The so-called doubling problem in the lattice description of fermions led to a proof that under certain circumstances chiral gauge theories cannot be defined on the lattice. This is called the no-go theorem. It implies that if Γ/sub/A is defined on a lattice then its infrared limit, which should correspond to the quantum description of the classical action for the slowly varying fields on lattice scale, is inevitably a vector like theory. In particular, if not circumvented, the no-go theorem implies that there is no lattice formulation of the Standard Weinberg-Salam theory or SU(5) GUT, even though the fermions belong to anomaly-free representations of the gauge group. This talk aims to explain one possible attempt at bypassing the no-go theorem. 20 refs
A definition of lattice BRS invariance is given. The requirement of lattice BRS invariance successfully replaces that of local gauge invariance as a principle for selecting allowed actions. This replacement also works to any finite order in perturbation theory, but, on the nonperturbative level one encounters an obstacle reflecting the existence of an even number of solutions to the gauge fixing problem. The problem of latticizing the classical action for open bosonic strings discovered by Witten is discussed and a possible direction for dealing with it is pointed out. 3 refs
Non-perturbative phenomena are essential to understanding quantum chromodynamics (QCD), the theory of the strong interactions. The particles observed are mesons and baryons, but the fundamental fields are quarks and gluons. Most properties of the hadrons are inaccessible in perturbation theory. Aside from their mere existence, the most blatant example is the mass spectrum. The lack of an accurate, reasonably precise, calculation of the mass spectrum is a major piece of unfinished business for theoretical particle physics. In addition, a wide variety of other non-perturbative calculations in QCD are necessary to interpret ongoing experiments. For example, it is impossible to extract the Cabibbo-Kobayashi-Maskawa angles without knowing matrix elements of operators in the K, D and B mesons. Furthermore, non-perturbative analyses of quarkonia can determine the strong coupling constant with uncertainties already comparable to perturbative analyses of high-energy data. These lectures cover lattice field theory, the only general, systematic approach that can address quantitatively the non-perturbative questions raised above. Sects. 2--8 explain how to formulate quantum field theory on a lattice and why lattice field theory is theoretically well-founded. Sect. 9 sketches some analytic calculations in scalar lattice field theory. They serve as an example of how lattice field theory can contribute to particle physics without necessarily using computers. Sect. 10 turns to the most powerful tool in lattice field theory: large-scale Monte Carlo integration of the functional integral. Instead of discussing algorithms in gory detail, the general themes of computational field theory are discussed. The methods needed for spectroscopy, weak matrix elements, and the strong coupling constant are reviewed. 52 refs., 7 figs., 1 tab
The finite-element method enables us to convert the operator differential equations of a quantum field theory into operator difference equations. These difference equations are consistent with the requirements of quantum mechanics and they do not exhibit fermion doubling, a problem that frequently plagues lattice treatments of fermions. Guage invariance can also be incorporated into the difference equations. On a finite lattice the operator difference equations can be solved in closed form. For the case of the Schwinger model the anomaly is computed and results in excellent agreement are obtained with the known continuum value
LATTICE: an interactive lattice computer code
LATTICE is a computer code which enables an interactive user to calculate the functions of a synchrotron lattice. This program satisfies the requirements at LBL for a simple interactive lattice program by borrowing ideas from both TRANSPORT and SYNCH. A fitting routine is included
Kinyon, Michael
2012-01-01
Categorical skew lattices are a variety of skew lattices on which the natural partial order is especially well behaved. While most skew lattices of interest are categorical, not all are. They are characterized by a countable family of forbidden subalgebras. We also consider the subclass of strictly categorical skew lattices.
Reactor lattice transport calculations
The present lecture is a continuation of the lecture on Introduction to the Neutron Transport Phenomena. It comprises three aspects of lattice calculations. First the idea of a reactor lattice is introduced. Then the main definitions used in reactor lattice analysis are given, and finally two basic methods applied for solution of the transport equations are defined. Several remarks on secondary results from lattice transport calculations are added. (author)
Sober Topological Molecular Lattices
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.
Querying Relational Concept Lattices
Azmeh, Zeina; Huchard, Marianne; Napoli, Amedeo; Rouane Hacene, Amine Mohamed; Valtchev, Petko
2011-01-01
Relational Concept Analysis (RCA) constructs conceptual abstractions from objects described by both own properties and inter-object links, while dealing with several sorts of objects. RCA produces lattices for each category of objects and those lattices are connected via relational attributes that are abstractions of the initial links. Navigating such interrelated lattice family in order to find concepts of interest is not a trivial task due to the potentially large size of the lattices and t...
