Automated Lattice Perturbation Theory
Energy Technology Data Exchange (ETDEWEB)
Monahan, Christopher
2014-11-01
I review recent developments in automated lattice perturbation theory. Starting with an overview of lattice perturbation theory, I focus on the three automation packages currently "on the market": HiPPy/HPsrc, Pastor and PhySyCAl. I highlight some recent applications of these methods, particularly in B physics. In the final section I briefly discuss the related, but distinct, approach of numerical stochastic perturbation theory.
Chiral Perturbation Theory With Lattice Regularization
Ouimet, P P A
2005-01-01
In this work, alternative methods to regularize chiral perturbation theory are discussed. First, Long Distance Regularization will be considered in the presence of the decuplet of the lightest spin 32 baryons for several different observables. This serves motivation and introduction to the use of the lattice regulator for chiral perturbation theory. The mesonic, baryonic and anomalous sectors of chiral perturbation theory will be formulated on a lattice of space time points. The consistency of the lattice as a regulator will be discussed in the context of the meson and baryon masses. Order a effects will also be discussed for the baryon masses, sigma terms and magnetic moments. The work will close with an attempt to derive an effective Wess-Zumino-Witten Lagrangian for Wilson fermions at non-zero a. Following this discussion, there will be a proposal for a phenomenologically useful WZW Lagrangian at non-zero a.
Perturbative and nonperturbative renormalization in lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Goeckeler, M. [Regensburg Univ. (Germany). Institut fuer Theoretische Physik; Horsley, R. [University of Edinburgh (United Kingdom). School of Physics and Astronomy; Perlt, H. [Leipzig Univ. (DE). Institut fuer Theoretische Physik] (and others)
2010-03-15
We investigate the perturbative and nonperturbative renormalization of composite operators in lattice QCD restricting ourselves to operators that are bilinear in the quark fields (quark-antiquark operators). These include operators which are relevant to the calculation of moments of hadronic structure functions. The nonperturbative computations are based on Monte Carlo simulations with two flavors of clover fermions and utilize the Rome-Southampton method also known as the RI-MOM scheme. We compare the results of this approach with various estimates from lattice perturbation theory, in particular with recent two-loop calculations. (orig.)
Higher representations on the lattice: perturbative studies
Del Debbio, Luigi; Panagopoulos, Haralambos; Sannino, Francesco
2008-01-01
We present analytical results to guide numerical simulations with Wilson fermions in higher representations of the colour group. The ratio of $\\Lambda$ parameters, the additive renormalization of the fermion mass, and the renormalization of fermion bilinears are computed in perturbation theory, including cactus resummation. We recall the chiral Lagrangian for the different patterns of symmetry breaking that can take place with fermions in higher representations, and discuss the possibility of an Aoki phase as the fermion mass is reduced at finite lattice spacing.
Chiral perturbation theory for lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Baer, Oliver
2010-07-21
The formulation of chiral perturbation theory (ChPT) for lattice Quantum Chromodynamics (QCD) is reviewed. We start with brief summaries of ChPT for continuum QCD as well as the Symanzik effective theory for lattice QCD. We then review the formulation of ChPT for lattice QCD. After an additional chapter on partial quenching and mixed action theories various concrete applications are discussed: Wilson ChPT, staggered ChPT and Wilson ChPT with a twisted mass term. The remaining chapters deal with the epsilon regime with Wilson fermions and selected results in mixed action ChPT. Finally, the formulation of heavy vector meson ChPT with Wilson fermions is discussed. (orig.)
Lattice-motivated holomorphic nearly perturbative QCD
Ayala, César; Cvetič, Gorazd; Kögerler, Reinhart
2017-07-01
Newer lattice results indicate that, in the Landau gauge at low spacelike momenta, the gluon propagator and the ghost dressing function are finite nonzero. This leads to a definition of the QCD running coupling, in a specific scheme, that goes to zero at low spacelike momenta. We construct a running coupling which fulfills these conditions, and at the same time reproduces to a high precision the perturbative behavior at high momenta. The coupling is constructed in such a way that it reflects qualitatively correctly the holomorphic (analytic) behavior of spacelike observables in the complex plane of the squared momenta, as dictated by the general principles of quantum field theories. Further, we require the coupling to reproduce correctly the nonstrange semihadronic decay rate of tau lepton which is the best measured low-momentum QCD observable with small higher-twist effects. Subsequent application of the Borel sum rules to the V + A spectral functions of tau lepton decays, as measured by OPAL Collaboration, determines the values of the gluon condensate and of the V + A six-dimensional condensate, and reproduces the data to a significantly higher precision than the usual \\overline{{MS}} running coupling.
Lattice-motivated holomorphic nearly perturbative QCD
Ayala, Cesar; Kogerler, Reinhart
2016-01-01
Newer lattice results indicate that, in the Landau gauge at low spacelike momenta, the gluon propagator and the ghost dressing function are finite nonzero. This leads to a definition of the QCD running coupling, in a specific scheme, that goes to zero at low spacelike momenta. We construct a running coupling which fulfills these conditions, and at the same time reproduces to a high precision the perturbative behavior at high momenta. The coupling is constructed in such a way that it reflects qualitatively correctly the holomorphic (analytic) behavior of spacelike observables in the complex plane of the squared momenta, as dictated by the general principles of Quantum Field Theories. Further, we require the coupling to reproduce correctly the nonstrange semihadronic decay rate of tau lepton which is the best measured low-momentum QCD observable with negligible higher-twist effects. Subsequent application of the Borel sum rules to the V+A spectral functions of tau lepton decays, as measured by OPAL Collaboratio...
Automated Methods in Chiral Perturbation Theory on the Lattice
Borasoy, B; Krebs, H; Lewis, R; Borasoy, Bugra; Hippel, Georg M. von; Krebs, Hermann; Lewis, Randy
2005-01-01
We present a method to automatically derive the Feynman rules for mesonic chiral perturbation theory with a lattice regulator. The Feynman rules can be output both in a human-readable format and in a form suitable for an automated numerical evaluation of lattice Feynman diagrams. The automated method significantly simplifies working with improved or extended actions. Some applications to the study of finite-volume effects will be presented.
Perfect Lattice Perturbation Theory A Study of the Anharmonic Oscillator
Bietenholz, W
1999-01-01
As an application of perfect lattice perturbation theory, we construct an O(\\lambda) perfect lattice action for the anharmonic oscillator analytically in momentum space. In coordinate space we obtain a set of 2-spin and 4-spin couplings \\propto \\lambda, which we evaluate for various masses. These couplings never involve variables separated by more than two lattice spacings. The O(\\lambda) perfect action is simulated and compared to the standard action. We discuss the improvement for the first two energy gaps \\Delta E_1, \\Delta E_2 and for the scaling quantity \\Delta E_2 / \\Delta E1 in different regimes of the interaction parameter, and of the correlation length.
Applications Of Chiral Perturbation Theory To Lattice Qcd
Van de Water, R S
2005-01-01
Quantum chromodynamics (QCD) is the fundamental theory that describes the interaction of quarks and gluons. Thus, in principle, one should be able to calculate all properties of hadrons from the QCD Lagrangian. It turns out, however, that such calculations can only be performed numerically on a computer using the nonperturbative method of lattice QCD, in which QCD is simulated on a discrete spacetime grid. Because lattice simulations use unphysically heavy quark masses (for computational reasons), lattice results must be connected to the real world using expressions calculated in chiral perturbation theory (χPT), the low-energy effective theory of QCD. Moreover, because real spacetime is continuous, they must be extrapolated to the continuum using an extension of χPT that includes lattice discretization effects, such as staggered χPT. This thesis is organized as follows. We motivate the need for lattice QCD and present the basic methodology in Chapter 1. We describe a common approximat...
Wilberding, James
2015-01-01
Embryology was a subject that inspired great cross-disciplinary discussion in antiquity, and Plato's Timaeus made an important contribution to this discussion, though Plato's precise views have remained a matter of controversy, especially regarding three key questions pertaining to the generation and nature of the seed: whether there is a female seed; what the nature of seed is; and whether the seed contains a preformed human being. In this paper I argue that Plato's positions on these three issues can be adequately determined, even if some other aspects of his theory cannot. In particular, it is argued that (i) Plato subscribes to the encephalo-myelogenic theory of seed, though he places particular emphasis on the soul being the true seed; (ii) Plato is a two-seed theorist, yet the female seed appears to make no contribution to reproduction; and (iii) Plato cannot be an advocate of preformationism.
Renormalisation and off-shell improvement in lattice perturbation theory
Capitani, S; Horsley, R; Perlt, H; Rakow, P E L; Schierholz, G; Schiller, A
2001-01-01
We discuss the improvement of flavour non-singlet point and one-link lattice quark operators, which describe the quark currents and the first moment of the DIS structure functions respectively. Suitable bases of improved operators are given, and the corresponding renormalisation factors and improvement coefficients are calculated in one-loop lattice perturbation theory, using the Sheikholeslami-Wohlert (clover) action. To this order we achieve off-shell improvement by eliminating the effect of contact terms. We use massive fermions, and our calculations are done keeping all terms up to first order in the lattice spacing, for arbitrary m^2/p^2, in a general covariant gauge. We also compare clover fermions with fermions satisfying the Ginsparg-Wilson relation, and show how to remove O(a) effects off-shell in this case too, and how this is in many aspects simpler than for clover fermions. Finally, tadpole improvement is also considered.
Perturbative scanning probe microscopy on a Kagome lattice of superconducting microwave resonators
Underwood, Devin; Shanks, Will; Li, Andy C. Y.; Koch, Jens; Houck, Andrew
2015-03-01
Microwave photons confined to a lattice of coupled resonators, each coupled to its own superconducting qubit have been predicted to exhibit matter like quantum phases. Realizing such a lattice-based quantum simulator presents a daunting experimental challenge; as such, new tools and measurement techniques are a necessary precursor. Here, we present measurements of the internal mode structure of microwave photons on a 49-site Kagome lattice of capacitively coupled coplanar waveguide resonators without qubits. By scanning a probe with a sapphire tip over the surface of a single lattice site, the resonant frequency was detuned, thus forming a local defect in the lattice. This perturbation resulted in measurable shifts in the lattice spectrum, which were used to extract the mode weights at the perturbed site. By perturbing each lattice site it was possible to reconstruct a complete map of different normal mode weights within the entire lattice. Additionally we present experimental evidence of a frustrated flat band that arises from the Kagome lattice geometry.
Comparing the QCD potential in Perturbative QCD and Lattice QCD at large distances
Recksiegel, S
2003-01-01
We compare the perturbatively calculated QCD potential to that obtained from lattice calculations in the theory without light quark flavours. We examine E_tot(r) = 2 m_pole + V_QCD(r) by re-expressing it in the MSbar mass m = m^MSbar(m^MSbar) and by choosing specific prescriptions for fixing the scale mu (dependent on r and m). By adjusting m so as to maximise the range of convergence, we show that perturbative and lattice calculations agree up to 3 r_0 ~ 7.5 GeV^-1 (r_0 is the Sommer scale) within the perturbative uncertainty of order Lambda^3 r^2.
The use of Schoonschip and form in perturbative lattice calculations
Capitani, S; Capitani, Stefano; Rossi, Giancarlo
1995-01-01
Using the formal languages Schoonschip and Form, we have developed general codes that are able to carry out all the algebraic manipulations needed to perform analytic lattice calculations, starting from the elementary building blocks (propagators and vertices) of each Feynman diagram. The main difficulty resides in the fact that, although there are many built in instructions to deal with Dirac gamma-matrices, Schoonschip and Form have been conceived having in mind a continuum theory, which is invariant with respect to the Lorentz group. On the lattice, on the contrary, a field theory is only invariant with respect to the hypercubic group, contained in the (euclidean) Lorentz group and not every pair of equal indices should be summed over. Being impossible to directly use the `gammatrics' of Schoonschip and Form as they are, special routines have been developed to correctly treat gamma matrices on the lattice, while using as much as possible of the built in Schoonschip and Form commands. We have used our codes...
Non-perturbative renormalization of static-light four-fermion operators in quenched lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Palombi, F. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Papinutto, M.; Pena, C. [CERN, Geneva (Switzerland). Physics Dept., Theory Div.; Wittig, H. [Mainz Univ. (Germany). Inst. fuer Kernphysik
2007-06-15
We perform a non-perturbative study of the scale-dependent renormalization factors of a multiplicatively renormalizable basis of {delta}B=2 parity-odd four-fermion operators in quenched lattice QCD. Heavy quarks are treated in the static approximation with various lattice discretizations of the static action. Light quarks are described by nonperturbatively O(a) improved Wilson-type fermions. The renormalization group running is computed for a family of Schroedinger functional (SF) schemes through finite volume techniques in the continuum limit. We compute non-perturbatively the relation between the renormalization group invariant operators and their counterparts renormalized in the SF at a low energy scale. Furthermore, we provide non-perturbative estimates for the matching between the lattice regularized theory and all the SF schemes considered. (orig.)
Constraining the Higgs boson mass: A non-perturbative lattice study
Jansen, Karl; Nagy, Attila
2012-01-01
We present non-perturbatively obtained results for upper and lower Higgs boson mass bounds using a chiral invariant lattice formulation of the Higgs-Yukawa sector of the standard model. We determine the mass bounds both, for a standard model top quark mass and for a possible fourth quark generation with masses up to 700GeV.
Kim, Taekwang; Kitazawa, Masakiyo
2016-01-01
We analyze the production rate of photons from the thermal medium above the deconfinement temperature with a quark propagator obtained from a lattice QCD numerical simulation. The photon-quark vertex is determined gauge-invariantly, so as to satisfy the Ward-Takahashi identity. The obtained photon production rate shows a suppression compared to perturbative results.
Apparently non-invariant terms of nonlinear sigma models in lattice perturbation theory
Harada, Koji; Kubo, Hirofumi; Yamamoto, Yuki
2009-01-01
Apparently non-invariant terms (ANTs) which appear in loop diagrams for nonlinear sigma models (NLSs) are revisited in lattice perturbation theory. The calculations have been done mostly with dimensional regularization so far. In order to establish that the existence of ANTs is independent of the regularization scheme, and of the potential ambiguities in the definition of the Jacobian of the change of integration variables from group elements to "pion" fields, we employ lattice regularization, in which everything (including the Jacobian) is well-defined. We show explicitly that lattice perturbation theory produces ANTs in the four-point functions of the "pion" fields at one-loop and the Jacobian does not play an important role in generating ANTs.
Perturbative subtraction of lattice artifacts in the computation of renormalization constants
Constantinou, M; Gockeler, M; Horsley, R; Panagopoulos, H; Perlt, H; Rakow, P E L; Schierholz, G; Schiller, A
2012-01-01
The determination of renormalization factors is of crucial importance. They relate the observables obtained on finite, discrete lattices to their measured counterparts in the continuum in a suitable renormalization scheme. Therefore, they have to be computed as precisely as possible. A widely used approach is the nonperturbative Rome-Southampton method. It requires, however, a careful treatment of lattice artifacts. They are always present because simulations are done at lattice spacings $a$ and momenta $p$ with $ap$ not necessarily small. In this paper we try to suppress these artifacts by subtraction of one-loop contributions in lattice perturbation theory. We compare results obtained from a complete one-loop subtraction with those calculated for a subtraction of $O(a^2)$.
New Approach for IIR Adaptive Lattice Filter Structure Using Simultaneous Perturbation Algorithm
Martinez, Jorge Ivan Medina; Nakano, Kazushi; Higuchi, Kohji
Adaptive infinite impulse response (IIR), or recursive, filters are less attractive mainly because of the stability and the difficulties associated with their adaptive algorithms. Therefore, in this paper the adaptive IIR lattice filters are studied in order to devise algorithms that preserve the stability of the corresponding direct-form schemes. We analyze the local properties of stationary points, a transformation achieving this goal is suggested, which gives algorithms that can be efficiently implemented. Application to the Steiglitz-McBride (SM) and Simple Hyperstable Adaptive Recursive Filter (SHARF) algorithms is presented. Also a modified version of Simultaneous Perturbation Stochastic Approximation (SPSA) is presented in order to get the coefficients in a lattice form more efficiently and with a lower computational cost and complexity. The results are compared with previous lattice versions of these algorithms. These previous lattice versions may fail to preserve the stability of stationary points.
Energy Technology Data Exchange (ETDEWEB)
Goeckeler, M.; Schaefer, A. [Regensburg Univ. (Germany). Inst. fuer Physik 1 - Theoretische Physik; Horsley, R. [Edinburgh Univ. (United Kingdom). School of Physics; Perlt, H.; Schiller, A. [Leipzig Univ. (Germany). Inst. fuer Theoretische Physik; Rakow, P.E.L. [Liverpool Univ. (United Kingdom). Theoretical Physics Division, Dept. of Mathematical Sciences; Schierholz, G. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC]|[Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2006-06-15
We consider the renormalisation of lattice QCD operators with one and two covariant derivatives related to the first and second moments of generalised parton distributions and meson distribution amplitudes. Employing the clover fermion action we calculate their non-forward quark matrix elements in one-loop lattice perturbation theory. For some representations of the hypercubic group commonly used in simulations we determine the sets of all possible mixing operators and compute the matrices of renormalisation factors in one-loop approximation. We describe how tadpole improvement is applied to the results. (Orig.)
B-physics from non-perturbatively renormalized HQET in two-flavour lattice QCD
Bernardoni, Fabio; Bulava, John; Della Morte, Michele; Fritzsch, Patrick; Garron, Nicolas; Gerardin, Antoine; Heitger, Jochen; von Hippel, Georg M; Simma, Hubert
2013-01-01
We report on the ALPHA Collaboration's lattice B-physics programme based on N_f=2 O(a) improved Wilson fermions and HQET, including all NLO effects in the inverse heavy quark mass, as well as non-perturbative renormalization and matching, to fix the parameters of the effective theory. Our simulations in large physical volume cover 3 lattice spacings a ~ (0.08-0.05) fm and pion masses down to 190 MeV to control continuum and chiral extrapolations. We present the status of results for the b-quark mass and the B_(s)-meson decay constants, f_B and f_{B_s}.
Filsafat Ketuhanan Menurut Plato
Directory of Open Access Journals (Sweden)
Ivan Th.J Weismann
2005-06-01
Full Text Available Plato adalah filsuf pertama yang menulis secara filosofis dan secara sistematik teologis mengenai konsep Ketuhanan sehingga dapatlah dikatakan bahwa ia adalah peletqk dasar bagi ilmu teologia dan memberikan pengaruh besar bagi perkembanganfilsafat Barat khususnya tentangkonsep Ketuhanan. Pemikiran Plato tentang Ketuhanan adalah upayanya untuk mereformasi konsep Ketuhanan yang terdapat pada masyarakat Yunani kuno. Tulisan ini berupaya menganalisis dan memahami Ketuhanan menurut Plato agar pembaca masa kini dapat mengerti lebih dalam lagi tentong konsep Ketuhanan yang dipahami masyarakat Yunani kuno dan khususnya menurut Plato, dan juga dapat dijadikan sebagai bahan perbandingan bagifilsafat Ketuhanan pada masa kini. Filsafat Ketuhanan menurut Plato ini penulis jelaskan dengan memperhatikandimensi metafisika, epistemologi, dan etika.
Non-perturbative test of the Witten-Veneziano formula from lattice QCD
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Cichy, Krzysztof [Goethe-Universität, Institut für Theoretische Physik,Max-von-Laue-Straße 1, Frankfurt a.M., D-60438 (Germany); NIC, DESY,Platanenallee 6, Zeuthen, D-15738 (Germany); Adam Mickiewicz University, Faculty of Physics,Umultowska 85, Poznan, 61-614 (Poland); Garcia-Ramos, Elena [NIC, DESY,Platanenallee 6, Zeuthen, D-15738 (Germany); Humboldt Universität zu Berlin,Newtonstr. 15, Berlin, D-12489 (Germany); Jansen, Karl [NIC, DESY,Platanenallee 6, Zeuthen, D-15738 (Germany); Ottnad, Konstantin [Institut für Strahlen- und Kernphysik (Theorie),Nussallee 14-16, Bonn 53115 Germania (Germany); Urbach, Carsten [Institut für Strahlen- und Kernphysik (Theorie),Nussallee 14-16, Bonn 53115 Germania (Germany); Bethe Center for Theoretical Physics,Nussallee 12, Universität Bonn, Bonn, D-53115 (Germany); Collaboration: The ETM collaboration
2015-09-03
We compute both sides of the Witten-Veneziano formula using lattice techniques. For the one side we perform dedicated quenched simulations and use the spectral projector method to determine the topological susceptibility in the pure Yang-Mills theory. The other side we determine in lattice QCD with N{sub f}=2+1+1 dynamical Wilson twisted mass fermions including for the first time also the flavour singlet decay constant. The Witten-Veneziano formula represents a leading order expression in the framework of chiral perturbation theory and we also employ leading order chiral perturbation theory to relate the flavor singlet decay constant to the relevant decay constant parameters in the quark flavor basis and flavor non-singlet decay constants. After taking the continuum and the SU(2) chiral limits we compare both sides and find good agreement within uncertainties.
Non-perturbative improvement of quark mass renormalization in two-flavour lattice QCD
Fritzsch, Patrick; Tantalo, Nazario
2010-01-01
We non-perturbatively determine the renormalization constant and the improvement coefficients relating the renormalized current and subtracted quark mass in O(a) improved two-flavour lattice QCD. We employ the Schr\\"odinger functional scheme and fix the physical extent of the box by working at a constant value of the renormalized coupling. Our calculation yields results which cover two regions of bare parameter space. One is the weak-coupling region suitable for volumes of about half a fermi. By making simulations in this region, quarks as heavy as the bottom can be propagated with the full relativistic QCD action and renormalization problems in HQET can be solved non-perturbatively by a matching to QCD in finite volume. The other region refers to the common parameter range in large-volume simulations of two-flavour lattice QCD, where our results have particular relevance for charm physics applications.
Non-perturbative test of the Witten-Veneziano formula from lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Cichy, Krzysztof [Frankfurt Univ. (Germany). Inst. fuer Theoretische Physik; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Poznan Univ. (Poland). Faculty of Physics; Garcia-Ramos, Elena [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Humboldt-Universitaet, Berlin (Germany); Jansen, Karl [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Ottnad, Konstantin; Urbach, Carsten [Bonn Univ. (Germany). Institut fuer Strahlen- und Kernphysik; Bonn Univ. (Germany). Bethe Center for Theoretical Physics; Collaboration: The ETM collaboration
2015-10-15
We compute both sides of the Witten-Veneziano formula using lattice techniques. For the one side we perform dedicated quenched simulations and use the spectral projector method to determine the topological susceptibility in the pure Yang-Mills theory. The other side we determine in lattice QCD with N{sub f}=2 +1+1 dynamical Wilson twisted mass fermions including for the first time also the flavour singlet decay constant. The Witten-Veneziano formula represents a leading order expression in the framework of chiral perturbation theory and we also employ leading order chiral perturbation theory to relate the flavor singlet decay constant to the relevant decay constant parameters in the quark flavor basis and flavor non-singlet decay constants. After taking the continuum and the SU(2) chiral limits we compare both sides and find good agreement within uncertainties.
Effects of non-perturbatively improved dynamical fermions in QCD at fixed lattice spacing
Allton, C R; Bowler, K C; Garden, J; Hart, A; Hepburn, D; Irving, A C; Joó, B; Kenway, R D; Maynard, C M; McNeile, C; Michael, C; Pickles, S M; Sexton, J C; Sharkey, K J; Sroczynski, Z; Talevi, M; Teper, M; Wittig, H
2002-01-01
We present results for the static inter-quark potential, lightest glueballs, light hadron spectrum and topological susceptibility using a non-perturbatively improved action on a $16^3\\times 32$ lattice at a set of values of the bare gauge coupling and bare dynamical quark mass chosen to keep the lattice size fixed in physical units ($\\sim 1.7$ fm). By comparing these measurements with a matched quenched ensemble, we study the effects due to two degenerate flavours of dynamical quarks. With the greater control over residual lattice spacing effects which these methods afford, we find some evidence of charge screening and some minor effects on the light hadron spectrum over the range of quark masses studied ($M_{PS}/M_{V}\\ge0.58$). More substantial differences between quenched and unquenched simulations are observed in measurements of topological quantities.
Energy Technology Data Exchange (ETDEWEB)
Hesse, Dirk
2012-07-13
The author developed the pastor software package for automated lattice perturbation theory calculations in the Schroedinger functional scheme. The pastor code consists of two building blocks, dealing with the generation of Feynman rules and Feynman diagrams respectively. Accepting a rather generic class of lattice gauge and fermion actions, passed to the code in a symbolic form as input, a low level part of pastor will generate Feynman rules to an arbitrary order in the bare coupling with a trivial or an Abelian background field. The second, high level part of pastor is a code generator whose output relies on the vertex generator. It writes programs that evaluate Feynman diagrams for a class of Schroedinger functional observables up to one loop order automatically, the relevant O(a) improvement terms are taken into account. We will describe the algorithms used for implementation of both parts of the code in detail, and provide cross checks with perturbative and non-perturbative data to demonstrate the correctness of our code. We demonstrate the usefulness of the pastor package through various applications taken from the matching process of heavy quark effective theory with quantum chromodynamics. We have e.g. completed a one loop analysis for new candidates for matching observables timely and with rather small effort, highlighting two advantages of an automated software setup. The results that were obtained so far will be useful as a guideline for further non-perturbative studies.
Validation of lattice code 'EXCEL' with TIC experiments on uniform and regularly perturbed lattices
Energy Technology Data Exchange (ETDEWEB)
Ramakrishna, A., E-mail: anantatmula.ramakrishna@gmail.co [Atomic Energy Regulatory Board, Niyamak Bhavan, Anushaktinagar, Mumbai 400 094 (India); Jagannathan, V. [Light Water Reactors Physics Section, Reactor Physics Design Division, Bhabha Atomic Research Centre, Mumbai 400 085 (India); Jain, R.P. [IIT Bombay, Mumbai (India)
2010-12-15
Temporary International Collective (TIC) was established in 1972 by an agreement among seven countries, namely, Bulgaria, Czechoslovakia, Germany, Hungary, Poland, Romania and Union of Soviet Socialist Republics. The main objective of TIC was to provide the experimental data for the reactor physics analysis of water cooled and water moderated power reactors (WWER). Extensive experimental work for different core configurations was carried out by TIC countries to investigate the physics behaviour of WWER lattices and the results were published in TIC volumes. Two VVER-1000 MWe reactors are currently in an advanced stage of construction and due for commissioning in Kudankulam, Tamil Nadu, India. Indigenous development of in-core fuel management computer codes for the analysis of hexagonal lattice cores is also in an advanced stage to address various design, operation and safety issues of VVER type cores. The validation of the above TIC lattice experiments will help in the identification of deficiencies in reactor physics design computational codes and the associated nuclear data libraries. In this paper, TIC experiments on uniform and regularly perturbed lattices have been analyzed as part of the validation of indigenous computer codes, EXCEL, TRIHEX-FA and HEXPIN developed at Light Water Reactors Physics Section, B.A.R.C. Neutron-nuclear multi-group cross-section libraries in WIMS/D format in 69/172 energy groups have been released by IAEA at the conclusion of WIMS library update project (WLUP). In the present study we have used libraries based on ENDF/B-6, ENDF/B-7, JEFF3.1 and JENDL3.2 evaluated nuclear datasets. The results of the theoretical analyses bring out the performance of the code system and various cross-section libraries.
[Plato psychiatrist, Foucault platonic].
Mathov, Nicolás
2016-05-01
This work explores the links between the concepts of "soul", "law" and "word" in Plato's work, in order to highlight the importance and the centrality of the philosophical-therapeutic dimension in the Greek philosopher's thought. In that way, this work pretends to show that "contemporary" problems usually discussed within "Human Sciences" in general, and Psychiatry in particular, should confront their knowledge with Plato's work, mainly due to the profound influence his ideas have had in our Greco-Christian culture. In that sense, and with that objective, this work also explores Michel Foucault's lucid and controversial interpretation of Plato.
Canfora, Fabrizio; Pais, Pablo; Rosa, Luigi; Zerwekh, Alfonso
2016-01-01
In this paper it is analyzed the compatibility of the non-perturbative equations of state of quarks and gluons arising from the lattice with some natural requirements for self gravitating objects at equilibrium: the existence of an equation of state (namely, the possibility to define the pressure as a function of the energy density), the absence of superluminal propagation and Le Chatelier's principle. It is discussed under which conditions it is possible to extract an equation of state (in the above sense) from the non-perturbative propagators arising from the fits of the last lattice data. In particular, in the quarks case, there is a small but non vanishing range of temperatures in which it is not possible to define a single-valued functional relation between density and pressure. Interestingly enough, a small change of the parameters appearing in the fit of the lattice quark propagator (of around 10\\%) can guarantee the fulfillment of all the three conditions (keeping alive, at the same time, the violatio...
New lessons from the nucleon mass, lattice QCD and heavy baryon chiral perturbation theory
Walker-Loud, A
2008-01-01
I will review heavy baryon chiral perturbation theory for the nucleon delta degrees of freedom and then examine the recent dynamical lattice calculations of the nucleon mass from the BMW, ETM, JLQCD, LHP, MILC, NPLQCD, PACS-CS, QCDSF/UKQCD and RBC/UKQCD Collaborations. Performing the chiral extrapolations of these results, one finds remarkable agreement with the physical nucleon mass, from each lattice data set. However, a careful examination of the lattice data and the resulting extrapolation functions reveals some unexpected results, serving to highlight the significant challenges in performing chiral extrapolations of baryon quantities. All the N_f=2+1 dynamical results can be quantitatively described by theoretically unmotivated fit function linear in the pion mass with m_pi ~ 750 -190 MeV. When extrapolated to the physical point, the results are in striking agreement with the physical nucleon mass. I will argue that knowledge of each lattice datum of the nucleon mass is required at the 1-2% level, includ...
Charmless chiral perturbation theory for N_f=2+1+1 twisted mass lattice QCD
Bar, Oliver
2014-01-01
The chiral Lagrangian describing the low-energy behavior of N_f=2+1+1 twisted mass lattice QCD is constructed through O(a^2). In contrast to existing results the effects of a heavy charm quark are consistently removed, leaving behind a charmless 3-flavor Lagrangian. This Lagrangian is used to compute the pion and kaon masses to one loop in a regime where the pion mass splitting is large and taken as a leading order effect. In comparison with continuum chiral perturbation theory additional chiral logarithms are present in the results. In particular, chiral logarithms involving the neutral pion mass appear. These predict rather large finite volume corrections in the kaon mass which roughly account for the finite volume effects observed in lattice data.
Pondy, Dorothy, Comp.
The catalog was compiled to assist instructors in planning community college and university curricula using the 48 computer-assisted accountancy lessons available on PLATO IV (Programmed Logic for Automatic Teaching Operation) for first semester accounting courses. It contains information on lesson access, lists of acceptable abbreviations for…
Control Data's Education Offering: "Plato Would Have Enjoyed PLATO"
Datamation, 1976
1976-01-01
Programmed Learning and Teaching Operation (PLATO) distributes instructional materials in the form of text, numbers, animated drawings and other graphics for individualized, self-paced learning. (Author)
Application of perturbation theory to lattice calculations based on method of cyclic characteristics
Assawaroongruengchot, Monchai
Perturbation theory is a technique used for the estimation of changes in performance functionals, such as linear reaction rate ratio and eigenvalue affected by small variations in reactor core compositions. Here the algorithm of perturbation theory is developed for the multigroup integral neutron transport problems in 2D fuel assemblies with isotropic scattering. The integral transport equation is used in the perturbative formulation because it represents the interconnecting neutronic systems of the lattice assemblies via the tracking lines. When the integral neutron transport equation is used in the formulation, one needs to solve the resulting integral transport equations for the flux importance and generalized flux importance functions. The relationship between the generalized flux importance and generalized source importance functions is defined in order to transform the generalized flux importance transport equations into the integro-differential equations for the generalized adjoints. Next we develop the adjoint and generalized adjoint transport solution algorithms based on the method of cyclic characteristics (MOCC) in DRAGON code. In the MOCC method, the adjoint characteristics equations associated with a cyclic tracking line are formulated in such a way that a closed form for the adjoint angular function can be obtained. The MOCC method then requires only one cycle of scanning over the cyclic tracking lines in each spatial iteration. We also show that the source importance function by CP method is mathematically equivalent to the adjoint function by MOCC method. In order to speed up the MOCC solution algorithm, a group-reduction and group-splitting techniques based on the structure of the adjoint scattering matrix are implemented. A combined forward flux/adjoint function iteration scheme, based on the group-splitting technique and the common use of a large number of variables storing tracking-line data and exponential values, is proposed to reduce the
DEFF Research Database (Denmark)
Larsen, Øjvind
2012-01-01
Plato is normally taken as one of the founders of Western political philosophy, not at least with his Republic. Here, he constructs a hierarchy of forms of governments, beginning with aristocracy at the top as a critical standard for the other forms of governments, and proceeding through timocrac......’ funeral oration is used to show that Pericles presented a democratic political philosophy that can serve as a counterpoint to Plato’s political philosophy in the Republic....
Mackenzie, Jim
2014-01-01
There is more to be said about two of the topics Chris Peers addresses in his article "Freud, Plato and Irigaray: A morpho-logic of teaching and learning" (2012, Educational Philosophy and Theory, 44, 760-774), namely the Socratic method of teaching and Plato's stance with regard to women and feminism. My purpose in this article is…
PLATO Sitcom Dialogs for Russian.
Dawson, Clayton; Provenzano, Nolen
1981-01-01
Situation comedy (sitcom) dialogs that are included in PLATO lessons for first year Russian students are described. These comprehension exercises make use of both the touch panel and the audio capabilities of PLATO. The sitcom dialogs were written by a native speaker of Russian and are based on the vocabulary in the textbook plus a small number of…
Mackenzie, Jim
2014-01-01
There is more to be said about two of the topics Chris Peers addresses in his article "Freud, Plato and Irigaray: A morpho-logic of teaching and learning" (2012, Educational Philosophy and Theory, 44, 760-774), namely the Socratic method of teaching and Plato's stance with regard to women and feminism. My purpose in this article is…
Korcyl, Piotr
2016-01-01
We determine quark mass dependent order $a$ improvement terms of the form $b_Jam$ for non-singlet scalar, pseudoscalar, vector and axialvector currents using correlators in coordinate space on a set of CLS ensembles. These have been generated employing non-perturbatively improved Wilson Fermions and the tree-level L\\"uscher-Weisz gauge action at $\\beta = 3.4, 3.46, 3.55$ and $3.7$, corresponding to lattice spacings ranging from $a \\approx 0.085$ fm down to $0.05$ fm. In the $N_f=2+1$ flavour theory two types of improvement coefficients exist: $b_J$, proportional to non-singlet quark mass combinations, and $\\bar{b}_J$ (or $\\tilde{b}_J$), proportional to the trace of the quark mass matrix. Combining our non-perturbative determinations with perturbative results, we quote Pad\\'e approximants parameterizing the $b_J$ improvement coefficients within the above window of lattice spacings. We also give preliminary results for $\\tilde{b}_J$ at $\\beta=3.4$.
Microbranching in mode-I fracture in a randomly perturbed lattice
Heizler, Shay I.; Kessler, David A.; Elbaz, Yonatan S.
2013-08-01
We study mode-I fracture in lattices using atomistic simulations with randomly distributed bond lengths. By using a small parameter that measures the variation of the bond length between the atoms in perfect lattices and using a three-body force law, simulations reproduce the qualitative behavior of the beyond-steady-state cracks in the high-velocity regime, including reasonable microbranching. In particular, the effect of the lattice structure on the crack appears minimal, even though in terms of the physical properties such as the structure factor g(r) and the radial or angular distributions, these lattices share the physical properties of perfect lattices rather than those of an amorphous material (e.g., the continuous random network model). A clear transition can be seen between steady-state cracks, where a single crack propagates in the midline of the sample, and the regime of unstable cracks, where microbranches start to appear near the main crack, in line with previous experimental results. This is seen in both a honeycomb lattice and a fully hexagonal lattice. This model reproduces the main physical features of propagating cracks in brittle materials, including the total length of microbranches as a function of driving displacement and the increasing amplitude of oscillations of the electrical resistance. In addition, preliminary indications of power-law behavior of the microbranch shapes can be seen, potentially reproducing one of the most intriguing experimental results of brittle fracture. There was found to exist a critical degree of disorder, i.e., a sharp threshold between the cleaving behavior characterizing perfect lattices and the microbranching behavior that characterizes amorphous materials.
Constantinou, Martha; Frezzotti, Roberto; Lubicz, Vittorio; Panagopoulos, Haralambos; Skouroupathis, Apostolos; Stylianou, Fotos
2010-01-01
In this work we calculate the corrections to the amputated Green's functions of 4-fermion operators, in 1-loop Lattice Perturbation theory. One of the novel aspects of our calculations is that they are carried out to O(a^2) (a: lattice spacing). We employ the Wilson/clover action for massless fermions (also applicable for the twisted mass action in the chiral limit) and a family of Symanzik improved actions for gluons. Our calculations have been carried out in a general covariant gauge. Results have been obtained for several popular choices of values for the Symanzik coefficients. While our Green's function calculations regard any pointlike 4-fermion operators which do not mix with lower dimension ones, we pay particular attention to DF=2 operators, both Parity Conserving and Parity Violating (F: flavour). We compute the perturbative renormalization constants for a complete basis of 4-fermion operators and we study their mixing pattern. For some of the actions considered here, even O(a^0) results did not exis...
Directory of Open Access Journals (Sweden)
Zahra Nouri Sanghdehi
2017-07-01
Full Text Available One of the greatest problems in Plato that appears in different forms in his works is the relation of nomos and phusis. This thesis has been in fifth century B.C as the contradiction of phusis and nomos among big thinkers. In this essay, we tried to investigate the relation of phusis and nomos in Plato’s thoughts according to current theories of the contradiction of these in dialogues Gorgias, Republic and Protagoras. Plato tries to minimize consequences of belief to contradiction of phusis and nomos in social and political life by assertion large scale relation between phusis and nomos. Plato depicts the ultimate solution of this problem in Law. There he accounts nomos as raised from phusis that is sub sovereignty of divine. Indeed union of phusis and gods in Plato’s thought is sanction for the identity of phusis and nomos.
Calculation of the Perturbative Expansion of Wilson Operators on the Lattice
Liu, Da-Qing; Wu, Ji-Min; Chen, Ying
2001-11-01
We introduce an approach to expand gauge-invariant Wilson operators on the lattice. This approach is based on the non-Abelian-Stokes theorem and overcomes the disadvantages of the Luscher-Weisz method. It is also suitable for expanding any Wilson operator.
Calculation of the Perturbative Expansion of Wilson Operators on the Lattice
Institute of Scientific and Technical Information of China (English)
刘大庆; 吴济民; 陈莹
2001-01-01
We introduce an approach to expand gauge-invariant Wilson operators on the lattice. This approach is based on the non-Abelian-Stokes theorem and overcomes the disadvantages of the Luscher-Weisz method. It is also suitable for expanding any Wilson operator.
What is Plato? Inference and Allusion in Plato's "Sophist."
Quandahl, Ellen
1989-01-01
Discusses inference and allusion in the dialogue in Plato's Sophist. Examines the sense in which a locution is used, distinguishing among senses of the verb to be, and sets the ball rolling for the development of logic and the whole metaphysics of categories of being. (RAE)
Stochastic perturbation of the linear tune and diffusion for simple lattice models
Energy Technology Data Exchange (ETDEWEB)
Bazzani, A. [INFN sezione di Bologna, University of Bologna, v. Irnerio n.46, 40126 Bologna (Italy). E-mail: bazzani (at) bo.infn.it; Giovannozzi, M. [CERN PS division v. Irnerio n.46, 40126 Bologna (Italy). E-mail: bazzani (at) bo.infn.it; Turchetti, G. [INFN sezione di Bologna, University of Bologna, v. Irnerio n.46, 40126 Bologna (Italy). E-mail: bazzani (at) bo.infn.it
1995-09-01
We analyse the particle diffusion in the betatronic motion due to a random noise in the tune parameter. We explicitly consider the lattice of the CERN Super Proton Synchrotron in the special set up used in the experimental sessions to study the beam stability. A Fokker-Planck equation is derived for the distribution function in the action variables. We compare the results of the tracking with the analytical results in the flat beam approximation.
The B-meson mass splitting from non-perturbative quenched lattice QCD
Grozin, A G; Marquard, P; Meyer, H B; Piclum, J H; Sommer, R; Steinhauser, M
2007-01-01
We perform the non-perturbative (quenched) renormalization of the chromo-magnetic operator in Heavy Quark Effective Theory and its three-loop matching to QCD. At order 1/m of the expansion, the operator is responsible for the mass splitting between the pseudoscalar and vector B-mesons. These new computed factors are affected by an uncertainty negligible in comparison to the known bare matrix element of the operator between B-states. Furthermore, they push the quenched determination of the spin splitting for the Bs-meson much closer to its experimental value than the previous perturbatively renormalized computations. The renormalization factor for three commonly used heavy quark actions and the Wilson gauge action and useful parametrizations of the matching coefficient are provided.
Perturbation Theory for PT-Symmetric Sinusoidal Optical Lattices at the Symmetry-Breaking Threshold
Jones, H F
2011-01-01
The $PT$ symmetric potential $V_0[\\cos(2\\pi x/a)+i\\lambda\\sin(2\\pi x/a)]$ has a completely real spectrum for $\\lambda\\le 1$, and begins to develop complex eigenvalues for $\\lambda>1$. At the symmetry-breaking threshold $\\lambda=1$ some of the eigenvectors become degenerate, giving rise to a Jordan-block structure for each degenerate eigenvector. In general this is expected to give rise to a secular growth in the amplitude of the wave. However, it has been shown in a recent paper by Longhi, by numerical simulation and by the use of perturbation theory, that for an initial wave packet this growth is suppressed, giving instead a constant maximum amplitude. We revisit this problem by developing the perturbation theory further. We verify that the results found by Longhi persist to second order, and with different input wave packets we are able to see the seeds in perturbation theory of the phenomenon of birefringence first discovered by El-Ganainy et al.
Korcyl, Piotr
2016-01-01
We determine quark mass dependent order $a$ improvement terms of the form $b_J am$ for non-singlet scalar, pseudoscalar, vector and axialvector currents, using correlators in coordinate space. We use a set of CLS ensembles comprising non-perturbatively improved Wilson Fermions and the tree-level Luescher-Weisz gauge action at $\\beta=3.4,3.46,3.55$ and $\\beta=3.7$, corresponding to lattice spacings $a$ ranging from $0.05$ fm to $0.09$ fm. We report the values of the $b_J$ improvement coefficients which are proportional to non-singlet quark mass combinations and also discuss the possibility of determining the $\\bar{b}_J$ coefficients which are proportional to the trace of the quark mass matrix.
Energy-momentum tensor on the lattice: non-perturbative renormalization in Yang--Mills theory
Giusti, Leonardo
2015-01-01
We construct an energy-momentum tensor on the lattice which satisfies the appropriate Ward Identities (WIs) and has the right trace anomaly in the continuum limit. It is defined by imposing suitable WIs associated to the Poincare` invariance of the continuum theory. These relations come forth when the length of the box in the temporal direction is finite, and they take a particularly simple form if the coordinate and the periodicity axes are not aligned. We implement the method for the SU(3) Yang--Mills theory discretized with the standard Wilson action in presence of shifted boundary conditions in the (short) temporal direction. By carrying out extensive numerical simulations, the renormalization constants of the traceless components of the tensor are determined with a precision of roughly half a percent for values of the bare coupling constant in the range 0<= g^2_0<=1.
Bulava, John; Heitger, Jochen; Wittemeier, Christian
2016-01-01
We non-perturbatively determine the renormalization factor of the axial vector current in lattice QCD with $N_f=3$ flavors of Wilson-clover fermions and the tree-level Symanzik-improved gauge action. The (by now standard) renormalization condition is derived from the massive axial Ward identity and it is imposed among Schr\\"{o}dinger functional states with large overlap on the lowest lying hadronic state in the pseudoscalar channel, in order to reduce kinematically enhanced cutoff effects. We explore a range of couplings relevant for simulations at lattice spacings of $\\approx 0.09$ fm and below. An interpolation formula for $Z_A(g_0^2)$, smoothly connecting the non-perturbative values to the 1-loop expression, is provided together with our final results.
Energy Technology Data Exchange (ETDEWEB)
Hehl, H.
2002-07-01
This thesis has studied the range of validity of the chiral random matrix theory in QCD on the example of the quenched staggered Dirac operator. The eigenvalues of this operator in the neighbourhood of zero are essential for the understanding of the spontaneous breaking of the chiral symmetry and the phase transition connected with this. The phase transition cannot be understood in the framework of perturbation theory, so that the formulation of QCD on the lattice has been chosen as the only non-perturbative approach. In order to circumvent both the problem of the fermion doubling and to study chiral properties on the lattice with acceptable numerical effort, quenched Kogut-Susskind fermions have been applied. The corresponding Dirac operator can be completely diagonalized by the Lanczos procedure of Cullum and Willoughby. Monte carlo simulations on hypercubic lattice have been performed and the Dirac operators of very much configurations diagonalized at different lattice lengths and coupling constants. The eigenvalue correlations on the microscopic scale are completely described by the chiral random matrix theory for the topological sector zero, which has been studied by means of the distribution of the smallest eigenvalue, the microscopic spectral density and the corresponding 2-point correlation function. The found universal behaviour shows, that on the scale of the lowest eigenvalue only completely general properties of the theory are important, but not the full dynamics. In order to determine the energy scale, from which the chiral random matrix theory losses its validity, - the Thouless energy - with the scalar susceptibilities observables have been analyzed, which are because of their spectral mass dependence sensitive on this. For each combination of the lattice parameter so the deviation point has been identified.
