribution to the amplitude the cosine of the Regge action in agreement with previous studies. We also consider the asymptotics of the SU(2) 6j-symbol using the non-commutative phase space path integral for the Ponzano-Regge model, and explain the connection of our results to the previous asymptotic results in terms of coherent states.

The framed Standard Model (II) — A first test against experiment

NASA Astrophysics Data System (ADS)

Chan, Hong-Mo; Tsou, Sheung Tsun

2015-10-01

Apart from the qualitative features described in Paper I (Ref. 1), the renormalization group equation derived for the rotation of the fermion mass matrices are amenable to quantitative study. The equation depends on a coupling and a fudge factor and, on integration, on 3 integration constants. Its application to data analysis, however, requires the input from experiment of the heaviest generation masses mt, mb, mτ, mν3 all of which are known, except for mν3. Together then with the theta-angle in the QCD action, there are in all 7 real unknown parameters. Determining these 7 parameters by fitting to the experimental values of the masses mc, mμ, me, the CKM elements |Vus|, |Vub|, and the neutrino oscillation angle sin2θ 13, one can then calculate and compare with experiment the following 12 other quantities ms, mu/md, |Vud|, |Vcs|, |Vtb|, |Vcd|, |Vcb|, |Vts|, |Vtd|, J, sin22θ 12, sin22θ 23, and the results all agree reasonably well with data, often to within the stringent experimental error now achieved. Counting the predictions not yet measured by experiment, this means that 17 independent parameters of the standard model are now replaced by 7 in the FSM.

A review of path-independent integrals in elastic-plastic fracture mechanics

NASA Technical Reports Server (NTRS)

Kim, Kwang S.; Orange, Thomas W.

1988-01-01

The objective of this paper is to review the path-independent (P-I) integrals in elastic plastic fracture mechanics which have been proposed in recent years to overcome the limitations imposed on the J-integral. The P-I integrals considered are the J-integral by Rice (1968), the thermoelastic P-I integrals by Wilson and Yu (1979) and Gurtin (1979), the J-integral by Blackburn (1972), the J(theta)-integral by Ainsworth et al. (1978), the J-integral by Kishimoto et al. (1980), and the Delta-T(p) and Delta T(p)-asterisk integrals by Alturi et al. (1982). The theoretical foundation of the P-I integrals is examined with an emphasis on whether or not the path independence is maintained in the presence of nonproportional loading and unloading in the plastic regime, thermal gradient, and material inhomogeneities. The simularities, difference, salient features, and limitations of the P-I integrals are discussed. Comments are also made with regard to the physical meaning, the possibility of experimental measurement, and computational aspects.

A review of path-independent integrals in elastic-plastic fracture mechanics, task 4

NASA Technical Reports Server (NTRS)

Kim, K. S.

1985-01-01

The path independent (P-I) integrals in elastic plastic fracture mechanics which have been proposed in recent years to overcome the limitations imposed on the J integral are reviewed. The P-I integrals considered herein are the J integral by Rice, the thermoelastic P-I integrals by Wilson and Yu and by Gurtin, the J* integral by Blackburn, the J sub theta integral by Ainsworth et al., the J integral by Kishimoto et al., and the delta T sub p and delta T* sub p integrals by Atluri et al. The theoretical foundation of these P-I integrals is examined with emphasis on whether or not path independence is maintained in the presence of nonproportional loading and unloading in the plastic regime, thermal gradients, and material inhomogeneities. The similarities, differences, salient features, and limitations of these P-I integrals are discussed. Comments are also made with regard to the physical meaning, the possibility of experimental measurement, and computational aspects.

77 FR 33486 - Certain Integrated Circuit Packages Provided With Multiple Heat-Conducting Paths and Products...

Federal Register 2010, 2011, 2012, 2013, 2014

2012-06-06

... INTERNATIONAL TRADE COMMISSION [Docket No. 2899] Certain Integrated Circuit Packages Provided With... complaint entitled Certain Integrated Circuit Packages Provided With Multiple Heat-Conducting Paths and..., telephone (202) 205-2000. The public version of the complaint can be accessed on the Commission's electronic...