Bulava, John; Heitger, Jochen; Wittemeier, Christian
2015-01-01
The coefficient c_A required for O(a) improvement of the axial current in lattice QCD with N_f=3 flavors of Wilson fermions and the tree-level Symanzik-improved gauge action is determined non-perturbatively. The standard improvement condition using Schroedinger functional boundary conditions is employed at constant physics for a range of couplings relevant for simulations at lattice spacings of ~ 0.09 fm and below. We define the improvement condition projected onto the zero topological charge sector of the theory, in order to avoid the problem of possibly insufficient tunneling between topological sectors in our simulations at the smallest bare coupling. An interpolation formula for c_A(g_0^2) is provided together with our final results.
The Method of Hypothesis in Plato's Philosophy
Directory of Open Access Journals (Sweden)
Malihe Aboie Mehrizi
2016-09-01
Full Text Available The article deals with the examination of method of hypothesis in Plato's philosophy. This method, respectively, will be examined in three dialogues of Meno, Phaedon and Republic in which it is explicitly indicated. It will be shown the process of change of Plato’s attitude towards the position and usage of the method of hypothesis in his realm of philosophy. In Meno, considering the geometry, Plato attempts to introduce a method that can be used in the realm of philosophy. But, ultimately in Republic, Plato’s special attention to the method and its importance in the philosophical investigations, leads him to revise it. Here, finally Plato introduces the particular method of philosophy, i.e., the dialectic
Plato's Anti-Kohlbergian Program for Moral Education
Jonas, Mark E.
2016-01-01
Following Lawrence Kohlberg it has been commonplace to regard Plato's moral theory as "intellectualist", where Plato supposedly believes that becoming virtuous requires nothing other than "philosophical knowledge or intuition of the ideal form of the good". This is a radical misunderstanding of Plato's educational programme,…
THEORY OF LOVE IN PLATO'S PHILOSOPHY
Directory of Open Access Journals (Sweden)
ZOHREH MOZAFARI
2015-01-01
Full Text Available The article presents a philosophical analysis of the phenomenon of Plato’s love. It is noted that a large number of works are devoted to the philosophy of Plato’s love, but not all aspects of his philosophy are studied, for example the problems of erotosophy of Plato. Phenomenon of love interested philosophers since ancient times. The first attempts to explain the phenomenon of love appeared in ancient times. These attempts were made by ancient philosophers Socrates, Plato and Aristotle. Platonism is a multifaceted teaching; identification of all possibilities of Plato’s erotic philosophy which can supplement other fields of philosophy is important and topical.
Quoting Plato in Porphyrius' Cuestiones homericas
Directory of Open Access Journals (Sweden)
Lucía Rodríguez‑Noriega Guillén
2016-08-01
Full Text Available This paper studies the quotations of Plato in Porphyry’s Homeric Questions,including their typology (literal quotation, allusion, paraphrase, etc., their beingor not direct citations, their function in the work, and their possible parallels inother authors.
Plato's problem an introduction to mathematical platonism
Panza, M
2013-01-01
What is mathematics about? And how can we have access to the reality it is supposed to describe? The book tells the story of this problem, first raised by Plato, through the views of Aristotle, Proclus, Kant, Frege, Gödel, Benacerraf, up to the most recent debate on mathematical platonism.
Rauer, H.; et al., [Unknown; Hekker, S.
2014-01-01
PLATO 2.0 has recently been selected for ESA’s M3 launch opportunity (2022/24). Providing accurate key planet parameters (radius, mass, density and age) in statistical numbers, it addresses fundamental questions such as: How do planetary systems form and evolve? Are there other systems with planets
Results of the 1975 Delaware PLATO Project.
Hofstetter, Fred T.
During the Spring semester of 1975, the University of Delaware initiated a PLATO project with the dual purpose of demonstrating how a computer system might function in a university and of evaluating what part such a system might play in the future of the university and its supporting community. The demonstration phase of the project, which…
Socrates, Plato, "Eros" and Liberal Education
McPherran, Mark L.
2010-01-01
This paper focuses on the educational method--the "elenchos"--of Plato's Socrates, arguing, against some prominent interpretations, that it is love, both "eros" and "philia", that is the key that links Socrates' philosophy with his education. This analysis, of course, raises some difficult questions regarding the relationship between teacher and…
Plato's Protagoras: Professional Models, Ethical Concerns.
Gregory, Marshall W.
1983-01-01
In Plato's model his clear criticism of Protagorean careerism and his negotiation with Socratic radicalism shows he is a centrist cultivating criticism and open discourse. In an age when academe seems to have lost a sense of its identify and function in society, its most enduring contributions are criticism and discourse. (MLW)
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.
2017-01-01
The following results are obtained for the Cauchy problem with localized initial data for the crystal lattice vibration equations with continuous and discrete time: (i) the asymptotics of the solution is determined by Lagrangian manifolds with singularities ("punctured" Lagrangian manifolds); (ii) Maslov's canonical operator is defined on such manifolds as a modification of a new representation recently obtained for the canonical operator by the present authors together with A. I. Shafarevich (Dokl. Ross. Akad. Nauk 46 (6), 641-644 (2016)); (iii) the projection of the Lagrangian manifold onto the configuration plane specifies a bounded oscillation region, whose boundary (which is naturally referred to as the leading edge front) is determined by the Hamiltonians corresponding to the limit wave equations; (iv) the leading edge front is a special caustic, which possibly contains stronger focal points. These observations, together with earlier results, lead to efficient formulas for the wave field in a neighborhood of the leading edge front.
Brambilla, Michele
2013-01-01
Numerical Stochastic Perturbation Theory was able to get three- (and even four-) loop results for finite Lattice QCD renormalization constants. More recently, a conceptual and technical framework has been devised to tame finite size effects, which had been reported to be significant for (logarithmically) divergent renormalization constants. In this work we present three-loop results for fermion bilinears in the Lattice QCD regularization defined by tree-level Symanzik improved gauge action and n_f=2 Wilson fermions. We discuss both finite and divergent renormalization constants in the RI'-MOM scheme. Since renormalization conditions are defined in the chiral limit, our results also apply to Twisted Mass QCD, for which non-perturbative computations of the same quantities are available. We emphasize the importance of carefully accounting for both finite lattice space and finite volume effects. In our opinion the latter have in general not attracted the attention they would deserve.
What scientists can learn from Plato's Symposium
van Emmerik, Tim
2015-04-01
Conferences and scientific meetings are as old as science itself. The ancient Greeks where (in)famous for organizing so-called symposiums. During a symposium (from Greek, drinking together), attendees followed a program that contained both social and scientific aspects, focused around a certain topic. Whilst drinking and eating, all participants were expected to share their vision on the topic of interest by giving an oral presentation. The goal of these meetings was to arrive at a new common understanding and to come closer to the truth. Plato et al. knew very well how to organize an effective scientific conference, which should make use overthink the way we are organizing present-day conferences. Scientific meetings aim to connect researchers, share research and unravel the truth. The question is now: how do we get this done effectively? Plato knew that discussing science with strangers is difficult and he believed that talking about heavy matter could be done best when combined with social events. What if we try to go back to the times of Plato and model our conferences after the ancient symposiums? We might drop laying on couches and covering ourselves in ivy and flowers. However, a mix of social and scientific events will contribute to achieving the ultimate goal of why scientists go to conferences: to connect, to share and to unravel the truth.
Molde, H.; Zwick, D.; Muskulus, M.
2014-12-01
Support structures for offshore wind turbines are contributing a large part to the total project cost, and a cost saving of a few percent would have considerable impact. At present support structures are designed with simplified methods, e.g., spreadsheet analysis, before more detailed load calculations are performed. Due to the large number of loadcases only a few semimanual design iterations are typically executed. Computer-assisted optimization algorithms could help to further explore design limits and avoid unnecessary conservatism. In this study the simultaneous perturbation stochastic approximation method developed by Spall in the 1990s was assessed with respect to its suitability for support structure optimization. The method depends on a few parameters and an objective function that need to be chosen carefully. In each iteration the structure is evaluated by time-domain analyses, and joint fatigue lifetimes and ultimate strength utilization are computed from stress concentration factors. A pseudo-gradient is determined from only two analysis runs and the design is adjusted in the direction that improves it the most. The algorithm is able to generate considerably improved designs, compared to other methods, in a few hundred iterations, which is demonstrated for the NOWITECH 10 MW reference turbine.
From Plato to Orwell: Utopian Rhetoric in a Dystopian World.
Deatherage, Scott
Plato's "Republic" and George Orwell's "1984" both posit visionary worlds, one where humans are virtuous and understand what Plato refers to as "the Good," and the other where citizens are pawns of a government which uses language as a form of tyranny and control. Despite these overarching differences in philosophical…
A Summary of Plato Curriculum and Research Materials.
Lyman, Elisabeth R.
PLATO (programmed Logic for Automatic Teaching Operations) is a computer-based teaching system which was developed in the Coordinated Science Laboratory at the University of Illinois to explore the possibilities of automation in individual instruction. The history of the PLATO program is summarized here, along with a list of courses which used…
From Plato to Orwell: Utopian Rhetoric in a Dystopian World.
Deatherage, Scott
Plato's "Republic" and George Orwell's "1984" both posit visionary worlds, one where humans are virtuous and understand what Plato refers to as "the Good," and the other where citizens are pawns of a government which uses language as a form of tyranny and control. Despite these overarching differences in philosophical…
Plato the Pederast: Rhetoric and Cultural Procreation in the Dialogues.
Ervin, Elizabeth
1993-01-01
Examines Plato's Dialogues by reading them through two cultural lenses: the role of eros in classical Greece and its analogous relationship to language and rhetoric; and the educational function of eros within the ancient institution of pederasty. Shows how the cultural values of ancient Greece manifested themselves in Plato's erotic educational…
Plato's Philosophy of Education and the Common Core Debate
Murphy, Madonna M.
2015-01-01
This paper examines Plato's Philosophy of Education asking what he would say about the current Common Core initiative which is to better help students to become college and career ready. Plato would be in favor of the common core in as much as the standards are tied to specific skills needed in various career jobs as he was a proponent of…
Fourth Summative Report of the Delaware PLATO Project.
Hofstetter, Fred T.
A brief history of the Delaware PLATO project and descriptions of new developments in facilities, applications, user services, research, evaluation, and courseware produced since the Third Summative Report (1978) are provided, as well as an overview of PLATO applications at the University of Delaware. Sample lessons, illustrations, and activity…
Fifth Summative Report of the Delaware PLATO Project.
Hofstetter, Fred T.
A brief history of the Delaware PLATO project and descriptions of the new developments in facilities, applications, user services, research, evaluation, and courseware produced since the Fourth Summative Report (1979) are provided, as well as an overview of PLATO applications at the University of Delaware. Sample lessons, illustrations, and…
Third Summative Report of the Delaware PLATO Project.
Hofstetter, Fred T.
Descriptions of new developments in the areas of facilities, applications, user services, support staff, research, evaluation, and courseware production since the Second Summative Report (1977) are provided, as well as a summative overview of PLATO applications at the University of Delaware. Through the purchase of its own PLATO system, this…
Plato's ghost the modernist transformation of mathematics
Gray, Jeremy
2008-01-01
Plato's Ghost is the first book to examine the development of mathematics from 1880 to 1920 as a modernist transformation similar to those in art, literature, and music. Jeremy Gray traces the growth of mathematical modernism from its roots in problem solving and theory to its interactions with physics, philosophy, theology, psychology, and ideas about real and artificial languages. He shows how mathematics was popularized, and explains how mathematical modernism not only gave expression to the work of mathematicians and the professional image they sought to create for themselves, but how modernism also introduced deeper and ultimately unanswerable questions
Pemikiran Epistemologi Barat: dari Plato Sampai Gonseth
Directory of Open Access Journals (Sweden)
Nunu Burhanuddin
2015-06-01
Full Text Available This paper riviewing the Western epistemology thought. The theme focuses on Plato to Gonseth. The Epistemology that referred in this article, is to think about "how humans acquire knowledge?". From this then appear four types of sect modern western epistemology thought, namely: sect of empiricism, rationalism sect, kantinian sect, sect of positivism. Furthermore, the social positivism sciences developed by Comte leaves serious problems associated with the loss of the role of the subject. This problem being the background of epistemology philosophy appears that by Emund Husserl developed through the phenomenology, Habermas through hermeneutics, and Ferdinand Gonseth through critical theory.
Rauer, H; Aerts, C; Appourchaux, T; Benz, W; Brandeker, A; Christensen-Dalsgaard, J; Deleuil, M; Gizon, L; Güdel, M; Janot-Pacheco, E; Mas-Hesse, M; Pagano, I; Piotto, G; Pollacco, D; Santos, N C; Smith, A; -C., J; Suárez,; Szabó, R; Udry, S; Adibekyan, V; Alibert, Y; Almenara, J -M; Amaro-Seoane, P; Eiff, M Ammler-von; Antonello, E; Ball, W; Barnes, S; Baudin, F; Belkacem, K; Bergemann, M; Birch, A; Boisse, I; Bonomo, A S; Borsa, F; Brandão, I M; Brocato, E; Brun, S; Burleigh, M; Burston, R; Cabrera, J; Cassisi, S; Chaplin, W; Charpinet, S; Chiappini, C; Csizmadia, Sz; Cunha, M; Damasso, M; Davies, M B; Deeg, H J; Fialho, F de Oliveira; DÍaz, R F; Dreizler, S; Dreyer, C; Eggenberger, P; Ehrenreich, D; Eigmüller, P; Erikson, A; Farmer, R; Feltzing, S; Figueira, P; Forveille, T; Fridlund, M; García, R; Giuffrida, G; Godolt, M; da Silva, J Gomes; Goupil, M -J; Granzer, T; Grenfell, J L; Grotsch-Noels, A; Günther, E; Haswell, C A; Hatzes, A P; Hébrard, G; Hekker, S; Helled, R; Heng, K; Jenkins, J M; Khodachenko, M L; Kislyakova, K G; Kley, W; Kolb, U; Krivova, N; Kupka, F; Lammer, H; Lanza, A F; Lebreton, Y; Magrin, D; Marcos-Arenal, P; Marrese, P M; Marques, J P; Martins, J; Mathis, S; Mathur, S; Messina, S; Miglio, A; Montalban, J; Montalto, M; Monteiro, M J P F G; Moradi, H; Moravveji, E; Mordasini, C; Morel, T; Mortier, A; Nascimbeni, V; Nielsen, M B; Noack, L; Norton, A J; Ofir, A; Oshagh, M; Ouazzani, R -M; Pápics, P; Parro, V C; Petit, P; Plez, B; Poretti, E; Quirrenbach, A; Ragazzoni, R; Raimondo, G; Rainer, M; Reese, D R; Redmer, R; Reffert, S; Rojas-Ayala, B; Roxburgh, I W; Solanki, S K; Salmon, S; Santerne, A; Schneider, J; Schou, J; Schuh, S; Schunker, H; Silva-Valio, A; Silvotti, R; Skillen, I; Snellen, I; Sohl, F; Sousa, A S; Sozzetti, A; Stello, D; Strassmeier, K G; Švanda, M; Szabó, G M; Tkachenko, A; Valencia, D; van Grootel, V; Vauclair, S D; Ventura, P; Wagner, F W; Walton, N A; Weingrill, J; Werner, S C; Wheatley, P J; Zwintz, K
2013-01-01
PLATO 2.0 is a mission candidate for ESA's M3 launch opportunity (2022/24). It addresses fundamental questions such as: How do planetary systems form and evolve? Are there other systems with planets like ours, able to develop life? The PLATO 2.0 instrument consists of 34 small aperture telescopes providing a wide field-of-view and a large photometric magnitude range. It targets bright stars in wide fields to detect and characterize planets down to Earth-size by photometric transits, whose masses can then be determined by ground-based radial-velocity follow-up measurements. Asteroseismology will be performed for stars <=11mag to obtain highly accurate stellar parameters, including masses and ages. The combination of bright targets and asteroseismology results in high accuracy for the bulk planet parameters: 2%, 4-10% and 10% for planet radii, masses and ages, respectively. The foreseen baseline observing strategy includes two long pointings (2-3 years) to detect and bulk characterize planets reaching into t...
Plato on Metaphysical Explanation: Does 'Participating' Mean Nothing?
Directory of Open Access Journals (Sweden)
Christine J. Thomas
2014-12-01
Full Text Available According to Aristotle, Plato's efforts at metaphysical explanation not only fail, they are nonsensical. In particular, Plato's appeals to Forms as metaphysically explanatory of the sensibles that participate in them is "empty talk" since "'participating' means nothing" (Met. 992a28-9. I defend Plato against Aristotle's charge by identifying a particular, substantive model of metaphysical predication as the favored model of Plato's late ontology. The model posits two basic metaphysical predication relations: self-predication and participation. In order to understand the participation relation, it is important first to understand how Plato's Forms are self-predicative paradigms. According to the favored model, Forms are self-predicative paradigms insofar as they are ideal, abstract encoders of structural essences. Sensibles participate in Forms by exemplifying the structures encoded in the Forms. Given plausible conditions on metaphysical explanation, Plato's appeals to abstract Forms as metaphysically explanatory of sensibles is a reasonable competitor for Aristotle's appeals to natural, substantial forms. At the very least, Plato's appeals to a participation relation are not empty.
Technology validation of the PLATO CCD at ESA
Prod'homme, Thibaut; Verhoeve, Peter; Beaufort, Thierry; Duvet, Ludovic; Lemmel, Frederic; Smit, Hans; Blommaert, Sander; Oosterbroek, Tim; van der Luijt, Cornelis; Visser, Ivo; Heijnen, Jerko; Butler, Bart
2016-07-01
PLATO { PLAnetary Transits and Oscillations of stars { is the third medium-class mission to be selected in the European Space Agency (ESA) Science and Robotic Exploration Cosmic Vision programme. Due for launch in 2025, the payload makes use of a large format (8 cm x 8 cm) Charge-Coupled Devices (CCDs) the e2v CCD270 operated at 4 MHz. The manufacture of such large device in large quantity constitutes an unprecedented effort. To de-risk the PLATO CCD procurement and aid the mission definition process, ESA's Payload Technology Validation team is characterizing the electro-optical performance of a number of PLATO devices before and after proton irradiation.
A scientific approach to Plato's Atlantis
Directory of Open Access Journals (Sweden)
Massimo Rapisarda
2015-09-01
Full Text Available The myth of Atlantis is hard to die. This attempt to use scientific evidence to give it the final smash ends up with the doubt that it might not be totally unsubstantiated. The time of the supposed existence of Atlantis (around twelve thousand years ago was, in fact, characterized by technological revolutions, acknowledged by archaeology, and abrupt climate changes, documented by geology. In principle, it cannot therefore be ruled out that some of those dramatic events left a memory, later used by Plato as a basis for its tale. The climate changes involved the majority of the northern hemisphere, thus all the ancient civilizations (Egyptian, Mesopotamian, Indian and Chinese could have preserved reminiscence, but it is clear that the events occurring closer to Greece would have been more accessible to Plato. Among the Mediterranean sites that experienced the cataclysms of the beginning of the Holocene, a good candidate to host a primordial civilization might have been the archipelago then existing in the Strait of Sicily, a natural maritime link between Tunisia and Italy, prized by the presence of an obsidian source at Pantelleria. Eleven thousand five hundred years ago, a sudden sea level rise erased the archipelago, submerging the possible settlements, but Pantelleria obsidian ores are still there and could provide a significant clue. In fact, the potential discovery of artefacts, originating from a source now submerged by the sea level rise, would imply that the collection of the mineral took place when it was still emerged, namely at the time of Atlantis. Even if such discovery would not be sufficient to prove the existence of the mythical island, it would be enough to shake up the timeline of the human occupation in the region.
Intra-Socratic Polemics: The Symposia of Plato and Xenophon
Directory of Open Access Journals (Sweden)
Gabriel Danzig
2010-11-01
Full Text Available Textual relationships between the two Symposia suggest that Xenophon wrote first, prompting Plato to write Socrates' critique of Phaedrus, to which Xenophon responded by appending his ch. 8.
Rationality and Motivation: Moral Psychology in Plato's Socratic Dialogues
Ivars Neiders
2011-01-01
"Rationality and Motivation: Moral Psychology in Plato's Socratic Dialogues" Annotation The dissertation "Rationality and Motivation: Moral Psychology in Plato's Socratic Dialogues" is a philosophical study of Socratic views in moral psychology. Particular attention is paid to what the author calls (1) Doxastic competence and (2) Orectic competence. It is argued that according to Socrates these two different epistemic relations are important aspects of our self-understanding. The doxast...
What Plato and Murdoch Think About Love
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Shadi Shakouri
2012-07-01
Full Text Available There are many interpretations of love and lots of scholars write and talk on love; however, what exactly is the meaning of love? Iris Murdoch’s works are an accumulation of emotional relationships and feelings of love. Her great subject is love, both sexual and non-sexual, and her characters are the portrayal of a small group of people caught up in convoluted ties of love and hate, with Eros ruling over them (Cohen 22. Murdoch was one of the most respected British writers and philosophers of the second half of the twentieth century and, of course, the postwar period. In Murdoch’s novels, love is one of the central themes—marriage, as the institution of love, more often binds than frees. Her characters are mainly ego-centric people who struggle to love and are often overwhelmed by the factor of self-obsession, jealousy, ambition, fascination with suffering and charismatic power. They are absolutely ordinary people with a consuming demand for love, and mental and physical exile. Murdoch was inspired by Plato’s ideas in many ways. Like art, here again Plato’s idea of love is more skeptical than Murdoch’s, whereas Murdoch kept it only as a way to the Good, creation, and happiness. Murdoch and Plato saw love more as a Freudian concept, the Eros, the word that comes from the name of the first Greek god of love. Both the philosophers, Plato and Murdoch, believed that this erotic longing and desires revived by Eros can led to a new direction, a way toward virtue and truth. Her protagonist or marginalized characters are usually tackling it with either vulgarity or the heavenly, which results in creation, art or salvation. Murdoch, as a major moral philosopher, usually grasps the chances to encapsulate her moral visions in her works, and created novels that should be counted as meditations on human love and goodness. Keywords: Eros, erotic love and real artwork, moral philosopher, The Black Prince
Reversing Plato’s Anti-Democratism: Castoriadis’ “Quirky” Plato
Wendy C. Hamblet
2008-01-01
This paper considers the conflicting "loves" of Cornelius Castoriadis--his love for the ancients, and especially Plato, and for the common person of the demos. A detailed study of Castoriadis' analysis of Plato's Statesman exposes that Castoriadis attempts to resolve the paradox by rereading Plato as a radical democrat. I argue that this unorthodox reading is at best "quirky, " (a charge Castoriadis levels at Plato) at worst a groundless sophism. However, I conjecture that Castoriadis' readin...
Eugenics concept: from Plato to present.
Güvercin, C H; Arda, B
2008-01-01
All prospective studies and purposes to improve cure and create a race that would be exempt of various diseases and disabilities are generally defined as eugenic procedures. They aim to create the "perfect" and "higher" human being by eliminating the "unhealthy" prospective persons. All of the supporting actions taken in order to enable the desired properties are called positive eugenic actions; the elimination of undesired properties are defined as negative eugenics. In addition, if such applications and approaches target the public as a whole, they are defined as macro-eugenics. On the other hand, if they only aim at individuals and/or families, they are called micro-eugenics. As generally acknowledged, Galton re-introduced eugenic proposals, but their roots stretch as far back as Plato. Eugenic thoughts and developments were widely accepted in many different countries beginning with the end of the 19th to the first half of the 20th centuries. Initially, the view of negative eugenics that included compulsory sterilizations of handicapped, diseased and "lower" classes, resulted in tens of thousands being exterminated especially in the period of Nazi Germany. In the 1930s, the type of micro positive eugenics movement found a place within the pro-natalist policies of a number of countries. However, it was unsuccessful since the policy was not able to become effective enough and totally disappeared in the 1960s. It was no longer a fashionable movement and left a deep impression on public opinion after the long years of war. However, developments in genetics and its related fields have now enabled eugenic thoughts to reappear under the spotlight and this is creating new moral dilemmas from an ethical perspective.
Positure in Plato's Laws: An Introduction to Figuration on Civic Education
Hall, Joshua M.
2016-01-01
Purpose: The aim of the research was to determine the benefits of applying the new Figuration philosophy of dance, based in part on Plato, to civic education. Design/methodology: A close phenomenological reading of Plato's "The Laws," with a strategic focus on its account of the concept of posture. Findings: Plato considers posture to be…
Plato's Cosmic Theology: A Rationale for a Polytheistic Astrology?
Henriques, André
2015-05-01
Plato's cosmology influenced classical astronomy and religion, but was in turn influenced by the polytheistic context of its time. Throughout his texts, including the cosmological treatise Timaeus, and the discussions on the soul in the Phaedrus, Plato (c.428-c.348 BC) established what can be generalised as Platonic cosmological thought. An understanding of the philosophical and mythical levels of Platonic thought can provide a rationale for polytheistic and astrological worldviews, pointing to some cosmological continuity, alongside major shifts, from ancient Greek religion to the astrological thought of ancient astronomers such as Claudius Ptolemy.
ESA's CCD test bench for the PLATO mission
Beaufort, Thierry; Duvet, Ludovic; Bloemmaert, Sander; Lemmel, Frederic; Prod'homme, Thibaut; Verhoeve, Peter; Smit, Hans; Butler, Bart; van der Luijt, Cornelis; Heijnen, Jerko; Visser, Ivo
2016-08-01
PLATO { PLAnetary Transits and Oscillations of stars { is the third medium-class mission to be selected in the European Space Agency (ESA) Science and Robotic Exploration Cosmic Vision programme. Due for launch in 2025, the payload makes use of a large format (8 cm x 8 cm) Charge-Coupled Devices (CCDs), the e2v CCD270 operated at 4 MHz and at -70 C. To de-risk the PLATO CCD qualification programme initiated in 2014 and support the mission definition process, ESA's Payload Technology Validation section from the Future Missions Office has developed a dedicated test bench.
A Data Bank Experience on the PLATO System.
Schwab, Wallace; St-Denis, Richard
1980-01-01
Current theories on terminology and lexicography which underlie the logical components of the terminology bank set up on the PLATO system and established standards are briefly presented. The units that were essential to developing the bank are discussed. References are listed. (Author)
Plato and Play: Taking Education Seriously in Ancient Greece
D'Angour, Armand
2013-01-01
In this article, the author outlines Plato's notions of play in ancient Greek culture and shows how the philosopher's views on play can be best appreciated against the background of shifting meanings and evaluations of play in classical Greece. Play--in various forms such as word play, ritual, and music--proved central to the development of…
Stonecutter Mills, Inc., Isothermal Community College. PLATO Evaluation Series.
Sherman, Greg
Stonecutter Mills, Inc., is a textile manufacturing company with a major production facility in Spindale, North Carolina. In the past few years, Stonecutter Mills employees have been given an opportunity to spend up to 2 hours a week on company time to participate in PLATO-supported learning at Isothermal Community College. Employees could choose…
Future development of the PLATO Observatory for Antarctic science
Ashley, Michael C. B.; Bonner, Colin S.; Everett, Jon R.; Lawrence, Jon S.; Luong-Van, Daniel; McDaid, Scott; McLaren, Campbell; Storey, John W. V.
2010-07-01
PLATO is a self-contained robotic observatory built into two 10-foot shipping containers. It has been successfully deployed at Dome A on the Antarctic plateau since January 2008, and has accumulated over 730 days of uptime at the time of writing. PLATO provides 0.5{1kW of continuous electrical power for a year from diesel engines running on Jet-A1, supplemented during the summertime with solar panels. One of the 10-foot shipping containers houses the power system and fuel, the other provides a warm environment for instruments. Two Iridium satellite modems allow 45 MB/day of data to be transferred across the internet. Future enhancements to PLATO, currently in development, include a more modular design, using lithium iron-phosphate batteries, higher power output, and a light-weight low-power version for eld deployment from a Twin Otter aircraft. Technologies used in PLATO include a CAN (Controller Area Network) bus, high-reliability PC/104 com- puters, ultracapacitors for starting the engines, and fault-tolerant redundant design.
The CGE-PLATO Electronic Laboratory Station Structure and Operation.
Neal, J. P.
An electronic laboratory station was designed for student use in learning electronic instrumentation and measurement by means of the computer-guided experimentation (CGE) system. The station features rack-mounted electronic laboratory equipment on a laboratory table adjacent to a PLATO IV terminal. An integrated logic system behind the laboratory…
Pursuing the Good, Ethics and Metaphysics in Plato s Republic
Institute of Scientific and Technical Information of China (English)
Douglas; Cairns; Fritz-Gregor; Herrmann; Terry; Penner
2008-01-01
‘Pursuing the good’ is an old subject in both social history of ancient Greece and Greek philosophy studies. There is hardly anything new when we talk about virtue or morality in the time of Plato and Aristotle. In the area of Greek history, many books and articles on or relevant to that
Eschatological narrative in Plato: between logos and myth
Directory of Open Access Journals (Sweden)
Francesc Casadesús Bordoy
2016-08-01
Full Text Available In his dialogues, Plato frequently resorted to alternate and intertwine his dialectic expositions with images and allegories, aiming to illustrate his arguments. This paper analyses in detail his use of the opposition between logos and myth tointroduce his descriptions of Hades
Go Tell Alcibiades: Tragedy, Comedy, and Rhetoric in Plato's "Symposium"
Crick, Nathan; Poulakos, John
2008-01-01
Plato's "Symposium" is a significant but neglected part of his elaborate and complex attitude toward rhetoric. Unlike the intellectual discussion of the "Gorgias" or the unscripted conversation of the "Phaedrus," the "Symposium" stages a feast celebrating and driven by the forces of "Eros." A luxuriously stylish performance rather than a rational…
The Cost of PLATO in a University Environment.
Hofstetter, Fred T.
1983-01-01
This analysis of the cost-effectiveness of the University of Delaware's own PLATO system discusses the initial expense of acquiring the system, decreases in unit cost as number of users increased, capital investment in hardware, expenditures and funding sources, comparisons of actual and projected costs, and benefits of individualized instruction.…
Second Summative Report of the Delaware PLATO Project.
Hofstetter, Fred T.
Begun on an experimental basis in March 1975, the ongoing PLATO project at the University of Delaware has become an established part of the University's academic program. This descriptive report is divided into three sections: (1) project history and development, including organization, utilization, instructor and author training, and projections…
Dodecahedrane—The chemical transliteration of Plato's universe (A Review)
Paquette, Leo A.
1982-07-01
The development of chemical interest in three of Plato's five convex polyhedra is described from an historical perspective. The successful synthesis of 1,16-dimethyldodecahedrane and its structural characteristics are outlined. Finally, an account of recent work leading to the still more aesthetically appealing and ultrasymmetric parent dodecahedrane is given.
Instantaneous stochastic perturbation theory
Lüscher, Martin
2015-01-01
A form of stochastic perturbation theory is described, where the representative stochastic fields are generated instantaneously rather than through a Markov process. The correctness of the procedure is established to all orders of the expansion and for a wide class of field theories that includes all common formulations of lattice QCD.
Arete and physics: The lesson of Plato's "Timaeus"
Wolfe, John R.
Plato's Timaeus is traditionally read as a work dedicated to the sole purpose of describing the origin and nature of the cosmos, as a straightforward attempt by Plato to produce a peri phuseos treatise. In accord with this reading, the body of Timaeus' monologue is then seen as nothing more than an attempt by Plato to convey his own cosmological doctrines. I propose an alternative to the view that the Timaeus is nothing more than a textbook of Platonic physics. The Timaeus is rather squarely focused on the human being, in her moral and political dimensions, and on her relation to the natural world as a whole. Ultimately, this account of the human being is intended to provide part of the answer to the question of how society can produce good citizens and leaders, and thus serves to provide a theoretical basis for the practices of paideia. When viewed in this light many of the curious features of the Timaeus appear less strange. The various parts of the dialogue: the dramatic introduction, Critias' tale of the Ancient Athenians, and Timaeus' monologue can be seen as each contributing to an investigation of a single topic. It further allows us to understand why Plato chooses to employ Timaeus the Locrian as the principle speaker of the dialogue rather than Socrates. Finally, when read in this way, the Timaeus no longer appears as an outlier in the Platonic corpus, as a work devoted to a radically different subject matter than the rest of his writings. It can be seen as dedicated to the same issues which preoccupied Plato throughout his entire life, as about the determination of the best life and providing the tools with which to realize it.
Quinn, Bill; Foshay, Rob; Morris, Barbara
The "PLATO[R] Math Expeditions" and "PLATO[R] Projects for the Real World" curricula are designed to implement effective, research-based instructional practices. "Math Expeditions" is designed to give elementary grade users the mathematics skills and practice needed to solve real-life problems. Across the eight…
THE JOURNEY OF TRUTH: FROM PLATO TO ZOLA
Directory of Open Access Journals (Sweden)
Ribut Basuki
1999-01-01
Full Text Available Western theater theory and criticism is generally considered to be set forth by the Greeks. Plato was "the first theater critic" with his negative comments about theater owing to his idealistic views about "the truth." Then came Aristotle who used a different viewpoint from that of Plato, saying that there is "truth" in theater. However, hostile criticism on theater came back in the Middle Ages, championed by Tertulian before Aristotelian theory was revived by the neo-classicists such as Scaliger and Castelvetro. Theater theory and criticism discourse was then made more alive by the romanticists who disagreed with the neo-classicists' rigid rules on theater. As the influence of science became dominant in the theater world, naturalism and realism emerged and became the mainstream of theater theory and criticism until well into the twentieth century.
The necessity of dialectics according to Plato and Adorno
DEFF Research Database (Denmark)
Olsen, Anne-Marie Eggert
2009-01-01
The paper deals with the notion of philosophy as, on the one hand, an academic or scientific discipline and, on the other, something perhaps superior to the disciplines and in any case dealing with what is not a 'disciplinary' matter. Through an interpretation of Plato's concept of dialectics and...... and Adorno's understanding of philosophy as expression (Ausdruck) it is proposed that this two-fold nature of philosophy is what makes dialectics necessary....
Optical and dark characterization of the PLATO CCD at ESA
Verhoeve, Peter; Prod'homme, Thibaut; Oosterbroek, Tim; Duvet, Ludovic; Beaufort, Thierry; Blommaert, Sander; Butler, Bart; Heijnen, Jerko; Lemmel, Frederic; van der Luijt, Cornelis; Smit, Hans; Visser, Ivo
2016-07-01
PLATO - PLAnetary Transits and Oscillations of stars - is the third medium-class mission (M3) to be selected in the European Space Agency (ESA) Science and Robotic Exploration Cosmic Vision programme. It is due for launch in 2025 with the main objective to find and study terrestrial planets in the habitable zone around solar-like stars. The payload consists of >20 cameras; with each camera comprising 4 Charge-Coupled Devices (CCDs), a large number of flight model devices procured by ESA shall ultimately be integrated on the spacecraft. The CCD270 - specially designed and manufactured by e2v for the PLATO mission - is a large format (8 cm x 8 cm) back-illuminated device operating at 4 MHz pixel rate and coming in two variants: full frame and frame transfer. In order to de-risk the PLATO CCD procurement and aid the mission definition process, ESA's Payload Technology Validation section is currently validating the PLATO CCD270. This validation consists in demonstrating that the device achieves its specified electrooptical performance in the relevant environment: operated at 4 MHz, at cold and before and after proton irradiation. As part of this validation, CCD270 devices have been characterized in the dark as well as optically with respect to performance parameters directly relevant for the photometric application of the CCDs. Dark tests comprise the measurement of gain sensitivity to bias voltages, charge injection tests, and measurement of hot and variable pixels after irradiation. In addition, the results of measurements of Quantum Efficiency for a range of angles of incidence, intra- pixel response (non-)uniformity, and response to spot illumination, before and after proton irradiation. In particular, the effect of radiation induced degradation of the charge transfer efficiency on the measured charge in a star-like spot has been studied as a function of signal level and of position on the pixel grid, Also, the effect of various levels of background light on the
Resummation of Cactus Diagrams in Lattice QCD
Panagopoulos, H
1998-01-01
We show how to perform a resummation, to all orders in perturbation theory, of a certain class of gauge invariant diagrams in Lattice QCD. These diagrams are often largely responsible for lattice artifacts. Our resummation leads to an improved perturbative expansion. Applied to a number of cases of interest, this expansion yields results remarkably close to corresponding nonperturbative estimates.
The Philosopher's Arete or theStructure of Plato's Parmenides
Directory of Open Access Journals (Sweden)
Raúl Gutierrez
1998-12-01
Full Text Available The controversy conceming the unity of Plato's Parmenides and the meaning of its first part is stillongoing. The A. proposes a solution, pointing out its structural coincidence with the Republic's simile of the line. This leads him to confine young Socrates in the segment that corresponds to óuivoux and old Parmenides in the vór¡olc; segment. As the one who "possesses insight" of truth based on his apprehension of the One-Good. Parmenides is the actual representative of the philosopher's arete.
Perfect and Quasi-Perfect Lattice Actions
Bietenholz, W
1998-01-01
Perfect lattice actions are exiting with several respects: they provide new insight into conceptual questions of the lattice regularization, and quasi-perfect actions could enable a great leap forward in the non-perturbative solution of QCD. We try to transmit a flavor of them, also beyond the lattice community.
Tibial plato leveling osteotomy / Osteotomia de nivelamento do plato da tíbia
Directory of Open Access Journals (Sweden)
Julia Maria Matera
2008-08-01
Full Text Available The tibial plateau leveling osteotomy (TPLO is a relatively new and innovative surgical treatment for the cranial cruciate ligament rupture in the canine species. The real intent of the procedure is to provide functional stability to the stifle joint by eliminating or neutralizing the cranial tibial thrust during weight bearing instead to restore the cranial cruciate ligament function. The proposal of this study is to report a review of the TPLO procedure, emphasizing procedure, surgical technique, post operative care and complications. The TPLO procedure consists in a radial osteotomy in the tibial plato and rotation of the caudal plateau in order to obtain a desired angle. After the leveling of the tibial plateau, a bone plate and screws are used to stabilize the osteotomy until bone is healed up. The complications that have been associated with the procedure include tibial tuberosity fracture and patellar tendon tendinosis. This procedure has become increasingly more popular for surgical treatment of cranial cruciate ligament injuries in large breed dog. The long term clinical results have not been completely elucidated yet. It has been showed that this technique doesn’t halt the degenerative joint disease.A osteotomia do platô da tíbia (TPLO é um tratamento relativamente novo e inovador para a ruptura do ligamento cruzado cranial (RLCC na espécie canina. Ao invés de restaurar a função do ligamento, o procedimento promove estabilidade funcional para a articulação do joelho, por eliminar ou neutralizar a força tibial cranial durante a sustentação de peso. A proposta do presente estudo é revisar a técnica de TPLO, enfatizando o procedimento, técnica cirúrgica, cuidados pós-operatórios e complicações. A técnica da TPLO consiste na realização de uma osteotomia circular do platô da tíbia com rotação de sua porção caudal até a obtenção do ângulo desejado. Após o nivelamento do platô da tíbia, placa e parafusos
Reversing Plato’s Anti-Democratism: Castoriadis’ “Quirky” Plato
Directory of Open Access Journals (Sweden)
Hamblet, Wendy C.
2008-12-01
Full Text Available This paper considers the conflicting "loves" of Cornelius Castoriadis--his love for the ancients, and especially Plato, and for the common person of the demos. A detailed study of Castoriadis' analysis of Plato's Statesman exposes that Castoriadis attempts to resolve the paradox by rereading Plato as a radical democrat. I argue that this unorthodox reading is at best "quirky, " (a charge Castoriadis levels at Plato at worst a groundless sophism. However, I conjecture that Castoriadis' reading may not constitute a serious attempt to describe a Platonic politics, so much as a prescriptive reading of what otherwise might have been, given certain strands of political generosity evident elsewhere in Plato's corpus.
Applications Of Chiral Perturbation Theory
Mohta, V
2005-01-01
Effective field theory techniques are used to describe the spectrum and interactions of hadrons. The mathematics of classical field theory and perturbative quantum field theory are reviewed. The physics of effective field theory and, in particular, of chiral perturbation theory and heavy baryon chiral perturbation theory are also reviewed. The geometry underlying heavy baryon chiral perturbation theory is described in detail. Results by Coleman et. al. in the physics literature are stated precisely and proven. A chiral perturbation theory is developed for a multiplet containing the recently- observed exotic baryons. A small coupling expansion is identified that allows the calculation of self-energy corrections to the exotic baryon masses. Opportunities in lattice calculations are discussed. Chiral perturbation theory is used to study the possibility of two multiplets of exotic baryons mixed by quark masses. A new symmetry constraint on reduced partial widths is identified. Predictions in the literature based ...
Energy Technology Data Exchange (ETDEWEB)
ORGINOS,K.
2003-01-07
I review the current status of hadronic structure computations on the lattice. I describe the basic lattice techniques and difficulties and present some of the latest lattice results; in particular recent results of the RBC group using domain wall fermions are also discussed. In conclusion, lattice computations can play an important role in understanding the hadronic structure and the fundamental properties of Quantum Chromodynamics (QCD). Although some difficulties still exist, several significant steps have been made. Advances in computer technology are expected to play a significant role in pushing these computations closer to the chiral limit and in including dynamical fermions. RBC has already begun preliminary dynamical domain wall fermion computations [49] which we expect to be pushed forward with the arrival of QCD0C. In the near future, we also expect to complete the non-perturbative renormalization of the relevant derivative operators in quenched QCD.
Radiation, Thermal Gradient and Weight: a threefold dilemma for PLATO
Magrin, Demetrio; Ragazzoni, Roberto; Bruno, Giordano; Piazza, Daniele; Borsa, Francesco; Ghigo, Mauro; Mogulsky, Valery; Bergomi, Maria; Biondi, Federico; Chinellato, Simonetta; Dima, Marco; Farinato, Jacopo; Greggio, Davide; Gullieuszik, Marco; Marafatto, Luca; Viotto, Valentina; Munari, Matteo; Pagano, Isabella; Sicilia, Daniela; Basso, Stefano; Spiga, Daniele; Bandy, Timothy; Brändli, Mathias; Benz, Willy; De Roche, Thierry; Rieder, Martin; Brandeker, Alexis; Klebor, Maximilian; Schweitzer, Mario; Wieser, Matthias; Erikson, Anders; Rauer, Heike
2016-07-01
The project PLAnetary Transits and Oscillations of stars (PLATO) is one of the selected medium class (M class) missions in the framework of the ESA Cosmic Vision 2015-2025 program. The mean scientific goal of PLATO is the discovery and study of extrasolar planetary systems by means of planetary transits detection. The opto mechanical subsystem of the payload is made of 32 normal telescope optical units (N-TOUs) and 2 fast telescope optical units (FTOUs). The optical configuration of each TOU is an all refractive design based on six properly optimized lenses. In the current baseline, in front of each TOU a Suprasil window is foreseen. The main purposes of the entrance window are to shield the following lenses from possible damaging high energy radiation and to mitigate the thermal gradient that the first optical element will experience during the launch from ground to space environment. In contrast, the presence of the window increases the overall mass by a non-negligible quantity. We describe here the radiation and thermal analysis and their impact on the quality and risks assessment, summarizing the trade-off process with pro and cons on having or dropping the entrance window in the optical train.
Manufacturing and alignment tolerance analysis through Montecarlo approach for PLATO
Magrin, Demetrio; Ragazzoni, Roberto; Bergomi, Maria; Biondi, Federico; Chinellato, Simonetta; Dima, Marco; Farinato, Jacopo; Greggio, Davide; Gullieuszik, Marco; Marafatto, Luca; Viotto, Valentina; Munari, Matteo; Pagano, Isabella; Sicilia, Daniela; Basso, Stefano; Borsa, Francesco; Ghigo, Mauro; Spiga, Daniele; Bandy, Timothy; Brändli, Mathias; Benz, Willy; Bruno, Giordano; De Roche, Thierry; Piazza, Daniele; Rieder, Martin; Brandeker, Alexis; Klebor, Maximilian; Mogulsky, Valery; Schweitzer, Mario; Wieser, Matthias; Erikson, Anders; Rauer, Heike
2016-07-01
The project PLAnetary Transits and Oscillations of stars (PLATO) is one of the selected medium class (M class) missions in the framework of the ESA Cosmic Vision 2015-2025 program. The main scientific goal of PLATO is the discovery and study of extrasolar planetary systems by means of planetary transits detection. According to the current baseline, the scientific payload consists of 34 all refractive telescopes having small aperture (120mm) and wide field of view (diameter greater than 37 degrees) observing over 0.5-1 micron wavelength band. The telescopes are mounted on a common optical bench and are divided in four families of eight telescopes with an overlapping line-of-sight in order to maximize the science return. Remaining two telescopes will be dedicated to support on-board star-tracking system and will be specialized on two different photometric bands for science purposes. The performance requirement, adopted as merit function during the analysis, is specified as 90% enclosed energy contained in a square having size 2 pixels over the whole field of view with a depth of focus of +/-20 micron. Given the complexity of the system, we have followed a Montecarlo analysis approach for manufacturing and alignment tolerances. We will describe here the tolerance method and the preliminary results, speculating on the assumed risks and expected performances.
Kozma, Gady
2012-01-01
We proved earlier that every measurable function on the circle, after a uniformly small perturbation, can be written as a power series (i.e. a series of exponentials with positive frequencies), which converges almost everywhere. Here we show that this result is basically sharp: the perturbation cannot be made smooth or even H\\"older. We discuss also a similar problem for perturbations with lacunary spectrum.
Volume reduction through perturbative Wilson loops
Perez, Margarita Garcia; Okawa, Masanori
2016-01-01
We derive the perturbative expansion of Wilson loops to order g^4 in a SU(N) lattice gauge theory with twisted boundary conditions. Our expressions show that the thermodynamic limit is attained at infinite N for any number of lattice sites and allow to quantify the deviations from volume independence at finite large N as a function of the twist.
Love as an Object of Initiation in Plato's Philosophy
Directory of Open Access Journals (Sweden)
Euaggelia Maraggianou
2007-07-01
Full Text Available Initiation ( muvhsh was the first stage of the ancient mysteries celebrating Demeter, the earth-goddess, and her daughter Kore, soon identified with Persephone or Persephasa, a pre-Greek deity of the underworld. Next came the stage of contemplation ( ejpopteiva , at which worshippers were shown a vision of the goddess of Hades. This led them to identify themselves with her, thus reaching the highest form of happiness. The Eleusinian Mysteries were inseparably linked to the Orphic doctrine, which in its turn influenced the thought of Plato. Plato sees love as an object of initiation and as one of the greatest mysteries of human existence. Plato’s dialogues, Phaedrus and Symposium, contain expressions borrowed directly from the vocabulary of the Mysteries. Although neither Socrates in Phaedrus nor Diotima in Symposium make any explicit reference to the mystic ceremonies, it is certain that both allude to them in expounding the mysteries of spiritual life. The latter has to start at the stage of physical love in order to end up in the contemplation of Ideas. The mystery into which Socrates is initiated by Diotima is the following: there is a mystic stairway leading from the earth to the sky, from man to God. It is made visible by Love, and its steps are represented by different kinds of beauty. The ascent is a gradual one, with a long stop at each of the stages. In this way Love, disciplined by philosophy and spiritualised by increasing de-personalisation, ends up in the Intellectual, conceiving the latter with an intuitive insight. By this spiritual process, one is purified, led to the road of salvation and enabled to participate in the Divine.
PLATO as it is : A legacy mission for Galactic archaeology
Miglio, A.; Chiappini, C.; Mosser, B.; Davies, G. R.; Freeman, K.; Girardi, L.; Jofré, P.; Kawata, D.; Rendle, B. M.; Valentini, M.; Casagrande, L.; Chaplin, W. J.; Gilmore, G.; Hawkins, K.; Holl, B.; Appourchaux, T.; Belkacem, K.; Bossini, D.; Brogaard, K.; Goupil, M.-J.; Montalbán, J.; Noels, A.; Anders, F.; Rodrigues, T.; Piotto, G.; Pollacco, D.; Rauer, H.; Prieto, C. Allende; Avelino, P. P.; Babusiaux, C.; Barban, C.; Barbuy, B.; Basu, S.; Baudin, F.; Benomar, O.; Bienaymé, O.; Binney, J.; Bland-Hawthorn, J.; Bressan, A.; Cacciari, C.; Campante, T. L.; Cassisi, S.; Christensen-Dalsgaard, J.; Combes, F.; Creevey, O.; Cunha, M. S.; Jong, R. S.; Laverny, P.; Degl'Innocenti, S.; Deheuvels, S.; Depagne, É.; Ridder, J.; Matteo, P. Di; Mauro, M. P. Di; Dupret, M.-A.; Eggenberger, P.; Elsworth, Y.; Famaey, B.; Feltzing, S.; García, R. A.; Gerhard, O.; Gibson, B. K.; Gizon, L.; Haywood, M.; Handberg, R.; Heiter, U.; Hekker, S.; Huber, D.; Ibata, R.; Katz, D.; Kawaler, S. D.; Kjeldsen, H.; Kurtz, D. W.; Lagarde, N.; Lebreton, Y.; Lund, M. N.; Majewski, S. R.; Marigo, P.; Martig, M.; Mathur, S.; Minchev, I.; Morel, T.; Ortolani, S.; Pinsonneault, M. H.; Plez, B.; Moroni, P. G. Prada; Pricopi, D.; Recio-Blanco, A.; Reylé, C.; Robin, A.; Roxburgh, I. W.; Salaris, M.; Santiago, B. X.; Schiavon, R.; Serenelli, A.; Sharma, S.; Aguirre, V. Silva; Soubiran, C.; Steinmetz, M.; Stello, D.; Strassmeier, K. G.; Ventura, P.; Ventura, R.; Walton, N. A.; Worley, C. C.
2017-07-01
Deciphering the assembly history of the Milky Way is a formidable task, which becomes possible only if one can produce high-resolution chrono-chemo-kinematical maps of the Galaxy. Data from large-scale astrometric and spectroscopic surveys will soon provide us with a well-defined view of the current chemo-kinematical structure of the Milky Way, but will only enable a blurred view on the temporal sequence that led to the present-day Galaxy. As demonstrated by the (ongoing) exploitation of data from the pioneering photometric missions CoRoT, Kepler, and K2, asteroseismology provides the way forward: solar-like oscillating giants are excellent evolutionary clocks thanks to the availability of seismic constraints on their mass and to the tight age-initial-mass relation they adhere to. In this paper we identify five key outstanding questions relating to the formation and evolution of the Milky Way that will need precise and accurate ages for large samples of stars to be addressed, and we identify the requirements in terms of number of targets and the precision on the stellar properties that are needed to tackle such questions. By quantifying the asteroseismic yields expected from PLATO for red-giant stars, we demonstrate that these requirements are within the capabilities of the current instrument design, provided that observations are sufficiently long to identify the evolutionary state and allow robust and precise determination of acoustic-mode frequencies. This will allow us to harvest data of sufficient quality to reach a 10% precision in age. This is a fundamental pre-requisite to then reach the more ambitious goal of a similar level of accuracy, which will only be possible if we have to hand a careful appraisal of systematic uncertainties on age deriving from our limited understanding of stellar physics, a goal which conveniently falls within the main aims of PLATO's core science.
Angiographic outcomes in the PLATO Trial (Platelet Inhibition and Patient Outcomes)
National Research Council Canada - National Science Library
Kunadian, Vijay; James, Stefan K; Wojdyla, Daniel M; Zorkun, Cafer; Wu, Jinhui; Storey, Robert F; Steg, Ph Gabriel; Katus, Hugo; Emanuelsson, Hakan; Horrow, Jay; Maya, Juan; Wallentin, Lars; Harrington, Robert A; Gibson, C Michael
2013-01-01
The PLATO (Platelet Inhibition and Patient Outcomes) angiographic substudy sought to compare the efficacy of ticagrelor versus clopidogrel with respect to angiographic outcomes before and after PCI in the setting of acute coronary syndrome...
The Legacies of Literacy: From Plato to Freire through Harvey Graff.
Gee, James Paul
1989-01-01
Reviews "The Legacies of Literacy: Continuities and Contradictions in Western Culture and Society" (Harvey G. Graff). Discusses the historical role of literacy education as a tool for liberation, emphasizing the viewpoints of Plato and Freire. (FMW)
Genesis 2–3 and Alcibiades's speech in Plato's Symposium : A ...
African Journals Online (AJOL)
Genesis 2–3 and Alcibiades's speech in Plato's Symposium : A cultural critical reading. ... interpretation can arise from the analysis of Alcibiades's speech compared to M- and LXX-Genesis ... EMAIL FREE FULL TEXT EMAIL FREE FULL TEXT
Prospects for detecting decreasing exoplanet frequency with main sequence age using PLATO
Veras, Dimitri; Mustill, Alexander J; Pollacco, Don
2015-01-01
The space mission PLATO will usher in a new era of exoplanetary science by expanding our current inventory of transiting systems and constraining host star ages, which are currently highly uncertain. This capability might allow PLATO to detect changes in planetary system architecture with time, particularly because planetary scattering due to Lagrange instability may be triggered long after the system was formed. Here, we utilize previously published instability timescale prescriptions to determine PLATO's capability to detect a trend of decreasing planet frequency with age for systems with equal-mass planets. For two-planet systems, our results demonstrate that PLATO may detect a trend for planet masses which are at least as massive as super-Earths. For systems with three or more planets, we link their initial compactness to potentially detectable frequency trends in order to aid future investigations when these populations will be better characterized.
Plato's Charmides as a Political Act: Apologetics and the Promotion of Ideology
National Research Council Canada - National Science Library
Danzig, Gabriel
2013-01-01
By showing that Critias and Socrates understood the same matters differently, Plato was able to treat seriously ideas that came to be associated with the Thirty and with Socrates while shielding himself from criticism...
Schwab, Wallace; St-Denis, Richard
1980-01-01
Describes the elements and functioning of the terminology bank of the PLATO (Programmed Loqic for Automated Teaching Operation) system. Discusses contemporary terminology and lexicography notions on which the bank is based and outlines the tasks performed through PLATERM. (MES)
Schwab, Wallace; St-Denis, Richard
1980-01-01
Describes the elements and functioning of the terminology bank of the PLATO (Programmed Loqic for Automated Teaching Operation) system. Discusses contemporary terminology and lexicography notions on which the bank is based and outlines the tasks performed through PLATERM. (MES)
Chakrabarti, J; Bagchi, B; Chakrabarti, Jayprokas; Basu, Asis; Bagchi, Bijon
2000-01-01
Fermions on the lattice have bosonic excitations generated from the underlying periodic background. These, the lattice bosons, arise near the empty band or when the bands are nearly full. They do not depend on the nature of the interactions and exist for any fermion-fermion coupling. We discuss these lattice boson solutions for the Dirac Hamiltonian.
Weisz, Peter; Majumdar, Pushan
2012-03-01
Lattice gauge theory is a formulation of quantum field theory with gauge symmetries on a space-time lattice. This formulation is particularly suitable for describing hadronic phenomena. In this article we review the present status of lattice QCD. We outline some of the computational methods, discuss some phenomenological applications and a variety of non-perturbative topics. The list of references is severely incomplete, the ones we have included are text books or reviews and a few subjectively selected papers. Kronfeld and Quigg (2010) supply a reasonably comprehensive set of QCD references. We apologize for the fact that have not covered many important topics such as QCD at finite density and heavy quark effective theory adequately, and mention some of them only in the last section "In Brief". These topics should be considered in further Scholarpedia articles.
Chiral Fermions on the Lattice
Bietenholz, Wolfgang
2010-01-01
In the last century the non-perturbative regularization of chiral fermions was a long-standing problem. We review how this problem was finally overcome by the formulation of a modified but exact form of chiral symmetry on the lattice. This also provides a sound definition of the topological charge of lattice gauge configurations. We illustrate a variety of applications to QCD in the p-, the epsilon- and the delta-regime, where simulation results can now be related to Random Matrix Theory and Chiral Perturbation Theory. The latter contains Low Energy Constants as free parameters, and we comment on their evaluation from first principles of QCD.
Hadron Physics from Lattice QCD
2016-01-01
We sketch the basic ideas of the lattice regularization in Quantum Field Theory, the corresponding Monte Carlo simulations, and applications to Quantum Chromodynamics (QCD). This approach enables the numerical measurement of observables at the non-perturbative level. We comment on selected results, with a focus on hadron masses and the link to Chiral Perturbation Theory. At last we address two outstanding issues: topological freezing and the sign problem.
A non-perturbative study of massive gauge theories
DEFF Research Database (Denmark)
Della Morte, Michele; Hernandez, Pilar
2013-01-01
We consider a non-perturbative formulation of an SU(2) massive gauge theory on a space-time lattice, which is also a discretised gauged non-linear chiral model. The lattice model is shown to have an exactly conserved global SU(2) symmetry. If a scaling region for the lattice model exists and the ...
Testing gauge-invariant perturbation theory
Törek, Pascal
2016-01-01
Gauge-invariant perturbation theory for theories with a Brout-Englert-Higgs effect, as developed by Fr\\"ohlich, Morchio and Strocchi, starts out from physical, exactly gauge-invariant quantities as initial and final states. These are composite operators, and can thus be considered as bound states. In case of the standard model, this reduces almost entirely to conventional perturbation theory. This explains the success of conventional perturbation theory for the standard model. However, this is due to the special structure of the standard model, and it is not guaranteed to be the case for other theories. Here, we review gauge-invariant perturbation theory. Especially, we show how it can be applied and that it is little more complicated than conventional perturbation theory, and that it is often possible to utilize existing results of conventional perturbation theory. Finally, we present tests of the predictions of gauge-invariant perturbation theory, using lattice gauge theory, in three different settings. In ...
Properties of the Quark Gluon Plasma: A lattice perspective
Karsch, Frithjof
2007-01-01
We discuss results from lattice calculations for a few observables that are sensitive to different length scales in the high temperature phase of QCD and can give insight into its non-perturbative structure. We compare lattice results with perturbative calculations at high temperature obtained for vanishing and non-vanishing quark chemical potential.
The PLATO Dome A site-testing observatory: Power generation and control systems
Lawrence, J. S.; Ashley, M. C. B.; Hengst, S.; Luong-van, D. M.; Storey, J. W. V.; Yang, H.; Zhou, X.; Zhu, Z.
2009-06-01
The atmospheric conditions above Dome A, a currently unmanned location at the highest point on the Antarctic plateau, are uniquely suited to astronomy. For certain types of astronomy Dome A is likely to be the best location on the planet, and this has motivated the development of the Plateau Observatory (PLATO). PLATO was deployed to Dome A in early 2008. It houses a suite of purpose-built site-testing instruments designed to quantify the benefits of Dome A site for astronomy, and science instruments designed to take advantage of the observing conditions. The PLATO power generation and control system is designed to provide continuous power and heat, and a high-reliability command and communications platform for these instruments. PLATO has run and collected data throughout the winter 2008 season completely unattended. Here we present a detailed description of the power generation, power control, thermal management, instrument interface, and communications systems for PLATO, and an overview of the system performance for 2008.
Gaia and WEAVE/WxES: Supporting the PLATO Exoplanet Hunter
Walton, N. A.
2016-10-01
This paper briefly describes the powerful linkages between the Gaia and PLATO missions and the potential for WEAVE in the study of exoplanet populations, for instance through the proposed WxES survey. Gaia successfully launched in December 2013, and over the course of its nominal five year mission will discover, via their astrometric signatures, upwards of 20 000 massive Jupiter sized long period planets at distances out to several hundred parsecs around all star types. In addition Gaia will discover up to a thousand short period hot Jupiters around M stars. PLATO, to launch in 2024, will through precision photometry, observe in detail some million host stars, and will detect, via the transit technique, planets down to Earth masses. PLATO will observe two fields of over 2 000 square degrees for 2-3 years each. At least one of these will be in the northern hemisphere. WEAVE has the potential to provide detailed chemical characterization of the host stars of the Gaia and PLATO exoplanet systems. This will enable insights into, for instance, metallicity of the host star correlations against both massive exoplanets (perhaps confirming current relationships), and lower mass exoplanets. We note how the rapid exploitation of such a potential WEAVE survey could be achieved, utilizing the WEAVE processing systems being developed at the IoA, Cambridge, coupled with efficient interfaces to both Gaia and PLATO data products, that are also being generated at the IoA.
Quantum Gravity on the Lattice
Hamber, Herbert W
2009-01-01
I review the lattice approach to quantum gravity, and how it relates to the non-trivial ultraviolet fixed point scenario of the continuum theory. After a brief introduction covering the general problem of ultraviolet divergences in gravity and other non-renormalizable theories, I cover the general methods and goals of the lattice approach. An underlying theme is an attempt at establishing connections between the continuum renormalization group results, which are mainly based on diagrammatic perturbation theory, and the recent lattice results, which should apply to the strong gravity regime and are inherently non-perturbative. A second theme in this review is the ever-present natural correspondence between infrared methods of strongly coupled non-abelian gauge theories on the one hand, and the low energy approach to quantum gravity based on the renormalization group and universality of critical behavior on the other. Towards the end of the review I discuss possible observational consequences of path integral q...
Wang, Da-Wei; Zhu, Shi-Yao; Scully, Marlan O
2014-01-01
We show that the timed Dicke states of a collection of three-level atoms can form a tight-binding lattice in the momentum space. This lattice, coined the superradiance lattice (SL), can be constructed based on an electromagnetically induced transparency (EIT) system. For a one-dimensional SL, we need the coupling field of the EIT system to be a standing wave. The detuning between the two components of the standing wave introduces an effective electric field. The quantum behaviours of electrons in lattices, such as Bloch oscillations, Wannier-Stark ladders, Bloch band collapsing and dynamic localization can be observed in the SL. The SL can be extended to two, three and even higher dimensions where no analogous real space lattices exist and new physics are waiting to be explored.
Introduction to lattice gauge theory
Gupta, R.
The lattice formulation of Quantum Field Theory (QFT) can be exploited in many ways. We can derive the lattice Feynman rules and carry out weak coupling perturbation expansions. The lattice then serves as a manifestly gauge invariant regularization scheme, albeit one that is more complicated than standard continuum schemes. Strong coupling expansions: these give us useful qualitative information, but unfortunately no hard numbers. The lattice theory is amenable to numerical simulations by which one calculates the long distance properties of a strongly interacting theory from first principles. The observables are measured as a function of the bare coupling g and a gauge invariant cut-off approx. = 1/alpha, where alpha is the lattice spacing. The continuum (physical) behavior is recovered in the limit alpha yields 0, at which point the lattice artifacts go to zero. This is the more powerful use of lattice formulation, so in these lectures the author focuses on setting up the theory for the purpose of numerical simulations to get hard numbers. The numerical techniques used in Lattice Gauge Theories have their roots in statistical mechanics, so it is important to develop an intuition for the interconnection between quantum mechanics and statistical mechanics.
Sommer, Rainer
1997-01-01
We review the O(a) improvement of lattice QCD with special emphasis on the motivation for performing the improvement programme non-perturbatively and the general concepts of on-shell improvement. The present status of the calculations of various improvement coefficients (perturbative and non-perturbative) is reviewed, as well as the computation of the isospin current normalization constants $Z_A$ and $Z_V$. We comment on recent results for hadronic observables obtained in the improved theory.
Lattice Quantum Chromodynamics
Sachrajda, C. T.
2016-10-01
I review the the application of the lattice formulation of QCD and large-scale numerical simulations to the evaluation of non-perturbative hadronic effects in Standard Model Phenomenology. I present an introduction to the elements of the calculations and discuss the limitations both in the range of quantities which can be studied and in the precision of the results. I focus particularly on the extraction of the QCD parameters, i.e. the quark masses and the strong coupling constant, and on important quantities in flavour physics. Lattice QCD is playing a central role in quantifying the hadronic effects necessary for the development of precision flavour physics and its use in exploring the limits of the Standard Model and in searches for inconsistencies which would signal the presence of new physics.
Lattices of dielectric resonators
Trubin, Alexander
2016-01-01
This book provides the analytical theory of complex systems composed of a large number of high-Q dielectric resonators. Spherical and cylindrical dielectric resonators with inferior and also whispering gallery oscillations allocated in various lattices are considered. A new approach to S-matrix parameter calculations based on perturbation theory of Maxwell equations, developed for a number of high-Q dielectric bodies, is introduced. All physical relationships are obtained in analytical form and are suitable for further computations. Essential attention is given to a new unified formalism of the description of scattering processes. The general scattering task for coupled eigen oscillations of the whole system of dielectric resonators is described. The equations for the expansion coefficients are explained in an applicable way. The temporal Green functions for the dielectric resonator are presented. The scattering process of short pulses in dielectric filter structures, dielectric antennas and lattices of d...
Lattice Quantum Chromodynamics
Sachrajda, C T
2016-01-01
I review the the application of the lattice formulation of QCD and large-scale numerical simulations to the evaluation of non-perturbative hadronic effects in Standard Model Phenomenology. I present an introduction to the elements of the calculations and discuss the limitations both in the range of quantities which can be studied and in the precision of the results. I focus particularly on the extraction of the QCD parameters, i.e. the quark masses and the strong coupling constant, and on important quantities in flavour physics. Lattice QCD is playing a central role in quantifying the hadronic effects necessary for the development of precision flavour physics and its use in exploring the limits of the Standard Model and in searches for inconsistencies which would signal the presence of new physics.
5D Maximally Supersymmetric Yang-Mills on the Lattice
Joseph, Anosh
2016-01-01
We provide details of the lattice construction of five-dimensional maximally supersymmetric Yang-Mills theory. The lattice theory is supersymmetric, gauge invariant and free from spectrum doublers. Such a supersymmetric lattice formulation is interesting as it can be used for non-perturbative explorations of the five-dimensional theory, which has a known gravitational dual.
The role of the poet in Plato's ideal cities of Callipolis and Magnesia
Directory of Open Access Journals (Sweden)
Gerard Naddaf
2008-01-01
Full Text Available Plato's attitude toward the poets and poetry has always been a flashpoint of debate, controversy and notoriety, but most scholars have failed to see their central role in the ideal cities of the Republic and the Laws, that is, Callipolis and Magnesia. In this paper, I argue that in neither dialogue does Plato "exile" the poets, but, instead, believes they must, like all citizens, exercise the expertise proper to their profession, allowing them the right to become full-fledged participants in the productive class. Moreover, attention to certain details reveals that Plato harnesses both positive and negative factors in poetry to bring his ideal cities closer to a practical realization. The status of the poet and his craft in this context has rarely to my knowledge been addressed.
PLATO - the next-generation AASTINO for robotic site-testing on the Antarctic plateau
Hengst, S.; Lawrence, J.; Luong-van, D.; Everett, J.; Ashley, M. C. B.; Storey, J. W. V.; Hall, S.
2006-08-01
A new site-testing facility, PLATO (Plateau Observatory), is under development at UNSW for deployment to remote sites on the Antarctic Plateau including Dome A. The new facility will adopt many of the features of the AASTINO (Automated Astrophysical Site Testing InterNational Observatory) facility at Dome C. PLATO will autonomously control a flexible site testing and observing instrument suite, monitored via the Iridium satellite network. A challenging aspect of PLATO is to maximise the reliability of the power source while minimising fuel consumption. We are building a low pressure, low temperature environmental chamber to simulate operation at the highest altitudes (4,100 m at Dome A). Two types of engines will be tested: a single-cylinder diesel engine and a Stirling engine.
Manipulation and control of a bichromatic lattice
Thomas, Claire; Barter, Thomas; Daiss, Severin; Leung, Zephy; Stamper-Kurn, Dan
2015-05-01
Recent experiments with ultracold atoms in optical lattices have had great success emulating the simple models of condensed matter systems. These experiments are typically performed with a single site per unit cell. We realize a lattice with up to four sites per unit cell by overlaying an attractive triangular lattice with a repulsive one at twice the wavelength. The relative displacement of the two lattices determines the particular structure. One available configuration is the kagome lattice, which has a flat energy band. In the flat band all kinetic energy states are degenerate, so we have the opportunity to explore a regime where interactions dominate. This bichromatic lattice requires careful stabilization, but offers an opportunity to manipulate the unit cell and band structure by perturbing the lattices relative to one another. I will discuss recent progress.
Efficient methods for solving discrete topology design problems in the PLATO-N project
DEFF Research Database (Denmark)
Canh, Nam Nguyen; Stolpe, Mathias
This paper considers the general multiple load structural topology design problems in the framework of the PLATO-N project. The problems involve a large number of discrete design variables and were modeled as a non-convex mixed 0–1 program. For the class of problems considered, a global optimizat......This paper considers the general multiple load structural topology design problems in the framework of the PLATO-N project. The problems involve a large number of discrete design variables and were modeled as a non-convex mixed 0–1 program. For the class of problems considered, a global...
The quest for a poetics of goodness in plato and aristotle
Dairo Orozco
2012-01-01
The paper, which compares Plato and Aristotle’s different approaches towards artistic activity, is divided into three parts. The first part discusses Plato’s Ion on mimesis and technē, as well as the role that poetry plays in the Republic. The second section offers an account of Aristotle’s idea of happiness as the end of action. Thelast section of this study deals with an attempt to reconcile Plato and Aristotle’s attitude towards mimetic art in a treatise by a Neoplatonic renaissance thinke...
A Similar Comparison between the Thought of Plato and Confucius on Social Hierarchy and Elitism
Institute of Scientific and Technical Information of China (English)
杨馥遥
2014-01-01
The spring-autumn period and warring state period of Chinese thoughts coincide strikingly with the thoughts of the Hel enic Age in the west. Plato and Confucius, the two outstanding seminal thinkers have shaped the philosophy of their respective cultures through some similar means and thoughts which definitely meet at a series of significant points. The highlight of the academic thesis lies in the comparison of the general similarities be-tween Plato and Confucius especial y in terms of social hierarchy and elitism.
Perturbative renormalization of the electric field correlator
Christensen, C
2016-01-01
The momentum diffusion coefficient of a heavy quark in a hot QCD plasma can be extracted as a transport coefficient related to the correlator of two colour-electric fields dressing a Polyakov loop. We determine the perturbative renormalization factor for a particular lattice discretization of this correlator within Wilson's SU(3) gauge theory, finding a ~12% NLO correction for values of the bare coupling used in the current generation of simulations. The impact of this result on existing lattice determinations is commented upon, and a possibility for non-perturbative renormalization through the gradient flow is pointed out.
Perturbative renormalization of the electric field correlator
Directory of Open Access Journals (Sweden)
C. Christensen
2016-04-01
Full Text Available The momentum diffusion coefficient of a heavy quark in a hot QCD plasma can be extracted as a transport coefficient related to the correlator of two colour-electric fields dressing a Polyakov loop. We determine the perturbative renormalization factor for a particular lattice discretization of this correlator within Wilson's SU(3 gauge theory, finding a ∼12% NLO correction for values of the bare coupling used in the current generation of simulations. The impact of this result on existing lattice determinations is commented upon, and a possibility for non-perturbative renormalization through the gradient flow is pointed out.
Perturbative renormalization of the electric field correlator
Christensen, C.; Laine, M.
2016-04-01
The momentum diffusion coefficient of a heavy quark in a hot QCD plasma can be extracted as a transport coefficient related to the correlator of two colour-electric fields dressing a Polyakov loop. We determine the perturbative renormalization factor for a particular lattice discretization of this correlator within Wilson's SU(3) gauge theory, finding a ∼ 12% NLO correction for values of the bare coupling used in the current generation of simulations. The impact of this result on existing lattice determinations is commented upon, and a possibility for non-perturbative renormalization through the gradient flow is pointed out.
Zima, W; De Ridder, J; Salmon, S; Catala, C; Kjeldsen, H; Aerts, C
2010-01-01
The PLATO satellite mission project is a next generation ESA Cosmic Vision satellite project dedicated to the detection of exo-planets and to asteroseismology of their host-stars using ultra-high precision photometry. The main goal of the PLATO mission is to provide a full statistical analysis of exo-planetary systems around stars that are bright and close enough for detailed follow-up studies. Many aspects concerning the design trade-off of a space-based instrument and its performance can best be tackled through realistic simulations of the expected observations. The complex interplay of various noise sources in the course of the observations made such simulations an indispensable part of the assessment study of the PLATO Payload Consortium. We created an end-to-end CCD simulation software-tool, dubbed PLATOSim, which simulates photometric time-series of CCD images by including realistic models of the CCD and its electronics, the telescope optics, the stellar field, the pointing uncertainty of the satellite ...
Perturbatively improving RI-MOM renormalization constants
Energy Technology Data Exchange (ETDEWEB)
Constantinou, M.; Costa, M.; Panagopoulos, H. [Cyprus Univ. (Cyprus). Dept. of Physics; Goeckeler, M. [Regensburg Univ. (Germany). Institut fuer Theoretische Physik; Horsley, R. [Edinburgh Univ. (United Kingdom). School of Physics; Perlt, H.; Schiller, A. [Leipzig Univ. (Germany). Inst. fuer Theoretische Physik; Rakow, P.E.L. [Liverpool Univ. (United Kingdom). Dept. of Mathematical Sciences; Schhierholz, G. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2013-03-15
The determination of renormalization factors is of crucial importance in lattice QCD. They relate the observables obtained on the lattice to their measured counterparts in the continuum in a suitable renormalization scheme. Therefore, they have to be computed as precisely as possible. A widely used approach is the nonperturbative Rome-Southampton method. It requires, however, a careful treatment of lattice artifacts. In this paper we investigate a method to suppress these artifacts by subtracting one-loop contributions to renormalization factors calculated in lattice perturbation theory. We compare results obtained from a complete one-loop subtraction with those calculated for a subtraction of contributions proportional to the square of the lattice spacing.
Perturbatively improving RI-MOM renormalization constants
Energy Technology Data Exchange (ETDEWEB)
Constantinou, M.; Costa, M.; Panagopoulos, H. [Cyprus Univ. (Cyprus). Dept. of Physics; Goeckeler, M. [Regensburg Univ. (Germany). Institut fuer Theoretische Physik; Horsley, R. [Edinburgh Univ. (United Kingdom). School of Physics; Perlt, H.; Schiller, A. [Leipzig Univ. (Germany). Inst. fuer Theoretische Physik; Rakow, P.E.L. [Liverpool Univ. (United Kingdom). Dept. of Mathematical Sciences; Schhierholz, G. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2013-03-15
The determination of renormalization factors is of crucial importance in lattice QCD. They relate the observables obtained on the lattice to their measured counterparts in the continuum in a suitable renormalization scheme. Therefore, they have to be computed as precisely as possible. A widely used approach is the nonperturbative Rome-Southampton method. It requires, however, a careful treatment of lattice artifacts. In this paper we investigate a method to suppress these artifacts by subtracting one-loop contributions to renormalization factors calculated in lattice perturbation theory. We compare results obtained from a complete one-loop subtraction with those calculated for a subtraction of contributions proportional to the square of the lattice spacing.
ST-elevation acute coronary syndromes in the Platelet Inhibition and Patient Outcomes (PLATO) trial
DEFF Research Database (Denmark)
Armstrong, Paul W; Siha, Hany; Fu, Yuling;
2012-01-01
Ticagrelor, when compared with clopidogrel, reduced the 12-month risk of vascular death/myocardial infarction and stroke in patients with ST-elevation acute coronary syndromes intended to undergo primary percutaneous coronary intervention in the PLATelet inhibition and patient Outcomes (PLATO) tr...
Democratic Freedom and the Concept of Freedom in Plato and Aristotle
Directory of Open Access Journals (Sweden)
Mogens Herman Hansen
2010-11-01
Full Text Available Among the several meanings of eleutheria used by Greeks in the classical period, democratic freedom is rejected by both Plato and Aristotle, who do not articulate a theory of political freedom but rather confine eleutheria to a social context.
Freud, Plato and Irigaray: A Morpho-Logic of Teaching and Learning
Peers, Chris
2012-01-01
This article discusses two well-known texts that respectively describe learning and teaching, drawn from the work of Freud and Plato. These texts are considered in psychoanalytic terms using a methodology drawn from the philosophy of Luce Irigaray. In particular the article addresses Irigaray's approach to the analysis of speech and utterance as a…
Dialectic of Eros and Myth of the Soul in Plato's Phaedrus
DEFF Research Database (Denmark)
Larsen, Jens Kristian
2010-01-01
In this paper, I question a widespread reading of a passage in the last part of the Phaedrus dealing with the science of dialectic. According to this reading, the passage announces a new method peculiar to the later Plato aiming at defining natural kinds. I show that the Phaedrus itself does not ...
Evaluation of a Three Year Health Sciences PLATO IV Computer-Based Education Project.
Sorlie, William E.; Essex, Diane L.
Significant findings of the comprehensive evaluation of a computer-based curriculum in the basic medical sciences using the PLATO IV computer system are presented. The study was conducted by the Office of Curriculum and Evaluation (OCE) of the School of Basic Medical Sciences (SBMS) at the University of Illinois, Urbana/Champaign (UC). It was…
Cost of Initial Development of PLATO Instruction in Veterinary Medicine. CERL Report X-43.
Grimes, George M.
An academic program instituting the PLATO system of computer-assisted instruction at the University of Illinois College of Veterinary Medicine is discussed. Procedures involved setting up an organization, establishing an administrative system, studying capabilities of the system, studying factors making a lesson suitable for programming, and…
From Dialogos to Dialogue: The Use of the Term from Plato to the Second Century CE
Directory of Open Access Journals (Sweden)
Katarzyna Jazdzewska
2014-02-01
Full Text Available In Plato the verb διαλέγεσθαι is far more common than the noun, and both denote question-and-answer discussions; it was only in the Hellenistic period that διάλογος became a genre term, though its other meanings survived.
Two examples of the relation between the contemporary science and Plato
Antonello, Elio
2016-01-01
The philosopher Plato is remembered even today by scientists, and his writings are still inspiring the scientific research. In the present short note (intended essentially for public outreach) two examples are briefly illustrated: 1) the European space project that bears his name, dedicated to the discovery of exoplanets; 2) the discussion about platonism in contemporary physics.
Quinn, David W.; Quinn, Nancy W.
Apache Junction Unified School District, Arizona, has embarked on a 5-year program of instructional improvement using technology. PLATO Elementary reading and mathematics products were installed in the district's elementary and middle schools at the beginning of the 1999-2000 school year. This evaluation studied the use and preliminary student…
Friedman, Lawrence B.
Taking a philosophical approach based on what Plato, Aristotle, and Descartes said about knowledge, this paper addresses some of the murkiness in the conceptual space surrounding the issue of whether prior knowledge does or does not facilitate text comprehension. Specifically, the paper first develops a non-exhaustive typology of cases in which…
Shim, Seung Hwan
2008-01-01
This study proposes the ideal role of teachers through the examination of Plato, Confucius, Buber, and Freire on the subject. Teachers not only contribute to the development of individuals and societies but also attain self-realization through teaching. As such, the role of teachers is important as a goal as well as a means. To examine such role,…
Genesis 2–3 and Alcibiades's speech in Plato's Symposium: A ...
African Journals Online (AJOL)
2015-08-26
Aug 26, 2015 ... Friedländer 1975:26f; Gauss 1958:111–117) is the last speech in Plato's ... leader (450–404/3 BCE), appears to be in a great state of intoxication .... command (Gn 2:18: 'You are free to eat of all the trees in the garden.
Freud, Plato and Irigaray: A Morpho-Logic of Teaching and Learning
Peers, Chris
2012-01-01
This article discusses two well-known texts that respectively describe learning and teaching, drawn from the work of Freud and Plato. These texts are considered in psychoanalytic terms using a methodology drawn from the philosophy of Luce Irigaray. In particular the article addresses Irigaray's approach to the analysis of speech and utterance as a…
From Plato to Erikson: How the War on "Bad Play" Has Impoverished Higher Education
Carnes, Mark C.
2015-01-01
For centuries, the titans of educational reform--Plato, Rousseau, Dewey, Piaget, Erikson, Csikszentmihalyi and others--have championed the educational benefits of play. Yet many professors and administrators are boggled by the idea of playing academic games in college. They instantly dismiss faculty initiatives like "Reacting to the…
Perturbative thermodynamics at nonzero isospin density for cold QCD
Graf, Thorben; Fraga, Eduardo S
2015-01-01
We use next-to-leading-order in perturbation theory to investigate the effects of a finite isospin density on the thermodynamics of cold strongly interacting matter. Our results include nonzero quark masses and are compared to lattice data.
Perturbative thermodynamics at nonzero isospin density for cold QCD
Graf, Thorben; Schaffner-Bielich, Juergen; Fraga, Eduardo S.
2016-04-01
We use next-to-leading order in perturbation theory to investigate the effects of a finite isospin density on the thermodynamics of cold strongly interacting matter. Our results include nonzero quark masses and are compared to lattice data.
Donnellan, Thomas; Maxwell, E A; Plumpton, C
1968-01-01
Lattice Theory presents an elementary account of a significant branch of contemporary mathematics concerning lattice theory. This book discusses the unusual features, which include the presentation and exploitation of partitions of a finite set. Organized into six chapters, this book begins with an overview of the concept of several topics, including sets in general, the relations and operations, the relation of equivalence, and the relation of congruence. This text then defines the relation of partial order and then partially ordered sets, including chains. Other chapters examine the properti
Bietenholz, W; Pepe, M; Wiese, U -J
2010-01-01
We consider lattice field theories with topological actions, which are invariant against small deformations of the fields. Some of these actions have infinite barriers separating different topological sectors. Topological actions do not have the correct classical continuum limit and they cannot be treated using perturbation theory, but they still yield the correct quantum continuum limit. To show this, we present analytic studies of the 1-d O(2) and O(3) model, as well as Monte Carlo simulations of the 2-d O(3) model using topological lattice actions. Some topological actions obey and others violate a lattice Schwarz inequality between the action and the topological charge $Q$. Irrespective of this, in the 2-d O(3) model the topological susceptibility $\\chi_t = \\l/V$ is logarithmically divergent in the continuum limit. Still, at non-zero distance the correlator of the topological charge density has a finite continuum limit which is consistent with analytic predictions. Our study shows explicitly that some cla...
Digital lattice gauge theories
Zohar, Erez; Farace, Alessandro; Reznik, Benni; Cirac, J. Ignacio
2017-02-01
We propose a general scheme for a digital construction of lattice gauge theories with dynamical fermions. In this method, the four-body interactions arising in models with 2 +1 dimensions and higher are obtained stroboscopically, through a sequence of two-body interactions with ancillary degrees of freedom. This yields stronger interactions than the ones obtained through perturbative methods, as typically done in previous proposals, and removes an important bottleneck in the road towards experimental realizations. The scheme applies to generic gauge theories with Lie or finite symmetry groups, both Abelian and non-Abelian. As a concrete example, we present the construction of a digital quantum simulator for a Z3 lattice gauge theory with dynamical fermionic matter in 2 +1 dimensions, using ultracold atoms in optical lattices, involving three atomic species, representing the matter, gauge, and auxiliary degrees of freedom, that are separated in three different layers. By moving the ancilla atoms with a proper sequence of steps, we show how we can obtain the desired evolution in a clean, controlled way.
The perturbative ghost propagator in Landau gauge from numerical stochastic perturbation theory
Di Renzo, F; Perlt, H; Schiller, A; Torrero, C
2008-01-01
We present one- and two-loop results for the ghost propagator in Landau gauge calculated in Numerical Stochastic Perturbation Theory (NSPT). The one-loop results are compared with available standard Lattice Perturbation Theory in the infinite-volume limit. We discuss in detail how to perform the different necessary limits in the NSPT approach and discuss a recipe to treat logarithmic terms by introducing ``finite-lattice logs''. We find agreement with the one-loop result from standard Lattice Perturbation Theory and estimate, from the non-logarithmic part of the ghost propagator in two-loop order, the unknown constant contribution to the ghost self-energy in the RI'-MOM scheme in Landau gauge. That constant vanishes within our numerical accuracy.
Non-perturbative Heavy Quark Effective Theory
DEFF Research Database (Denmark)
Della Morte, Michele; Heitger, Jochen; Simma, Hubert;
2015-01-01
We review a lattice strategy how to non-perturbatively determine the coefficients in the HQET expansion of all components of the heavy-light axial and vector currents, including 1/m_h-corrections. We also discuss recent preliminary results on the form factors parameterizing semi-leptonic B-decays...
Non-perturbative Heavy Quark Effective Theory
DEFF Research Database (Denmark)
Della Morte, Michele; Heitger, Jochen; Simma, Hubert
2015-01-01
We review a lattice strategy how to non-perturbatively determine the coefficients in the HQET expansion of all components of the heavy-light axial and vector currents, including 1/m_h-corrections. We also discuss recent preliminary results on the form factors parameterizing semi-leptonic B-decays...
Gravitational Perturbation in Topological Phonon Space
Institute of Scientific and Technical Information of China (English)
李芳昱; 罗俊; 唐孟希
1994-01-01
The effect of gravitational wave (GW) on phonon in crystal lattice space with spiral dislocation is expressed as a gravitational perturbation in topological phonon space with background of the spiral dislocation.This is a new-type effect form of the GW field to the phonon.The corresponding phonon solutions are given.
Latest results from lattice N=4 supersymmetric Yang--Mills
Schaich, David; Damgaard, Poul H; Giedt, Joel
2016-01-01
We present some of the latest results from our numerical investigations of N=4 supersymmetric Yang--Mills theory formulated on a space-time lattice. Based on a construction that exactly preserves a single supersymmetry at non-zero lattice spacing, we recently developed an improved lattice action that is now being employed in large-scale calculations. Here we update our studies of the static potential using this new action, also applying tree-level lattice perturbation theory to improve the analysis of the potential itself. Considering relatively weak couplings, we obtain results for the Coulomb coefficient that are consistent with continuum perturbation theory.
Molecular Cluster Perturbation Theory. I. Formalism
Byrd, Jason N; Molt,, Robert W; Bartlett, Rodney J; Sanders, Beverly A; Lotrich, Victor F
2014-01-01
We present second-order molecular cluster perturbation theory (MCPT(2)), a methodology to calculate arbitrarily large systems with explicit calculation of individual wavefunctions in a coupled cluster framework. This new MCPT(2) framework uses coupled cluster perturbation theory and an expansion in terms of molecular dimer interactions to obtain molecular wavefunctions that are infinite order in both the electronic fluctuation operator and all possible dimer (and products of dimers) interactions. The MCPT(2) framework has been implemented in the new SIA/ACES parallel architecture, making use of the advanced dynamic memory control and fine grained parallelism to perform very large explicit molecular cluster calculations. To illustrate the power of this method, we have computed energy shifts and lattice site dipole moments for the polar and non-polar configurations of solid hydrogen fluoride by scaling an explicit lattice to the bulk limit. The explicit lattice size without periodic boundary conditions was scal...
Algebraic Lattices in QFT Renormalization
Borinsky, Michael
2016-07-01
The structure of overlapping subdivergences, which appear in the perturbative expansions of quantum field theory, is analyzed using algebraic lattice theory. It is shown that for specific QFTs the sets of subdivergences of Feynman diagrams form algebraic lattices. This class of QFTs includes the standard model. In kinematic renormalization schemes, in which tadpole diagrams vanish, these lattices are semimodular. This implies that the Hopf algebra of Feynman diagrams is graded by the coradical degree or equivalently that every maximal forest has the same length in the scope of BPHZ renormalization. As an application of this framework, a formula for the counter terms in zero-dimensional QFT is given together with some examples of the enumeration of primitive or skeleton diagrams.
The deconfinement transition on coarse lattices
Bliss, D W; Lepage, G P
1996-01-01
We compute the critical temperature T_c for the deconfinement transition of pure QCD on coarse lattices, with N_t = 2, 3, 4, and lattice spacings from .33 fm to .15 fm. We employ a perturbatively improved gluon action designed to remove order a^2 and \\alpha_s a^2 errors. We find that T_c in units of the charmonium 1P--1S splitting and the torelon mass is independent of a to within approximately 5\\%.
Lattice QCD and the Jefferson Laboratory Program
Energy Technology Data Exchange (ETDEWEB)
Jozef Dudek, Robert Edwards, David Richards, Konstantinos Orginos
2011-06-01
Lattice gauge theory provides our only means of performing \\textit{ab initio} calculations in the non-perturbative regime. It has thus become an increasing important component of the Jefferson Laboratory physics program. In this paper, we describe the contributions of lattice QCD to our understanding of hadronic and nuclear physics, focusing on the structure of hadrons, the calculation of the spectrum and properties of resonances, and finally on deriving an understanding of the QCD origin of nuclear forces.
Lattice quantum chromodynamics with approximately chiral fermions
Energy Technology Data Exchange (ETDEWEB)
Hierl, Dieter
2008-05-15
In this work we present Lattice QCD results obtained by approximately chiral fermions. We use the CI fermions in the quenched approximation to investigate the excited baryon spectrum and to search for the {theta}{sup +} pentaquark on the lattice. Furthermore we developed an algorithm for dynamical simulations using the FP action. Using FP fermions we calculate some LECs of chiral perturbation theory applying the epsilon expansion. (orig.)
Gauge-Higgs Unification on the Lattice
Irges, Nikos; Yoneyama, Kyoko
2012-01-01
The simplest Gauge-Higgs Unification model is a five-dimensional SU(2) gauge theory compactified on the S^1/Z_2 orbifold, such that on the four-dimensional boundaries of space-time there is an unbroken U(1) symmetry and a complex scalar, the latter identified with the Higgs boson. Perturbatively the U(1) remains spontaneously unbroken. Earlier lattice Monte Carlo simulations revealed however that the spontaneous breaking of the U(1) does occur at the non-perturbative level. Here, we verify the Monte Carlo result via an analytical lattice Mean-Field expansion.
Extra-dimensional models on the lattice
Knechtli, Francesco
2016-01-01
In this review we summarize the ongoing effort to study extra-dimensional gauge theories with lattice simulations. In these models the Higgs field is identified with extra-dimensional components of the gauge field. The Higgs potential is generated by quantum corrections and is protected from divergencies by the higher dimensional gauge symmetry. Dimensional reduction to four dimensions can occur through compactification or localization. Gauge-Higgs unification models are often studied using perturbation theory. Numerical lattice simulations are used to go beyond these perturbative expectations and to include non-perturbative effects. We describe the known perturbative predictions and their fate in the strongly-coupled regime for various extra-dimensional models.
Eigenspectrum Noise Subtraction Methods in Lattice QCD
Guerrero, Victor; Wilcox, Walter
2010-01-01
We propose a new noise subtraction method, which we call "eigenspectrum subtraction", which uses low eigenmode information to suppress statistical noise at low quark mass. This is useful for lattice calculations involving disconnected loops or all-to-all propagators. It has significant advantages over perturbative subtraction methods. We compare unsubtracted, eigenspectrum and perturbative error bar results for the scalar operator on a small Wilson QCD matrix.
Cosmological density perturbations from perturbed couplings
Tsujikawa, S
2003-01-01
The density perturbations generated when the inflaton decay rate is perturbed by a light scalar field $\\chi$ are studied. By explicitly solving the perturbation equations for the system of two scalar fields and radiation, we show that even in low energy-scale inflation nearly scale-invariant spectra of scalar perturbations with an amplitude set by observations are obtained through the conversion of $\\chi$ fluctuations into adiabatic density perturbations. We demonstrate that the spectra depend on the average decay rate of the inflaton & on the inflaton fluctuations. We then apply this new mechanism to string cosmologies & generalized Einstein theories and discuss the conditions under which scale-invariant spectra are possible.
Plato, Wilde, and Woolf: the poetics of homoerotic "intercourse" in A Room of One's Own.
Vanita, Ruth
2010-01-01
This article places Woolf in the context of homoerotic literary ancestry. It suggests that the overall argument in A Room of One's Own owes a debt to Wilde's 1891 pamphlet The Soul of Man under Socialism. It also examines Woolf's controversial meditation on male-female collaboration and intercourse in A Room, and suggests a homoerotic reading of this meditation, drawing on images and ideas of literary transmission and creation from Plato's Symposium.
The philosopher Socrates had exophthalmos (a term coined by Plato) and probably Graves' disease.