BOOK REVIEW: Path Integrals in Field Theory: An Introduction

NASA Astrophysics Data System (ADS)

Ryder, Lewis

2004-06-01

In the 1960s Feynman was known to particle physicists as one of the people who solved the major problems of quantum electrodynamics, his contribution famously introducing what are now called Feynman diagrams. To other physicists he gained a reputation as the author of the Feynman Lectures on Physics; in addition some people were aware of his work on the path integral formulation of quantum theory, and a very few knew about his work on gravitation and Yang--Mills theories, which made use of path integral methods. Forty years later the scene is rather different. Many of the problems of high energy physics are solved; and the standard model incorporates Feynman's path integral method as a way of proving the renormalisability of the gauge (Yang--Mills) theories involved. Gravitation is proving a much harder nut to crack, but here also questions of renormalisability are couched in path-integral language. What is more, theoretical studies of condensed matter physics now also appeal to this technique for quantisation, so the path integral method is becoming part of the standard apparatus of theoretical physics. Chapters on it appear in a number of recent books, and a few books have appeared devoted to this topic alone; the book under review is a very recent one. Path integral techniques have the advantage of enormous conceptual appeal and the great disadvantage of mathematical complexity, this being partly the result of messy integrals but more fundamentally due to the notions of functional differentiation and integration which are involved in the method. All in all this subject is not such an easy ride. Mosel's book, described as an introduction, is aimed at graduate students and research workers in particle physics. It assumes a background knowledge of quantum mechanics, both non-relativistic and relativistic. After three chapters on the path integral formulation of non-relativistic quantum mechanics there are eight chapters on scalar and spinor field theory, followed by three on gauge field theories---quantum electrodynamics and Yang--Mills theories, Faddeev--Popov ghosts and so on.There is no treatment of the quantisation of gravity.Thus in about 200 pages the reader has the chance to learn in some detail about a most important area of modern physics. The subject is tough but the style is clear and pedagogic, results for the most part being derived explicitly. The choice of topics included is main-stream and sensible and one has a clear sense that the author knows where he is going and is a reliable guide. Path Integrals in Field Theory is clearly the work of a man with considerable teaching experience and is recommended as a readable and helpful account of a rather non-trivial subject.

Higgs boson self-coupling from two-loop analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alhendi, H. A.; National Center for Mathematics and Physics, KACST P. O. Box 6086, Riyadh 11442; Barakat, T.

2010-09-01

The scale invariant of the effective potential of the standard model at two loop is used as a boundary condition under the assumption that the two-loop effective potential approximates the full effective potential. This condition leads with the help of the renormalization-group functions of the model at two loop to an algebraic equation of the scalar self-coupling with coefficients that depend on the gauge and the top quark couplings. It admits only two real positive solutions. One of them, in the absence of the gauge and top quark couplings, corresponds to the nonperturbative ultraviolet fixed point of the scalar renormalization-groupmore » function and the other corresponds to the perturbative infrared fixed point. The dependence of the scalar coupling on the top quark and the strong couplings at two-loop radiative corrections is analyzed.« less

Renormalization of the global quantum correlation and monogamy relation in the anisotropic Heisenberg XXZ model

NASA Astrophysics Data System (ADS)

Qin, Meng; Ren, Zhong-Zhou; Zhang, Xin

2016-01-01

In this study, the global quantum correlation, monogamy relation and quantum phase transition of the Heisenberg XXZ model are investigated by the method of quantum renormalization group. We obtain, analytically, the expressions of the global negativity, the global measurement-induced disturbance and the monogamy relation for the system. The result shows that for a three-site block state, the partial transpose of an asymmetric block can get stronger entanglement than that of the symmetric one. The residual entanglement and the difference of the monogamy relation of measurement-induced disturbance show a scaling behavior with the size of the system becoming large. Moreover, the monogamy nature of entanglement measured by negativity exists in the model, while the nonclassical correlation quantified by measurement-induced disturbance violates the monogamy relation and demonstrates polygamy.

Charged polymers in high dimensions

NASA Technical Reports Server (NTRS)

Kantor, Yacov

1990-01-01

A Monte Carlo study of charged polymers with either homogeneously distributed frozen charges or with mobile charges has been performed in four and five space dimensions. The results are consistent with the renormalization-group predictions and contradict the predictions of Flory-type theory. Introduction of charge mobility does not modify the behavior of the polymers.

Spin-adapted matrix product states and operators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Keller, Sebastian, E-mail: sebastian.keller@phys.chem.ethz.ch; Reiher, Markus, E-mail: markus.reiher@phys.chem.ethz.ch

Matrix product states (MPSs) and matrix product operators (MPOs) allow an alternative formulation of the density matrix renormalization group algorithm introduced by White. Here, we describe how non-abelian spin symmetry can be exploited in MPSs and MPOs by virtue of the Wigner–Eckart theorem at the example of the spin-adapted quantum chemical Hamiltonian operator.

Recursive renormalization group theory based subgrid modeling

NASA Technical Reports Server (NTRS)

Zhou, YE

1991-01-01

Advancing the knowledge and understanding of turbulence theory is addressed. Specific problems to be addressed will include studies of subgrid models to understand the effects of unresolved small scale dynamics on the large scale motion which, if successful, might substantially reduce the number of degrees of freedom that need to be computed in turbulence simulation.