Papapetrou, Peter D
2015-01-01
According to a previously published theory, Socrates was afflicted with temporal lobe epilepsy since his childhood. Plato, Xenophon, and Aristoxenus described Socrates as having exophthalmos, probably diplopia, and some symptoms compatible with hyperthyroidism. Using these data, we theorize that Socrates had Graves' disease. In order to determine a cause of his temporal lobe epilepsy, we speculate that the philosopher also had autoimmune thyroiditis and Hashimoto encephalopathy during his childhood and his epilepsy may have been a sequel to this hypothesized encephalopathy.
Rare Kaon Decays on the Lattice
Isidori, Gino; Turchetti, P; Isidori, Gino; Martinelli, Guido; Turchetti, Paolo
2006-01-01
We show that long distance contributions to the rare decays K -> pi nu nu-bar and K -> pi l+ l- can be computed using lattice QCD. The proposed approach requires well established methods, successfully applied in the calculations of electromagnetic and semileptonic form factors. The extra power divergences, related to the use of weak four-fermion operators, can be eliminated using only the symmetries of the lattice action without ambiguities or complicated non-perturbative subtractions. We demonstrate that this is true even when a lattice action with explicit chiral symmetry breaking is employed. Our study opens the possibility of reducing the present uncertainty in the theoretical predictions for these decays.
Investigating jet quenching on the lattice
Panero, Marco; Schäfer, Andreas
2014-01-01
Due to the dynamical, real-time, nature of the phenomenon, the study of jet quenching via lattice QCD simulations is not straightforward. In this contribution, however, we show how one can extract information about the momentum broadening of a hard parton moving in the quark-gluon plasma, from lattice calculations. After discussing the basic idea (originally proposed by Caron-Huot), we present a recent study, in which we estimated the jet quenching parameter non-perturbatively, from the lattice evaluation of a particular set of gauge-invariant operators.
Energy Technology Data Exchange (ETDEWEB)
Schaefer, Stefan [DESY (Germany). Neumann Inst. for Computing
2016-11-01
These configurations are currently in use in many on-going projects carried out by researchers throughout Europe. In particular this data will serve as an essential input into the computation of the coupling constant of QCD, where some of the simulations are still on-going. But also projects computing the masses of hadrons and investigating their structure are underway as well as activities in the physics of heavy quarks. As this initial project of gauge field generation has been successful, it is worthwhile to extend the currently available ensembles with further points in parameter space. These will allow to further study and control systematic effects like the ones introduced by the finite volume, the non-physical quark masses and the finite lattice spacing. In particular certain compromises have still been made in the region where pion masses and lattice spacing are both small. This is because physical pion masses require larger lattices to keep the effects of the finite volume under control. At light pion masses, a precise control of the continuum extrapolation is therefore difficult, but certainly a main goal of future simulations. To reach this goal, algorithmic developments as well as faster hardware will be needed.
The instrument control unit of the ESA-PLATO 2.0 mission
Focardi, M.; Pezzuto, S.; Cosentino, R.; Giusi, G.; Pancrazzi, M.; Noce, V.; Ottensamer, R.; Steller, M.; Di Giorgio, A. M.; Pace, E.; Plasson, P.; Peter, G.; Pagano, I.
2016-07-01
PLATO 2.0 has been selected by ESA as the third medium-class Mission (M3) of the Cosmic Vision Program. Its Payload is conceived for the discovery of new transiting exoplanets on the disk of their parent stars and for the study of planetary system formation and evolution as well as to answer fundamental questions concerning the existence of other planetary systems like our own, including the presence of potentially habitable new worlds. The PLATO Payload design is based on the adoption of four sets of short focal length telescopes having a large field of view in order to exploit a large sky coverage and to reach, at the same time, the needed photometry accuracy and signalto- noise ratio (S/N) within a few tens of seconds of exposure time. The large amount of data produced by the telescope is collected and processed by means of the Payload's Data Processing System (DPS) composed by many processing electronics units. This paper gives an overview of the PLATO 2.0 DPS, mainly focusing on the architecture and processing capabilities of its Instrument Control Unit (ICU), the electronic subsystem acting as the main interface between the Payload (P/L) and the Spacecraft (S/C).
Effective Field Theories and Lattice QCD
Bernard, C
2015-01-01
I describe some of the many connections between lattice QCD and effective field theories, focusing in particular on chiral effective theory, and, to a lesser extent, Symanzik effective theory. I first discuss the ways in which effective theories have enabled and supported lattice QCD calculations. Particular attention is paid to the inclusion of discretization errors, for a variety of lattice QCD actions, into chiral effective theory. Several other examples of the usefulness of chiral perturbation theory, including the encoding of partial quenching and of twisted boundary conditions, are also described. In the second part of the talk, I turn to results from lattice QCD for the low energy constants of the two- and three-flavor chiral theories. I concentrate here on mesonic quantities, but the dependence of the nucleon mass on the pion mass is also discussed. Finally I describe some recent preliminary lattice QCD calculations by the MILC Collaboration relating to the three-flavor chiral limit.
Ultracold Quantum Gases and Lattice Systems: Quantum Simulation of Lattice Gauge Theories
Wiese, U -J
2013-01-01
Abelian and non-Abelian gauge theories are of central importance in many areas of physics. In condensed matter physics, Abelian U(1) lattice gauge theories arise in the description of certain quantum spin liquids. In quantum information theory, Kitaev's toric code is a Z(2) lattice gauge theory. In particle physics, Quantum Chromodynamics (QCD), the non-Abelian SU(3) gauge theory of the strong interactions between quarks and gluons, is non-perturbatively regularized on a lattice. Quantum link models extend the concept of lattice gauge theories beyond the Wilson formulation, and are well suited for both digital and analog quantum simulation using ultracold atomic gases in optical lattices. Since quantum simulators do not suffer from the notorious sign problem, they open the door to studies of the real-time evolution of strongly coupled quantum systems, which are impossible with classical simulation methods. A plethora of interesting lattice gauge theories suggests itself for quantum simulation, which should al...
Monte Carlo methods in continuous time for lattice Hamiltonians
Huffman, Emilie
2016-01-01
We solve a variety of sign problems for models in lattice field theory using the Hamiltonian formulation, including Yukawa models and simple lattice gauge theories. The solutions emerge naturally in continuous time and use the dual representation for the bosonic fields. These solutions allow us to construct quantum Monte Carlo methods for these problems. The methods could provide an alternative approach to understanding non-perturbative dynamics of some lattice field theories.
Mixed action computations on fine dynamical lattices
Bernardoni, F; Hernandez, P; Necco, S; Pena, C
2009-01-01
We report on our first experiences in simulating Neuberger valence fermions on CLS $N_f=2$ configurations with light sea quark masses and small lattice spacings. Valence quark masses are considered that allow to explore the matching to (partially quenched) chiral perturbation theory both in the $\\epsilon$- and $p$-regimes. The setup is discussed, and first results are presented for spectral observables.
TRAVELING WAVES CONNECTING EQUILIBRIUM AND PERIODIC ORBIT FOR DELAYED LATTICE DIFFERENTIAL EQUATION
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
A class of lattice with time delay and nonlocal response is considered.By transforming the lattice delay differential system into an integral equations in a Banach space,we reduces a singular perturbation problem to a regular perturbation problem.Traveling wave solution therefore is obtained by applying Liapunov-Schmidt method and the implicit function theorem.
Resummation of Cactus Diagrams in the Clover Improved Lattice Formulation of QCD
Panagopoulos, H
1999-01-01
We extend to the clover improved lattice formulation of QCD the resummation of cactus diagrams, i.e. a certain class of tadpole-like gauge invariant diagrams. Cactus resummation yields an improved perturbative expansion. We apply it to the lattice renormalization of some two-fermion operators improving their one-loop perturbative estimates.
Dual Lattice of ℤ-module Lattice
Directory of Open Access Journals (Sweden)
Futa Yuichi
2017-07-01
Full Text Available In this article, we formalize in Mizar [5] the definition of dual lattice and their properties. We formally prove that a set of all dual vectors in a rational lattice has the construction of a lattice. We show that a dual basis can be calculated by elements of an inverse of the Gram Matrix. We also formalize a summation of inner products and their properties. Lattice of ℤ-module is necessary for lattice problems, LLL(Lenstra, Lenstra and Lovász base reduction algorithm and cryptographic systems with lattice [20], [10] and [19].
Nuclear effective field theory on the lattice
Krebs, H; Epelbaum, E; Lee, D; ner, Ulf-G Mei\\ss
2008-01-01
In the low-energy region far below the chiral symmetry breaking scale (which is of the order of 1 GeV) chiral perturbation theory provides a model-independent approach for quantitative description of nuclear processes. In the two- and more-nucleon sector perturbation theory is applicable only at the level of an effective potential which serves as input in the corresponding dynamical equation. To deal with the resulting many-body problem we put chiral effective field theory (EFT) on the lattice. Here we present the results of our lattice EFT study up to next-to-next-to-leading order in the chiral expansion. Accurate description of two-nucleon phase-shifts and ground state energy ratio of dilute neutron matter up to corrections of higher orders shows that lattice EFT is a promising tool for a quantitative description of low-energy few- and many-body systems.
Interstitial single resistor in a network of resistors application of the lattice Green's function
Energy Technology Data Exchange (ETDEWEB)
Owaidat, M Q; Khalifeh, J M [Department of Physics, University of Jordan, Amman-11942 (Jordan); Hijjawi, R S, E-mail: jkalifa@ju.edu.j [Department of Physics, Mutah University (Jordan)
2010-09-17
The resistance between two arbitrary nodes of a network of resistors is studied when the network is perturbed by connecting an extra resistor between two arbitrary nodes in the perfect lattice. The lattice Green's function and the resistance of the perturbed network are expressed in terms of those of the perfect lattice by solving Dyson's equation. A comparison is carried out between numerical and experimental results for a square lattice.
Resummation of Cactus Diagrams in Lattice QCD, to all Orders
Panagopoulos, H
2000-01-01
We show how to perform a resummation, to all orders in perturbation theory, of a certain class of gauge invariant tadpole-like diagrams in Lattice QCD. These diagrams are often largely responsible for lattice artifacts. Our resummation leads to an improved perturbative expansion. Applied to a number of cases of interest, e.g. the lattice renormalization of some two-fermion operators, this expansion yields results remarkably close to corresponding nonperturbative estimates. We consider in our study both the Wilson and the clover action for fermions.
Nucleon structure from lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Dinter, Simon
2012-11-13
In this thesis we compute within lattice QCD observables related to the structure of the nucleon. One part of this thesis is concerned with moments of parton distribution functions (PDFs). Those moments are essential elements for the understanding of nucleon structure and can be extracted from a global analysis of deep inelastic scattering experiments. On the theoretical side they can be computed non-perturbatively by means of lattice QCD. However, since the time lattice calculations of moments of PDFs are available, there is a tension between these lattice calculations and the results from a global analysis of experimental data. We examine whether systematic effects are responsible for this tension, and study particularly intensively the effects of excited states by a dedicated high precision computation. Moreover, we carry out a first computation with four dynamical flavors. Another aspect of this thesis is a feasibility study of a lattice QCD computation of the scalar quark content of the nucleon, which is an important element in the cross-section of a heavy particle with the nucleon mediated by a scalar particle (e.g. Higgs particle) and can therefore have an impact on Dark Matter searches. Existing lattice QCD calculations of this quantity usually have a large error and thus a low significance for phenomenological applications. We use a variance-reduction technique for quark-disconnected diagrams to obtain a precise result. Furthermore, we introduce a new stochastic method for the calculation of connected 3-point correlation functions, which are needed to compute nucleon structure observables, as an alternative to the usual sequential propagator method. In an explorative study we check whether this new method is competitive to the standard one. We use Wilson twisted mass fermions at maximal twist in all our calculations, such that all observables considered here have only O(a{sup 2}) discretization effects.
Shear Viscosity from Lattice QCD
Mages, Simon W; Fodor, Zoltán; Schäfer, Andreas; Szabó, Kálmán
2015-01-01
Understanding of the transport properties of the the quark-gluon plasma is becoming increasingly important to describe current measurements at heavy ion collisions. This work reports on recent efforts to determine the shear viscosity h in the deconfined phase from lattice QCD. The main focus is on the integration of the Wilson flow in the analysis to get a better handle on the infrared behaviour of the spectral function which is relevant for transport. It is carried out at finite Wilson flow time, which eliminates the dependence on the lattice spacing. Eventually, a new continuum limit has to be carried out which sends the new regulator introduced by finite flow time to zero. Also the non-perturbative renormalization strategy applied for the energy momentum tensor is discussed. At the end some quenched results for temperatures up to 4 : 5 T c are presented
Non-perturbative quark mass renormalization
Capitani, S.; Luescher, M.; Sint, S.; Sommer, R.; Weisz, P.; Wittig, H.
1998-01-01
We show that the renormalization factor relating the renormalization group invariant quark masses to the bare quark masses computed in lattice QCD can be determined non-perturbatively. The calculation is based on an extension of a finite-size technique previously employed to compute the running coupling in quenched QCD. As a by-product we obtain the $\\Lambda$--parameter in this theory with completely controlled errors.
Convergent series for lattice models with polynomial interactions
Ivanov, Aleksandr S.; Sazonov, Vasily K.
2017-01-01
The standard perturbative weak-coupling expansions in lattice models are asymptotic. The reason for this is hidden in the incorrect interchange of the summation and integration. However, substituting the Gaussian initial approximation of the perturbative expansions by a certain interacting model or regularizing original lattice integrals, one can construct desired convergent series. In this paper we develop methods, which are based on the joint and separate utilization of the regularization and new initial approximation. We prove, that the convergent series exist and can be expressed as re-summed standard perturbation theory for any model on the finite lattice with the polynomial interaction of even degree. We discuss properties of such series and study their applicability to practical computations on the example of the lattice ϕ4-model. We calculate expectation value using the convergent series, the comparison of the results with the Borel re-summation and Monte Carlo simulations shows a good agreement between all these methods.
Convergent series for lattice models with polynomial interactions
Ivanov, Aleksandr S
2016-01-01
The standard perturbative weak-coupling expansions in lattice models are asymptotic. The reason for this is hidden in the incorrect interchange of the summation and integration. However, substituting the Gaussian initial approximation of the perturbative expansions by a certain interacting model or regularizing original lattice integrals, one can construct desired convergent series. In this paper we develop methods, which are based on the joint and separate utilization of the regularization and new initial approximation. We prove, that the convergent series exist and can be expressed as the re-summed standard perturbation theory for any model on the finite lattice with the polynomial interaction of even degree. We discuss properties of such series and make them applicable to practical computations. The workability of the methods is demonstrated on the example of the lattice $\\phi^4$-model. We calculate the operator $\\langle\\phi_n^2\\rangle$ using the convergent series, the comparison of the results with the Bo...
Echoes in Plato's cave : ontology of sound objects in computer music and analysis
Marsden, Alan
2014-01-01
The sonic aspects of Plato's analogy of the cave is taken as a starting point for thought experiments to investigate the objective nature of sound, and the idea of quasi-Platonic forms in music. Sounds are found to be objects in a way that sights or appearances are not, and it is only in the presence of technology that they become artificial. When recognition, control and communication about sound come into play, abstract concepts emerge, but there is no reason to give these the priority stat...
Ontological Questions in Schelling’s Late Philosophy: Plato and Aristotle
Directory of Open Access Journals (Sweden)
Jean-François Courtine
2010-09-01
Full Text Available The purpose of the article is to understand the reasons and procedures employed by F. W. Schelling in his Plato and Aristotle re-appropriation, and to extract the authentically ontological thematic of it. It makes a path through the Schelling’s late writings and letters, to construct a complete view about the relation between this appropriation and the possibility of the constitution of a positive philosophy, as a particular science, in opposition to a negative philosophy, understood as metaphysics.
Numbers Rule The Vexing Mathematics of Democracy, from Plato to the Present
Szpiro, George G
2010-01-01
Since the very birth of democracy in ancient Greece, the simple act of voting has given rise to mathematical paradoxes that have puzzled some of the greatest philosophers, statesmen, and mathematicians. Numbers Rule traces the epic quest by these thinkers to create a more perfect democracy and adapt to the ever-changing demands that each new generation places on our democratic institutions. In a sweeping narrative that combines history, biography, and mathematics, George Szpiro details the fascinating lives and big ideas of great minds such as Plato, Pliny the Younger, Ramon Llull, Pierre Simo
Topics in Effective Field Theory for Lattice QCD
Walker-Loud, A
2006-01-01
In this work, we extend and apply effective field theory techniques to systematically understand a subset of lattice artifacts which pollute the lattice correlation functions for a few processes of physical interest. Where possible, we compare to existing lattice QCD calculations. In particular, we extend the heavy baryon Lagrangian to the next order in partially quenched chiral perturbation theory and use it to compute the masses of the lightest spin-1/2 and spin-3/2 baryons to next-to-next-to leading order. We then construct the twisted mass chiral Lagrangian for baryons and apply it to compute the lattice spacing corrections to the baryon masses simulated with twisted mass lattice QCD. We extend computations of the nucleon electromagnetic structure to account for finite volume effects, as these observables are particularly sensitive to the finite extent of the lattice. We resolve subtle peculiarities for lattice QCD simulations of polarizabilities and we show that using background field techniques, one can...
Brane World Cosmological Perturbations
Casali, A G; Wang, B; Casali, Adenauer G.; Abdalla, Elcio; Wang, Bin
2004-01-01
We consider a brane world and its gravitational linear perturbations. We present a general solution of the perturbations in the bulk and find the complete perturbed junction conditions for generic brane dynamics. We also prove that (spin 2) gravitational waves in the great majority of cases can only arise in connection with a non-vanishing anisotropic stress. This has far reaching consequences for inflation in the brane world. Moreover, contrary to the case of the radion, perturbations are stable.
Quantum Finite Elements for Lattice Field Theory
Brower, Richard C; Gasbarro, Andrew; Raben, Timothy; Tan, Chung-I; Weinberg, Evan
2016-01-01
Viable non-perturbative methods for lattice quantum field theories on curved manifolds are difficult. By adapting features from the traditional finite element methods (FEM) and Regge Calculus, a new simplicial lattice Quantum Finite Element (QFE) Lagrangian is constructed for fields on a smooth Riemann manifold. To reach the continuum limit additional counter terms must be constructed to cancel the ultraviolet distortions. This is tested by the comparison of phi 4-th theory at the Wilson-Fisher fixed point with the exact Ising (c =1/2) CFT on a 2D Riemann sphere. The Dirac equation is also constructed on a simplicial lattice approximation to a Riemann manifold by introducing a lattice vierbein and spin connection on each link. Convergence of the QFE Dirac equation is tested against the exact solution for the 2D Riemann sphere. Future directions and applications to Conformal Field Theories are suggested.
Proton–proton fusion in lattice effective field theory
Directory of Open Access Journals (Sweden)
Gautam Rupak
2015-02-01
Full Text Available The proton–proton fusion rate is calculated at low energy in a lattice effective field theory (EFT formulation. The strong and the Coulomb interactions are treated non-perturbatively at leading order in the EFT. The lattice results are shown to accurately describe the low energy cross section within the validity of the theory at energies relevant to solar physics. In prior works in the literature, Coulomb effects were generally not included in non-perturbative lattice calculations. Work presented here is of general interest in nuclear lattice EFT calculations that involve Coulomb effects at low energy. It complements recent developments of the adiabatic projection method for lattice calculations of nuclear reactions.
DEFF Research Database (Denmark)
Santocanale, Luigi
2002-01-01
A μ-lattice is a lattice with the property that every unary polynomial has both a least and a greatest fix-point. In this paper we define the quasivariety of μ-lattices and, for a given partially ordered set P, we construct a μ-lattice JP whose elements are equivalence classes of games in a preor...
Further Precise Determinations of $\\alpha_s$ from Lattice QCD
Davies, C T H; Lepage, G P; McCallum, P; Shigemitsu, J; Sloan, J
1997-01-01
We present a new determination of the strong coupling constant from lattice QCD simulations. We use four different short-distance quantities to obtain the coupling, three different (infrared) meson splittings to tune the simulation parameters, and a wide range of lattice spacings, quark masses, and lattice volumes to test for systematic errors. Our final result consists of ten different determinations of $\\alpha^{(3)}_{P}(8.2 GeV)$, which agree well with each other and with our previous results. The most accurate of these, when evolved perturbatively to the $Z^0$ mass, gives obtained from other recent lattice simulations.
Philosophy and Mathematics in the Teaching of Plato: the Development of Idea and Modernity
Directory of Open Access Journals (Sweden)
Mikhailova N. V.
2014-01-01
Full Text Available It is well known that the largest philosophers differently explain the origin of mathematics. This question was investigated in antiquity, a substantial and decisive role in this respect was played by the Platonic doctrine. Therefore, discussing this issue the problem of interaction of philosophy and mathematics in the teachings of Plato should be taken into consideration. Many mathematicians believe that abstract mathematical objects belong in a certain sense to the world of ideas and that consistency of objects and theories really describes mathematical reality, as Plato quite clearly expressed his views on math, according to which mathematical concepts objectively exist as distinct entities between the world of ideas and the world of material things. In the context of foundations of mathematics, so called “Gödel’s Platonism” is of particular interest. It is shown in the article how Platonic objectification of mathematical concepts contributes to the development of modern mathematics by revealing philosophical understanding of the nature of abstraction. To substantiate his point of view, the author draws the works of contemporary experts in the field of philosophy of mathematics.
The PLATO Simulator: Modelling of High-Precision High-Cadence Space-Based Imaging
Marcos-Arenal, P; De Ridder, J; Aerts, C; Huygen, R; Samadi, R; Green, J; Piotto, G; Salmon, S; Catala, C; Rauer, H
2014-01-01
Many aspects of the design trade-off of a space-based instrument and its performance can best be tackled through simulations of the expected observations. The complex interplay of various noise sources in the course of the observations make such simulations an indispensable part of the assessment and design study of any space-based mission. We present a formalism to model and simulate photometric time series of CCD images by including models of the CCD and its electronics, the telescope optics, the stellar field, the jitter movements of the spacecraft, and all important natural noise sources. This formalism has been implemented in a versatile end-to-end simulation software tool, called PLATO Simulator, specifically designed for the PLATO space mission to be operated from L2, but easily adaptable to similar types of missions. We provide a detailed description of several noise sources and discuss their properties, in connection with the optical design, the allowable level of jitter, the quantum efficiency of th...
Automated generation of lattice QCD Feynman rules
Energy Technology Data Exchange (ETDEWEB)
Hart, A.; Mueller, E.H. [Edinburgh Univ. (United Kingdom). SUPA School of Physics and Astronomy; von Hippel, G.M. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Horgan, R.R. [Cambridge Univ. (United Kingdom). DAMTP, CMS
2009-04-15
The derivation of the Feynman rules for lattice perturbation theory from actions and operators is complicated, especially for highly improved actions such as HISQ. This task is, however, both important and particularly suitable for automation. We describe a suite of software to generate and evaluate Feynman rules for a wide range of lattice field theories with gluons and (relativistic and/or heavy) quarks. Our programs are capable of dealing with actions as complicated as (m)NRQCD and HISQ. Automated differentiation methods are used to calculate also the derivatives of Feynman diagrams. (orig.)
Lattice methods and effective field theory
Nicholson, Amy N
2016-01-01
Lattice field theory is a non-perturbative tool for studying properties of strongly interacting field theories, which is particularly amenable to numerical calculations and has quantifiable systematic errors. In these lectures we apply these techniques to nuclear Effective Field Theory (EFT), a non-relativistic theory for nuclei involving the nucleons as the basic degrees of freedom. The lattice formulation of [1,2] for so-called pionless EFT is discussed in detail, with portions of code included to aid the reader in code development. Systematic and statistical uncertainties of these methods are discussed at length, and extensions beyond pionless EFT are introduced in the final Section.
Singlet vs Nonsinglet Perturbative Renormalization of Fermion Bilinears
Constantinou, M; Panagopoulos, H; Spanoudes, G
2016-01-01
In this paper we present the perturbative evaluation of the difference between the renormalization functions of flavor singlet and nonsinglet bilinear quark operators on the lattice. The computation is performed to two loops and to lowest order in the lattice spacing, for a class of improved lattice actions, including Wilson, tree-level (TL) Symanzik and Iwasaki gluons, twisted mass and SLiNC Wilson fermions, as well as staggered fermions with twice stout-smeared links. In the staggered formalism, the stout smearing procedure is also applied to the definition of bilinear operators.
Magrini, James Michael
2014-01-01
Incorporating Gadamer and other thinkers from the continental tradition, this essay is a close and detailed hermeneutic, phenomenological, and ontological study of the dialectic practice of Plato's Socrates--it radicalizes and refutes the Socrates-as-teacher model that educators from scholar academic ideology embrace.
Klecka, Joseph A.
This report describes various aspects of lesson production and use of the PLATO system at Chanute Air Force Base. The first chapter considers four major factors influencing lesson production: (1) implementation of the "lean approach," (2) the Instructional Systems Development (ISD) role in lesson production, (3) the transfer of…
A Plan for the Evaluation of a Project to Develop Basic Medical Sciences Lessons on PLATO IV.
Jones, Les A.; And Others
A project to introduce PLATO IV computer-assisted instruction (CAI) in medical sciences education for health professionals was implemented at the School of Basic Medical Sciences at the University of Illinois. This paper describes the plan for evaluation of the project. Using a student questionnaire and additional general questions, the…
Arsenty, Richard P.; Kieffer, George H.
This paper describes a study of the teaching effectiveness of computer-assisted instruction using the PLATO system at the University of Illinois in a first level biology course. College enrollment, class rank, final grade, and time study data of the control and experimental groups were obtained from master rosters. A questionnaire administered to…
Mintz, Avi I.
2016-01-01
Background/Context: In one of the classics of educational philosophy, a key issue is remains unsettled. In Plato's "Republic," Socrates makes a case for the importance of a comprehensive education. Socrates is unclear, however, about whether the producer class is eligible for this comprehensive education. Purpose/Objective: Previous…
Magrini, James Michael
2014-01-01
Incorporating Gadamer and other thinkers from the continental tradition, this essay is a close and detailed hermeneutic, phenomenological, and ontological study of the dialectic practice of Plato's Socrates--it radicalizes and refutes the Socrates-as-teacher model that educators from scholar academic ideology embrace.
Improved Lattice Renormalization Group Techniques
Petropoulos, Gregory; Hasenfratz, Anna; Schaich, David
2013-01-01
We compute the bare step-scaling function $s_b$ for SU(3) lattice gauge theory with $N_f = 12$ massless fundamental fermions, using the non-perturbative Wilson-flow-optimized Monte Carlo Renormalization Group two-lattice matching technique. We use a short Wilson flow to approach the renormalized trajectory before beginning RG blocking steps. By optimizing the length of the Wilson flow, we are able to determine an $s_b$ corresponding to a unique discrete $\\beta$ function, after a few blocking steps. We carry out this study using new ensembles of 12-flavor gauge configurations generated with exactly massless fermions, using volumes up to $32^4$. The results are consistent with the existence of an infrared fixed point (IRFP) for all investigated lattice volumes and number of blocking steps. We also compare different renormalization schemes, each of which indicates an IRFP at a slightly different value of the bare coupling, as expected for an IR-conformal theory.
Perturbative tests of non-perturbative counting
Dabholkar, Atish; Gomes, João
2010-03-01
We observe that a class of quarter-BPS dyons in mathcal{N} = 4 theories with charge vector ( Q, P) and with nontrivial values of the arithmetic duality invariant I := gcd( Q∧ P) are nonperturbative in one frame but perturbative in another frame. This observation suggests a test of the recently computed nonperturbative partition functions for dyons with nontrivial values of the arithmetic invariant. For all values of I, we show that the nonperturbative counting yields vanishing indexed degeneracy for this class of states everywhere in the moduli space in precise agreement with the perturbative result.
Generalized Supersymmetric Perturbation Theory
Institute of Scientific and Technical Information of China (English)
B. G(o)n(ǖ)l
2004-01-01
@@ Using the basic ingredient of supersymmetry, a simple alternative approach is developed to perturbation theory in one-dimensional non-relativistic quantum mechanics. The formulae for the energy shifts and wavefunctions do not involve tedious calculations which appear in the available perturbation theories. The model applicable in the same form to both the ground state and excited bound states, unlike the recently introduced supersymmetric perturbation technique which, together with other approaches based on logarithmic perturbation theory, are involved within the more general framework of the present formalism.
Density matrix perturbation theory.
Niklasson, Anders M N; Challacombe, Matt
2004-05-14
An orbital-free quantum perturbation theory is proposed. It gives the response of the density matrix upon variation of the Hamiltonian by quadratically convergent recursions based on perturbed projections. The technique allows treatment of embedded quantum subsystems with a computational cost scaling linearly with the size of the perturbed region, O(N(pert.)), and as O(1) with the total system size. The method allows efficient high order perturbation expansions, as demonstrated with an example involving a 10th order expansion. Density matrix analogs of Wigner's 2n+1 rule are also presented.
Imaging Photon Lattice States by Scanning Defect Microscopy
Underwood, D. L.; Shanks, W. E.; Li, Andy C. Y.; Ateshian, Lamia; Koch, Jens; Houck, A. A.
2016-04-01
Microwave photons inside lattices of coupled resonators and superconducting qubits can exhibit surprising matterlike behavior. Realizing such open-system quantum simulators presents an experimental challenge and requires new tools and measurement techniques. Here, we introduce scanning defect microscopy as one such tool and illustrate its use in mapping the normal-mode structure of microwave photons inside a 49-site kagome lattice of coplanar waveguide resonators. Scanning is accomplished by moving a probe equipped with a sapphire tip across the lattice. This locally perturbs resonator frequencies and induces shifts of the lattice resonance frequencies, which we determine by measuring the transmission spectrum. From the magnitude of mode shifts, we can reconstruct photon field amplitudes at each lattice site and thus create spatial images of the photon-lattice normal modes.
Universality and the approach to the continuum limit in lattice gauge theory
De Divitiis, G M; Guagnelli, M; Lüscher, Martin; Petronzio, Roberto; Sommer, Rainer; Weisz, P; Wolff, U; de Divitiis, G; Frezzotti, R; Guagnelli, M; Luescher, M; Petronzio, R; Sommer, R; Weisz, P; Wolff, U
1995-01-01
The universality of the continuum limit and the applicability of renormalized perturbation theory are tested in the SU(2) lattice gauge theory by computing two different non-perturbatively defined running couplings over a large range of energies. The lattice data (which were generated on the powerful APE computers at Rome II and DESY) are extrapolated to the continuum limit by simulating sequences of lattices with decreasing spacings. Our results confirm the expected universality at all energies to a precision of a few percent. We find, however, that perturbation theory must be used with care when matching different renormalized couplings at high energies.
Evidence for a Lattice Weak Gravity Conjecture
Heidenreich, Ben; Rudelius, Tom
2016-01-01
The Weak Gravity Conjecture postulates the existence of superextremal charged particles, i.e. those with mass smaller than or equal to their charge in Planck units. We present further evidence for our recent observation that in known examples a much stronger statement is true: an infinite tower of superextremal particles of different charges exists. We show that effective Kaluza-Klein field theories and perturbative string vacua respect the Sublattice Weak Gravity Conjecture, namely that a finite index sublattice of the full charge lattice exists with a superextremal particle at each site. In perturbative string theory we show that this follows from modular invariance. However, we present counterexamples to the stronger possibility that a superextremal state exists at every lattice site, including an example in which the lightest charged state is subextremal. The Sublattice Weak Gravity Conjecture has many implications both for abstract theories of quantum gravity and for real-world physics. For instance, it ...
Stabilizing Perturbative Yang-Mills Free Energy with Gribov Quantization
Fukushima, Kenji
2013-01-01
We evaluate the free energy of the Yang-Mills theory using the Gribov quantization that copes with non-perturbative resummation. The magnetic scale is automatically incorporated in the framework and we find it efficient to stabilize the perturbative expansion of the free energy. In the range of the temperature T=T_c~2T_c major uncertainty in our results comes from the non-perturbative running coupling that is adopted from the lattice simulation, while the convergence above 2T_c is impressively robust.
Molecular cluster perturbation theory. I. Formalism
Byrd, Jason N.; Jindal, Nakul; Molt, Robert W., Jr.; Bartlett, Rodney J.; Sanders, Beverly A.; Lotrich, Victor F.
2015-11-01
We present second-order molecular cluster perturbation theory (MCPT(2)), a linear scaling methodology to calculate arbitrarily large systems with explicit calculation of individual wave functions in a coupled-cluster framework. This new MCPT(2) framework uses coupled-cluster perturbation theory and an expansion in terms of molecular dimer interactions to obtain molecular wave functions that are infinite order in both the electronic fluctuation operator and all possible dimer (and products of dimers) interactions. The MCPT(2) framework has been implemented in the new SIA/Aces4 parallel architecture, making use of the advanced dynamic memory control and fine-grained parallelism to perform very large explicit molecular cluster calculations. To illustrate the power of this method, we have computed energy shifts, lattice site dipole moments, and harmonic vibrational frequencies via explicit calculation of the bulk system for the polar and non-polar polymorphs of solid hydrogen fluoride. The explicit lattice size (without using any periodic boundary conditions) was expanded up to 1000 HF molecules, with 32,000 basis functions and 10,000 electrons. Our obtained HF lattice site dipole moments and harmonic vibrational frequencies agree well with the existing literature.
Campos, R G; Campos, Rafael G.; Tututi, Eduardo S.
2002-01-01
It is shown that the nonlocal Dirac operator yielded by a lattice model that preserves chiral symmetry and uniqueness of fields, approaches to an ultralocal and invariant under translations operator when the size of the lattice tends to zero.
New integrable lattice hierarchies
Energy Technology Data Exchange (ETDEWEB)
Pickering, Andrew [Area de Matematica Aplicada, ESCET, Universidad Rey Juan Carlos, c/ Tulipan s/n, 28933 Mostoles, Madrid (Spain); Zhu Zuonong [Departamento de Matematicas, Universidad de Salamanca, Plaza de la Merced 1, 37008 Salamanca (Spain) and Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200030 (China)]. E-mail: znzhu2@yahoo.com.cn
2006-01-23
In this Letter we give a new integrable four-field lattice hierarchy, associated to a new discrete spectral problem. We obtain our hierarchy as the compatibility condition of this spectral problem and an associated equation, constructed herein, for the time-evolution of eigenfunctions. We consider reductions of our hierarchy, which also of course admit discrete zero curvature representations, in detail. We find that our hierarchy includes many well-known integrable hierarchies as special cases, including the Toda lattice hierarchy, the modified Toda lattice hierarchy, the relativistic Toda lattice hierarchy, and the Volterra lattice hierarchy. We also obtain here a new integrable two-field lattice hierarchy, to which we give the name of Suris lattice hierarchy, since the first equation of this hierarchy has previously been given by Suris. The Hamiltonian structure of the Suris lattice hierarchy is obtained by means of a trace identity formula.
``Heavy-water Lattice and Heavy-Quark''
Maksoed, Ssi, Wh-
Refer to Birgitt Roettger-Roessler: ``Feelings at the Margins'', 2014 retrieved the Vienna, 2006 UNIDO Research Programme: Combating Marginalization and Poverty through Industrial Development/COMPID. Also from Vienna, on Feb 18-22, 1963 reported Technical Report Series 20 about ``Heavy Water Lattice''. Failed to relates scale-invariant properties of public-Debt growth to convergence in perturbation theory, sought JH Field: ``Convergence & Gauge Dependence Properties:..''. Furthers, in GP Lepage: ``On the Viabilities of Lattice Perturbation Theory'', 1992 stated: ``in terms of physical quantities, like the heavy-quark potential, greatly enhanced the predictive power of lattice perturbation theory''. Acknowledgements to HE. Mr. H. TUK SETYOHADI, Jl. Sriwijaya Raya 3, South-Jakarta, INDONESIA.
Cosmological phase transitions from lattice field theory
Energy Technology Data Exchange (ETDEWEB)
Jansen, Karl [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2011-11-22
In this proceedings contribution we discuss the fate of the electroweak and the quantum chromodynamics phase transitions relevant for the early stage of the universe at non-zero temperature. These phase transitions are related to the Higgs mechanism and the breaking of chiral symmetry, respectively. We will review that non-perturbative lattice field theory simulations show that these phase transitions actually do not occur in nature and that physical observables show a completely smooth behaviour as a function of the temperature.
The Theory of Argumentation within Language and its relation to Plato, Saussure and Benveniste
Directory of Open Access Journals (Sweden)
Cristiane Dall'Cortivo-Lebler
2014-12-01
Full Text Available The Theory of Argumentation within Language, developed by Oswald Ducrot, Jean-Claude Anscombre and Marion Carel, has experienced along its development different phases and forms, constantly seeking to align to what its main developer, Oswald Ducrot, called external hypotheses and internal hypotheses. This paper discusses the presence of Linguistic Theories and Philosophy in Ducrot’s work regarding concepts of Plato, Ferdinand de Saussure and Émile Benveniste, which constitute its external assumptions. The presence of these concepts culminated in the creation of different concepts that comprise the Linguistic Semantics, and gave it a specific point of view about language that emphasizes the internal relationships among language components and understands that speech is the result of a linguistic activity where an “I” speaks to a “you”.
Efficient methods for solving discrete topology design problems in the PLATO-N project
DEFF Research Database (Denmark)
Canh, Nam Nguyen; Stolpe, Mathias
This paper considers the general multiple load structural topology design problems in the framework of the PLATO-N project. The problems involve a large number of discrete design variables and were modeled as a non-convex mixed 0–1 program. For the class of problems considered, a global...... optimization method based on the branch-and-cut concept was developed and implemented. In the method a large number of continuous relaxations were solved. We also present an algorithm for generating cuts to strengthen the quality of the relaxations. Several heuristics were also investigated to obtain efficient...... algorithms. The branch and cut method is used to solve benchmark examples which can be used to validate other methods and heuristics....
Alternative communication network designs for an operational Plato 4 CAI system
Mobley, R. E., Jr.; Eastwood, L. F., Jr.
1975-01-01
The cost of alternative communications networks for the dissemination of PLATO IV computer-aided instruction (CAI) was studied. Four communication techniques are compared: leased telephone lines, satellite communication, UHF TV, and low-power microwave radio. For each network design, costs per student contact hour are computed. These costs are derived as functions of student population density, a parameter which can be calculated from census data for one potential market for CAI, the public primary and secondary schools. Calculating costs in this way allows one to determine which of the four communications alternatives can serve this market least expensively for any given area in the U.S. The analysis indicates that radio distribution techniques are cost optimum over a wide range of conditions.
Banishing the Poet: The Pedagogical Function of Mythology in the Dialogues of Plato
Directory of Open Access Journals (Sweden)
Javier Martínez
2013-06-01
Full Text Available This text attempts to develop a sound justification for Plato’s pedagogical use of myth in the dialogues. In particular, I seek to resolve a seeming contradiction: why Plato personally made use of myths in spite of his many statements that seem to contradict such a pedagogical approach, especially his edict that poets and myth-makers be banished from his republic for the danger their works pose to the attainment of true philosophical wisdom. An analysis of the centrality of myths to the dialogues is carried out, followed by a discussion of the place of muthos in its Ionian historical context. This establishes the basis for resolving the contradiction through the division of muthos into two distinct modes: the fantastic and the eikastic.
Arete and Gender-Differentiation in Socrates/Plato and Aristotle
Directory of Open Access Journals (Sweden)
Thomas Robinson
1998-12-01
Full Text Available The article grapples with the question whether Plato believed that, in the matter of arete, the female psyche had a built-in inclination to immorality in a way that the male psyche did not, and was therefore assuch signiticantly different from the male psyche. It is argued that the evidence of the Timaeus ( and, to some lesser degree, of the Laws suggests very strongly that he did, though fortunately the political consequence she drew from this (in the Laws tum out to be positive rather than negative. Aristotle, by contrast,it is argued, while still holding to the lamentable theory of the inferiority of woman, talks of ditl'eringquanta of (one and the same arete in male and female souls, rather than a difference in their very arete.
Non-perturbative study of QCD correlators
Lokhov, A Y
2006-01-01
This PhD dissertation is devoted to a non-perturbative study of QCD correlators. The main tool that we use is lattice QCD. We concentrated our efforts on the study of the main correlators of the pure Yang - Mills theory in the Landau gauge, namely the ghost and the gluon propagators. We are particularly interested in determining the $\\Lqcd$ parameter. It is extracted by means of perturbative predictions available up to NNNLO. The related topic is the influence of non-perturbative effects that show up as appearance of power-corrections to the low-momentum behaviour of the Green functions. A new method of removing these power corrections allows a better estimate of $\\Lqcd$. Our result is $\\Lambda^{n_f=0}_{\\ms} = 269(5)^{+12}_{-9}$ MeV. Another question that we address is the infrared behaviour of Green functions, at momenta of order and below $\\Lqcd$. At low energy the momentum dependence of the propagators changes considerably, and this is probably related to confinement. The lattice approach allows to check t...
Perturbative Topological Field Theory
Dijkgraaf, Robbert
We give a review of the application of perturbative techniques to topological quantum field theories, in particular three-dimensional Chern-Simons-Witten theory and its various generalizations. To this end we give an introduction to graph homology and homotopy algebras and the work of Vassiliev and Kontsevich on perturbative knot invariants.
Perturbing supersymmetric black hole
Onozawa, H; Mishima, T; Ishihara, H; Onozawa, Hisashi; Okamura, Takashi; Mishima, Takashi; Ishihara, Hideki
1996-01-01
An investigation of the perturbations of the Reissner-Nordstr\\"{o}m black hole in the N=2 supergravity is presented. In the extreme case, the black hole responds to the perturbation of each field in the same manner. This is possibly because we can match the modes of the graviton, gravitino, and photon using supersymmetry transformations.
Sober Topological Molecular Lattices
Institute of Scientific and Technical Information of China (English)
张德学; 李永明
2003-01-01
A topological molecular lattice (TML) is a pair (L, T), where L is a completely distributive lattice and r is a subframe of L. There is an obvious forgetful functor from the category TML of TML's to the category Loc of locales. In this note,it is showed that this forgetful functor has a right adjoint. Then, by this adjunction,a special kind of topological molecular lattices called sober topological molecular lattices is introduced and investigated.
Platón y el silogismo Plato and the syllogism
Directory of Open Access Journals (Sweden)
Manuel Correia Machuca
2010-03-01
Full Text Available La cuestión de si Platón pudo ser el autor de una primera noción de deducción silogística (un método que Aristóteles hizo conocido a través de una definición y un progreso teórico en los Analíticos Primeros fue discutida en la antigüedad y, desde entonces, debatida por varios comentaristas. En este artículo, comento dos pasajes de la literatura post-aristotélica, uno atestiguado por Boecio (que se remonta a Alejandro de Afrodisia y el otro presente en Juan Filópono, en su comentario a los Analíticos Primeros. El artículo intenta mostrar que estos pasajes contienen información suficiente para favorecer a Platón como conocedor de la técnica deductiva silogística, aunque no para conferirle el desarrollo de la metodología silogística.The question of whether Plato could be the author of a first concept of syllogistic deduction (a method that Aristotle made known by means of a definition and a theoretical improvement in his Prior Analytics was known in the antiquity and from that time, the question has usually examined by several commentators. In this article, I comment on two passages of post-Aristotelian tradition; one is given by Boethius (which stems from Alexander of Aphrodisias and the other was given by Johannes Philoponus in his commentary on Prior Analytics. The article intends to show that these passages contain information that is sufficient to come to an opinion favoring Plato, although it does not imply that they are sufficient to confer him the syllogistic method.
Frame independent cosmological perturbations
Energy Technology Data Exchange (ETDEWEB)
Prokopec, Tomislav; Weenink, Jan, E-mail: t.prokopec@uu.nl, E-mail: j.g.weenink@uu.nl [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, Leuvenlaan 4, 3585 CE Utrecht (Netherlands)
2013-09-01
We compute the third order gauge invariant action for scalar-graviton interactions in the Jordan frame. We demonstrate that the gauge invariant action for scalar and tensor perturbations on one physical hypersurface only differs from that on another physical hypersurface via terms proportional to the equation of motion and boundary terms, such that the evolution of non-Gaussianity may be called unique. Moreover, we demonstrate that the gauge invariant curvature perturbation and graviton on uniform field hypersurfaces in the Jordan frame are equal to their counterparts in the Einstein frame. These frame independent perturbations are therefore particularly useful in relating results in different frames at the perturbative level. On the other hand, the field perturbation and graviton on uniform curvature hypersurfaces in the Jordan and Einstein frame are non-linearly related, as are their corresponding actions and n-point functions.
Non-perturbative lorentzian quantum gravity, causality and topology change
Ambjørn, J.; Loll, R.
1998-01-01
We formulate a non-perturbative lattice model of two-dimensional Lorentzian quantum gravity by performing the path integral over geometries with a causal structure. The model can be solved exactly at the discretized level. Its continuum limit coincides with the theory obtained by quantizing 2d conti
Stability analysis for solitons in PT-symmetric optical lattices
Nixon, Sean; Yang, Jianke
2012-01-01
Stability of solitons in parity-time (PT)-symmetric periodic potentials (optical lattices) is analyzed in both one- and two-dimensional systems. First we show analytically that when the strength of the gain-loss component in the PT lattice rises above a certain threshold (phase-transition point), an infinite number of linear Bloch bands turn complex simultaneously. Second, we show that while stable families of solitons can exist in PT lattices, increasing the gain-loss component has an overall destabilizing effect on soliton propagation. Specifically, when the gain-loss component increases, the parameter range of stable solitons shrinks as new regions of instability appear. Thirdly, we investigate the nonlinear evolution of unstable PT solitons under perturbations, and show that the energy of perturbed solitons can grow unbounded even though the PT lattice is below the phase transition point.
Nonlinear Realization of Chiral Symmetry on the Lattice
Chandrasekharan, S; Steffen, F D; Wiese, U J
2003-01-01
We formulate lattice theories in which chiral symmetry is realized nonlinearly on the fermion fields. In this framework the fermion mass term does not break chiral symmetry. This property allows us to use the Wilson term to remove the doubler fermions while maintaining exact chiral symmetry on the lattice. Our lattice formulation enables us to address non-perturbative questions in effective field theories of baryons interacting with pions and in models involving constituent quarks interacting with pions and gluons. We show that a system containing a non-zero density of static baryons interacting with pions can be studied on the lattice without encountering complex action problems. In our formulation one can also decide non-perturbatively if the chiral quark model of Georgi and Manohar provides an appropriate low-energy description of QCD. If so, one could understand why the non-relativistic quark model works.
Atkinson, D; van Steenwijk, F.J.
The resistance between two arbitrary nodes in an infinite square lattice of:identical resistors is calculated, The method is generalized to infinite triangular and hexagonal lattices in two dimensions, and also to infinite cubic and hypercubic lattices in three and more dimensions. (C) 1999 American
Lattice Regularization and Symmetries
Hasenfratz, Peter; Von Allmen, R; Allmen, Reto von; Hasenfratz, Peter; Niedermayer, Ferenc
2006-01-01
Finding the relation between the symmetry transformations in the continuum and on the lattice might be a nontrivial task as illustrated by the history of chiral symmetry. Lattice actions induced by a renormalization group procedure inherit all symmetries of the continuum theory. We give a general procedure which gives the corresponding symmetry transformations on the lattice.
Lattice Theories with Nonlinearly Realized Chiral Symmetry
Chandrasekharan, S; Steffen, F D; Wiese, U J
2003-01-01
We present the lattice formulation of effective Lagrangians in which chiral symmetry is realized nonlinearly on the fermion fields. In this framework both the Wilson term removing unphysical doubler fermions and the fermion mass term do not break chiral symmetry. Our lattice formulation allows us to address non-perturbative questions in effective theories of baryons interacting with pions and in models involving constitutent quarks interacting with pions and gluons. With the presented methods, a system containing a non-zero density of static baryons interacting with pions can be studied on the lattice without encountering a complex action problem. This might lead to new insights into the phase diagram of strongly interacting matter at non-zero chemical potential.
Rare kaon decays on the lattice
Energy Technology Data Exchange (ETDEWEB)
Isidori, Gino [INFN, Laboratori Nazionali di Frascati, I-00044 Frascati (Italy)]. E-mail: gino.isidori@lnf.infn.it; Martinelli, Guido [Dipartimento di Fisica, Universita di Roma ' La Sapienza' and INFN, Sezione di Roma, P.le A. Moro 2, I-00185 Rome (Italy); Turchetti, Paolo [Dipartimento di Fisica, Universita di Roma ' La Sapienza' and INFN, Sezione di Roma, P.le A. Moro 2, I-00185 Rome (Italy)
2006-02-02
We show that long-distance contributions to the rare decays K->{pi}{nu}{nu}-bar and K->{pi}-bar {sup +}-bar {sup -} can be computed using lattice QCD. The proposed approach requires well established methods, successfully applied in the calculations of electromagnetic and semileptonic form factors. The extra power divergences, related to the use of weak four-fermion operators, can be eliminated using only the symmetries of the lattice action without ambiguities or complicated non-perturbative subtractions. We demonstrate that this is true even when a lattice action with explicit chiral symmetry breaking is employed. Our study opens the possibility of reducing the present uncertainty in the theoretical predictions for these decays.
Thermal dilepton rates from quenched lattice QCD
Ding, H -T; Kaczmarek, O; Karsch, F; Laermann, E; Mukherjee, S; Müller, M; Soeldner, W
2013-01-01
We present new lattice results on the continuum extrapolation of the vector current correlation function. Lattice calculations have been carried out in the deconfined phase at a temperature of 1.1 Tc, extending our previous results at 1.45 Tc, utilizing quenched non-perturbatively clover-improved Wilson fermions and light quark masses. A systematic analysis on multiple lattice spacings allows to perform the continuum limit of the correlation function and to extract spectral properties in the continuum limit. Our current analysis suggests the results for the electrical conductivity are proportional to the temperature and the thermal dilepton rates in the quark gluon plasma are comparable for both temperatures. Preliminary results of the continuum extrapolated correlation function at finite momenta, which relates to thermal photon rates, are also presented.
Neutron-antineutron oscillations on the lattice
Buchoff, Michael I; Wasem, Joseph
2012-01-01
One possible low energy process due to beyond the Standard Model (BSM) physics is the neutron-antineutron transition, where baryon number changes by two units. In addition to providing a source of baryon number violation in the early universe, interactions of this kind are natural in grand unified theories (GUTs) with Majorana neutrinos that violate lepton number. Bounds on these oscillations can greatly restrict a variety of GUTs, while a non-zero signal would be a "smoking gun" for new physics; however, to make a reliable prediction, the six-quark nucleon-antinucleon matrix elements must first be calculated non-perturbatively via lattice QCD. We review the current understanding of this quantity, describe the lattice formalism, and present preliminary results from $32^3\\times256$ clover-Wilson lattices with a pion mass of 390 MeV.
Lattice Three-Dimensional Skyrmions Revisited
Charalampidis, E G; Kevrekidis, P G
2014-01-01
In the continuum a skyrmion is a topological nontrivial map between Riemannian manifolds, and a stationary point of a particular energy functional. This paper describes lattice analogues of the aforementioned skyrmions, namely a natural way of using the topological properties of the three-dimensional continuum Skyrme model to achieve topological stability on the lattice. In particular, using fixed point iterations, numerically exact lattice skyrmions are constructed; and their stability under small perturbations is verified by means of linear stability analysis. While stable branches of such solutions are identified, it is also shown that they possess a particularly delicate bifurcation structure, especially so in the vicinity of the continuum limit. The corresponding bifurcation diagram is elucidated and a prescription for selecting the branch asymptoting to the well-known continuum limit is given. Finally, the robustness of the solutions by virtue of direct numerical simulations is corroborated.
Lattice Induced Frequency Shifts in Sr Optical Lattice Clocks at the $10^{-17}$ Level
Westergaard, Philip G; Lorini, Luca; Lecallier, Arnaud; Burt, Eric; Zawada, Michal; Millo, Jacques; Lemonde, Pierre
2011-01-01
We present a comprehensive study of the frequency shifts associated with the lattice potential for a Sr lattice clock. By comparing two such clocks with a frequency stability reaching $5\\times 10^{-17}$ after a one hour integration time, and varying the lattice depth up to $U_0=900 \\, E_r$ with $E_r$ being the recoil energy, we evaluate lattice related shifts with an unprecedented accuracy. We put the first experimental upper bound on the recently predicted frequency shift due to the magnetic dipole (M1) and electric quadrupole (E2) interactions. This upper bound is significantly smaller than the theoretical upper limit. We also give a new upper limit on the effect of hyperpolarizability with an improvement by more than one order of magnitude. Finally, we report the first observation of the vector and tensor shifts in a lattice clock. Combining these measurements, we show that all known lattice related perturbation will not affect the clock accuracy down to the $10^{-17}$ level, even for very deep lattices, u...
Habib, A.; Menouni, M.; Pangaud, P.; Fenzi, C.; Colledani, G.; Moureau, G.; Escarguel, A.; Morel, C.
2017-01-01
PLATO is a prototype hybrid X-ray photon counting detector that has been designed to meet the specifications for plasma diagnostics for the WEST tokamak platform (Tungsten (W) Environment in Steady-state Tokamak) in southern France, with potential perspectives for ITER. PLATO represents a customized solution that fulfills high sensitivity, low dispersion and high photon counting rate. The PLATO prototype matrix is composed of 16 × 18 pixels with a 70 μm pixel pitch. New techniques have been used in analog sensitive blocks to minimize noise coupling through supply rails and substrate, and to suppress threshold dispersion across the matrix. The PLATO ASIC is designed in CMOS 0.13 μm technology and was submitted for a fabrication run in June 2016. The chip is designed to be bump-bonded to a silicon sensor. This paper presents pixel architecture as well as simulation results while highlighting novel solutions.
Perturbative static four-quark potentials
Lang, J; Green, A M
1995-01-01
A first attempt to understand hadron dynamics at low energies in terms of the fundamental quark and gluon degrees of freedom incorporates the effects of the gluonic field into a potential depending only on the spatial positions of the quarks, which are considered in the infinite mass limit. A suitable framework for calculating such potentials between static quarks, i.e.\\ a generalization of the Wilson loop will be discussed. Making a connection with recent Monte Carlo lattice simulations for the lowest two energies of a system of two quarks and two antiquarks, the static qq\\bar{q}\\bar{q}-potential will be calculated in perturbation theory to fourth order. The result will be shown to be exactly equal to the prediction of a straightforward two-body approach, which in Monte Carlo lattice simulations has been found to be a reasonable approximation for very small interquark distances.
Rong, Shu-Jun; Liu, Qiu-Yu
2012-04-01
The puma model on the basis of the Lorentz and CPT violation may bring an economical interpretation to the conventional neutrinos oscillation and part of the anomalous oscillations. We study the effect of the perturbation to the puma model. In the case of the first-order perturbation which keeps the (23) interchange symmetry, the mixing matrix element Ue3 is always zero. The nonzero mixing matrix element Ue3 is obtained in the second-order perturbation that breaks the (23) interchange symmetry.
Topics in lattice QCD and effective field theory
Buchoff, Michael I.
Quantum Chromodynamics (QCD) is the fundamental theory that governs hadronic physics. However, due to its non-perturbative nature at low-energy/long distances, QCD calculations are difficult. The only method for performing these calculations is through lattice QCD. These computationally intensive calculations approximate continuum physics with a discretized lattice in order to extract hadronic phenomena from first principles. However, as in any approximation, there are multiple systematic errors between lattice QCD calculation and actual hardronic phenomena. Developing analytic formulae describing the systematic errors due to the discrete lattice spacings is the main focus of this work. To account for these systematic effects in terms of hadronic interactions, effective field theory proves to be useful. Effective field theory (EFT) provides a formalism for categorizing low-energy effects of a high-energy fundamental theory as long as there is a significant separation in scales. An example of this is in chiral perturbation theory (chiPT), where the low-energy effects of QCD are contained in a mesonic theory whose applicability is a result of a pion mass smaller than the chiral breaking scale. In a similar way, lattice chiPT accounts for the low-energy effects of lattice QCD, where a small lattice spacing acts the same way as the quark mass. In this work, the basics of this process are outlined, and multiple original calculations are presented: effective field theory for anisotropic lattices, I=2 pipi scattering for isotropic, anisotropic, and twisted mass lattices. Additionally, a combination of effective field theory and an isospin chemical potential on the lattice is proposed to extract several computationally difficult scattering parameters. Lastly, recently proposed local, chiral lattice actions are analyzed in the framework of effective field theory, which illuminates various challenges in simulating such actions.
Perfect Actions and Operators for Lattice QCD
Wiese, Uwe-Jens
1996-05-01
Wilson's renormalization group implies that lattice actions located on a renormalized trajectory emanating from a fixed point represent perfect discretizations of continuum physics. With a perfect action the spectrum of a lattice theory is identical with the one of the continuum theory even at finite lattice spacing. Similarly, perfect operators yield cut-off independent matrix elements. Hence, continuum QCD can in principle be reconstructed from a lattice with finite spacing. In practice it is difficult to construct perfect actions and perfect operators explicitly. Here perturbation theory is used to derive perfect actions for quarks and gluons by performing a block renormalization group transformation directly from the continuum. The renormalized trajectory for free massive quarks is identified and a parameter in the renormalization group transformation is tuned such that for 1-d configurations the perfect action reduces to the nearest neighbor Wilson fermion action. Then the 4-d perfect action turns out to be extremely local as well, which is vital for numerical simulations. The fixed point action for free gluons is also obtained by blocking from the continuum. For 2-d configurations it reduces to the standard plaquette action, and for 4-d configurations it is still very local. With interactions between quarks and gluons switched on the perfect quark-gluon and 3-gluon vertex functions are computed analytically. In particular, a perfect clover term can be extracted from the quark-gluon vertex. The perturbatively perfect action is directly applicable to heavy quark physics. The construction of a perfect QCD action for light quarks should include nonperturbative effects, which is possible using numerical methods. Classically perfect quark and gluon fields are constructed as well. They allow to interpolate the continuum fields from the lattice data. In this way one can obtain information about space-time regions between lattice points. The classically perfect fields
Improving perturbation theory with cactus diagrams
Constantinou, M; Skouroupathis, A; Constantinou, Martha; Panagopoulos, Haralambos; Skouroupathis, Apostolos
2006-01-01
We study a systematic improvement of perturbation theory for gauge fields on the lattice [hep-lat/0606001]; the improvement entails resumming, to all orders in the coupling constant, a dominant subclass of tadpole diagrams. This method, originally proposed for the Wilson gluon action, is extended here to encompass all possible gluon actions made of closed Wilson loops; any fermion action can be employed as well. The effect of resummation is to replace various parameters in the action (coupling constant, Symanzik and clover coefficient) by ``dressed'' values; the latter are solutions to certain coupled integral equations, which are easy to solve numerically. Some positive features of this method are: a) It is gauge invariant, b) it can be systematically applied to improve (to all orders) results obtained at any given order in perturbation theory, c) it does indeed absorb in the dressed parameters the bulk of tadpole contributions. Two different applications are presented: The additive renormalization of fermio...
Perturbations of planar algebras
Das, Paramita; Gupta, Ved Prakash
2010-01-01
We introduce the concept of {\\em weight} of a planar algebra $P$ and construct a new planar algebra referred as the {\\em perturbation of $P$} by the weight. We establish a one-to-one correspondence between pivotal structures on 2-categories and perturbations of planar algebras by weights. To each bifinite bimodule over $II_1$-factors, we associate a {\\em bimodule planar algebra} bimodule corresponds naturally with sphericality of the bimodule planar algebra. As a consequence of this, we reproduce an extension of Jones' theorem (of associating 'subfactor planar algebras' to extremal subfactors). Conversely, given a bimodule planar algebra, we construct a bifinite bimodule whose associated bimodule planar algebra is the one which we start with using perturbations and Jones-Walker-Shlyakhtenko-Kodiyalam-Sunder method of reconstructing an extremal subfactor from a subfactor planar algebra. We show that the perturbation class of a bimodule planar algebra contains a unique spherical unimodular bimodule planar algeb...
Introduction to perturbation techniques
Nayfeh, Ali H
2011-01-01
Similarities, differences, advantages and limitations of perturbation techniques are pointed out concisely. The techniques are described by means of examples that consist mainly of algebraic and ordinary differential equations. Each chapter contains a number of exercises.
Lattice Models of Quantum Gravity
Bittner, E R; Holm, C; Janke, W; Markum, H; Riedler, J
1998-01-01
Standard Regge Calculus provides an interesting method to explore quantum gravity in a non-perturbative fashion but turns out to be a CPU-time demanding enterprise. One therefore seeks for suitable approximations which retain most of its universal features. The $Z_2$-Regge model could be such a desired simplification. Here the quadratic edge lengths $q$ of the simplicial complexes are restricted to only two possible values $q=1+\\epsilon\\sigma$, with Ising model. To test whether this simpler model still contains the essential qualities of the standard Regge Calculus, we study both models in two dimensions and determine several observables on the same lattice size. In order to compare expectation values, e.g. of the average curvature or the Liouville field susceptibility, we employ in both models the same functional integration measure. The phase structure is under current investigation using mean field theory and numerical simulation.
Technicolor and Lattice Gauge Theory
Chivukula, R Sekhar
2010-01-01
Technicolor and other theories of dynamical electroweak symmetry breaking invoke chiral symmetry breaking triggered by strong gauge-dynamics, analogous to that found in QCD, to explain the observed W, Z, and fermion masses. In this talk we describe why a realistic theory of dynamical electroweak symmetry breaking must, relative to QCD, produce an enhanced fermion condensate. We quantify the degree to which the technicolor condensate must be enhanced in order to yield the observed quark masses, and still be consistent with phenomenological constraints on flavor-changing neutral-currents. Lattice studies of technicolor and related theories provide the only way to demonstrate that such enhancements are possible and, hopefully, to discover viable candidate models. We comment briefly on the current status of non-perturbative investigations of dynamical electroweak symmetry breaking, and provide a "wish-list" of phenomenologically-relevant properties that are important to calculate in these theories
Pion structure from lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Javadi Motaghi, Narjes
2015-05-12
In this thesis we use lattice QCD to compute the second Mellin moments of pion generalized parton distributions and pion electromagnetic form factors. For our calculations we are able to analyze a large set of gauge configurations with 2 dynamical flavours using non-perturbatively the improved Wilson-Sheikholeslami-Wohlert fermionic action pion masses ranging down to 151 MeV. By employing improved smearing we were able to suppress excited state contamination. However, our data in the physical quark mass limit show that some excited state contamination remains. We show the non-zero sink momentum is optimal for the computation of the electromagnetic form factors and generalized form factors at finite momenta.
Perturbations around black holes
Wang, B
2005-01-01
Perturbations around black holes have been an intriguing topic in the last few decades. They are particularly important today, since they relate to the gravitational wave observations which may provide the unique fingerprint of black holes' existence. Besides the astrophysical interest, theoretically perturbations around black holes can be used as testing grounds to examine the proposed AdS/CFT and dS/CFT correspondence.
Perturbations and quantum relaxation
Kandhadai, Adithya
2016-01-01
We investigate whether small perturbations can cause relaxation to quantum equilibrium over very long timescales. We consider in particular a two-dimensional harmonic oscillator, which can serve as a model of a field mode on expanding space. We assume an initial wave function with small perturbations to the ground state. We present evidence that the trajectories are highly confined so as to preclude relaxation to equilibrium even over very long timescales. Cosmological implications are briefly discussed.
Non-perturbative renormalization of quark bilinear operators and B_K using domain wall fermions
Aoki, Y; Christ, N H; Dawson, C; Donnellan, M A; Izubuchi, T; Juttner, A; Li, S; Mawhinney, R D; Noaki, J; Sachrajda, Christopher T C; Soni, A; Tweedie, R J; Yamaguchi, A
2007-01-01
We present a calculation of the renormalization coefficients of the quark bilinear operators and the K-Kbar mixing parameter B_K. The coefficients relating the bare lattice operators to those in the RI/MOM scheme are computed non-perturbatively and then matched perturbatively to the MSbar scheme. The coefficients are calculated on the RBC/UKQCD 2+1 flavor dynamical lattice configurations. Specifically we use a 16^3 x 32 lattice volume, the Iwasaki gauge action at beta=2.13 and domain wall fermions with L_s=16.
The K+ K+ scattering length from Lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Silas Beane; Thomas Luu; Konstantinos Orginos; Assumpta Parreno; Martin Savage; Aaron Torok; Andre Walker-Loud
2007-09-11
The K+K+ scattering length is calculated in fully-dynamical lattice QCD with domain-wall valence quarks on the MILC asqtad-improved gauge configurations with fourth-rooted staggered sea quarks. Three-flavor mixed-action chiral perturbation theory at next-to-leading order, which includes the leading effects of the finite lattice spacing, is used to extrapolate the results of the lattice calculation to the physical value of mK + /fK + . We find mK^+ aK^+ K^+ = â~0.352 Â± 0.016, where the statistical and systematic errors have been combined in quadrature.
Inhomogeneous atomic Bose-Fermi mixtures in cubic lattices.
Cramer, M; Eisert, J; Illuminati, F
2004-11-05
We determine the ground state properties of inhomogeneous mixtures of bosons and fermions in cubic lattices and parabolic confining potentials. For finite hopping we determine the domain boundaries between Mott-insulator plateaux and hopping-dominated regions for lattices of arbitrary dimension within mean-field and perturbation theory. The results are compared with a new numerical method that is based on a Gutzwiller variational approach for the bosons and an exact treatment for the fermions. The findings can be applied as a guideline for future experiments with trapped atomic Bose-Fermi mixtures in optical lattices.
Aspects of lattice N=4 supersymmetric Yang--Mills
Schaich, David
2015-01-01
Non-perturbative investigations of $\\mathcal N = 4$ supersymmetric Yang--Mills theory formulated on a space-time lattice have advanced rapidly in recent years. Large-scale numerical calculations are currently being carried out based on a construction that exactly preserves a single supersymmetry at non-zero lattice spacing. A recent development is the creation of an improved lattice action through a new procedure to regulate flat directions in a manner compatible with this supersymmetry, by modifying the moduli equations. In this proceedings I briefly summarize this new procedure and discuss the parameter space of the resulting improved action that is now being employed in numerical calculations.
Institute of Scientific and Technical Information of China (English)
RONG Shu-Jun; LIU Qiu-Yu
2012-01-01
The puma model on the basis of the Lorentz and CPT violation may bring an economical interpretation to the conventional neutrinos oscillation and part of the anomalous oscillations.We study the effect of the perturbation to the puma model.In the case of the first-order perturbation which keeps the (23) interchange symmetry,the mixing matrix element Ue3 is always zero.The nonzero mixing matrix element Ue3 is obtained in the second-order perturbation that breaks the (23) interchange symmetry.%The puma model on the basis of the Lorentz and CPT violation may bring an economical interpretation to the conventional neutrinos oscillation and part of the anomalous oscillations. We study the effect of the perturbation to the puma model. In the case of the first-order perturbation which keeps the (23) interchange symmetry, the mixing matrix element Ue3 is always zero. The nonzero mixing matrix element Ue3 is obtained in the second-order perturbation that breaks the (23) interchange symmetry.
Two-loop thermodynamics of warm and dense (isospin and baryo-chemical potential) perturbative QCD
Energy Technology Data Exchange (ETDEWEB)
Graf, Thorben [Institut fuer Theoretische Physik, Goethe Universitaet, Frankfurt am Main (Germany); Schaffner-Bielich, Juergen [Institut fuer Theoretische Physik, Goethe Universitaet, Frankfurt am Main (Germany); Fraga, Eduardo S. [Instituto de Fisica, Universidade Federal do Rio de Janeiro, Rio de Janeiro (Brazil)
2014-07-01
We present a perturbative calculation of the thermodynamical potential of quantum chromodynamics at nonvanishing temperatures for different values of the isospin and baryo-chemical potential. A comparison to recent lattice calculations at nonvanishing isospin is performed and the region of the break-down of the perturbative calculations are delineated. Finally, we study the thermodynamic potential at high chemical potentials and low temperatures where the perturbative scheme should be also applicable.
NSPT study of the three-loop lattice gluon propagator in Landau gauge
Torrero, C; Ilgenfritz, E -M; Perlt, H; Schiller, A
2010-01-01
By means of Numerical Stochastic Perturbation Theory (NSPT), we calculate the lattice gluon propagator up to three loops of perturbation theory in the limits of infinite volume and vanishing lattice spacing. Based on known anomalous dimensions and a parametrization of both the hypercubic symmetry group H(4) and finite-size effects, we calculate the non-leading-log and non-logarithmic contributions iteratively, starting with the first-loop expression.
Coulomb Artifacts and Bottomonium Hyperfine Splitting in Lattice NRQCD
Liu, Tao; Rayyan, Ahmed
2016-01-01
We study the role of the lattice artifacts associated with the Coulomb binding effects in the analysis of the heavy quarkonium within lattice NRQCD. We find that a "na\\"ive" perturbative matching generates spurious linear Coulomb artifacts, which result in a large systematic error in the lattice predictions for the heavy quarkonium spectrum. This effect is responsible, in particular, for the discrepancy between the recent determinations of the bottomonium hyperfine splitting in the radiatively improved lattice NRQCD [1, 2]. We show that the correct matching procedure which provides full control over discretization errors is based on the asymptotic expansion of the lattice theory about the continuum limit, which gives $M_{\\Upsilon(1S)}-M_{\\eta_b(1S)}=52.9\\pm 5.5~{\\rm MeV}$ [1].
Jammed lattice sphere packings
Kallus, Yoav; Marcotte, Étienne; Torquato, Salvatore
2013-01-01
We generate and study an ensemble of isostatic jammed hard-sphere lattices. These lattices are obtained by compression of a periodic system with an adaptive unit cell containing a single sphere until the point of mechanical stability. We present detailed numerical data about the densities, pair correlations, force distributions, and structure factors of such lattices. We show that this model retains many of the crucial structural features of the classical hard-sphere model and propose it as a...
On Traveling Waves in Lattices: The Case of Riccati Lattices
Dimitrova, Zlatinka
2012-09-01
The method of simplest equation is applied for analysis of a class of lattices described by differential-difference equations that admit traveling-wave solutions constructed on the basis of the solution of the Riccati equation. We denote such lattices as Riccati lattices. We search for Riccati lattices within two classes of lattices: generalized Lotka-Volterra lattices and generalized Holling lattices. We show that from the class of generalized Lotka-Volterra lattices only the Wadati lattice belongs to the class of Riccati lattices. Opposite to this many lattices from the Holling class are Riccati lattices. We construct exact traveling wave solutions on the basis of the solution of Riccati equation for three members of the class of generalized Holling lattices.
Renormalization Constants of Quark Operators for the Non-Perturbatively Improved Wilson Action
Becirevic, D; Lubicz, V; Martinelli, G; Papinutto, Mauro; Reyes, J
2004-01-01
We present the results of an extensive lattice calculation of the renormalization constants of bilinear and four-quark operators for the non-perturbatively O(a)-improved Wilson action. The results are obtained in the quenched approximation at four values of the lattice coupling by using the non-perturbative RI/MOM renormalization method. Several sources of systematic uncertainties, including discretization errors and final volume effects, are examined. The contribution of the Goldstone pole, which in some cases may affect the extrapolation of the renormalization constants to the chiral limit, is non-perturbatively subtracted. The scale independent renormalization constants of bilinear quark operators have been also computed by using the lattice chiral Ward identities approach and compared with those obtained with the RI-MOM method. For those renormalization constants the non-perturbative estimates of which have been already presented in the literature we find an agreement which is typically at the level of 1%...
Energy Technology Data Exchange (ETDEWEB)
Shindler, A. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2007-07-15
I review the theoretical foundations, properties as well as the simulation results obtained so far of a variant of the Wilson lattice QCD formulation: Wilson twisted mass lattice QCD. Emphasis is put on the discretization errors and on the effects of these discretization errors on the phase structure for Wilson-like fermions in the chiral limit. The possibility to use in lattice simulations different lattice actions for sea and valence quarks to ease the renormalization patterns of phenomenologically relevant local operators, is also discussed. (orig.)
Exact quantization conditions for the relativistic Toda lattice
Hatsuda, Yasuyuki
2015-01-01
Inspired by recent connections between spectral theory and topological string theory, we propose exact quantization conditions for the relativistic Toda lattice of N particles. These conditions involve the Nekrasov-Shatashvili free energy, which resums the perturbative WKB expansion, but they require in addition a non-perturbative contribution, which is related to the perturbative result by an S-duality transformation of the Planck constant. We test the quantization conditions against explicit calculations of the spectrum for N=3. Our proposal can be generalized to arbitrary toric Calabi--Yau manifolds and might solve the corresponding quantum integrable system of Goncharov and Kenyon.
Exact quantization conditions for the relativistic Toda lattice
Hatsuda, Yasuyuki; Mariño, Marcos
2016-05-01
Inspired by recent connections between spectral theory and topological string theory, we propose exact quantization conditions for the relativistic Toda lattice of N particles. These conditions involve the Nekrasov-Shatashvili free energy, which resums the perturbative WKB expansion, but they require in addition a non-perturbative contribution, which is related to the perturbative result by an S-duality transformation of the Planck constant. We test the quantization conditions against explicit calculations of the spectrum for N = 3. Our proposal can be generalized to arbitrary toric Calabi-Yau manifolds and might solve the corresponding quantum integrable system of Goncharov and Kenyon.
Clustering under Perturbation Resilience
Balcan, Maria Florina
2011-01-01
Recently, Bilu and Linial \\cite{BL} formalized an implicit assumption often made when choosing a clustering objective: that the optimum clustering to the objective should be preserved under small multiplicative perturbations to distances between points. They showed that for max-cut clustering it is possible to circumvent NP-hardness and obtain polynomial-time algorithms for instances resilient to large (factor $O(\\sqrt{n})$) perturbations, and subsequently Awasthi et al. \\cite{ABS10} considered center-based objectives, giving algorithms for instances resilient to O(1) factor perturbations. In this paper, we greatly advance this line of work. For the $k$-median objective, we present an algorithm that can optimally cluster instances resilient to $(1 + \\sqrt{2})$-factor perturbations, solving an open problem of Awasthi et al.\\cite{ABS10}. We additionally give algorithms for a more relaxed assumption in which we allow the optimal solution to change in a small $\\epsilon$ fraction of the points after perturbation. ...
Di Renzo, F; Schröder, Y; Torrero, C
2008-01-01
The pressure of QCD admits at high temperatures a factorization into purely perturbative contributions from ``hard'' thermal momenta, and slowly convergent as well as non-perturbative contributions from ``soft'' thermal momenta. The latter can be related to various effective gluon condensates in a dimensionally reduced effective field theory, and measured there through lattice simulations. Practical measurements of one of the relevant condensates have suffered, however, from difficulties in extrapolating convincingly to the continuum limit. In order to gain insight on this problem, we employ Numerical Stochastic Perturbation Theory to estimate the problematic condensate up to 4-loop order in lattice perturbation theory. Our results seem to confirm the presence of ``large'' disretization effects, going like $a\\ln(1/a)$, where $a$ is the lattice spacing. For definite conclusions, however, it would be helpful to repeat the corresponding part of our study with standard lattice perturbation theory techniques.
The characters of nonlinear vibration in the two-dimensional discrete monoatomic lattice
Institute of Scientific and Technical Information of China (English)
XU Quan; TIAN Qiang
2005-01-01
The two-dimensional discrete monoatomic lattice is analyzed. Taking nearest-neighbor interaction into account, the characters of the nonlinear vibration in two-dimensional discrete monoatomic lattice are described by the two-dimensional cubic nonlinear Schrodinger equation. Considering the quartic nonlinear potential, the two-dimensional discrete-soliton trains and the solutions perturbed by the neck mode are presented.
Renormalized Cosmological Perturbation Theory
Crocce, M
2006-01-01
We develop a new formalism to study nonlinear evolution in the growth of large-scale structure, by following the dynamics of gravitational clustering as it builds up in time. This approach is conveniently represented by Feynman diagrams constructed in terms of three objects: the initial conditions (e.g. perturbation spectrum), the vertex (describing non-linearities) and the propagator (describing linear evolution). We show that loop corrections to the linear power spectrum organize themselves into two classes of diagrams: one corresponding to mode-coupling effects, the other to a renormalization of the propagator. Resummation of the latter gives rise to a quantity that measures the memory of perturbations to initial conditions as a function of scale. As a result of this, we show that a well-defined (renormalized) perturbation theory follows, in the sense that each term in the remaining mode-coupling series dominates at some characteristic scale and is subdominant otherwise. This is unlike standard perturbatio...
The Polarized Structure Function $g_{2} A Lattice Study Revisited
Göckeler, M; Kürzinger, W; Oelrich, H; Rakow, P; Schierholz, G
1999-01-01
A recent lattice calculation of the spin-dependent structure function g_2 is revisited. It has been recognized that the twist-three operator, which gives rise to d_2, mixes non-perturbatively with operators of lower dimensions under renormalization. This changes the results substantially.
HAFNIUM IMPLANTED IN IRON .1. LATTICE LOCATION AND ANNEALING BEHAVIOR
DEBAKKER, JMGJ; PLEITER, F; SMULDERS, PJM
1993-01-01
Perturbed angular correlation, Rutherford backscattering and channelling experiments were conducted to study the lattice location and annealing behaviour of 110 keV hafnium ions implanted into iron single crystals. It was found that a fraction of 11-25% of the implanted hafnium atoms are located at
Hafnium implanted in iron 1. Lattice location and annealing behavior
de Bakker, J.M.G.J.; Pleiter, F; Smulders, P.J M
1993-01-01
Perturbed angular correlation, Rutherford backscattering and channelling experiments were conducted to study the lattice location and annealing behaviour of 110 keV hafnium ions implanted into iron single crystals. It was found that a fraction of 11-25% of the implanted hafnium atoms are located at
Hafnium implanted in iron 1. Lattice location and annealing behavior
de Bakker, J.M.G.J.; Pleiter, F; Smulders, P.J M
1993-01-01
Perturbed angular correlation, Rutherford backscattering and channelling experiments were conducted to study the lattice location and annealing behaviour of 110 keV hafnium ions implanted into iron single crystals. It was found that a fraction of 11-25% of the implanted hafnium atoms are located at
Lattice study of ChPT beyond QCD
Appelquist, Thomas; Babich, Ron; Brower, Richard C; Cheng, Michael; Clark, Michael A; Cohen, Saul D; Fleming, George T; Kiskis, Joseph; Neil, Ethan T; Osborn, James C; Rebbi, Claudio; Schaich, David; Vranas, Pavlos
2010-01-01
We describe initial results by the Lattice Strong Dynamics (LSD) collaboration of a study into the variation of chiral properties of chiral properties of SU(3) Yang-Mills gauge theory as the number of massless flavors changes from $N_f = 2$ to $N_f = 6$, with a focus on the use of chiral perturbation theory.
Yukawa model on a lattice: two body states
De Soto, F; Roiesnel, C; Boucaud, P; Leroy, J P; Pène, O; Boucaud, Ph.
2007-01-01
We present first results of the solutions of the Yukawa model as a Quantum Field Theory (QFT) solved non perturbatively with the help of lattice calculations. In particular we will focus on the possibility of binding two nucleons in the QFT, compared to the non relativistic result.
From Pericles to Plato – from democratic political praxis to totalitarian political philosophy
Directory of Open Access Journals (Sweden)
Øjvind Larsen
2012-03-01
Full Text Available Plato is normally taken as one of the founders of Western political philosophy, not at least with his Republic. Here, he constructs a hierarchy of forms of governments, beginning with aristocracy at the top as a critical standard for the other forms of governments, and proceeding through timocracy and oligarchy to democracy and tyranny at the bottom. Following Karl Popper, the paper argues that Plato’s is a totalitarian philosophy that emphasizes the similarities between democracy and tyranny, which it considers to be the two worst forms of government. Plato’s denigration of democracy has dominated the tradition of political philosophy until recent times. This paper, however, shows that political philosophy in fact originates in democracy, especially as developed by the sophists and that philosophy is only a form of sophism with a similar origin in ancient Greek democracy. A discussion of Pericles’ funeral oration is used to show that Pericles presented a democratic political philosophy that can serve as a counterpoint to Plato’s political philosophy in the Republic.
Plato's Concept of Justice%论柏拉图的正义观
Institute of Scientific and Technical Information of China (English)
刘欣如
2015-01-01
本文以柏拉图的作品《申辩》、《斐多》、《理想国》为切入点,论述了正义是在应在的位置上做应做之事、正义的本质是灵魂的一种属性以及正义的产生,并通过作品提供的背景和对话讨论了正义之人和不义之人的区别、正义的种类、正义行为的动机、正义的各种不同状态等问题.%In this paper, the works of Plato,"defense","Phaedo","Utopia"as the starting point, discusses the justice should be done is to do things in a position to be in, the nature of justice is an attribute of the soul, and justice generation, background and dialogue and through providing discussed works of justice and the unrighteous man of distinction, just the kind of moti-vation act of justice, justice of various states and other issues.
Directory of Open Access Journals (Sweden)
Epelbaum E.
2010-04-01
Full Text Available We review recent progress on nuclear lattice simulations using chiral eﬀective ﬁeld theory. We discuss lattice results for dilute neutron matter at next-to-leading order, three-body forces at next-to-next-toleading order, isospin-breaking and Coulomb eﬀects, and the binding energy of light nuclei.
Non-perturbative studies of QCD at small quark masses
Energy Technology Data Exchange (ETDEWEB)
Wennekers, J.
2006-07-15
We investigate the quenched approximation of lattice QCD with numerical simulations of Ginsparg-Wilson fermions, which are a fermion discretisation with exact chiral symmetry. We compute the renormalisation constant of the scalar density, which allows to extrapolate the chiral condensate to the continuum limit. Furthermore we match lattice results of matrix elements describing hadronic kaon decays to Chiral Perturbation Theory in finite volume and at almost vanishing quark mass. The resulting low-energy constants in the considered SU(4)-flavour symmetric case indicate a substantial contribution of low scale QCD effects to the {delta}I = 1/2 rule. (Orig.)
Determining the QCD coupling from lattice vacuum polarization
Hudspith, Renwick J; Maltman, Kim; Shintani, Eigo
2015-01-01
The QCD coupling appears in the perturbative expansion of the current-current two-point (vacuum polarization) function. Any lattice calculation of vacuum polarization is plagued by several competing non-perturbative effects at small momenta and by discretization errors at large momenta. We work in an intermediate region, computing the vacuum polarization for many off-axis momentum directions on the lattice. Having many momentum directions provides a way to monitor and account for lattice artifacts. Our results are competitive with, and have certain systematic advantages over, the alternate phenomenological determination of the strong coupling from the same light quark vacuum polarization produced by sum rule analyses of hadronic tau decay data.
Stability of trapped Bose-Einstein condensates in one-dimensional tilted optical lattice potential
Institute of Scientific and Technical Information of China (English)
Fang Jian-Shu; Liao Xiang-Ping
2011-01-01
Using the direct perturbation technique, this paper obtains a general perturbed solution of the Bose-Einstein condensates trapped in one-dimensional tilted optical lattice potential. We also gave out two necessary and sufficient conditions for boundedness of the perturbed solution. Theoretical analytical results and the corresponding numerical results show that the perturbed solution of the Bose-Einstein condensate system is unbounded in general and indicate that the Bose-Einstein condensates are Lyapunov-unstable. However, when the conditions for boundedness of the perturbed solution are satisfied, then the Bose-Einstein condensates are Lyapunov-stable.
DEFF Research Database (Denmark)
jora, Renata; Schechter, Joseph; Naeem Shahid, M.
2009-01-01
We study the effects of the perturbation which violates the permutation symmetry of three Majorana neutrinos but preserves the well known (23) interchange symmetry. This is done in the presenceof an arbitrary Majorana phase which serves to insure the degeneracy of the three neutrinos at the unper...
Cosmological perturbations in antigravity
Oltean, Marius; Brandenberger, Robert
2014-10-01
We compute the evolution of cosmological perturbations in a recently proposed Weyl-symmetric theory of two scalar fields with oppositely signed conformal couplings to Einstein gravity. It is motivated from the minimal conformal extension of the standard model, such that one of these scalar fields is the Higgs while the other is a new particle, the dilaton, introduced to make the Higgs mass conformally symmetric. At the background level, the theory admits novel geodesically complete cyclic cosmological solutions characterized by a brief period of repulsive gravity, or "antigravity," during each successive transition from a big crunch to a big bang. For simplicity, we consider scalar perturbations in the absence of anisotropies, with potential set to zero and without any radiation. We show that despite the necessarily wrong-signed kinetic term of the dilaton in the full action, these perturbations are neither ghostlike nor tachyonic in the limit of strongly repulsive gravity. On this basis, we argue—pending a future analysis of vector and tensor perturbations—that, with respect to perturbative stability, the cosmological solutions of this theory are viable.
DiNicolantonio, James J; Can, Mehmet Mustafa; Serebruany, Victor L
2013-04-15
Extreme rates of vascular and all-cause mortality especially in the clopidogrel arm of the Platelet Inhibition and Patient Outcomes (PLATO) non-USA cohort raise concerns of data integrity, and call for independent verification of vital records in the national death registries. Four recent acute coronary syndrome (ACS) trials: Thrombin Receptor Antagonist for Clinical Event Reduction in Acute Coronary Syndrome (TRACER), Anti-Xa therapy to lower cardiovascular events in addition to standard therapy in subjects with acute coronary syndrome (ATLAS-ACS 2), Trial to Assess Improvement in Therapeutic Outcomes by Optimizing Platelet Inhibition with Prasugrel (TRITON), and the Thrombin Receptor Antagonist in Secondary Prevention of Atherothrombotic Ischemic Events (TRA 2P), provide a valuable opportunity to match lost in follow-up (LIFU) with mortality rates among similar ACS studies. To compare the LIFU from PLATO, TRACER, ATLAS-ACS 2, TRITON-TIMI 38 and TRA 2P trials. The disturbingly high (8.9%-14.7%) LIFU in PLATO was no match to LIFU in TRACER (0.1%), ATLAS ACS 2 (0.3%), TRITON (0.1%) and TRA 2P (0.1%). In fact, such an astronomical (49-147 fold higher) PLATO LIFU rate should result in less mortality compared to the other ACS trials since no event can be reported or adjudicated if the patient has been lost. Adjusting LIFU rate revealed that vascular (5.55%) and all cause (6.05%) mortality in PLATO was even more disparate than in TRACER (3.2% and 4.9%), ATLAS-ACS 2 (4.1% and 4.5%), TRITON-TIMI 38 (2.4% and 3.2%) and TRA 2P (3.0% and 5.3%) control arms, respectfully. Moreover, the incomplete CV follow-up in the ATLAS ACS 2 trial was later revealed to be around 12%, which lead to the rejection of rivaroxaban for the treatment of ACS. PLATO's LIFU rate was just as high, if not higher, than seen in ATLAS ACS 2. The chance to die in PLATO far exceeds the mortality risks observed in the clopidogrel arms of four recent ACS trials, which becomes especially evident after
Renormalization of the momentum density on the lattice using shifted boundary conditions
Robaina, Daniel
2013-01-01
In order to extract transport quantities from energy-momentum-tensor (EMT) correlators in Lattice QCD there is a strong need for a non-perturbative renormalization of these operators. This is due to the fact that the lattice regularization explicitly breaks translational invariance, invalidating the non-renormalization-theorem. Here we present a non-perturbative calculation of the renormalization constant of the off-diagonal components of the EMT in SU(3) pure gauge theory using lattices with shifted boundary conditions. This allows us to induce a non-zero momentum in the system controlled by the shift parameter and to determine the normalization of the momentum density operator.
High order multiplication perturbation method for singular perturbation problems
Institute of Scientific and Technical Information of China (English)
张文志; 黄培彦
2013-01-01
This paper presents a high order multiplication perturbation method for sin-gularly perturbed two-point boundary value problems with the boundary layer at one end. By the theory of singular perturbations, the singularly perturbed two-point boundary value problems are first transformed into the singularly perturbed initial value problems. With the variable coeﬃcient dimensional expanding, the non-homogeneous ordinary dif-ferential equations (ODEs) are transformed into the homogeneous ODEs, which are then solved by the high order multiplication perturbation method. Some linear and nonlinear numerical examples show that the proposed method has high precision.
Lattice QCD with overlap fermions on GPUs
Walk, B.; Wittig, H.; Schömer, E.
2012-08-01
Lattice QCD is widely considered the correct theory of the strong force and is able to make quantitative statements in the low energy regime where perturbation theory is not applicable. The partition function of lattice QCD can be mapped onto a statistical mechanics system which then allows for the use of calculational methods such as Monte Carlo simulations. In recent years, the enormous success of GPU programming has also arrived at the lattice community. In this article, we give a short overview of Lattice QCD and motivate this need for large computing power. In our simulations we concentrate on a specific fermionic discretization, so-called Neuberger-Dirac fermions, which respect an exact chiral symmetry. We will discuss the algorithms we use in our GPU implementation which turns out to be an order of magnitude faster then the conventional CPU-equivalent. As an application we present results on the eigenvalue spectra in QCD and compare them to analytical calculations from Random Matrix Theory.
Lattice QCD spectroscopy for hadronic CP violation
Directory of Open Access Journals (Sweden)
Jordy de Vries
2017-03-01
In this work we propose a strategy to calculate these couplings by using spectroscopic lattice QCD techniques. Instead of directly calculating the pion–nucleon coupling constants, a challenging task, we use chiral symmetry relations that link the pion–nucleon couplings to nucleon sigma terms and mass splittings that are significantly easier to calculate. In this work, we show that these relations are reliable up to next-to-next-to-leading order in the chiral expansion in both SU(2 and SU(3 chiral perturbation theory. We conclude with a brief discussion about practical details regarding the required lattice QCD calculations and the phenomenological impact of an improved understanding of CP-violating matrix elements.
Fixed Point Actions for Lattice Fermions
Bietenholz, W
1994-01-01
The fixed point actions for Wilson and staggered lattice fermions are determined by iterating renormalization group transformations. In both cases a line of fixed points is found. Some points have very local fixed point actions. They can be used to construct perfect lattice actions for asymptotically free fermionic theories like QCD or the Gross-Neveu model. The local fixed point actions for Wilson fermions break chiral symmetry, while in the staggered case the remnant $U(1)_e \\otimes U(1)_o$ symmetry is preserved. In addition, for Wilson fermions a nonlocal fixed point is found that corresponds to free chiral fermions. The vicinity of this fixed point is studied in the Gross-Neveu model using perturbation theory.
Vacuum polarization and chiral lattice fermions
Randjbar-Daemi, S.; Strathdee, J.
1996-02-01
The vacuum polarization due to chiral fermions on a 4-dimensional Euclidean lattice is calculated according to the overlap prescription. The fermions are coupled to weak and slowly varying background gauge and Higgs fields, and the polarization tensor is given by second order perturbation theory. In this order the overlap constitutes a gauge-invariant regularization of the fermion vacuum amplitude. Its low-energy-long-wavelength behaviour can be computed explicitly and we verify that it coincides with the Feynman graph result obtainable, for example, by dimensional regularization of continuum gauge theory. In particular, the Standard Model Callan-Symanzik RG functions are recovered. Moreover, there are no residual lattice artefacts such as a dependence on Wilson-type mass parameters.
Lattice fermions in the Schwinger model
Bodwin, Geoffrey T.; Kovacs, Eve V.
1987-05-01
We obtain exact solutions for the continuum limit of the lattice Schwinger model, using the Lagrangian formulations of the Wilson, ``naive,'' Kogut-Susskind, and Drell-Weinstein-Yankielowicz (DWY) lattice fermion derivatives. We examine the mass gap, the anomaly, and the chiral order parameter . As expected, our results for the Wilson formulation are consistent with those of the continuum theory and our results for the ``naive'' formulation exhibit spectrum doubling. In the Kogut-Susskind case, the U(1) anomaly is doubled, but vanishes. In solving the DWY version of the model, we make use of a proposal for resumming perturbation theory due to Rabin. The Lagrangian formulation of the DWY Schwinger model displays spectrum doubling and a mass gap that is √2 times the continuum one. The U(1) anomaly graph is nonvanishing and noncovariant in the continuum limit, but has a vanishing divergence. The chiral order parameter also vanishes.
Vacuum polarization and chiral lattice fermions
Strathdee, J A
1995-01-01
The vacuum polarization due to chiral fermions on a 4--dimensional Euclidean lattice is calculated according to the overlap prescription. The fermions are coupled to weak and slowly varying background gauge and Higgs fields, and the polarization tensor is given by second order perturbation theory. In this order the overlap constitutes a gauge invariant regularization of the fermion vacuum amplitude. Its low energy -- long wavelength behaviour can be computed explicitly and we verify that it coincides with the Feynman graph result obtainable, for example, by dimensional regularization of continuum gauge theory. In particular, the Standard Model Callan--Symanzik RG functions are recovered. Moreover, there are no residual lattice artefacts such as a dependence on Wilson--type mass parameters.
Improving the lattice axial vector current
Energy Technology Data Exchange (ETDEWEB)
Horsley, R. [Edinburgh Univ. (United Kingdom). School of Physics and Astronomy; Nakamura, Y. [RIKEN Advanced Institute for Computational Science, Kobe (Japan); Perlt, H.; Schiller, A. [Leipzig Univ. (Germany). Inst. fuer Theoretische Physik; Rakow, P.E.L. [Liverpool Univ. (United Kingdom). Theoretical Physics Div.; Schierholz, G. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Zanotti, J.M. [Adelaide Univ. (Australia). CSSM, Dept. of Physics
2015-11-15
For Wilson and clover fermions traditional formulations of the axial vector current do not respect the continuum Ward identity which relates the divergence of that current to the pseudoscalar density. Here we propose to use a point-split or one-link axial vector current whose divergence exactly satisfies a lattice Ward identity, involving the pseudoscalar density and a number of irrelevant operators. We check in one-loop lattice perturbation theory with SLiNC fermion and gauge plaquette action that this is indeed the case including order O(a) effects. Including these operators the axial Ward identity remains renormalisation invariant. First preliminary results of a nonperturbative check of the Ward identity are also presented.
Improving the lattice axial vector current
Horsley, R; Perlt, H; Rakow, P E L; Schierholz, G; Schiller, A; Zanotti, J M
2015-01-01
For Wilson and clover fermions traditional formulations of the axial vector current do not respect the continuum Ward identity which relates the divergence of that current to the pseudoscalar density. Here we propose to use a point-split or one-link axial vector current whose divergence exactly satisfies a lattice Ward identity, involving the pseudoscalar density and a number of irrelevant operators. We check in one-loop lattice perturbation theory with SLiNC fermion and gauge plaquette action that this is indeed the case including order $O(a)$ effects. Including these operators the axial Ward identity remains renormalisation invariant. First preliminary results of a nonperturbative check of the Ward identity are also presented.
Von Smekal, L; Sternbeck, A; Williams, A G
2007-01-01
We propose a modified lattice Landau gauge based on stereographically projecting the link variables on the circle S^1 -> R for compact U(1) or the 3-sphere S^3 -> R^3 for SU(2) before imposing the Landau gauge condition. This can reduce the number of Gribov copies exponentially and solves the Gribov problem in compact U(1) where it is a lattice artifact. Applied to the maximal Abelian subgroup this might be just enough to avoid the perfect cancellation amongst the Gribov copies in a lattice BRST formulation for SU(N), and thus to avoid the Neuberger 0/0 problem. The continuum limit of the Landau gauge remains unchanged.
Jammed lattice sphere packings.
Kallus, Yoav; Marcotte, Étienne; Torquato, Salvatore
2013-12-01
We generate and study an ensemble of isostatic jammed hard-sphere lattices. These lattices are obtained by compression of a periodic system with an adaptive unit cell containing a single sphere until the point of mechanical stability. We present detailed numerical data about the densities, pair correlations, force distributions, and structure factors of such lattices. We show that this model retains many of the crucial structural features of the classical hard-sphere model and propose it as a model for the jamming and glass transitions that enables exploration of much higher dimensions than are usually accessible.
Jammed lattice sphere packings
Kallus, Yoav; Marcotte, Étienne; Torquato, Salvatore
2013-12-01
We generate and study an ensemble of isostatic jammed hard-sphere lattices. These lattices are obtained by compression of a periodic system with an adaptive unit cell containing a single sphere until the point of mechanical stability. We present detailed numerical data about the densities, pair correlations, force distributions, and structure factors of such lattices. We show that this model retains many of the crucial structural features of the classical hard-sphere model and propose it as a model for the jamming and glass transitions that enables exploration of much higher dimensions than are usually accessible.
Perturbations can enhance qauntum search
Bae, J; Bae, Joonwoo; Kwon, Younghun
2003-01-01
In general, a quantum algorithm wants to avoid decoherence or perturbation, since such factors may cause errors in the algorithm. In this letter, we will supply the answer to the interesting question: can the factors seemingly harmful to a quantum algorithm(for example, perturbations) enhance the algorithm? We show that some perturbations to the generalized quantum search Hamiltonian can reduce the running time and enhance the success probability. We also provide the narrow bound to the perturbation which can be beneficial to quantum search. In addition, we show that the error induced by a perturbation on the Farhi and Gutmann Hamiltonian can be corrected by another perturbation.
Pion electric polarizability from lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Alexandru, Andrei; Lujan, Michael; Freeman, Walter; Lee, Frank [The George Washington University, 725 21st St. NW, Washington DC, 20052 (United States)
2016-01-22
Electromagnetic polarizabilities are important parameters for understanding the interaction between photons and hadrons. For pions these quantities are poorly constrained experimentally since they can only be measured indirectly. New experiments at CERN and Jefferson Lab are planned that will measure the polarizabilities more precisely. Lattice QCD can be used to compute these quantities directly in terms of quark and gluons degrees of freedom, using the background field method. We present results for the electric polarizability for two different quark masses, light enough to connect to chiral perturbation theory. These are currently the lightest quark masses used in polarizability studies.
Kondo lattice without Nozieres exhaustion effect.
Energy Technology Data Exchange (ETDEWEB)
Kikoin, K.; Kiselev, M. N.; Materials Science Division; Ben-Gurion Univ. of the Negev; Ludwig-Maximilians Univ.
2006-01-01
We discuss the properties of layered Anderson/Kondo lattices with metallic electrons confined in 2D xy planes and local spins in insulating layers forming chains in the z direction. Each spin in this model possesses its own 2D Kondo cloud, so that the Nozieres exhaustion problem does not occur. The high-temperature perturbational description is matched to exact low-T Bethe-ansatz solution. The excitation spectrum of the model is gapless both in charge and spin sectors. The disordered phases and possible experimental realizations of the model are briefly discussed.
Quantum ideal hydrodynamics on the lattice
Burch, Tommy
2013-01-01
After discussing the problem of defining the hydrodynamic limit from microscopic scales, we give an introduction to ideal hydrodynamics in the Lagrange picture, and show that it can be viewed as a field theory, which can be quantized using the usual Feynman sum-over-paths prescription. We then argue that this picture can be connected to the usually neglected thermal microscopic scale in the hydrodynamic expansion. After showing that this expansion is generally non-perturbative, we show how the lattice can be used to understand the impact quantum and thermal fluctuations can have on the fluid behavior.
Quarkonia at $T>0$ and lattice QCD
Rothkopf, Alexander
2016-01-01
We report here on recent progress in the determination of S-wave and P-wave heavy-quarkonium states at finite temperature. Our results are based on the combination of effective field theories with numerical lattice QCD simulations. These non-perturbative tools allow us to compute the heavy-quarkonium in-medium spectral functions, from which we in turn determine the melting temperatures of individual states and estimate phenomenologically relevant observables, such as the $\\psi^\\prime$ to J/$\\psi$ ratio in heavy-ion collisions.
Nuclear Parity Violation from Lattice QCD
Kurth, Thorsten; Rinaldi, Enrico; Vranas, Pavlos; Nicholson, Amy; Strother, Mark; Walker-Loud, Andre
2015-01-01
The electroweak interaction at the level of quarks and gluons are well understood from precision measurements in high energy collider experiments. Relating these fundamental parameters to Hadronic Parity Violation in nuclei however remains an outstanding theoretical challenge. One of the most interesting observables in this respect is the parity violating hadronic neutral current: it is hard to measure in collider experiments and is thus the least constrained observable of the Standard Model. Precision measurements of parity violating transitions in nuclei can help to improve these constraints. In these systems however, the weak interaction is masked by effects of the seven orders of magnitude stronger non-perturbative strong interaction. Therefore, in order to relate experimental measurements of the parity violating pion-nucleon couplings to the fundamental Lagrangian of the SM, these non-perturbative effects have to be well understood. In this paper, we are going to present a Lattice QCD approach for comput...
Non-renormalization theorem and cyclic Leibniz rule in lattice supersymmetry
Kato, Mitsuhiro; So, Hiroto
2014-01-01
We propose a lattice model of supersymmetric complex quantum mechanics which realizes the non-renormalization theorem on a lattice. In our lattice model, the Leibniz rule in the continuum, which cannot hold on a lattice due to a no-go theorem, is replaced by the cyclic Leibniz rule (CLR) for difference operators. It is shown that CLR allows two of four supercharges of the continuum theory to preserve while a naive lattice model can realize one supercharge at the most. A striking feature of our lattice model is that there are no quantum corrections to potential terms in any finite order of perturbation theory. This is one of characteristic properties of supersymmetric theories in the continuum. It turns out that CLR plays a crucial role in the proof of the non-renormalization theorem. This result suggests that CLR grasps an essence of supersymmetry on a lattice.
Aspects of perturbative unitarity
Anselmi, Damiano
2016-07-01
We reconsider perturbative unitarity in quantum field theory and upgrade several arguments and results. The minimum assumptions that lead to the largest time equation, the cutting equations and the unitarity equation are identified. Using this knowledge and a special gauge, we give a new, simpler proof of perturbative unitarity in gauge theories and generalize it to quantum gravity, in four and higher dimensions. The special gauge interpolates between the Feynman gauge and the Coulomb gauge without double poles. When the Coulomb limit is approached, the unphysical particles drop out of the cuts and the cutting equations are consistently projected onto the physical subspace. The proof does not extend to nonlocal quantum field theories of gauge fields and gravity, whose unitarity remains uncertain.
Aspects of perturbative unitarity
Anselmi, Damiano
2016-01-01
We reconsider perturbative unitarity in quantum field theory and upgrade several arguments and results. The minimum assumptions that lead to the largest time equation, the cutting equations and the unitarity equation are identified. Using this knowledge and a special gauge, we give a new, simpler proof of perturbative unitarity in gauge theories and generalize it to quantum gravity, in four and higher dimensions. The special gauge interpolates between the Feynman gauge and the Coulomb gauge without double poles. When the Coulomb limit is approached, the unphysical particles drop out of the cuts and the cutting equations are consistently projected onto the physical subspace. The proof does not extend to nonlocal quantum field theories of gauge fields and gravity, whose unitarity remains uncertain.
Degenerate Density Perturbation Theory
Palenik, Mark C
2016-01-01
Fractional occupation numbers can be used in density functional theory to create a symmetric Kohn-Sham potential, resulting in orbitals with degenerate eigenvalues. We develop the corresponding perturbation theory and apply it to a system of $N_d$ degenerate electrons in a harmonic oscillator potential. The order-by-order expansions of both the fractional occupation numbers and unitary transformations within the degenerate subspace are determined by the requirement that a differentiable map exists connecting the initial and perturbed states. Using the X$\\alpha$ exchange-correlation (XC) functional, we find an analytic solution for the first-order density and first through third-order energies as a function of $\\alpha$, with and without a self-interaction correction. The fact that the XC Hessian is not positive definite plays an important role in the behavior of the occupation numbers.
Large Spin Perturbation Theory
Alday, Luis F
2016-01-01
We consider conformal field theories around points of large twist degeneracy. Examples of this are theories with weakly broken higher spin symmetry and perturbations around generalised free fields. At the degenerate point we introduce twist conformal blocks. These are eigenfunctions of certain quartic operators and encode the contribution, to a given four-point correlator, of the whole tower of intermediate operators with a given twist. As we perturb around the degenerate point, the twist degeneracy is lifted. In many situations this breaking is controlled by inverse powers of the spin. In such cases the twist conformal blocks can be decomposed into a sequence of functions which we systematically construct. Decomposing the four-point correlator in this basis turns crossing symmetry into an algebraic problem. Our method can be applied to a wide spectrum of conformal field theories in any number of dimensions and at any order in the breaking parameter. As an example, we compute the spectrum of various theories ...
Cosmological Perturbations in Antigravity
Oltean, Marius
2014-01-01
We compute the evolution of cosmological perturbations in a recently proposed Weyl-symmetric theory of two scalar fields with oppositely-signed conformal couplings to Einstein gravity. It is motivated from the minimal conformal extension of the Standard Model, such that one of these scalar fields is the Higgs while the other is a new particle, the dilaton, introduced to make the Higgs mass conformally symmetric. At the background level, the theory admits novel geodesically-complete cyclic cosmological solutions characterized by a brief period of repulsive gravity, or "antigravity", during each successive transition from a Big Crunch to a Big Bang. We show that despite the necessarily wrong-signed kinetic term of the dilaton in the full action, its cosmological solutions are stable at the perturbative level.
Perturbatively charged holographic disorder
O'Keeffe, Daniel K
2015-01-01
Within the framework of holography applied to condensed matter physics, we study a model of perturbatively charged disorder in D=4 dimensions. Starting from initially uncharged AdS_4, a randomly fluctuating boundary chemical potential is introduced by turning on a bulk gauge field parameterized by a disorder strength and a characteristic scale k_0. Accounting for gravitational backreaction, we construct an asymptotically AdS solution perturbatively in the disorder strength. The disorder averaged geometry displays unphysical divergences in the deep interior. We explain how to remove these divergences and arrive at a well behaved solution. The disorder averaged DC conductivity is calculated and is found to contain a correction to the AdS result. The correction appears at second order in the disorder strength and scales inversely with k_0. We discuss the extension to a system with a finite initial charge density. The disorder averaged DC conductivity may be calculated by adopting a technique developed for hologr...
Degenerate density perturbation theory
Palenik, Mark C.; Dunlap, Brett I.
2016-09-01
Fractional occupation numbers can be used in density functional theory to create a symmetric Kohn-Sham potential, resulting in orbitals with degenerate eigenvalues. We develop the corresponding perturbation theory and apply it to a system of Nd degenerate electrons in a harmonic oscillator potential. The order-by-order expansions of both the fractional occupation numbers and unitary transformations within the degenerate subspace are determined by the requirement that a differentiable map exists connecting the initial and perturbed states. Using the X α exchange-correlation (XC) functional, we find an analytic solution for the first-order density and first- through third-order energies as a function of α , with and without a self-interaction correction. The fact that the XC Hessian is not positive definite plays an important role in the behavior of the occupation numbers.
Singh, Hardev; Herman, Tania De La Fuente; Showalter, Barry; Thompson, Spencer J.; Syzek, Elizabeth J.; Herman, Terence; Ahmad, Salahuddin
2012-10-01
This study compares the dosimetric differences in HDR brachytherapy treatment plans calculated with Nucletron's PLATO and Oncentra MasterPlan treatment planning systems (TPS). Ten patients (1 T1b, 1 T2a, 6 T2b, 2 T4) having cervical carcinoma, median age of 43.5 years (range, 34-79 years) treated with tandem & ring applicator in our institution were selected retrospectively for this study. For both Plato and Oncentra TPS, the same orthogonal films anterior-posterior (AP) and lateral were used to manually draw the prescription and anatomical points using definitions from the Manchester system and recommendations from the ICRU report 38. Data input for PLATO was done using a digitizer and Epson Expression 10000XL scanner was used for Oncentra where the points were selected on the images in the screen. The prescription doses for these patients were 30 Gy to points right A (RA) and left A (LA) delivered in 5 fractions with Ir-192 HDR source. Two arrangements: one dwell position and two dwell positions on the tandem were used for dose calculation. The doses to the patient points right B (RB) and left B (LB), and to the organs at risk (OAR), bladder and rectum for each patient were calculated. The mean dose and the mean percentage difference in dose calculated by the two treatment planning systems were compared. Paired t-tests were used for statistical analysis. No significant differences in mean RB, LB, bladder and rectum doses were found with p-values > 0.14. The mean percent difference of doses in RB, LB, bladder and rectum are found to be less than 2.2%, 1.8%, 1.3% and 2.2%, respectively. Dose calculations based on the two different treatment planning systems were found to be consistent and the treatment plans can be made with either system in our department without any concern.
Energy Technology Data Exchange (ETDEWEB)
Singh, Hardev; De La Fuente Herman, Tania; Showalter, Barry; Thompson, Spencer J.; Syzek, Elizabeth J.; Herman, Terence; Ahmad, Salahuddin [Department of Radiation Oncology, Peggy and Charles Stephenson Oklahoma Cancer Center, University of Oklahoma Health Sciences Center, Oklahoma City, OK 73104 (United States)
2012-10-23
This study compares the dosimetric differences in HDR brachytherapy treatment plans calculated with Nucletron's PLATO and Oncentra MasterPlan treatment planning systems (TPS). Ten patients (1 T1b, 1 T2a, 6 T2b, 2 T4) having cervical carcinoma, median age of 43.5 years (range, 34-79 years) treated with tandem and ring applicator in our institution were selected retrospectively for this study. For both Plato and Oncentra TPS, the same orthogonal films anterior-posterior (AP) and lateral were used to manually draw the prescription and anatomical points using definitions from the Manchester system and recommendations from the ICRU report 38. Data input for PLATO was done using a digitizer and Epson Expression 10000XL scanner was used for Oncentra where the points were selected on the images in the screen. The prescription doses for these patients were 30 Gy to points right A (RA) and left A (LA) delivered in 5 fractions with Ir-192 HDR source. Two arrangements: one dwell position and two dwell positions on the tandem were used for dose calculation. The doses to the patient points right B (RB) and left B (LB), and to the organs at risk (OAR), bladder and rectum for each patient were calculated. The mean dose and the mean percentage difference in dose calculated by the two treatment planning systems were compared. Paired t-tests were used for statistical analysis. No significant differences in mean RB, LB, bladder and rectum doses were found with p-values > 0.14. The mean percent difference of doses in RB, LB, bladder and rectum are found to be less than 2.2%, 1.8%, 1.3% and 2.2%, respectively. Dose calculations based on the two different treatment planning systems were found to be consistent and the treatment plans can be made with either system in our department without any concern.
Ooguri, H; Ooguri, Hirosi; Yin, Zheng
1996-01-01
These lecture notes are based on a course on string theories given by Hirosi Ooguri in the first week of TASI 96 Summer School at Boulder, Colorado. It is an introductory course designed to provide students with minimum knowledge before they attend more advanced courses on non-perturbative aspects of string theories in the School. The course consists of five lectures: 1. Bosonic String, 2. Toroidal Compactifications, 3. Superstrings, 4. Heterotic Strings, and 5. Orbifold Compactifications.
Testing chiral effective theory with quenched lattice QCD
Giusti, Leonardo; Necco, S; Peña, C; Wennekers, J; Wittig, H
2008-01-01
We investigate two-point correlation functions of left-handed currents computed in quenched lattice QCD with the Neuberger-Dirac operator. We consider two lattice spacings a~0.09,0.12 fm and two different lattice extents L~ 1.5, 2.0 fm; quark masses span both the p- and the epsilon-regimes. We compare the results with the predictions of quenched chiral perturbation theory, with the purpose of testing to what extent the effective theory reproduces quenched QCD at low energy. In the p-regime we test volume and quark mass dependence of the pseudoscalar decay constant and mass; in the epsilon-regime, we investigate volume and topology dependence of the correlators. While the leading order behaviour predicted by the effective theory is very well reproduced by the lattice data in the range of parameters that we explored, our numerical data are not precise enough to test next-to-leading order effects.
Testing chiral effective theory with quenched lattice QCD
Giusti, L.; Hernández, P.; Necco, S.; Pena, C.; Wennekers, J.; Wittig, H.
2008-05-01
We investigate two-point correlation functions of left-handed currents computed in quenched lattice QCD with the Neuberger-Dirac operator. We consider two lattice spacings a simeq 0.09,0.12 fm and two different lattice extents L simeq 1.5,2.0 fm; quark masses span both the p- and the epsilon-regimes. We compare the results with the predictions of quenched chiral perturbation theory, with the purpose of testing to what extent the effective theory reproduces quenched QCD at low energy. In the p-regime we test volume and quark mass dependence of the pseudoscalar decay constant and mass; in the epsilon-regime, we investigate volume and topology dependence of the correlators. While the leading order behaviour predicted by the effective theory is very well reproduced by the lattice data in the range of parameters that we explored, our numerical data are not precise enough to test next-to-leading order effects.
Noise source identification with the lattice Boltzmann method.
Vergnault, Etienne; Malaspinas, Orestis; Sagaut, Pierre
2013-03-01
In this paper the sound source identification problem is addressed with the use of the lattice Boltzmann method. To this aim, a time-reversed problem coupled to a complex differentiation method is used. In order to circumvent the inherent instability of the time-reversed lattice Boltzmann scheme, a method based on a split of the lattice Boltzmann equation into a mean and a perturbation component is used. Lattice Boltzmann method formulation around an arbitrary base flow is recalled and specific applications to acoustics are presented. The implementation of the noise source detection method for two-dimensional weakly compressible (low Mach number) flows is discussed, and the applicability of the method is demonstrated.
An atom interferometer with a shaken optical lattice
Weidner, C A; Kosloff, Ronnie; Anderson, and Dana Z
2016-01-01
We introduce shaken lattice interferometry with atoms trapped in a one-dimensional optical lattice. The atoms undergo an interferometer sequence of splitting, propagation, reflection, and recombination by phase modulation of the lattice through a sequence of shaking functions. Each function in the sequence is determined by a learning procedure that is implemented with a genetic algorithm. Numerical simulations determine the momentum state of the atoms, which is experimentally accessible with time-of-flight imaging. The shaking function is then optimized to achieve the desired state transitions. The sensitivity of the interferometer to perturbations such as those introduced by inertial forces scales the same way as for conventional matter wave interferometers. The shaken lattice interferometer may be optimized to sense signals of interest while rejecting others, such as the measurement of an AC signal while rejecting a DC bias.
O(N) Models with Topological Lattice Actions
Bietenholz, Wolfgang; Gerber, Urs; Niedermayer, Ferenc; Pepe, Michele; Rejón-Barrera, Fernando G; Wiese, Uwe-Jens
2013-01-01
A variety of lattice discretisations of continuum actions has been considered, usually requiring the correct classical continuum limit. Here we discuss "weird" lattice formulations without that property, namely lattice actions that are invariant under most continuous deformations of the field configuration, in one version even without any coupling constants. It turns out that universality is powerful enough to still provide the correct quantum continuum limit, despite the absence of a classical limit, or a perturbative expansion. We demonstrate this for a set of O(N) models (or non-linear $\\sigma$-models). Amazingly, such "weird" lattice actions are not only in the right universality class, but some of them even have practical benefits, in particular an excellent scaling behaviour.
Entangling the lattice clock: Towards Heisenberg-limited timekeeping
Weinstein, Jonathan D; Derevianko, Andrei
2009-01-01
We present a scheme for entangling the atoms of an optical lattice to reduce the quantum projection noise of a clock measurement. The divalent clock atoms are held in a lattice at a ``magic'' wavelength that does not perturb the clock frequency -- to maintain clock accuracy -- while an open-shell J=1/2 ``head'' atom is coherently transported between lattice sites via the lattice polarization. This polarization-dependent ``Archimedes' screw'' transport at magic wavelength takes advantage of the vanishing vector polarizability of the scalar, J=0, clock states of bosonic isotopes of divalent atoms. The on-site interactions between the clock atoms and the head atom are used to engineer entanglement and for clock readout.
Moments of nucleon generalized parton distributions from lattice QCD
Alexandrou, C; Constantinou, M; Harraud, P A; Guichon, P; Jansen, K; Kallidonis, C; Korzec, T; Papinutto, M
2011-01-01
We present results on the lower moments of the nucleon generalized parton distri butions within lattice QCD using two dynamical flavors of degenerate twisted mass fermions. Our simulations are performed on lattices with three different values of the lattice spacings, namely $a=0.089$ fm, $a=0.070$ fm and $a=0.056$ fm, allowing the investigation of cut-off effects. The volume dependence is examined using simulations on two lattices of spatial length $L=2.1$ fm and $L=2.8$ fm. The simulations span pion masses in the range of 260-470 MeV. Our results are renormalized non-perturbatively and the values are given in the $\\bar{\\rm MS}$ scheme at a scale $ \\mu=2$ GeV. They are chirally extrapolated to the physical point in order to compare with experiment. The consequences of these results on the spin carried by the quarks in the nucleon are investigated.
Chiral Random Matrix Theory and Chiral Perturbation Theory
Damgaard, P H
2011-01-01
Spontaneous breaking of chiral symmetry in QCD has traditionally been inferred indirectly through low-energy theorems and comparison with experiments. Thanks to the understanding of an unexpected connection between chiral Random Matrix Theory and chiral Perturbation Theory, the spontaneous breaking of chiral symmetry in QCD can now be shown unequivocally from first principles and lattice simulations. In these lectures I give an introduction to the subject, starting with an elementary discussion of spontaneous breaking of global symmetries.
Chiral Random Matrix Theory and Chiral Perturbation Theory
Energy Technology Data Exchange (ETDEWEB)
Damgaard, Poul H, E-mail: phdamg@nbi.dk [Niels Bohr International Academy and Discovery Center, The Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen (Denmark)
2011-04-01
Spontaneous breaking of chiral symmetry in QCD has traditionally been inferred indirectly through low-energy theorems and comparison with experiments. Thanks to the understanding of an unexpected connection between chiral Random Matrix Theory and chiral Perturbation Theory, the spontaneous breaking of chiral symmetry in QCD can now be shown unequivocally from first principles and lattice simulations. In these lectures I give an introduction to the subject, starting with an elementary discussion of spontaneous breaking of global symmetries.
Covariant Bardeen perturbation formalism
Vitenti, S. D. P.; Falciano, F. T.; Pinto-Neto, N.
2014-05-01
In a previous work we obtained a set of necessary conditions for the linear approximation in cosmology. Here we discuss the relations of this approach with the so-called covariant perturbations. It is often argued in the literature that one of the main advantages of the covariant approach to describe cosmological perturbations is that the Bardeen formalism is coordinate dependent. In this paper we will reformulate the Bardeen approach in a completely covariant manner. For that, we introduce the notion of pure and mixed tensors, which yields an adequate language to treat both perturbative approaches in a common framework. We then stress that in the referred covariant approach, one necessarily introduces an additional hypersurface choice to the problem. Using our mixed and pure tensors approach, we are able to construct a one-to-one map relating the usual gauge dependence of the Bardeen formalism with the hypersurface dependence inherent to the covariant approach. Finally, through the use of this map, we define full nonlinear tensors that at first order correspond to the three known gauge invariant variables Φ, Ψ and Ξ, which are simultaneously foliation and gauge invariant. We then stress that the use of the proposed mixed tensors allows one to construct simultaneously gauge and hypersurface invariant variables at any order.
Directory of Open Access Journals (Sweden)
Zaitsev Cornelius
2014-10-01
Full Text Available The article discusses the ancient idea of the soul that in the patristic era has been enriched by the perception of the methodology of ancient philosophy. Greek and Roman thinkers considered some properties of the soul, its immortality, revealed its “levels and strata” (Plato, Aristotle, expressed first guesses about the nature of sinful passions (the Stoics. But some aspects still remained unresolved so far. This is the issue of materiality or immateriality, of the soul, which "raised" in the Russian Empire in the 19th century (the dispute saints Theophan the Recluse and Ignatius Brianchaninov and remains relevant today.
Directory of Open Access Journals (Sweden)
Dan Disney
2008-01-01
Full Text Available This article is a language-based re-reading of Plato's exile of the poets via Wallace Stevens' poem-manifesto, "An Ordinary Evening in New Haven." I examine how philosophy and poetry use language differently in order to deconstruct an origin of the speech-acts -- wonder -- that I then identify as a phenomenological difference between philosophers and poets. I contend that the thinking-into-language of philosophers is based in theoria, comprehension, and a resulting closure of wonder. I contrast this with the processes of poets, who I show to be moving thought into language via gnosis, apprehension, and a phenomenology opening onto inexhaustible wonder.
Fink, Bruce
2015-02-01
What is love and what part does it play in psychoanalysis? Where are the analyst and the analysand situated in relation to the roles defined as those of the "lover" and the "beloved"? Jacques Lacan explores these and other questions in his soon-to-be-published Seminar VIII: Transference by providing an extensive commentary on Plato's most famous dialogue on love, the Symposium. This paper outlines some of the major points about love that grow out of Lacan's reading of the dialogue and examines their relevance to the analytic setting. Can the analyst be characterized as a sort of modern-day Socrates?
Lipstein, Arthur E
2014-01-01
We formulate the theory of a 2-form gauge field on a Euclidean spacetime lattice. In this approach, the fundamental degrees of freedom live on the faces of the lattice, and the action can be constructed from the sum over Wilson surfaces associated with each fundamental cube of the lattice. If we take the gauge group to be $U(1)$, the theory reduces to the well-known abelian gerbe theory in the continuum limit. We also propose a very simple and natural non-abelian generalization with gauge group $U(N) \\times U(N)$, which gives rise to $U(N)$ Yang-Mills theory upon dimensional reduction. Formulating the theory on a lattice has several other advantages. In particular, it is possible to compute many observables, such as the expectation value of Wilson surfaces, analytically at strong coupling and numerically for any value of the coupling.
Root lattices and quasicrystals
Baake, M.; Joseph, D.; Kramer, P.; Schlottmann, M.
1990-10-01
It is shown that root lattices and their reciprocals might serve as the right pool for the construction of quasicrystalline structure models. All noncrystallographic symmetries observed so far are covered in minimal embedding with maximal symmetry.
Superalloy Lattice Block Structures
Nathal, M. V.; Whittenberger, J. D.; Hebsur, M. G.; Kantzos, P. T.; Krause, D. L.
2004-01-01
Initial investigations of investment cast superalloy lattice block suggest that this technology will yield a low cost approach to utilize the high temperature strength and environmental resistance of superalloys in lightweight, damage tolerant structural configurations. Work to date has demonstrated that relatively large superalloy lattice block panels can be successfully investment cast from both IN-718 and Mar-M247. These castings exhibited mechanical properties consistent with the strength of the same superalloys measured from more conventional castings. The lattice block structure also accommodates significant deformation without failure, and is defect tolerant in fatigue. The potential of lattice block structures opens new opportunities for the use of superalloys in future generations of aircraft applications that demand strength and environmental resistance at elevated temperatures along with low weight.
Vector Lattice Vortex Solitons
Institute of Scientific and Technical Information of China (English)
WANG Jian-Dong; YE Fang-Wei; DONG Liang-Wei; LI Yong-Ping
2005-01-01
@@ Two-dimensional vector vortex solitons in harmonic optical lattices are investigated. The stability properties of such solitons are closely connected to the lattice depth Vo. For small Vo, vector vortex solitons with the total zero-angular momentum are more stable than those with the total nonzero-angular momentum, while for large Vo, this case is inversed. If Vo is large enough, both the types of such solitons are stable.
Pica, C; Lucini, B; Patella, A; Rago, A
2009-01-01
Technicolor theories provide an elegant mechanism for dynamical electroweak symmetry breaking. We will discuss the use of lattice simulations to study the strongly-interacting dynamics of some of the candidate theories, with matter fields in representations other than the fundamental. To be viable candidates for phenomenology, such theories need to be different from a scaled-up version of QCD, which were ruled out by LEP precision measurements, and represent a challenge for modern lattice computations.
Kiefel, Martin; Jampani, Varun; Gehler, Peter V.
2014-01-01
This paper presents a convolutional layer that is able to process sparse input features. As an example, for image recognition problems this allows an efficient filtering of signals that do not lie on a dense grid (like pixel position), but of more general features (such as color values). The presented algorithm makes use of the permutohedral lattice data structure. The permutohedral lattice was introduced to efficiently implement a bilateral filter, a commonly used image processing operation....
¿Solamente platos? Cerámicas de barniz rojo en el depósito ibérico del Zacatín (Granada)
Sánchez Moreno, Amparo; Niveau de Villedary y Mariñas, Ana María; Adroher Auroux, Andrés María
2015-01-01
Se presenta un conjunto homogéneo de platos de barniz rojo indígena con un perfil muy particular y sin paralelos conocidos por el momento. Dicho conjunto formaba parte del depósito ritual hallado en la granadina calle del Zacatín, una fosa junto al río Darro que se rellenó con los resultantes de un festín sagrado posiblemente en relación con el propio río. En este trabajo planteamos que estos platos fueron fabricados ex profeso para el ritual que tuvo lugar fuera de las murallas de Iliberri e...
Solitons in spiraling Vogel lattices
Kartashov, Yaroslav V; Torner, Lluis
2012-01-01
We address light propagation in Vogel optical lattices and show that such lattices support a variety of stable soliton solutions in both self-focusing and self-defocusing media, whose propagation constants belong to domains resembling gaps in the spectrum of a truly periodic lattice. The azimuthally-rich structure of Vogel lattices allows generation of spiraling soliton motion.
Convergent series for lattice models with polynomial interactions
Directory of Open Access Journals (Sweden)
Aleksandr S. Ivanov
2017-01-01
Full Text Available The standard perturbative weak-coupling expansions in lattice models are asymptotic. The reason for this is hidden in the incorrect interchange of the summation and integration. However, substituting the Gaussian initial approximation of the perturbative expansions by a certain interacting model or regularizing original lattice integrals, one can construct desired convergent series. In this paper we develop methods, which are based on the joint and separate utilization of the regularization and new initial approximation. We prove, that the convergent series exist and can be expressed as re-summed standard perturbation theory for any model on the finite lattice with the polynomial interaction of even degree. We discuss properties of such series and study their applicability to practical computations on the example of the lattice ϕ4-model. We calculate 〈ϕn2〉 expectation value using the convergent series, the comparison of the results with the Borel re-summation and Monte Carlo simulations shows a good agreement between all these methods.
Perturbation semigroup of matrix algebras
Neumann, N.; Suijlekom, W.D. van
2016-01-01
In this article we analyze the structure of the semigroup of inner perturbations in noncommutative geometry. This perturbation semigroup is associated to a unital associative *-algebra and extends the group of unitary elements of this *-algebra. We compute the perturbation semigroup for all matrix algebras.
Hadron physics from lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Schaefer, Andreas [Regensburg Univ. (Germany). Inst. for Theoretical Physics
2016-11-01
Particle physics experiments at modern high luminosity particle accelerators achieve orders of magnitude higher count rates than what was possible ten or twenty years ago. This extremely large statistics allows to draw far reaching conclusions even from minute signals, provided that these signals are well understood by theory. This is, however, ever more difficult to achieve. Presently, technical and scientific progress in general and experimental progress in particle physics in particular, shows typically an exponential growth rate. For example, data acquisition and analysis are, among many other factor, driven by the development of ever more efficient computers and thus by Moore's law. Theory has to keep up with this development by also achieving an exponential increase in precision, which is only possible using powerful computers. This is true for both types of calculations, analytic ones as, e.g., in quantum field perturbation theory, and purely numerical ones as in Lattice QCD. As stated above such calculations are absolutely indispensable to make best use of the extremely costly large particle physics experiments. Thus, it is economically reasonable to invest a certain percentage of the cost of accelerators and experiments in related theory efforts. The basic ideas behind Lattice QCD simulations are the following: Because quarks and gluons can never be observed individually but are always ''confined'' into colorless hadrons, like the proton, all quark-gluon states can be expressed in two different systems of basis states, namely in a quark-gluon basis and the basis of hadron states. The proton, e.g., is an eigenstate of the latter, a specific quark-gluon configuration is part of the former. In the quark-gluon basis a physical hadron, like a proton, is given by an extremely complicated multi-particle wave function containing all effects of quantum fluctuations. This state is so complicated that it is basically impossible to model it
Non-perturbative match of ultraviolet renormalon
Zakharov, V I
2003-01-01
The paper is motivated by observation of a kind of branes in the vacuum state of the lattice SU(2) gluodynamics. The branes represent two-dimensional vortices whose total area scales in physical units while the non-Abelian action diverges in the ultraviolet. We consider the question whether effects of the branes can be accommodated into the continuum theory. We demonstrate that at least in case of the gluon condensate (plaquette action) and of the heavy quark potential the contribution of the branes corresponds to the ultraviolet renormalon. Thus, the vortices might represent a non-perturbative match of the ultraviolet renormalon. Such an identification constrains, in turn, properties of the branes.
Exact lattice supersymmetry at the quantum level for N = 2 Wess-Zumino models in 1- and 2-dimensions
Asaka, Keisuke; D'Adda, Alessandro; Kawamoto, Noboru; Kondo, Yoshi
2016-08-01
Supersymmetric lattice Ward-Takahashi identities are investigated perturbatively up to two-loop corrections for super doubler approach of N = 2 lattice Wess-Zumino models in 1- and 2-dimensions. In this approach, notorious chiral fermion doublers are treated as physical particles and momentum conservation is modified in such a way that lattice Leibniz rule is satisfied. The two major difficulties to keep exact lattice supersymmetry are overcome. This formulation defines, however, nonlocal field theory. Nevertheless we confirm that exact supersymmetry on the lattice is realized for all supercharges at the quantum level. Delicate issues of associativity are also discussed.
Exact Lattice Supersymmetry at the Quantum Level for $N=2$ Wess-Zumino Models in 1- and 2-Dimensions
Asaka, Keisuke; Kawamoto, Noboru; Kondo, Yoshi
2016-01-01
Supersymmetric lattice Ward-Takahashi identities are investigated perturbatively up to two-loop corrections for super doubler approach of $N=2$ lattice Wess-Zumino models in 1- and 2-dimensions. In this approach notorious chiral fermion doublers are treated as physical particles and momentum conservation is modified in such a way that lattice Leibniz rule is satisfied. The two major difficulties to keep exact lattice supersymmetry are overcome. This formulation defines, however, nonlocal field theory. Nevertheless we confirm that exact supersymmetry on the lattice is realized for all supercharges at the quantum level. Delicate issues of associativity are also discussed.
Modularity and the spread of perturbations in complex dynamical systems
Kolchinsky, Artemy; Gates, Alexander J.; Rocha, Luis M.
2015-12-01
We propose a method to decompose dynamical systems based on the idea that modules constrain the spread of perturbations. We find partitions of system variables that maximize "perturbation modularity," defined as the autocovariance of coarse-grained perturbed trajectories. The measure effectively separates the fast intramodular from the slow intermodular dynamics of perturbation spreading (in this respect, it is a generalization of the "Markov stability" method of network community detection). Our approach captures variation of modular organization across different system states, time scales, and in response to different kinds of perturbations: aspects of modularity which are all relevant to real-world dynamical systems. It offers a principled alternative to detecting communities in networks of statistical dependencies between system variables (e.g., "relevance networks" or "functional networks"). Using coupled logistic maps, we demonstrate that the method uncovers hierarchical modular organization planted in a system's coupling matrix. Additionally, in homogeneously coupled map lattices, it identifies the presence of self-organized modularity that depends on the initial state, dynamical parameters, and type of perturbations. Our approach offers a powerful tool for exploring the modular organization of complex dynamical systems.
Perturbative quantum chromodynamics
1989-01-01
This book will be of great interest to advanced students and researchers in the area of high energy theoretical physics. Being the most complete and updated review volume on Perturbative QCD, it serves as an extremely useful textbook or reference book. Some of the reviews in this volume are the best that have been written on the subject anywhere. Contents: Factorization of Hard Processes in QCD (J C Collins, D E Soper & G Sterman); Exclusive Processes in Quantum Chromodynamics (S J Brodsky & G P Lepage); Coherence and Physics of QCD Jets (Yu L Dokshitzer, V A Khoze & S I Troyan); Pomeron in Qu
Beane, Silas R; Vuorinen, Aleksi
2009-01-01
We present a new formulation of effective field theory for nucleon-nucleon (NN) interactions which treats pion interactions perturbatively, and we offer evidence that the expansion converges satisfactorily to third order in the expansion, which we have computed analytically for s and d wave NN scattering. Starting with the Kaplan-Savage-Wise (KSW) expansion about the nontrivial fixed point corresponding to infinite NN scattering length, we cure the convergence problems with that theory by summing to all orders the singular short distance part of the pion tensor interaction. This method makes possible a host of high precision analytic few-body calculations in nuclear physics.
Non-Perturbative Renormalization
Mastropietro, Vieri
2008-01-01
The notion of renormalization is at the core of several spectacular achievements of contemporary physics, and in the last years powerful techniques have been developed allowing to put renormalization on a firm mathematical basis. This book provides a self-consistent and accessible introduction to the sophisticated tools used in the modern theory of non-perturbative renormalization, allowing an unified and rigorous treatment of Quantum Field Theory, Statistical Physics and Condensed Matter models. In particular the first part of this book is devoted to Constructive Quantum Field Theory, providi
Optimised Dirac operators on the lattice. Construction, properties and applications
Energy Technology Data Exchange (ETDEWEB)
Bietenholz, W. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik]|[Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2006-11-15
We review a number of topics related to block variable renormalisation group transformations of quantum fields on the lattice, and to the emerging perfect lattice actions. We first illustrate this procedure by considering scalar fields. Then we proceed to lattice fermions, where we discuss perfect actions for free fields, for the Gross-Neveu model and for a supersymmetric spin model. We also consider the extension to perfect lattice perturbation theory, in particular regarding the axial anomaly and the quark gluon vertex function. Next we deal with properties and applications of truncated perfect fermions, and their chiral correction by means of the overlap formula. This yields a formulation of lattice fermions, which combines exact chiral symmetry with an optimisation of further essential properties. We summarise simulation results for these so-called overlap-hypercube fermions in the two-flavour Schwinger model and in quenched QCD. In the latter framework we establish a link to Chiral Perturbation Theory, both, in the p-regime and in the epsilon-regime. In particular we present an evaluation of the leading Low Energy Constants of the chiral Lagrangian - the chiral condensate and the pion decay constant - from QCD simulations with extremely light quarks. (orig.)
Optimised Dirac operators on the lattice: construction, properties and applications
Energy Technology Data Exchange (ETDEWEB)
Bietenholz, Wolfgang [Humbolt-Universitaet zu Berlin (Germany). Inst. fuer Physik; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing (NIC)
2006-12-15
We review a number of topics related to block variable renormalisation group transformations of quantum fields on the lattice, and to the emerging perfect lattice actions. We first illustrate this procedure by considering scalar fields. Then we proceed to lattice fermions, where we discuss perfect actions for free fields, for the Gross-Neveu model and for a supersymmetric spin model. We also consider the extension to perfect lattice perturbation theory, in particular regarding the axial anomaly and the quark gluon vertex function. Next we deal with properties and applications of truncated perfect fermions, and their chiral correction by means of the overlap formula. This yields a formulation of lattice fermions, which combines exact chiral symmetry with an optimisation of further essential properties. We summarise simulation results for these so-called overlap-hypercube fermions in the two-flavour Schwinger model and in quenched QCD. In the latter framework we establish a link to Chiral Perturbation Theory, both, in the p-regime and in the e-regime. In particular we present an evaluation of the leading Low Energy Constants of the chiral Lagrangian - the chiral condensate and the pion decay constant - from QCD simulations with extremely light quarks. (author)
The micro-fascism of Plato's good citizen: producing (dis)order through the construction of risk.
O'Byrne, Patrick; Holmes, Dave
2007-04-01
The human body has come to be seen as forever susceptible to both external and internal hazards, which in many circumstances require immediate, heroic, and expensive intervention. In response to this, there has been a shift from a treatment-based healthcare model to one of prevention wherein nurses play an integral role by identifying and assessing risks for individuals, communities, and populations. This paper uses Deborah Lupton's outline of the spectrum of risk and applies the theoretical works of Foucault and Plato to demonstrate the means by which nurses maintain social order by identifying and counselling risk takers. It also utilizes the work of Deleuze and Guattari to illustrate how Plato's framework for creating social order through the creation of the good citizen can be viewed as a micro-fascist system, which has been adopted wholeheartedly by preventative health professionals. The goal of this paper is to present an alternate understanding of risk to provide nurses and other healthcare professionals with a non-traditional appreciation of certain aspects of their practice as researchers and clinicians.
Negação e diferença em Platão Negation and diference in Plato
Directory of Open Access Journals (Sweden)
Eliane Christina de Souza
2010-01-01
Full Text Available Platão, ao tratar da negação no diálogo Sofista, afirma que sempre que enunciamos o que não é, não enunciamos algo contrário ao que é, mas algo diferente. A negação significa cada parte da natureza da diferença em antítese ao que é. Tal tratamento da negação resulta da necessidade de resolver alguns problemas colocados pelo eleatismo. Propõe-se indicar esses problemas e examinar o tratamento que Platão dá ao não-ser como diferença.Plato, in dealing with negation in the dialogue Sophist, says that when we say what is not, we speak not of something that is the opposite of being, but of something different. Negation means each part of the nature of the difference in antithesis to what is. This treatment of negation results from the need to solve some problems posed by eleatism. It is proposed to indicate these problems and examine the treatment that Plato gives to non-being as difference.
Comparative Study of Meanings and Status of Imagination in Mathnavi and Platoâs Ideas
Directory of Open Access Journals (Sweden)
sh alyari
2013-02-01
Full Text Available Describing and explaining the nature of imagination and its function with regard to human being and ontology has always been one of the preoccupations of philosophers and thinkers. Plato is the first philosopher who considered an epistemological status for imagination and, by dividing the world into the world of reason and world of senses, he ascribed the knowledge of imagination to the world of senses. In different parts of Mathnavi, Molavi, the great Muslim-Iranian mystic, has paid much attention to imagination, its types, its status in the Knowledge of Man (both physical and metaphysical affairs and its various influences on the body, soul and mental states of any individual. Thus, the present article aims to compare the concept of imagination in the view of the two thinkers. For reaching such aim, while using a descriptive-comparative method, first, the definitions of imagination in Mathnavi and Platoâs ideas are investigated and, then, the similarities and differences of the two views are shown. The conclusion is that their ideas are similar with regard to unreality and shadowiness of the world and phenomena, the relation between imitation and imagination, deficiency and restrictions of imagination for understanding the reality, whereas their ideas are different regarding the power of imagination, its epistemological status and the meaning and influence of it.
Perturbative study of Yang-Mills theory in the infrared
Siringo, Fabio
2015-01-01
Pure Yang-Mills SU(N) theory is studied in four dimensional space and Landau gauge by a double perturbative expansion based on a massive free-particle propagator. By dimensional regularization, all diverging mass terms cancel exactly in the double expansion, without the need to include mass counterterms that would spoil the symmetry of the original Lagrangian. The emerging perturbation theory is safe in the infrared and shares the same behaviour of the standard perturbation theory in the UV. At one-loop, Gluon and ghost propagators are found in excellent agreement with the data of lattice simulations and an infrared-safe running coupling is derived. A natural scale m=0.5-0.6 GeV is extracted from the data for N=3.
A Bijection between Lattice-Valued Filters and Lattice-Valued Congruences in Residuated Lattices
Directory of Open Access Journals (Sweden)
Wei Wei
2013-01-01
Full Text Available The aim of this paper is to study relations between lattice-valued filters and lattice-valued congruences in residuated lattices. We introduce a new definition of congruences which just depends on the meet ∧ and the residuum →. Then it is shown that each of these congruences is automatically a universal-algebra-congruence. Also, lattice-valued filters and lattice-valued congruences are studied, and it is shown that there is a one-to-one correspondence between the set of all (lattice-valued filters and the set of all (lattice-valued congruences.
Determination of low-energy constants of Wilson chiral perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Herdoiza, Gregorio [Mainz Univ. (Germany). Inst fuer Kernphysik, PRISMA Cluster of Excellence; Univ. Autonoma de Madrid, Contoblanco (Spain). Dept. de Fisica Teorica; Univ. Autonoma de Madrid (Spain). Inst. de Fisica Teorica UAM/CSIC; Jansen, Karl [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Univ. Cyprus, Nicosia (Cyprus). Dept. of Physics; Michael, Chris [Liverpool Univ. (United Kingdom). Theoretical Physics Division; Ottnad, Konstantin; Urbach, Carsten [Bonn Univ. (Germany). Helmholtz-Institut fuer Strahlen und Kernphysik; Univ. Bonn (Germany). Bethe Center for Theoretical Physics; Collaboration: European Twisted Mass Collaboration
2013-03-15
By matching Wilson twisted mass lattice QCD determinations of pseudoscalar meson masses to Wilson Chiral Perturbation Theory we determine the low-energy constants W{sub 6}{sup '}, W{sub 8}{sup '} and their linear combination c{sub 2}. We explore the dependence of these low-energy constants on the choice of the lattice action and on the number of dynamical flavours.
Non-perturbative effects for the Quark-Gluon Plasma equation of state
Energy Technology Data Exchange (ETDEWEB)
Begun, V. V., E-mail: viktor.begun@gmail.com; Gorenstein, M. I., E-mail: goren@bitp.kiev.ua; Mogilevsky, O. A. [Bogolyubov Institute for Theoretical Physics (Ukraine)
2012-07-15
The non-perturbative effects for the Quark-Gluon Plasma (QGP) equation of state (EoS) are considered. The modifications of the bag model EoS are constructed to satisfy the main qualitative features observed for the QGP EoS in the lattice QCD calculations. A quantitative comparison with the lattice results is done for the SU(3) gluon plasma and for the QGP with dynamical quarks. Our analysis advocates a negative value of the bag constant B.
Non-perturbative effects for the Quark-Gluon Plasma equation of state
Begun, V. V.; Gorenstein, M. I.; Mogilevsky, O. A.
2012-07-01
The non-perturbative effects for the Quark-Gluon Plasma (QGP) equation of state (EoS) are considered. The modifications of the bag model EoS are constructed to satisfy the main qualitative features observed for the QGP EoS in the lattice QCD calculations. A quantitative comparison with the lattice results is done for the SU(3) gluon plasma and for the QGP with dynamical quarks. Our analysis advocates a negative value of the bag constant B.
Three loop HTL perturbation theory at finite temperature and chemical potential
Energy Technology Data Exchange (ETDEWEB)
Strickland, Michael [Department of Physics, Kent State University, Kent, OH 44242 (United States); Andersen, Jens O. [Department of Physics, Norwegian University of Science and Technology, N-7491 Trondheim (Norway); Bandyopadhyay, Aritra; Haque, Najmul; Mustafa, Munshi G. [Theory Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700064 (India); Su, Nan [Faculty of Physics, University of Bielefeld, D-33615 Bielefeld (Germany)
2014-11-15
In this proceedings contribution we present a recent three-loop hard-thermal-loop perturbation theory (HTLpt) calculation of the thermodynamic potential for a finite temperature and chemical potential system of quarks and gluons. We compare the resulting pressure, trace anomaly, and diagonal/off-diagonal quark susceptibilities with lattice data. We show that there is good agreement between the three-loop HTLpt analytic result and available lattice data.
Three loop HTL perturbation theory at finite temperature and chemical potential
Strickland, Michael; Bandyopadhyay, Aritra; Haque, Najmul; Mustafa, Munshi G; Su, Nan
2014-01-01
In this proceedings contribution we present a recent three-loop hard-thermal-loop perturbation theory (HTLpt) calculation of the thermodynamic potential for a finite temperature and chemical potential system of quarks and gluons. We compare the resulting pressure, trace anomaly, and diagonal/off-diagonal quark susceptibilities with lattice data. We show that there is good agreement between the three-loop HTLpt analytic result and available lattice data.
Gauge Invariant Cosmological Perturbation Theory
Durrer, R
1993-01-01
After an introduction to the problem of cosmological structure formation, we develop gauge invariant cosmological perturbation theory. We derive the first order perturbation equations of Einstein's equations and energy momentum ``conservation''. Furthermore, the perturbations of Liouville's equation for collisionless particles and Boltzmann's equation for Compton scattering are worked out. We fully discuss the propagation of photons in a perturbed Friedmann universe, calculating the Sachs--Wolfe effect and light deflection. The perturbation equations are extended to accommodate also perturbations induced by seeds. With these general results we discuss some of the main aspects of the texture model for the formation of large scale structure in the Universe (galaxies, clusters, sheets, voids). In this model, perturbations in the dark matter are induced by texture seeds. The gravitational effects of a spherically symmetric collapsing texture on dark matter, baryonic matter and photons are calculated in first orde...
Infinitesimal diffeomorfisms on the lattice
CERN. Geneva
2015-01-01
The energy-momentum tensor and local translation Ward identities constitute the essential toolkit to probe the response of a QFT to an infinitesimal change of geometry. This is relevant in a number of contexts. For instance in order to get the thermodynamical equation of state, one wants to study the response of a Euclidean QFT in a finite box to a change in the size of the box. The lattice formulation of QFTs is a prime tool to study their dynamics beyond perturbation theory. However Poincaré invariance is explicitly broken, and is supposed to be recovered only in the continuum limit. Approximate local Ward identities for translations can be defined, by they require some care for two reasons: 1) the energy-momentum tensor needs to be properly defined through a renormalization procedure; 2) the action of infinitesimal local translations (i.e. infinitesimal diffeomorfisms) is ill-defined on local observables. In this talk I will review the issues related to the renormalization of the energy-momentum tensor ...
Controlling quark mass determinations non-perturbatively in three-flavour QCD
Directory of Open Access Journals (Sweden)
Campos Isabel
2017-01-01
Full Text Available The determination of quark masses from lattice QCD simulations requires a non-perturbative renormalization procedure and subsequent scale evolution to high energies, where a conversion to the commonly used MS¯$\\overline {{\\rm{MS}}} $ scheme can be safely established. We present our results for the non-perturbative running of renormalized quark masses in Nf = 3 QCD between the electroweak and a hadronic energy scale, where lattice simulations are at our disposal. Recent theoretical advances in combination with well-established techniques allows to follow the scale evolution to very high statistical accuracy, and full control of systematic effects.
Controlling quark mass determinations non-perturbatively in three-flavour QCD
Campos, Isabel; Pena, Carlos; Preti, David; Ramos, Alberto; Vladikas, Anastassios
2016-01-01
The determination of quark masses from lattice QCD simulations requires a non-perturbative renormalization procedure and subsequent scale evolution to high energies, where a conversion to the commonly used MS-bar scheme can be safely established. We present our results for the non-perturbative running of renormalized quark masses in Nf=3 QCD between the electroweak and a hadronic energy scale, where lattice simulations are at our disposal. Recent theoretical advances in combination with well-established techniques allows to follow the scale evolution to very high statistical accuracy, and full control of systematic effects.
Knuth, Kevin H.
2009-12-01
Previous derivations of the sum and product rules of probability theory relied on the algebraic properties of Boolean logic. Here they are derived within a more general framework based on lattice theory. The result is a new foundation of probability theory that encompasses and generalizes both the Cox and Kolmogorov formulations. In this picture probability is a bi-valuation defined on a lattice of statements that quantifies the degree to which one statement implies another. The sum rule is a constraint equation that ensures that valuations are assigned so as to not violate associativity of the lattice join and meet. The product rule is much more interesting in that there are actually two product rules: one is a constraint equation arises from associativity of the direct products of lattices, and the other a constraint equation derived from associativity of changes of context. The generality of this formalism enables one to derive the traditionally assumed condition of additivity in measure theory, as well introduce a general notion of product. To illustrate the generic utility of this novel lattice-theoretic foundation of measure, the sum and product rules are applied to number theory. Further application of these concepts to understand the foundation of quantum mechanics is described in a joint paper in this proceedings.
Institute of Scientific and Technical Information of China (English)
WANG Peng
2011-01-01
Perturbation to Noether symmetry of discrete mechanico-electrical systems on an uniform lattice is investigated.First, Noether theorem of a system is presented. Secondly, the criterion of perturbation to Noether symmetry of the system is given. Based on the definition of adiabatic invariants, Noether adiabatic invariants of the system are obtained. Finally, An example is given to support these results.%@@ Perturbation to Noether symmetry of discrete mechanico-electrical systems on an uniform lattice is investigated.First, Noether theorem of a system is presented.Secondly , the criterion of perturbation to Noether symmetry of the system is given.Based on the definition of adiabatic invariants, Noether adiabatic invariants of the system are obtained .Finally, An example is given to support these results.
Some Applications of Hard Thermal Loop Perturbation Theory in Quark Gluon Plasma
Haque, Najmul
2014-01-01
This thesis is mainly devoted to the study of thermodynamics for quantum Chromodynamics. In this thesis I apply hard-thermal-loop perturbation theory, which is a gauge-invariant reorganization of the conventional perturbative expansion for quantum gauge theories to study the thermodynamics of QCD in leading-order, next-to-leading-order and next-to-next-to-leading order at finite temperature and finite chemical potential. I also discuss about various order diagonal and off-diagonale quark number susceptibilities in leading order as well as beyond leading order. For all the observables, I compare our results with available lattice QCD data and we find good agreement. Along-with the computation of thermodynamic quantities of hot and dense matter, I also discuss about low mass dilepton rate from hot and dense medium using both perturbative and non-perturbative models and compare them with those from lattice gauge theory and in-medium hadron gas.
From enemies to friends chiral symmetry on the lattice
Hernández, Pilar; Lellouch, L P; Hernandez, Pilar; Jansen, Karl; Lellouch, Laurent
2002-01-01
The physics of strong interactions is invariant under the exchange of left-handed and right-handed quarks, at least in the massless limit. This invariance is reflected in the chiral symmetry of quantum chromodynamics. Surprisingly, it has become clear only recently how to implement this important symmetry in lattice formulations of quantum field theories. We will discuss realizations of exact lattice chiral symmetry and give an example of the computation of a physical observable in quantum chromodynamics where chiral symmetry is important. This calculation is performed by relying on finite size scaling methods as predicted by chiral perturbation theory.
Properties of light pseudoscalars from lattice QCD with HISQ ensembles
Bazavov, A; DeTar, C; Freeman, W; Gottlieb, Steven; Heller, U M; Hetrick, J E; Kim, J; Laiho, J; Levkova, L; Lightman, M; Oktay, M; Osborn, J; Sugar, R L; Toussaint, D; Van de Water, R S
2011-01-01
We fit lattice-QCD data for light-pseudoscalar masses and decay constants, from HISQ configurations generated by MILC, to SU(3) staggered chiral perturbation theory. At present such fits have rather high values of chi^2/d.o.f., possibly due to the lack of ensembles with lighter-than-physical sea strange-quark masses. We propose solutions to this problem for future work. We also perform simple linear interpolations near the physical point on two ensembles with different lattice spacings, and obtain the preliminary result (f_K / f_pi)^phys = 1.1872(41) in the continuum limit.
Light Meson Physics from Maximally Twisted Mass Lattice QCD
Baron, R; Dimopoulos, P; Farchioni, F; Frezzotti, R; Gimenez, V; Herdoiza, G; Jansen, K; Lubicz, V; Michael, C; Muenster, G; Palao, D; Rossi, G C; Scorzato, L; Shindler, A; Simula, S; Sudmann, T; Urbach, C; Wenger, U
2009-01-01
We present a comprehensive investigation of light meson physics using maximally twisted mass fermions for two mass-degenerate quark flavours. By employing four values of the lattice spacing, spatial lattice extents ranging from 2.0 fm to 2.5 fm and pseudo scalar masses in the range 280 MeV to 650 MeV we control the major systematic effects of our calculation. This enables us to confront our data with chiral perturbation theory and extract low energy constants of the effective chiral Lagrangian and derived quantities, such as the light quark mass, with high precision.
Approaching the chiral point in two-flavour lattice simulations
Lottini, Stefano
2014-01-01
We investigate the behaviour of the pion decay constant and the pion mass in two-flavour lattice QCD, with the physical and chiral points as ultimate goal. Measurements come from the ensembles generated by the CLS initiative using the O(a)-improved Wilson formulation, with lattice spacing down to about 0.05 fermi and pion masses as low as 190 MeV. The applicability of SU(2) chiral perturbation theory is investigated, and various functional forms, and their range of validity, are compared. The physical scale is set through the kaon decay constant, whose measurement is enabled by inserting a third, heavier valence strange quark.
QCD Factorization and PDFs from Lattice QCD Calculation
Ma, Yan-Qing
2014-01-01
In this talk, we review a QCD factorization based approach to extract parton distribution and correlation functions from lattice QCD calculation of single hadron matrix elements of quark-gluon operators. We argue that although the lattice QCD calculations are done in the Euclidean space, the nonperturbative collinear behavior of the matrix elements are the same as that in the Minkowski space, and could be systematically factorized into parton distribution functions with infrared safe matching coefficients. The matching coefficients can be calculated perturbatively by applying the factorization formalism on to asymptotic partonic states.
Long distance part of $\\epsilon_K$ from lattice QCD
Bai, Ziyuan
2016-01-01
We demonstrate the lattice QCD calculation of the long distance contribution to $\\epsilon_K$. Due to the singular, short-distance structure of $\\epsilon_K$, we must perform a short-distance subtraction and introduce a corresponding low-energy constant determined from perturbation theory, which we calculate at Next Leading Order (NLO). We perform the calculation on a $24^3 \\times 64$ lattice with a pion mass of 329 MeV. This work is a complete calculation, which includes all connected and disconnected diagrams.
Responses of many-species predator-prey systems to perturbations
Esmaily, Shadi; Pleimling, Michel
2015-03-01
We study the responses of many-species predator-prey systems, both in the well-mixed case as well as on a two-dimensional lattice, to permanent and transient perturbations. In the case of a weak transient perturbation the system returns to the original steady state, whereas a permanent perturbation pushes the system into a new steady state. Using Monte Carlo simulations, we monitor the approach to stationarity after a perturbation through a variety of quantities, as for example time-dependent particle densities and correlation functions. Different types of perturbations are studied, ranging from a change in reaction rates to the injection of additional individuals into the system, the latter perturbation mimicking immigration. This work is supported by the US National Science Foundation through Grant DMR-1205309.
Csikor, Ferenc; Hegedüs, P; Piróth, A
1999-01-01
We present a one-loop calculation of the static potential in the SU(2)-Higgs model. The connection to the coupling constant definition used in lattice simulations is clarified. The consequences in comparing lattice simulations and perturbative results for finite temperature applications are explored.
Lattice Boltzmann Stokesian dynamics.
Ding, E J
2015-11-01
Lattice Boltzmann Stokesian dynamics (LBSD) is presented for simulation of particle suspension in Stokes flows. This method is developed from Stokesian dynamics (SD) with resistance and mobility matrices calculated using the time-independent lattice Boltzmann algorithm (TILBA). TILBA is distinguished from the traditional lattice Boltzmann method (LBM) in that a background matrix is generated prior to the calculation. The background matrix, once generated, can be reused for calculations for different scenarios, thus the computational cost for each such subsequent calculation is significantly reduced. The LBSD inherits the merits of the SD where both near- and far-field interactions are considered. It also inherits the merits of the LBM that the computational cost is almost independent of the particle shape.
Improved Lattice Radial Quantization
Brower, Richard C; Fleming, George T
2014-01-01
Lattice radial quantization was proposed in a recent paper by Brower, Fleming and Neuberger[1] as a nonperturbative method especially suited to numerically solve Euclidean conformal field theories. The lessons learned from the lattice radial quantization of the 3D Ising model on a longitudinal cylinder with 2D Icosahedral cross-section suggested the need for an improved discretization. We consider here the use of the Finite Element Methods(FEM) to descretize the universally-equivalent $\\phi^4$ Lagrangian on $\\mathbb R \\times \\mathbb S^2$. It is argued that this lattice regularization will approach the exact conformal theory at the Wilson-Fisher fixed point in the continuum. Numerical tests are underway to support this conjecture.
Graphene antidot lattice waveguides
DEFF Research Database (Denmark)
Pedersen, Jesper Goor; Gunst, Tue; Markussen, Troels
2012-01-01
We introduce graphene antidot lattice waveguides: nanostructured graphene where a region of pristine graphene is sandwiched between regions of graphene antidot lattices. The band gaps in the surrounding antidot lattices enable localized states to emerge in the central waveguide region. We model...... the waveguides via a position-dependent mass term in the Dirac approximation of graphene and arrive at analytical results for the dispersion relation and spinor eigenstates of the localized waveguide modes. To include atomistic details we also use a tight-binding model, which is in excellent agreement...... with the analytical results. The waveguides resemble graphene nanoribbons, but without the particular properties of ribbons that emerge due to the details of the edge. We show that electrons can be guided through kinks without additional resistance and that transport through the waveguides is robust against...
Digital lattice gauge theories
Zohar, Erez; Reznik, Benni; Cirac, J Ignacio
2016-01-01
We propose a general scheme for a digital construction of lattice gauge theories with dynamical fermions. In this method, the four-body interactions arising in models with $2+1$ dimensions and higher, are obtained stroboscopically, through a sequence of two-body interactions with ancillary degrees of freedom. This yields stronger interactions than the ones obtained through pertubative methods, as typically done in previous proposals, and removes an important bottleneck in the road towards experimental realizations. The scheme applies to generic gauge theories with Lie or finite symmetry groups, both Abelian and non-Abelian. As a concrete example, we present the construction of a digital quantum simulator for a $\\mathbb{Z}_{3}$ lattice gauge theory with dynamical fermionic matter in $2+1$ dimensions, using ultracold atoms in optical lattices, involving three atomic species, representing the matter, gauge and auxiliary degrees of freedom, that are separated in three different layers. By moving the ancilla atoms...
Perturbation theory of solid-liquid interfacial free energies of bcc metals.
Warshavsky, Vadim B; Song, Xueyu
2012-09-01
A perturbation theory is used to calculate bcc solid-liquid interfacial free energies of metallic systems with embedded-atom model potentials. As a reference system for bcc crystals we used a single-occupancy cell, hard-sphere bcc system. Good agreements between the perturbation theory results and the corresponding results from simulations are found. The strategy to extract hard-sphere bcc solid-liquid interfacial free energies may have broader applications for other crystal lattices.
Perturbative two- and three-loop coefficients from large $\\beta$ Monte Carlo
Lepage, G P; Shakespeare, N H; Trottier, H D
2000-01-01
Perturbative coefficients for Wilson loops and the static quark self-energy are extracted from Monte Carlo simulations at large beta on finite volumes, where all the lattice momenta are large. The Monte Carlo results are in excellent agreement with perturbation theory through second order. New results for third order coefficients are reported. Twisted boundary conditions are used to eliminate zero modes and to suppress Z_3 tunneling.
Oates, Chris
2012-06-01
Since they were first proposed in 2003 [1], optical lattice clocks have become one of the leading technologies for the next generation of atomic clocks, which will be used for advanced timing applications and in tests of fundamental physics [2]. These clocks are based on stabilized lasers whose frequency is ultimately referenced to an ultra-narrow neutral atom transition (natural linewidths magic'' value so as to yield a vanishing net AC Stark shift for the clock transition. As a result lattice clocks have demonstrated the capability of generating high stability clock signals with small absolute uncertainties (˜ 1 part in 10^16). In this presentation I will first give an overview of the field, which now includes three different atomic species. I will then use experiments with Yb performed in our laboratory to illustrate the key features of a lattice clock. Our research has included the development of state-of-the-art optical cavities enabling ultra-high-resolution optical spectroscopy (1 Hz linewidth). Together with the large atom number in the optical lattice, we are able to achieve very low clock instability (< 0.3 Hz in 1 s) [3]. Furthermore, I will show results from some of our recent investigations of key shifts for the Yb lattice clock, including high precision measurements of ultracold atom-atom interactions in the lattice and the dc Stark effect for the Yb clock transition (necessary for the evaluation of blackbody radiation shifts). [4pt] [1] H. Katori, M. Takamoto, V. G. Pal'chikov, and V. D. Ovsiannikov, Phys. Rev. Lett. 91, 173005 (2003). [0pt] [2] Andrei Derevianko and Hidetoshi Katori, Rev. Mod. Phys. 83, 331 (2011). [0pt] [3] Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L.-S. Ma, and C. W. Oates, Nature Photonics 5, 158 (2011).
Lattice thermal conductivity of minerals in the deep mantle condition
Dekura, H.; Tsuchiya, T.; Tsuchiya, J.
2011-12-01
Thermal transport property of materials under pressure and temperature is of importance for understanding the dynamics of the solid Earth and the thermal history. Both experimental and theoretical determinations of the thermal conductivity, however, still remain technically challenging particularly at the deep mantle condition. Recent progress in ab initio computational method based on the density-functional theory is now makes it possible to examine the transport phenomena including the lattice thermal conduction. The intrinsic bulk thermal conduction of insulator is caused by lattice anharmonicity owing to phonon-phonon interaction. The key parameter to predict lattice thermal conductivity is thus the anharmonic coupling constant. Earlier theoretical works calculated the lattice thermal conductivity of MgO with ab initio molecular dynamics simulation or finite difference lattice dynamics simulation (Nico de Koker, Phys. Rev. Lett. 103, 125902, 2009; X. Tang and J. Dong, Proc. Natl. Acad. Sci. U.S.A. 107, 4539, 2010). However, in these approaches, the simulation cell size could often be insufficient for accurate description of the long wavelength phonon scattering. This leads to a lack of the decay channels for the phonons. As an alternative approach, the anharmonic coupling strength between phonon modes can be evaluated within the density-functional perturbation theory. In this approach, the higher-order force tensors are calculated through a number of phonon decay channels obtained within the perturbative scheme taking care only of the primitive cell. We have been developing a technique for calculation of the phonon linewidth necessary to obtain the phonon lifetime. Then the lattice thermal conductivity is evaluated combining with additional harmonic-level of propeties. In this presentation, we show the behavior of lattice thermal conductivity in lower mantle minerals, and discuss the effects of pressure and temperature on their conductivities up to the deep
Energy Technology Data Exchange (ETDEWEB)
Catterall, Simon; Kaplan, David B.; Unsal, Mithat
2009-03-31
We provide an introduction to recent lattice formulations of supersymmetric theories which are invariant under one or more real supersymmetries at nonzero lattice spacing. These include the especially interesting case of N = 4 SYM in four dimensions. We discuss approaches based both on twisted supersymmetry and orbifold-deconstruction techniques and show their equivalence in the case of gauge theories. The presence of an exact supersymmetry reduces and in some cases eliminates the need for fine tuning to achieve a continuum limit invariant under the full supersymmetry of the target theory. We discuss open problems.
Grabisch, Michel
2008-01-01
We extend the notion of belief function to the case where the underlying structure is no more the Boolean lattice of subsets of some universal set, but any lattice, which we will endow with a minimal set of properties according to our needs. We show that all classical constructions and definitions (e.g., mass allocation, commonality function, plausibility functions, necessity measures with nested focal elements, possibility distributions, Dempster rule of combination, decomposition w.r.t. simple support functions, etc.) remain valid in this general setting. Moreover, our proof of decomposition of belief functions into simple support functions is much simpler and general than the original one by Shafer.
Charmed bottom baryon spectroscopy from lattice QCD
Brown, Zachary S; Meinel, Stefan; Orginos, Kostas
2014-01-01
We calculate the masses of baryons containing one, two, or three heavy quarks using lattice QCD. We consider all possible combinations of charm and bottom quarks, and compute a total of 36 different states with $J^P = \\frac12^+$ and $J^P = \\frac32^+$. We use domain-wall fermions for the up, down, and strange quarks, a relativistic heavy-quark action for the charm quarks, and nonrelativistic QCD for the bottom quarks. Our analysis includes results from two different lattice spacings and seven different pion masses. We perform extrapolations of the baryon masses to the continuum limit and to the physical pion mass using $SU(4|2)$ heavy-hadron chiral perturbation theory including $1/m_Q$ and finite-volume effects. For the 14 singly heavy baryons that have already been observed, our results agree with the experimental values within the uncertainties. We compare our predictions for the hitherto unobserved states with other lattice calculations and quark-model studies.
Lattice gauge theories and Monte Carlo algorithms
Energy Technology Data Exchange (ETDEWEB)
Creutz, M. (Brookhaven National Lab., Upton, NY (USA). Physics Dept.)
1989-07-01
Lattice gauge theory has become the primary tool for non-perturbative calculations in quantum field theory. These lectures review some of the foundations of this subject. The first lecture reviews the basic definition of the theory in terms of invariant integrals over group elements on lattice bonds. The lattice represents an ultraviolet cutoff, and renormalization group arguments show how the bare coupling must be varied to obtain the continuum limit. Expansions in the inverse of the coupling constant demonstrate quark confinement in the strong coupling limit. The second lecture turns to numerical simulation, which has become an important approach to calculating hadronic properties. Here I discuss the basic algorithms for obtaining appropriately weighted gauge field configurations. The third lecture turns to algorithms for treating fermionic fields, which still require considerably more computer time than needed for purely bosonic simulations. Some particularly promising recent approaches are based on global accept-reject steps and should display a rather favorable dependence of computer time on the system volume. (orig.).
Tate, Nicholas
2016-01-01
From Plato onwards many of the great Western thinkers have explored the nature of the arts, their contribution to society and their role in education. This has often involved a discussion of the potentially negative impact of the arts. The recurring message has been that the arts can warp judgment, elevate emotion at the expense of reason,…
Mintz, Avi I.
2014-01-01
Plato's "Apology of Socrates" contains a spirited account of Socrates' relationship with the city of Athens and its citizens. As Socrates stands on trial for corrupting the youth, surprisingly, he does not defend the substance and the methods of his teaching. Instead, he simply denies that he is a teacher. Many scholars have…
DEFF Research Database (Denmark)
Patel, Manesh R.; Becker, Richard C.; Wojdyla, Daniel M.;
Abstract 14299: Cardiovascular Events in Acute Coronary Syndrome Patients With Peripheral Arterial Disease Treated With Ticagrelor Compared to Clopidogrel: Data From the PLATO Trial Manesh R Patel1; Richard C Becker1; Daniel M Wojdyla2; Håkan Emanuelsson3; William Hiatt4; Jay Horrow5; Steen Husted6...
Direct perturbation method for perturbed complex Burgers equation
Institute of Scientific and Technical Information of China (English)
Cheng Xue-Ping; Lin Ji; Yao Jian-Ming
2009-01-01
So far, Lou's direct perturbation method has been applied successfully to solve the nonlinear Schrōdinger equa-tion(NLSE) hierarchy, such as the NLSE, the coupled NLSE, the critical NLSE, and the derivative NLSE. But to our knowledge, this method for other types of perturbed nonlinear evolution equations has still been lacking. In this paper, Lou's direct perturbation method is applied to the study of perturbed complex Burgers equation. By this method, we calculate not only the zero-order adiabatic solution, but also the first order modification.
Directory of Open Access Journals (Sweden)
Futa Yuichi
2016-03-01
Full Text Available In this article, we formalize the definition of lattice of ℤ-module and its properties in the Mizar system [5].We formally prove that scalar products in lattices are bilinear forms over the field of real numbers ℝ. We also formalize the definitions of positive definite and integral lattices and their properties. Lattice of ℤ-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lovász base reduction algorithm [14], and cryptographic systems with lattices [15] and coding theory [9].
Introduction to perturbation methods
Holmes, M
1995-01-01
This book is an introductory graduate text dealing with many of the perturbation methods currently used by applied mathematicians, scientists, and engineers. The author has based his book on a graduate course he has taught several times over the last ten years to students in applied mathematics, engineering sciences, and physics. The only prerequisite for the course is a background in differential equations. Each chapter begins with an introductory development involving ordinary differential equations. The book covers traditional topics, such as boundary layers and multiple scales. However, it also contains material arising from current research interest. This includes homogenization, slender body theory, symbolic computing, and discrete equations. One of the more important features of this book is contained in the exercises. Many are derived from problems of up- to-date research and are from a wide range of application areas.
An Algorithm on Generating Lattice Based on Layered Concept Lattice
Directory of Open Access Journals (Sweden)
Zhang Chang-sheng
2013-08-01
Full Text Available Concept lattice is an effective tool for data analysis and rule extraction, a bottleneck factor on impacting the applications of concept lattice is how to generate lattice efficiently. In this paper, an algorithm LCLG on generating lattice in batch processing based on layered concept lattice is developed, this algorithm is based on layered concept lattice, the lattice is generated downward layer by layer through concept nodes and provisional nodes in current layer; the concept nodes are found parent-child relationships upward layer by layer, then the Hasse diagram of inter-layer connection is generated; in the generated process of the lattice nodes in each layer, we do the pruning operations dynamically according to relevant properties, and delete some unnecessary nodes, such that the generating speed is improved greatly; the experimental results demonstrate that the proposed algorithm has good performance.
Applications of Cosmological Perturbation Theory
Christopherson, Adam J
2011-01-01
Cosmological perturbation theory is crucial for our understanding of the universe. The linear theory has been well understood for some time, however developing and applying the theory beyond linear order is currently at the forefront of research in theoretical cosmology. This thesis studies the applications of perturbation theory to cosmology and, specifically, to the early universe. Starting with some background material introducing the well-tested 'standard model' of cosmology, we move on to develop the formalism for perturbation theory up to second order giving evolution equations for all types of scalar, vector and tensor perturbations, both in gauge dependent and gauge invariant form. We then move on to the main result of the thesis, showing that, at second order in perturbation theory, vorticity is sourced by a coupling term quadratic in energy density and entropy perturbations. This source term implies a qualitative difference to linear order. Thus, while at linear order vorticity decays with the expan...
Evidence for hard chiral logarithms in quenched lattice QCD
Kim, S; Kim, Seyong; Sinclair, D K
1995-01-01
We present the first direct evidence that quenched QCD differs from full QCD in the chiral (m_q \\rightarrow 0) limit, as predicted by chiral perturbation theory, from our quenched lattice QCD simulations at \\beta = 6/g^2 = 6.0. We measured the spectrum of light hadrons on 16^3 \\times 64, 24^3 \\times 64 and 32^3 \\times 64, using staggered quarks of masses m_q=0.01, m_q=0.005 and m_q=0.0025. The pion masses showed clear evidence for logarithmic violations of the PCAC relation m_{\\pi}^2 \\propto m_q, as predicted by quenched chiral perturbation theory. The dependence on spatial lattice volume precludes this being a finite size effect. No evidence was seen for such chiral logarithms in the behaviour of the chiral condensate \\langle\\bar{\\psi}\\psi\\rangle.
Long-range interactions in lattice field theory
Energy Technology Data Exchange (ETDEWEB)
Rabin, J.M.
1981-06-01
Lattice quantum field theories containing fermions can be formulated in a chirally invariant way provided long-range interactions are introduced. It is established that in weak-coupling perturbation theory such a lattice theory is renormalizable when the corresponding continuum theory is, and that the continuum theory is indeed recovered in the perturbative continuum limit. In the strong-coupling limit of these theories one is led to study an effective Hamiltonian describing a Heisenberg antiferromagnet with long-range interactions. Block-spin renormalization group methods are used to find a critical rate of falloff of the interactions, approximately as inverse distance squared, which separates a nearest-neighbor-antiferromagnetic phase from a phase displaying identifiable long-range effects. A duality-type symmetry is present in some block-spin calculations.
Scalar mass corrections from compact extra dimensions on the lattice
Del Debbio, Luigi
2012-01-01
We explore the phase diagram of the SU(2) Yang-Mills theory in 5 dimensions by numerical simulations. The lattice system shows a dimensionally-reduced phase where the extra dimension is small compared to the four dimensional correlation length. In the low-energy regime of this phase, the system behaves like a four-dimensional gauge theory coupled to an adjoint scalar field. By tuning the bare parameters of the lattice model, we identify lines of constant physics, and analyse the behaviour of the non-perturbative scalar mass as a function of the compactification and the cut-off scales. The perturbative prediction that the effective theory contains a light particle with a mass that is independent of the cut-off is tested against non-pertubative results.
Shigaki, Kenta; Noda, Fumiaki; Yamamoto, Kazami; Machida, Shinji; Molodojentsev, Alexander; Ishi, Yoshihiro
2002-12-01
The JKJ high-intensity proton accelerator facility consists of a 400-MeV linac, a 3-GeV 1-MW rapid-cycling synchrotron and a 50-GeV 0.75-MW synchrotron. The lattice and beam dynamics design of the two synchrotrons are reported.
de Raedt, Hans; von der Linden, W.; Binder, K
1995-01-01
In this chapter we review methods currently used to perform Monte Carlo calculations for quantum lattice models. A detailed exposition is given of the formalism underlying the construction of the simulation algorithms. We discuss the fundamental and technical difficulties that are encountered and gi
Knuth, Kevin H
2009-01-01
Previous derivations of the sum and product rules of probability theory relied on the algebraic properties of Boolean logic. Here they are derived within a more general framework based on lattice theory. The result is a new foundation of probability theory that encompasses and generalizes both the Cox and Kolmogorov formulations. In this picture probability is a bi-valuation defined on a lattice of statements that quantifies the degree to which one statement implies another. The sum rule is a constraint equation that ensures that valuations are assigned so as to not violate associativity of the lattice join and meet. The product rule is much more interesting in that there are actually two product rules: one is a constraint equation arises from associativity of the direct products of lattices, and the other a constraint equation derived from associativity of changes of context. The generality of this formalism enables one to derive the traditionally assumed condition of additivity in measure theory, as well in...
Williamson, S. Gill
2010-01-01
Will the cosmological multiverse, when described mathematically, have easily stated properties that are impossible to prove or disprove using mathematical physics? We explore this question by constructing lattice multiverses which exhibit such behavior even though they are much simpler mathematically than any likely cosmological multiverse.
Phenomenology from lattice QCD
Lellouch, L P
2003-01-01
After a short presentation of lattice QCD and some of its current practical limitations, I review recent progress in applications to phenomenology. Emphasis is placed on heavy-quark masses and on hadronic weak matrix elements relevant for constraining the CKM unitarity triangle. The main numerical results are highlighted in boxes.
Noetherian and Artinian Lattices
Directory of Open Access Journals (Sweden)
Derya Keskin Tütüncü
2012-01-01
Full Text Available It is proved that if L is a complete modular lattice which is compactly generated, then Rad(L/0 is Artinian if, and only if for every small element a of L, the sublattice a/0 is Artinian if, and only if L satisfies DCC on small elements.
Green-Schwarz superstring on the lattice
Bianchi, L.; Bianchi, M. S.; Forini, V.; Leder, B.; Vescovi, E.
2016-07-01
We consider possible discretizations for a gauge-fixed Green-Schwarz action of Type IIB superstring. We use them for measuring the action, from which we extract the cusp anomalous dimension of planar N=4 SYM as derived from AdS/CFT, as well as the mass of the two AdS excitations transverse to the relevant null cusp classical string solution. We perform lattice simulations employing a Rational Hybrid Monte Carlo (RHMC) algorithm and two Wilson-like fermion discretizations, one of which preserves the global SO(6) symmetry the model. We compare our results with the expected behavior at various values of g=√{λ }/4π . For both the observables, we find a good agreement for large g, which is the perturbative regime of the sigma-model. For smaller values of g, the expectation value of the action exhibits a deviation compatible with the presence of quadratic divergences. After their non-perturbative subtraction the continuum limit can be taken, and suggests a qualitative agreement with the non-perturbative expectation from AdS/CFT. Furthermore, we detect a phase in the fermion determinant, whose origin we explain, that for small g leads to a sign problem not treatable via standard reweigthing. The continuum extrapolations of the observables in the two different discretizations agree within errors, which is strongly suggesting that they lead to the same continuum limit. Part of the results discussed here were presented earlier in [1].
Cosmological perturbations in massive bigravity
Energy Technology Data Exchange (ETDEWEB)
Lagos, Macarena; Ferreira, Pedro G., E-mail: m.lagos13@imperial.ac.uk, E-mail: p.ferreira1@physics.ox.ac.uk [Astrophysics, University of Oxford, DWB, Keble road, Oxford OX1 3RH (United Kingdom)
2014-12-01
We present a comprehensive analysis of classical scalar, vector and tensor cosmological perturbations in ghost-free massive bigravity. In particular, we find the full evolution equations and analytical solutions in a wide range of regimes. We show that there are viable cosmological backgrounds but, as has been found in the literature, these models generally have exponential instabilities in linear perturbation theory. However, it is possible to find stable scalar cosmological perturbations for a very particular choice of parameters. For this stable subclass of models we find that vector and tensor perturbations have growing solutions. We argue that special initial conditions are needed for tensor modes in order to have a viable model.
Nucleon isovector couplings from $N_f=2$ lattice QCD
Bali, Gunnar S; Glässle, Benjamin; Göckeler, Meinulf; Najjar, Johannes; Rödl, Rudolf H; Schäfer, Andreas; Schiel, Rainer W; Söldner, Wolfgang; Sternbeck, Andre
2014-01-01
We compute the axial, scalar, tensor and pseudoscalar isovector couplings of the nucleon as well as the induced tensor and pseudoscalar charges in lattice simulations with $N_f=2$ mass-degenerate non-perturbatively improved Wilson-Sheikholeslami-Wohlert fermions. The simulations are carried out down to a pion mass of 150 MeV and linear spatial lattice extents of up to 4.6 fm at three different lattice spacings ranging from approximately 0.08 fm to 0.06 fm. Possible excited state contamination is carefully investigated and finite volume effects are studied. The couplings, determined at these lattice spacings, are extrapolated to the physical pion mass. In this limit we find agreement with experimental results, where these exist, with the exception of the magnetic moment. A proper continuum limit could not be performed, due to our limited range of lattice constants, but no significant lattice spacing dependence is detected. Upper limits on discretization effects are estimated and these dominate the error budget...
Gauge-fixing approach to lattice chiral gauge theories
Bock, W; Shamir, Y; Bock, Wolfgang; Golterman, Maarten F.L.; Shamir, Yigal
1998-01-01
We review the status of our recent work on the gauge-fixing approach to lattice chiral gauge theories. New numerical results in the reduced version of a model with a U(1) gauge symmetry are presented which strongly indicate that the factorization of the correlation functions of the left-handed neutral and right-handed charged fermion fields, which we established before in perturbation theory, holds also nonperturbatively.
Cascades with coupled map lattices in preferential attachment community networks
Institute of Scientific and Technical Information of China (English)
Cui Di; Gao Zi-You; Zhao Xiao-Mei
2008-01-01
In this paper,cascading failure is studied by coupled map lattice (CML) methods in preferential attachment community networks.It is found that external perturbation R is increasing with modularity Q growing by simulation.In particular,the large modularity Q can hold off the cascading failure dynamic process in community networks.Furthermore,different attack strategies also greatly affect the cascading failure dynamic process. It is particularly significant to control cascading failure process in real community networks.
The accuracy of QCD perturbation theory at high energies
Dalla Brida, Mattia; Korzec, Tomasz; Ramos, Alberto; Sint, Stefan; Sommer, Rainer
2016-01-01
We discuss the determination of the strong coupling $\\alpha_\\mathrm{\\overline{MS}}^{}(m_\\mathrm{Z})$ or equivalently the QCD $\\Lambda$-parameter. Its determination requires the use of perturbation theory in $\\alpha_s(\\mu)$ in some scheme, $s$, and at some energy scale $\\mu$. The higher the scale $\\mu$ the more accurate perturbation theory becomes, owing to asymptotic freedom. As one step in our computation of the $\\Lambda$-parameter in three-flavor QCD, we perform lattice computations in a scheme which allows us to non-perturbatively reach very high energies, corresponding to $\\alpha_s = 0.1$ and below. We find that perturbation theory is very accurate there, yielding a three percent error in the $\\Lambda$-parameter, while data around $\\alpha_s \\approx 0.2$ is clearly insufficient to quote such a precision. It is important to realize that these findings are expected to be generic, as our scheme has advantageous properties regarding the applicability of perturbation theory.
Basis reduction for layered lattices
Torreão Dassen, Erwin
2011-01-01
We develop the theory of layered Euclidean spaces and layered lattices. We present algorithms to compute both Gram-Schmidt and reduced bases in this generalized setting. A layered lattice can be seen as lattices where certain directions have infinite weight. It can also be interpre
Spin qubits in antidot lattices
DEFF Research Database (Denmark)
Pedersen, Jesper Goor; Flindt, Christian; Mortensen, Niels Asger;
2008-01-01
and density of states for a periodic potential modulation, referred to as an antidot lattice, and find that localized states appear, when designed defects are introduced in the lattice. Such defect states may form the building blocks for quantum computing in a large antidot lattice, allowing for coherent...
Manifestly Gauge Covariant Treatment of Lattice Chiral Fermion
Suzuki, H
1997-01-01
We propose a lattice formulation of the chiral fermion which maximally respects the gauge symmetry and simultaneously is free of the unwanted species doublers. This is achieved by directly dealing with the lattice fermion propagator and the composite operators, rather than the lattice action and the fermionic determinant. The latter is defined as a functional integral of the expectation value of the gauge current operator with respect to the background gauge field. The gauge anomaly is characterized as a non-integrability of this integration process and, the determinant is defined only for anomaly free cases. Gauge singlet operators on the other hand are always regularized gauge invariantly. Some perturbative check is performed to confirm the gauge covariance and the absence of the doublers. This formulation can be applied rather straightforwardly to numerical simulations in the quenched approximation.
Axion cosmology, lattice QCD and the dilute instanton gas
Energy Technology Data Exchange (ETDEWEB)
Borsanyi, S. [Wuppertal Univ. (Germany). Dept. of Physics; Dierigl, M.; Ringwald, A. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Fodor, Z. [Wuppertal Univ. (Germany). Dept. of Physics; Forschungszentrum Juelich (Germany). Inst. for Advanced Simulation (IAS), Juelich Supercomputing Centre (JSC); Lorand Eoetvoes Univ., Budapest (Hungary). Inst. for Theoretical Physics; Katz, S.D. [Lorand Eoetvoes Univ., Budapest (Hungary). Inst. for Theoretical Physics; MTA-ELTE Lenduelet Lattice Gauge Theory Research Group, Budapest (Hungary); Mages, S.W. [Rgensburg Univ. (Germany); Forschungszentrum Juelich (Germany). Inst. for Advanced Simulation (IAS), Juelich Supercomputing Centre (JSC); Nogradi, D. [Lorand Eoetvoes Univ., Budapest (Hungary). Inst. for Theoretical Physics; MTA-ELTE Lenduelet Lattice Gauge Theory Research Group, Budapest (Hungary); Califonia Univ., Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics; Redondo, J. [Zaragoza Univ. (Spain). Dept. de Fisica Teorica; Max-Planck-Institut fuer Physik, Muenchen (Germany); Szabo, K.K. [Wuppertal Univ. (Germany). Dept. of Physics; Forschungszentrum Juelich (Germany). Inst. for Advanced Simulation (IAS), Juelich Supercomputing Centre (JSC)
2015-08-15
Axions are one of the most attractive dark matter candidates. The evolution of their number density in the early universe can be determined by calculating the topological susceptibility χ(T) of QCD as a function of the temperature. Lattice QCD provides an ab initio technique to carry out such a calculation. A full result needs two ingredients: physical quark masses and a controlled continuum extrapolation from non-vanishing to zero lattice spacings. We determine χ(T) in the quenched framework (infinitely large quark masses) and extrapolate its values to the continuum limit. The results are compared with the prediction of the dilute instanton gas approximation (DIGA). A nice agreement is found for the temperature dependence, whereas the overall normalization of the DIGA result still differs from the non-perturbative continuum extrapolated lattice results by a factor of order ten. We discuss the consequences of our findings for the prediction of the amount of axion dark matter.
Axion cosmology, lattice QCD and the dilute instanton gas
Directory of Open Access Journals (Sweden)
Sz. Borsanyi
2016-01-01
Full Text Available Axions are one of the most attractive dark matter candidates. The evolution of their number density in the early universe can be determined by calculating the topological susceptibility χ(T of QCD as a function of the temperature. Lattice QCD provides an ab initio technique to carry out such a calculation. A full result needs two ingredients: physical quark masses and a controlled continuum extrapolation from non-vanishing to zero lattice spacings. We determine χ(T in the quenched framework (infinitely large quark masses and extrapolate its values to the continuum limit. The results are compared with the prediction of the dilute instanton gas approximation (DIGA. A nice agreement is found for the temperature dependence, whereas the overall normalization of the DIGA result still differs from the non-perturbative continuum extrapolated lattice results by a factor of order ten. We discuss the consequences of our findings for the prediction of the amount of axion dark matter.
Axion cosmology, lattice QCD and the dilute instanton gas
Borsanyi, S; Fodor, Z; Katz, S D; Mages, S W; Nogradi, D; Redondo, J; Ringwald, A; Szabo, K K
2015-01-01
Axions are one of the most attractive dark matter candidates. The evolution of their number density in the early universe can be determined by calculating the topological susceptibility $\\chi(T)$ of QCD as a function of the temperature. Lattice QCD provides an ab initio technique to carry out such a calculation. A full result needs two ingredients: physical quark masses and a controlled continuum extrapolation from non-vanishing to zero lattice spacings. We determine $\\chi(T)$ in the quenched framework (infinitely large quark masses) and extrapolate its values to the continuum limit. The results are compared with the prediction of the dilute instanton gas approximation (DIGA). A nice agreement is found for the temperature dependence, whereas the overall normalization of the DIGA result still differs from the non-perturbative continuum extrapolated lattice results by a factor of order ten. We discuss the consequences of our findings for the prediction of the amount of axion dark matter.
Electroweak Phase Transition in the MSSM 4-Dimensional Lattice Simulations
Csikor, Ferenc; Hegedüs, P; Jakovác, A; Katz, S D; Piróth, A
2000-01-01
Recent lattice results have shown that there is no Standard Model (SM) electroweak phase transition (EWPT) for Higgs boson masses above \\approx 72 GeV, which is below the present experimental limit. According to perturbation theory and 3-dimensional (3d) lattice simulations there could be an EWPT in the Minimal Supersymmetric Standard Model (MSSM) that is strong enough for baryogenesis up to m_h \\approx 105 GeV. In this letter we present the results of our large scale 4-dimensional (4d) lattice simulations for the MSSM EWPT. We carried out infinite volume and continuum limit extrapolations, which show a somewhat weaker transition than suggested by 3d simulations. The upper bound of the lightest Higgs boson mass for a MSSM baryogenesis scenario is m_h = 97 +/- 4 GeV. We determined the properties of the bubble wall that are important for a successful baryogenesis.
Kaon matrix elements and CP violation from quenched lattice QCD
Cristian, Calin-Radu
We report the results of a calculation of the K → pipi matrix elements relevant for the DeltaI = 1/2 rule and epsilon '/epsilon in quenched lattice QCD using domain wall fermions at a fixed lattice spacing of a-1 ˜ 2 GeV. Working in the three-quark effective theory, where only the u, d and s quarks enter and which is known perturbatively to next-to-leading order; we calculate the lattice K → pi and K → |0> matrix elements of dimension six, four-fermion operators. Through lowest order chiral perturbation theory these yield K → pipi matrix elements, which we then normalize to continuum values through a non-perturbative renormalization technique. For the Delta I = 1/2 rule we find a value of 25.3 +/- 1.8 (statistical error only) compared to the experimental value of 22.2, with individual isospin amplitudes 10--20% below the experimental values. For epsilon '/epsilon; using known central values for standard model parameters, we calculate (-4.0 +/- 2.3) x 10-4 (statistical error only) compared to the current experimental average of (17.2 +/- 1.8) x 10-4. Because we find a large cancellation between the I = 0 and I = 2 contributions to epsilon'/epsilon, the result may be very sensitive to the approximations employed. Among these are the use of: quenched QCD, lowest order chiral perturbation theory and continuum perturbation theory below 1.3 GeV. We have also calculated the kaon B parameter, BK and find BK(2 GeV) = 0.532(11). Although currently unable to give a reliable systematic error; we have control over statistical errors and more simulations will yield information about the effects of the approximations on this first-principles determination of these important quantities.
Higgs Mass Triviality Bounds on F(4) Lattices
Klomfass, Markus
In order to accurately describe the cutoff dependence of the Higgs mass triviality bound, the varphi ^4 theory is formulated on an F_4 lattice which preserves Lorentz invariance to a higher degree than the commonly used hypercubic lattice. We solve this model non-perturbatively by evaluating the linked cluster expansion through 12th order following the approach of Luscher and Weisz. The results are continued across the transition line into the broken phase by integrating the perturbative renormalization group equations. In the Goldstone phase, the renormalized coupling never exceeds 2/3 of the tree level unitarity bound when Lambda /m_{R}>= 2. Our results confirm recent Monte Carlo data and we obtain as an upper bound for the Higgs mass m_{R }/f_pi=2.45(7) at Lambda/m_{R }=2. Attempting to produce a heavier Higgs on the lattice, additional four-derivative terms are introduced in the naive action which serve to parameterize the leading order cutoff effects. Using a cluster reflection algorithm of the Swendsen-Wang-Wolff type, we simulate this action on an F_4 lattice in a region where the region where the effects of the new terms are expected to be maximal. As an upper bound we now obtain M _sigma/f_pi~ 2.8, an increase of about 20% compared to the simplest non-linear action. Despite triviality, the scalar sector may thus not be weakly interacting.
Inversion of the perturbation series
Energy Technology Data Exchange (ETDEWEB)
Amore, Paolo [Facultad de Ciencias, Universidad de Colima, Bernal DIaz del Castillo 340, Colima, Colima (Mexico); Fernandez, Francisco M [INIFTA (Conicet, UNLP), Division Quimica Teorica, Diag 113 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)
2008-01-18
We investigate the inversion of the perturbation series and its resummation, and prove that it is related to a recently developed parametric perturbation theory. Results for some illustrative examples show that in some cases series reversion may improve the accuracy of the results.
Propagation of Ion Acoustic Perturbations
DEFF Research Database (Denmark)
Pécseli, Hans
1975-01-01
Equations describing the propagation of ion acoustic perturbations are considered, using the assumption that the electrons are Boltzman distributed and isothermal at all times. Quasi-neutrality is also considered.......Equations describing the propagation of ion acoustic perturbations are considered, using the assumption that the electrons are Boltzman distributed and isothermal at all times. Quasi-neutrality is also considered....
Path integral for inflationary perturbations
Prokopec, T.; Rigopoulos, G.
2010-01-01
The quantum theory of cosmological perturbations in single-field inflation is formulated in terms of a path integral. Starting from a canonical formulation, we show how the free propagators can be obtained from the well-known gauge-invariant quadratic action for scalar and tensor perturbations, and
Lattice Field Theory with the Sign Problem and the Maximum Entropy Method
Directory of Open Access Journals (Sweden)
Masahiro Imachi
2007-02-01
Full Text Available Although numerical simulation in lattice field theory is one of the most effective tools to study non-perturbative properties of field theories, it faces serious obstacles coming from the sign problem in some theories such as finite density QCD and lattice field theory with the θ term. We reconsider this problem from the point of view of the maximum entropy method.
Lattice simulation of the SU(2) chiral model at zero and non-zero pion density
Rindlisbacher, Tobias
2015-01-01
We propose a flux representation based lattice formulation of the partition function corresponding to the SU(2) principal chiral Lagrangian, including a chemical potential and scalar/pseudo-scalar source terms. Lattice simulations are then used to obtain non-perturbative properties of the theory, in particular its mass spectrum at zero and non-zero pion density. We also sketch a method to efficiently measure general one- and two-point functions during the worm updates.
Digital Quantum Simulation of Z2 Lattice Gauge Theories with Dynamical Fermionic Matter
Zohar, Erez; Farace, Alessandro; Reznik, Benni; Cirac, J. Ignacio
2017-02-01
We propose a scheme for digital quantum simulation of lattice gauge theories with dynamical fermions. Using a layered optical lattice with ancilla atoms that can move and interact with the other atoms (simulating the physical degrees of freedom), we obtain a stroboscopic dynamics which yields the four-body plaquette interactions, arising in models with (2 +1 ) and higher dimensions, without the use of perturbation theory. As an example we show how to simulate a Z2 model in (2 +1 ) dimensions.
Junction conditions of cosmological perturbations
Tomita, K
2004-01-01
The behavior of perturbations is studied in cosmological models which consist of two different homogeneous regions connected in a spherical shell boundary. The junction conditions for the metric perturbations and the displacements of the shell boundary are analyzed and the surface densities of the perturbed energy and momentum in the shell are derived, using Mukohyama's gauge-invariant formalism and the Israel discontinuity condition. In both homogeneous regions the perturbations of scalar, vector and tensor types are expanded using the 3-dimensional harmonic functions, but the model coupling among them is caused in the shell by the inhomogeneity. By treating the perturbations with odd and even parities separately, it is found, however, that we can have consistent displacements and surface densities for given metric parturbations
Perturbations in Massive Gravity Cosmology
Crisostomi, Marco; Pilo, Luigi
2012-01-01
We study cosmological perturbations for a ghost free massive gravity theory formulated with a dynamical extra metric that is needed to massive deform GR. In this formulation FRW background solutions fall in two branches. In the dynamics of perturbations around the first branch solutions, no extra degree of freedom with respect to GR ispresent at linearized level, likewise what is found in the Stuckelberg formulation of massive gravity where the extra metric isflat and non dynamical. In the first branch, perturbations are probably strongly coupled. On the contrary, for perturbations around the second branch solutions all expected degrees of freedom propagate. While tensor and vector perturbations of the physical metric that couples with matter follow closely the ones of GR, scalars develop an exponential Jeans-like instability on sub-horizon scales. On the other hand, around a de Sitter background there is no instability. We argue that one could get rid of the instabilities by introducing a mirror dark matter ...
Multiplicative perturbations of local -semigroups
Indian Academy of Sciences (India)
Chung-Cheng Kuo
2015-02-01
In this paper, we establish some left and right multiplicative perturbation theorems concerning local -semigroups when the generator of a perturbed local -semigroup $S(\\cdot)$ may not be densely defined and the perturbation operator is a bounded linear operator from $\\overline{D(A)}$ into () such that = on $\\overline{D(A)}$, which can be applied to obtain some additive perturbation theorems for local -semigroups in which is a bounded linear operator from $[D(A)]$ into () such that = on $\\overline{D(A)}$. We also show that the perturbations of a (local) -semigroup $S(\\cdot)$ are exponentially bounded (resp., norm continuous, locally Lipschitz continuous, or exponentially Lipschitz continuous) if $S(\\cdot)$ is.
Physical consequences of black holes in non-perturbative quantum gravity and inflationary cosmology
Reska, P.M.
2011-01-01
In this thesis the consequences of the presence of a Schwarzschild black hole in de Sitter space are studied in the setting of non-perturbative quantum gravity and in inflationary cosmology. We first review the formalism of Causal Dynamical Triangulations (CDT) which implements a lattice regularizat
DEFECTS IN CDS - IN DETECTED BY PERTURBED ANGULAR-CORRELATION SPECTROSCOPY (PAC)
MAGERLE, R; DEICHER, M; DESNICA, U; KELLER, R; PFEIFFER, W; PLEITER, F; SKUDLIK, H; WICHERT, T
1991-01-01
The local lattice environment of the donor In in CdS is investigated measuring the electric-field gradient at the site of the radioactive probe atom In-111 by the perturbed gamma-gamma angular correlation technique. It is shown that implantation of In into CdS with subsequent annealing drives 100% o
Non-perturbative Heavy Quark Effective Theory: An application to semi-leptonic B-decays
Della Morte, Michele; Simma, Hubert; Sommer, Rainer
2015-01-01
We review a lattice strategy how to non-perturbatively determine the coefficients in the HQET expansion of all components of the heavy-light axial and vector currents, including 1/m_h-corrections. We also discuss recent preliminary results on the form factors parameterizing semi-leptonic B-decays at the leading order in 1/m_h.
Energy Technology Data Exchange (ETDEWEB)
Gupta, R.
1998-12-31
The goal of the lectures on lattice QCD (LQCD) is to provide an overview of both the technical issues and the progress made so far in obtaining phenomenologically useful numbers. The lectures consist of three parts. The author`s charter is to provide an introduction to LQCD and outline the scope of LQCD calculations. In the second set of lectures, Guido Martinelli will discuss the progress they have made so far in obtaining results, and their impact on Standard Model phenomenology. Finally, Martin Luescher will discuss the topical subjects of chiral symmetry, improved formulation of lattice QCD, and the impact these improvements will have on the quality of results expected from the next generation of simulations.
Fractional lattice charge transport
Flach, Sergej; Khomeriki, Ramaz
2017-01-01
We consider the dynamics of noninteracting quantum particles on a square lattice in the presence of a magnetic flux α and a dc electric field E oriented along the lattice diagonal. In general, the adiabatic dynamics will be characterized by Bloch oscillations in the electrical field direction and dispersive ballistic transport in the perpendicular direction. For rational values of α and a corresponding discrete set of values of E(α) vanishing gaps in the spectrum induce a fractionalization of the charge in the perpendicular direction - while left movers are still performing dispersive ballistic transport, the complementary fraction of right movers is propagating in a dispersionless relativistic manner in the opposite direction. Generalizations and the possible probing of the effect with atomic Bose-Einstein condensates and photonic networks are discussed. Zak phase of respective band associated with gap closing regime has been computed and it is found converging to π/2 value. PMID:28102302
Borsanyi, Sz; Kampert, K H; Katz, S D; Kawanai, T; Kovacs, T G; Mages, S W; Pasztor, A; Pittler, F; Redondo, J; Ringwald, A; Szabo, K K
2016-01-01
We present a full result for the equation of state (EoS) in 2+1+1 (up/down, strange and charm quarks are present) flavour lattice QCD. We extend this analysis and give the equation of state in 2+1+1+1 flavour QCD. In order to describe the evolution of the universe from temperatures several hundreds of GeV to several tens of MeV we also include the known effects of the electroweak theory and give the effective degree of freedoms. As another application of lattice QCD we calculate the topological susceptibility (chi) up to the few GeV temperature region. These two results, EoS and chi, can be used to predict the dark matter axion's mass in the post-inflation scenario and/or give the relationship between the axion's mass and the universal axionic angle, which acts as a initial condition of our universe.
Solitons in nonlinear lattices
Kartashov, Yaroslav V; Torner, Lluis
2010-01-01
This article offers a comprehensive survey of results obtained for solitons and complex nonlinear wave patterns supported by purely nonlinear lattices (NLs), which represent a spatially periodic modulation of the local strength and sign of the nonlinearity, and their combinations with linear lattices. A majority of the results obtained, thus far, in this field and reviewed in this article are theoretical. Nevertheless, relevant experimental settings are surveyed too, with emphasis on perspectives for implementation of the theoretical predictions in the experiment. Physical systems discussed in the review belong to the realms of nonlinear optics (including artificial optical media, such as photonic crystals, and plasmonics) and Bose-Einstein condensation (BEC). The solitons are considered in one, two, and three dimensions (1D, 2D, and 3D). Basic properties of the solitons presented in the review are their existence, stability, and mobility. Although the field is still far from completion, general conclusions c...
Parametric lattice Boltzmann method
Shim, Jae Wan
2017-06-01
The discretized equilibrium distributions of the lattice Boltzmann method are presented by using the coefficients of the Lagrange interpolating polynomials that pass through the points related to discrete velocities and using moments of the Maxwell-Boltzmann distribution. The ranges of flow velocity and temperature providing positive valued distributions vary with regulating discrete velocities as parameters. New isothermal and thermal compressible models are proposed for flows of the level of the isothermal and thermal compressible Navier-Stokes equations. Thermal compressible shock tube flows are simulated by only five on-lattice discrete velocities. Two-dimensional isothermal and thermal vortices provoked by the Kelvin-Helmholtz instability are simulated by the parametric models.
Jipsen, Peter
1992-01-01
The study of lattice varieties is a field that has experienced rapid growth in the last 30 years, but many of the interesting and deep results discovered in that period have so far only appeared in research papers. The aim of this monograph is to present the main results about modular and nonmodular varieties, equational bases and the amalgamation property in a uniform way. The first chapter covers preliminaries that make the material accessible to anyone who has had an introductory course in universal algebra. Each subsequent chapter begins with a short historical introduction which sites the original references and then presents the results with complete proofs (in nearly all cases). Numerous diagrams illustrate the beauty of lattice theory and aid in the visualization of many proofs. An extensive index and bibliography also make the monograph a useful reference work.
International Lattice Data Grid
Davies, C T H; Kenway, R D; Maynard, C M
2002-01-01
We propose the co-ordination of lattice QCD grid developments in different countries to allow transparent exchange of gauge configurations in future, should participants wish to do so. We describe briefly UKQCD's XML schema for labelling and cataloguing the data. A meeting to further develop these ideas will be held in Edinburgh on 19/20 December 2002, and will be available over AccessGrid.
Weakly deformed soliton lattices
Energy Technology Data Exchange (ETDEWEB)
Dubrovin, B. (Moskovskij Gosudarstvennyj Univ., Moscow (USSR). Dept. of Mechanics and Mathematics)
1990-12-01
In this lecture the author discusses periodic and quasiperiodic solutions of nonlinear evolution equations of phi{sub t}=K (phi, phi{sub x},..., phi{sup (n)}), the so-called soliton lattices. After introducing the theory of integrable systems of hydrodynamic type he discusses their Hamiltonian formalism, i.e. the theory of Poisson brackets of hydrodynamic type. Then he describes the application of algebraic geometry to the effective integration of such equations. (HSI).
Crystallographic Lattice Boltzmann Method
Namburi, Manjusha; Krithivasan, Siddharth; Ansumali, Santosh
2016-01-01
Current approaches to Direct Numerical Simulation (DNS) are computationally quite expensive for most realistic scientific and engineering applications of Fluid Dynamics such as automobiles or atmospheric flows. The Lattice Boltzmann Method (LBM), with its simplified kinetic descriptions, has emerged as an important tool for simulating hydrodynamics. In a heterogeneous computing environment, it is often preferred due to its flexibility and better parallel scaling. However, direct simulation of realistic applications, without the use of turbulence models, remains a distant dream even with highly efficient methods such as LBM. In LBM, a fictitious lattice with suitable isotropy in the velocity space is considered to recover Navier-Stokes hydrodynamics in macroscopic limit. The same lattice is mapped onto a cartesian grid for spatial discretization of the kinetic equation. In this paper, we present an inverted argument of the LBM, by making spatial discretization as the central theme. We argue that the optimal spatial discretization for LBM is a Body Centered Cubic (BCC) arrangement of grid points. We illustrate an order-of-magnitude gain in efficiency for LBM and thus a significant progress towards feasibility of DNS for realistic flows. PMID:27251098
Adamatzky, Andrew
2015-01-01
The book gives a comprehensive overview of the state-of-the-art research and engineering in theory and application of Lattice Automata in design and control of autonomous Robots. Automata and robots share the same notional meaning. Automata (originated from the latinization of the Greek word “αυτόματον”) as self-operating autonomous machines invented from ancient years can be easily considered the first steps of robotic-like efforts. Automata are mathematical models of Robots and also they are integral parts of robotic control systems. A Lattice Automaton is a regular array or a collective of finite state machines, or automata. The Automata update their states by the same rules depending on states of their immediate neighbours. In the context of this book, Lattice Automata are used in developing modular reconfigurable robotic systems, path planning and map exploration for robots, as robot controllers, synchronisation of robot collectives, robot vision, parallel robotic actuators. All chapters are...
Hadroquarkonium from lattice QCD
Alberti, Maurizio; Bali, Gunnar S.; Collins, Sara; Knechtli, Francesco; Moir, Graham; Söldner, Wolfgang
2017-04-01
The hadroquarkonium picture [S. Dubynskiy and M. B. Voloshin, Phys. Lett. B 666, 344 (2008), 10.1016/j.physletb.2008.07.086] provides one possible interpretation for the pentaquark candidates with hidden charm, recently reported by the LHCb Collaboration, as well as for some of the charmoniumlike "X , Y , Z " states. In this picture, a heavy quarkonium core resides within a light hadron giving rise to four- or five-quark/antiquark bound states. We test this scenario in the heavy quark limit by investigating the modification of the potential between a static quark-antiquark pair induced by the presence of a hadron. Our lattice QCD simulations are performed on a Coordinated Lattice Simulations (CLS) ensemble with Nf=2 +1 flavors of nonperturbatively improved Wilson quarks at a pion mass of about 223 MeV and a lattice spacing of about a =0.0854 fm . We study the static potential in the presence of a variety of light mesons as well as of octet and decuplet baryons. In all these cases, the resulting configurations are favored energetically. The associated binding energies between the quarkonium in the heavy quark limit and the light hadron are found to be smaller than a few MeV, similar in strength to deuterium binding. It needs to be seen if the small attraction survives in the infinite volume limit and supports bound states or resonances.
A Mechanical Lattice Aid for Crystallography Teaching.
Amezcua-Lopez, J.; Cordero-Borboa, A. E.
1988-01-01
Introduces a 3-dimensional mechanical lattice with adjustable telescoping mechanisms. Discusses the crystalline state, the 14 Bravais lattices, operational principles of the mechanical lattice, construction methods, and demonstrations in classroom. Provides lattice diagrams, schemes of the lattice, and various pictures of the lattice. (YP)
Kenneth Wilson and lattice QCD
Ukawa, Akira
2015-01-01
We discuss the physics and computation of lattice QCD, a space-time lattice formulation of quantum chromodynamics, and Kenneth Wilson's seminal role in its development. We start with the fundamental issue of confinement of quarks in the theory of the strong interactions, and discuss how lattice QCD provides a framework for understanding this phenomenon. A conceptual issue with lattice QCD is a conflict of space-time lattice with chiral symmetry of quarks. We discuss how this problem is resolved. Since lattice QCD is a non-linear quantum dynamical system with infinite degrees of freedom, quantities which are analytically calculable are limited. On the other hand, it provides an ideal case of massively parallel numerical computations. We review the long and distinguished history of parallel-architecture supercomputers designed and built for lattice QCD. We discuss algorithmic developments, in particular the difficulties posed by the fermionic nature of quarks, and their resolution. The triad of efforts toward b...
Tolerance of edge cascades with coupled map lattices methods
Institute of Scientific and Technical Information of China (English)
Cui Di; Gao Zi-You; Zheng Jian-Feng
2009-01-01
This paper studies the cascading failure on random networks and scale-free networks by introducing the tolerance parameter of edge based on the coupled map lattices methods. The whole work focuses on investigating some indices including the number of failed edges, dynamic edge tolerance capacity and the perturbation of edge. In general, it assumes that the perturbation is attributed to the normal distribution in adopted simulations. By investigating the effectiveness of edge tolerance in scale-free and random networks, it finds that the larger tolerance parameter 位 can more efficiently delay the cascading failure process for scale-free networks than random networks. These results indicate that the cascading failure process can be effectively controlled by increasing the tolerance parameter A. Moreover, the simulations also show that, larger variance of perturbation can easily trigger the cascading failures than the smaller one. This study may be useful for evaluating efficiency of whole traffic systems, and for alleviating cascading failure in such systems.
The lowest-lying baryon masses in covariant SU(3)-flavor chiral perturbation theory
Martin-Camalich, J; Vacas, M J Vicente
2010-01-01
We present an analysis of the baryon-octet and -decuplet masses using covariant SU(3)-flavor chiral perturbation theory up to next-to-leading order. Besides the description of the physical masses we address the problem of the lattice QCD extrapolation. Using the PACS-CS collaboration data we show that a good description of the lattice points can be achieved at next-to-leading order with the covariant loop amplitudes and phenomenologically determined values for the meson-baryon couplings. Moreover, the extrapolation to the physical point up to this order is found to be better than the linear one given at leading-order by the Gell-Mann-Okubo approach. The importance that a reliable combination of lattice QCD and chiral perturbation theory may have for hadron phenomenology is emphasized with the prediction of the pion-baryon and strange-baryon sigma terms.
Disformal transformation of cosmological perturbations
Directory of Open Access Journals (Sweden)
Masato Minamitsuji
2014-10-01
Full Text Available We investigate the gauge-invariant cosmological perturbations in the gravity and matter frames in the general scalar–tensor theory where two frames are related by the disformal transformation. The gravity and matter frames are the extensions of the Einstein and Jordan frames in the scalar–tensor theory where two frames are related by the conformal transformation, respectively. First, it is shown that the curvature perturbation in the comoving gauge to the scalar field is disformally invariant as well as conformally invariant, which gives the predictions from the cosmological model where the scalar field is responsible both for inflation and cosmological perturbations. Second, in case that the disformally coupled matter sector also contributes to curvature perturbations, we derive the evolution equations of the curvature perturbation in the uniform matter energy density gauge from the energy (nonconservation in the matter sector, which are independent of the choice of the gravity sector. While in the matter frame the curvature perturbation in the uniform matter energy density gauge is conserved on superhorizon scales for the vanishing nonadiabatic pressure, in the gravity frame it is not conserved even if the nonadiabatic pressure vanishes. The formula relating two frames gives the amplitude of the curvature perturbation in the matter frame, once it is evaluated in the gravity frame.
Towards lattice-regularized Quantum Gravity
Diakonov, Dmitri
2011-01-01
Using the Cartan formulation of General Relativity, we construct a well defined lattice-regularized theory capable to describe large non-perturbative quantum fluctuations of the frame field (or the metric) and of the spin connection. To that end we need to present the tetrad by a composite field built as a bilinear combination of fermion fields. The theory is explicitly invariant under local Lorentz transformations and, in the continuum limit, under general covariant transformations, or diffeomorphisms. Being well defined for large and fast varying fields at the ultraviolet cutoff, the theory simultaneously has chances of reproducing standard General Relativity in the infrared continuum limit. The present regularization of quantum gravity opens new possibilities of its unification with the Standard Model.
A Lattice Determination of Light Quark Masses
Göckeler, M; Oelrich, H; Petters, D; Pleiter, D; Rakow, P E L; Schierholz, G; Stephenson, P
2000-01-01
A fully non-perturbative lattice determination of the up/down and strange quark masses is given for quenched QCD using both, $O(a)$ improved Wilson fermions and ordinary Wilson fermions. For the strange quark mass with $O(a)$ improved fermions we obtain $m^{\\msbar}_s(\\mu=2 {GeV}) = 105(4) {MeV}$, using the interquark force scale $r_0$. Due to quenching problems fits are only possible for quark masses larger than the strange quark mass. If we extrapolate our fits to the up/down quark mass we find for the average mass $m^{\\msbar}_l(\\mu=2 {GeV}) = 4.4(2) {MeV}$.
Lattice constraints on the thermal photon rate
Ghiglieri, J.; Kaczmarek, O.; Laine, M.; Meyer, F.
2016-07-01
We estimate the photon production rate from an SU(3) plasma at temperatures of about 1.1 Tc and 1.3 Tc . Lattice results for the vector current correlator at spatial momenta k ˜(2 -6 )T are extrapolated to the continuum limit and analyzed with the help of a polynomial interpolation for the corresponding spectral function, which vanishes at zero frequency and matches to high-precision perturbative results at large invariant masses. For small invariant masses the interpolation is compared with the next-to-leading-order (NLO) weak-coupling result, hydrodynamics, and a holographic model. At vanishing invariant mass we extract the photon rate which for k ≳3 T is found to be close to the NLO weak-coupling prediction. For k ≲2 T uncertainties remain large but the photon rate is likely to fall below the NLO prediction, in accordance with the onset of a strongly interacting behavior characteristic of the hydrodynamic regime.
Lattice constraints on the thermal photon rate
Ghiglieri, J; Laine, M; Meyer, F
2016-01-01
We estimate the photon production rate from an SU(3) plasma at temperatures of about 1.1Tc and 1.3Tc. Lattice results for the vector current correlator at spatial momenta k ~ (2-6)T are extrapolated to the continuum limit and analyzed with the help of a polynomial interpolation for the corresponding spectral function, which vanishes at zero frequency and matches to high-precision perturbative results at large invariant masses. For small invariant masses the interpolation is compared with the NLO weak-coupling result, hydrodynamics, and a holographic model. At vanishing invariant mass we extract the photon rate which for k \\gsim 3T is found to be close to the NLO weak-coupling prediction. For k \\lsim 2T uncertainties remain large but the photon rate is likely to fall below the NLO prediction, in accordance with the onset of a strongly interacting behaviour characteristic of the hydrodynamic regime.
Quantum Holonomy Theory, Lattice-Independent Formulation
Aastrup, Johannes
2016-01-01
Quantum holonomy theory is a candidate for a non-perturbative theory of quantum gravity coupled to fermions. The theory is based on the QHD-algebra, which essentially encodes how local degrees of freedom are moved on a three-dimensional manifold. In this paper we continue the development of the theory by providing a lattice-independent formulation. We first define a Dirac type operator over a configuration space of Ashtekar connections and use it to formulate a graded version of the QHD-algebra. Next we formulate necessary conditions for a state to exist on this algebra and use the GNS construction to build a kinematical Hilbert space. Finally we find that operators, that correspond to the Dirac and gravitational Hamiltonians in a semi-classical limit, are background independent.
Lattice thermal conductivity of LaSe
Energy Technology Data Exchange (ETDEWEB)
Li, Wei, E-mail: tolwwt@163.com [School of Physics and Telecommunication Engineering, South China Normal University, 510006 Guangzhou (China); Pan, Zhong-liang; Chen, Jun-fang; He, Qin-yu [School of Physics and Telecommunication Engineering, South China Normal University, 510006 Guangzhou (China); Wang, Teng [School of Computer, South China Normal University, 510631 Guangzhou (China)
2015-07-15
The phonon dispersions and phonon density of states of LaSe are obtained, based on density functional perturbation theory and the norm-conserving pseudo-potential method. An anomaly in calculated phonon dispersion curves is presented and interpreted as a Kohn anomaly. The heat capacity of LaSe is calculated then. For the three-phonon process scattering, the lowest non-harmonic cubic terms of the interatomic potential are considered to obtain single-phonon relaxation rate by applying the Fermi's golden rule. For the boundary scattering, the average phonon relaxation time was obtained. Considering two kinds of phonon scattering mechanisms, we obtain the lattice thermal conductivity of LaSe.
Entanglement of Distillation for Lattice Gauge Theories
Van Acoleyen, Karel; Bultinck, Nick; Haegeman, Jutho; Marien, Michael; Scholz, Volkher B.; Verstraete, Frank
2016-09-01
We study the entanglement structure of lattice gauge theories from the local operational point of view, and, similar to Soni and Trivedi [J. High Energy Phys. 1 (2016) 1], we show that the usual entanglement entropy for a spatial bipartition can be written as the sum of an undistillable gauge part and of another part corresponding to the local operations and classical communication distillable entanglement, which is obtained by depolarizing the local superselection sectors. We demonstrate that the distillable entanglement is zero for pure Abelian gauge theories at zero gauge coupling, while it is in general nonzero for the non-Abelian case. We also consider gauge theories with matter, and show in a perturbative approach how area laws—including a topological correction—emerge for the distillable entanglement. Finally, we also discuss the entanglement entropy of gauge fixed states and show that it has no relation to the physical distillable entropy.
Rho resonance parameters from lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Guo, Dehua; Alexandru, Andrei; Molina, Raquel; Döring, Michael
2016-08-01
We perform a high-precision calculation of the phase shifts for $\\pi$-$\\pi$ scattering in the I = 1, J = 1 channel in the elastic region using elongated lattices with two mass-degenerate quark favors ($N_f = 2$). We extract the $\\rho$ resonance parameters using a Breit-Wigner fit at two different quark masses, corresponding to $m_{\\pi} = 226$MeV and $m_{\\pi} = 315$MeV, and perform an extrapolation to the physical point. The extrapolation is based on a unitarized chiral perturbation theory model that describes well the phase-shifts around the resonance for both quark masses. We find that the extrapolated value, $m_{\\rho} = 720(1)(15)$MeV, is significantly lower that the physical rho mass and we argue that this shift could be due to the absence of the strange quark in our calculation.
Cosmological perturbations beyond linear order
CERN. Geneva
2013-01-01
Cosmological perturbation theory is the standard tool to understand the formation of the large scale structure in the Universe. However, its degree of applicability is limited by the growth of the amplitude of the matter perturbations with time. This problem can be tackled with by using N-body simulations or analytical techniques that go beyond the linear calculation. In my talk, I'll summarise some recent efforts in the latter that ameliorate the bad convergence of the standard perturbative expansion. The new techniques allow better analytical control on observables (as the matter power spectrum) over scales very relevant to understand the expansion history and formation of structure in the Universe.
The theory of singular perturbations
De Jager, E M
1996-01-01
The subject of this textbook is the mathematical theory of singular perturbations, which despite its respectable history is still in a state of vigorous development. Singular perturbations of cumulative and of boundary layer type are presented. Attention has been given to composite expansions of solutions of initial and boundary value problems for ordinary and partial differential equations, linear as well as quasilinear; also turning points are discussed. The main emphasis lies on several methods of approximation for solutions of singularly perturbed differential equations and on the mathemat
Density perturbations with relativistic thermodynamics
Maartens, R
1997-01-01
We investigate cosmological density perturbations in a covariant and gauge- invariant formalism, incorporating relativistic causal thermodynamics to give a self-consistent description. The gradient of density inhomogeneities splits covariantly into a scalar part, a rotational vector part that is determined by the vorticity, and a tensor part that describes the shape. We give the evolution equations for these parts in the general dissipative case. Causal thermodynamics gives evolution equations for viswcous stress and heat flux, which are coupled to the density perturbation equation and to the entropy and temperature perturbation equations. We give the full coupled system in the general dissipative case, and simplify the system in certain cases.
Instabilities in mimetic matter perturbations
Firouzjahi, Hassan; Gorji, Mohammad Ali; Mansoori, Seyed Ali Hosseini
2017-07-01
We study cosmological perturbations in mimetic matter scenario with a general higher derivative function. We calculate the quadratic action and show that both the kinetic term and the gradient term have the wrong sings. We perform the analysis in both comoving and Newtonian gauges and confirm that the Hamiltonians and the associated instabilities are consistent with each other in both gauges. The existence of instabilities is independent of the specific form of higher derivative function which generates gradients for mimetic field perturbations. It is verified that the ghost instability in mimetic perturbations is not associated with the higher derivative instabilities such as the Ostrogradsky ghost.
Perturbation Theory of Embedded Eigenvalues
DEFF Research Database (Denmark)
Engelmann, Matthias
We study problems connected to perturbation theory of embedded eigenvalues in two different setups. The first part deals with second order perturbation theory of mass shells in massive translation invariant Nelson type models. To this end an expansion of the eigenvalues w.r.t. fiber parameter up...... project gives a general and systematic approach to analytic perturbation theory of embedded eigenvalues. The spectral deformation technique originally developed in the theory of dilation analytic potentials in the context of Schrödinger operators is systematized by the use of Mourre theory. The group...
Gauge Invariant Effective Action in Abelian Chiral Gauge Theory on the Lattice
Suzuki, H
1999-01-01
Lüscher's recent formulation of Abelian chiral gauge theories on the lattice, in the vacuum (or perturbative) sector in infinite lattice volume, is re-interpreted in terms of the lattice covariant regularization. The gauge invariance of the effective action and the integrability of the gauge current in anomaly-free cases become transparent then. The real part of the effective action is simply one-half of that of the Dirac fermion and, when the Dirac operator has proper properties in the continuum limit, the imaginary part in the continuum limit reproduces the $\\eta$-invariant.}
Lattice heavy quark effective theory and the isgur-wise function
Hashimoto, S
1996-01-01
We compute the Isgur-Wise function using heavy quark effective theory formulated on the lattice. The non-relativistic kinetic energy term of the heavy quark is included to the action as well as terms remaining in the infinite quark mass limit. The classical velocity of the heavy quark is renormalized on the lattice and we determine the renormalized velocity non-perturbatively using the energy-momentum dispersion relation. The slope parameter of the Isgur-Wise function at zero recoil is obtained at \\beta=6.0 on a 24^3\\times 48 lattice for three values of m_{Q}.
Axial couplings of heavy hadrons from domain-wall lattice QCD
Detmold, William; Meinel, Stefan
2012-01-01
We calculate matrix elements of the axial current for static-light mesons and baryons in lattice QCD with dynamical domain wall fermions. We use partially quenched heavy hadron chiral perturbation theory in a finite volume to extract the axial couplings g_1, g_2, and g_3 from the data. These axial couplings allow the prediction of strong decay rates and enter chiral extrapolations of most lattice results in the b sector. Our calculations are performed with two lattice spacings and with pion masses down to 227 MeV.
Charm quark mass and D-meson decay constants from two-flavour lattice QCD
Heitger, Jochen; Schaefer, Stefan; Virotta, Francesco
2013-01-01
We present a computation of the charm quark's mass and the leptonic D-meson decay constants f_D and f_{D_s} in two-flavour lattice QCD with non-perturbatively O(a) improved Wilson quarks. Our analysis is based on the CLS configurations at two lattice spacings (a=0.065 and 0.048 fm, where the lattice scale is set by f_K) and pion masses ranging down to ~ 190 MeV at L*m_pi > 4, in order to perform controlled continuum and chiral extrapolations with small systematic uncertainties.
I=2 pi-pi Scattering from Fully-Dynamical Mixed-Action Lattice QCD
Beane, Silas R.; Bedaque, Paulo F.; Orginos, Kostas; Savage, Martin J.
2005-01-01
We compute the I=2 pi-pi scattering length at pion masses of m_pi ~ 294, 348 and 484 MeV in fully-dynamical lattice QCD using Luscher's finite-volume method. The calculation is performed with domain-wall valence-quark propagators on asqtad-improved MILC configurations with staggered sea quarks at a single lattice spacing, b ~ 0.125 fm. Chiral perturbation theory is used to perform the extrapolation of the scattering length from lattice quark masses down to the physical value, and we find m_pi...
Pseudoscalar decay constants from N_f=2+1+1 twisted mass lattice QCD
Farchioni, Federico; Jansen, Karl; Petschlies, Marcus; Urbach, Carsten
2010-01-01
We present first results for the pseudoscalar decay constants $f_K$, $f_D$ and $f_{D_s}$ from lattice QCD with N_f=2+1+1 flavours of dynamical quarks. The lattice simulations have been performed by the European Twisted Mass collaboration (ETMC) using maximally twisted mass quarks. For the pseudoscalar decay constants we follow a mixed action approach by using so called Osterwalder-Seiler fermions in the valence sector for strange and charm quarks. The data for two values of the lattice spacing and several values of the up/down quark mass is analysed using chiral perturbation theory.
The pion form factor from lattice QCD with two dynamical flavours
Energy Technology Data Exchange (ETDEWEB)
Broemmel, D. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Gruppe Theorie]|[Regensburg Univ. (Germany). Inst. fuer Physik 1 - Theoretische Physik; Diehl, M. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Gruppe Theorie; Goeckeler, M. [Regensburg Univ. (DE). Inst. fuer Physik 1 - Theoretische Physik] (and others)
2006-08-15
We compute the electromagnetic form factor of the pion using non-perturbatively O(a) improved Wilson fermions. The calculations are done for pion masses down to 400 MeV and for lattice spacings of 0.07-0.11 fm. We check for finite size effects by repeating some of the measurements on smaller lattices. The large number of lattice parameters we use allows us to extrapolate to the physical point. For the square of the charge radius we find left angle r{sup 2} right angle =0.440(19) fm{sup 2}, in good agreement with experiment. (orig.)
Lattice topology dictates photon statistics.
Kondakci, H Esat; Abouraddy, Ayman F; Saleh, Bahaa E A
2017-08-21
Propagation of coherent light through a disordered network is accompanied by randomization and possible conversion into thermal light. Here, we show that network topology plays a decisive role in determining the statistics of the emerging field if the underlying lattice is endowed with chiral symmetry. In such lattices, eigenmode pairs come in skew-symmetric pairs with oppositely signed eigenvalues. By examining one-dimensional arrays of randomly coupled waveguides arranged on linear and ring topologies, we are led to a remarkable prediction: the field circularity and the photon statistics in ring lattices are dictated by its parity while the same quantities are insensitive to the parity of a linear lattice. For a ring lattice, adding or subtracting a single lattice site can switch the photon statistics from super-thermal to sub-thermal, or vice versa. This behavior is understood by examining the real and imaginary fields on a lattice exhibiting chiral symmetry, which form two strands that interleave along the lattice sites. These strands can be fully braided around an even-sited ring lattice thereby producing super-thermal photon statistics, while an odd-sited lattice is incommensurate with such an arrangement and the statistics become sub-thermal.
Vector and Axial Currents in Wilson Chiral Perturbation Theory
Aoki, Sinya; Sharpe, Stephen R
2009-01-01
We reconsider the construction of the vector and axial-vector currents in Wilson Chiral Perturbation Theory (WChPT), the low-energy effective theory for lattice QCD with Wilson fermions. We discuss in detail the finite renormalization of the currents that has to be taken into account in order to properly match the currents. We explicitly show that imposing the chiral Ward identities on the currents does, in general, affect the axial-vector current at O(a). As an application of our results we compute the pion decay constant to one loop in the two flavor theory. Our result differs from previously published ones.
Casimir operator dependences of non-perturbative fermionic QCD amplitudes
Fried, H M; Hofmann, R
2015-01-01
In eikonal and quenched approximation, it is argued that the strong coupling fermionic QCD Green's functions and related amplitudes, when based on the newly discovered effective locality property, depart from a sole dependence on the SUc(3) quadratic Casimir operator, evaluated over the fundamental gauge group representation.Though noticed in non-relativistic Quark Models, an additional dependence on the cubic Casimir operator is in contradistinction with perturbation theory, and also with a number of non-perturbative approaches such as the MIT Bag, the Stochastic Vacuum Models and lattice simulations. It accounts for the full algebraic content of the rank-2 Lie algebra of SUc(3). We briefly discuss the orders of magnitude of quadratic and cubic Casimir operator contributions.
Blossier, B; De soto, F; Morenas, V; Gravina, M; Pène, O; Rodríguez-Quintero, J
2010-01-01
A non-perturbative calculation of the ghost-gluon running QCD coupling constant is performed using $N_f=2$ twisted-mass dynamical fermions. The extraction of $\\Lambda_{\\bar{MS}}$ in the chiral limit reveals the presence of a non-perturbative OPE contribution that is assumed to be dominated by a dimension-two $\\VEV{A^2}$ condensate. In this contest a novel method for calibrating the lattice spacing in lattice simulations is presented.
Complex 3D Vortex Lattice Formation by Phase-Engineered Multiple Beam Interference
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Jolly Xavier
2012-01-01
Full Text Available We present the computational results on the formation of diverse complex 3D vortex lattices by a designed superposition of multiple plane waves. Special combinations of multiples of three noncoplanar plane waves with a designed relative phase shift between one another are perturbed by a nonsingular beam to generate various complex 3D vortex lattice structures. The formation of complex gyrating lattice structures carrying designed vortices by means of relatively phase-engineered plane waves is also computationally investigated. The generated structures are configured with both periodic as well as transversely quasicrystallographic basis, while these whirling complex lattices possess a long-range order of designed symmetry in a given plane. Various computational analytical tools are used to verify the presence of engineered geometry of vortices in these complex 3D vortex lattices.
Polymers on disordered hierarchical lattices: A nonlinear combination of random variables
Energy Technology Data Exchange (ETDEWEB)
Cook, J. (Commissariat a l' Energie Atomique, Gif-sur-Yvette (France) Univ. of Edinburgh (England)); Derrida, B. (Commissariat a l' Energie Atomique, Gif-sur-Yvette (France))
1989-10-01
The problem of directed polymers on disordered hierarchical and hypercubic lattices is considered. For the hierarchical lattices the problem can be reduced to the study of the stable laws for combining random variables in a nonlinear way. The authors present the results of numerical simulations of two hierarchical lattices, finding evidence of a phase transition in one case. For a limiting case they extend the perturbation theory developed by Derrida and Griffiths to nonzero temperature and to higher order and use this approach to calculate thermal and geometrical properties (overlaps) of the model. In this limit they obtain an interpolation formula, allowing one to obtain the noninteger moments of the partition function from the integer moments. They obtain bounds for the transition temperature for hierarchical and hypercubic lattices, and some similarities between the problem on the two different types of lattice are discussed.
Spin-Lattice Order in One-Dimensional Conductors: Beyond the RKKY Effect
Schecter, Michael; Rudner, Mark S.; Flensberg, Karsten
2015-06-01
We investigate magnetic order in a lattice of classical spins coupled to an isotropic gas of one-dimensional conduction electrons via local exchange interactions. The frequently discussed Ruderman-Kittel-Kasuya-Yosida effective exchange model for this system predicts that spiral order is always preferred. Here we consider the problem nonperturbatively, and find that such order vanishes above a critical value of the exchange coupling that depends strongly on the lattice spacing. The critical coupling tends to zero as the lattice spacing becomes commensurate with the Fermi wave vector, signaling the breakdown of the perturbative Ruderman-Kittel-Kasuya-Yosida picture, and spiral order, even at weak coupling. We provide the exact phase diagram for arbitrary exchange coupling and lattice spacing, and discuss its stability. Our results shed new light on the problem of utilizing a spiral spin-lattice state to drive a one-dimensional superconductor into a topological phase.
Chaves Filho, V. L.; Lima, R. P. A.; Lyra, M. L.
2015-06-01
We investigate the modulational instability of uniform wavepackets governed by the discrete nonlinear Schrodinger equation in finite linear chains and square lattices. We show that, while the critical nonlinear coupling χMI above which modulational instability occurs remains finite in square lattices, it decays as 1/L in linear chains. In square lattices, there is a direct transition between the regime of stable uniform wavefunctions and the regime of asymptotically localized solutions with stationary probability distributions. On the other hand, there is an intermediate regime in linear chains for which the wavefunction dynamics develops complex breathing patterns. We analytically compute the critical nonlinear strengths for modulational instability in both lattices, as well as the characteristic time τ governing the exponential increase of perturbations in the vicinity of the transition. We unveil that the interplay between modulational instability and self-trapping phenomena is responsible for the distinct wavefunction dynamics in linear and square lattices.