Marichal, Jean-Luc
2007-01-01
We define the concept of weighted lattice polynomial functions as lattice polynomial functions constructed from both variables and parameters. We provide equivalent forms of these functions in an arbitrary bounded distributive lattice. We also show that these functions include the class of discrete Sugeno integrals and that they are characterized by a median based decomposition formula.
Zakrzewski, W J
2004-01-01
We consider some lattices and look at discrete Laplacians on these lattices. In particular we look at solutions of the equation $\\triangle(1)\\phi = \\triangle(2)Z$ where $\\triangle(1)$ and $\\triangle(2)$ are two such laplacians on the same lattice. We discuss solutions of this equation in some special cases.
In the last few years lattice gauge theory has become the primary tool for the study of nonperturbative phenomena in gauge theories. The lattice serves as an ultraviolet cutoff, rendering the theory well defined and amenable to numerical and analytical work. Of course, as with any cutoff, at the end of a calculation one must consider the limit of vanishing lattice spacing in order to draw conclusions on the physical continuum limit theory. The lattice has the advantage over other regulators that it is not tied to the Feynman expansion. This opens the possibility of other approximation schemes than conventional perturbation theory. Thus Wilson used a high temperature expansion to demonstrate confinement in the strong coupling limit. Monte Carlo simulations have dominated the research in lattice gauge theory for the last four years, giving first principle calculations of nonperturbative parameters characterizing the continuum limit. Some of the recent results with lattice calculations are reviewed
Lattice theory for nonspecialists
These lectures were delivered as part of the academic training programme at the NIKHEF-H. These lectures were intended primarily for experimentalists, and theorists not specializing in lattice methods. The goal was to present the essential spirit behind the lattice approach and consequently the author has concentrated mostly on issues of principle rather than on presenting a large amount of detail. In particular, the author emphasizes the deep theoretical infra-structure that has made lattice studies meaningful. At the same time, he has avoided the use of heavy formalisms as they tend to obscure the basic issues for people trying to approach this subject for the first time. The essential ideas are illustrated with elementary soluble examples not involving complicated mathematics. The following subjects are discussed: three ways of solving the harmonic oscillator problem; latticization; gauge fields on a lattice; QCD observables; how to solve lattice theories. (Auth.)
Spight, Marshall
2008-01-01
Relational lattice is a formal mathematical model for Relational algebra. It reduces the set of six classic relational algebra operators to two: natural join and inner union. We continue to investigate Relational lattice properties with emphasis onto axiomatic definition. New results include additional axioms, equational definition for set difference (more generally anti-join), and case study demonstrating application of the relational lattice theory for query transformations.
kunz, Milan
2006-01-01
Ferrers graphs and tables of partitions are treated as vectors. Matrix operations are used for simple proofs of identities concerning partitions. Interpreting partitions as vectors gives a possibility to generalize partitions on negative numbers. Partitions are then tabulated into lattices and some properties of these lattices are studied. There appears a new identity counting Ferrers graphs packed consecutively into isoscele form. The lattices form the base for tabulating combinatorial ident...
Lattice degeneracies of fermions
We present a detailed description of the minimal degeneracies of geometric (Kaehler) fermions on all the lattices of maximal symmetries in n = 1, ..., 4 dimensions. We also determine the isolated orbits of the maximal symmetry groups, which are related to the minimal numbers of ''naive'' fermions on the reciprocals of these lattices. It turns out that on the self-reciprocal lattices the minimal numbers of naive fermions are equal to the minimal numbers of degrees of freedom of geometric fermions. The description we give relies on the close connection of the maximal lattice symmetry groups with (affine) Weyl groups of root systems of (semi-) simple Lie algebras. (orig.)
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.)
Counting Hexagonal Lattice Animals
Mohammed, Mohamud
2002-01-01
We describe Maple packages for the automatic generation of generating functions(and series expansions) for counting lattice animals(fixed polyominoes), in the two-dimensional hexagonal lattice, of bounded but arbitrary width. Our Maple packages(complete with source code) are easy-to-use and available from my website.
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.
Active Optical Lattice Filters
Gary Evans; MacFarlane, Duncan L.; Govind Kannan; Jian Tong; Issa Panahi; Vishnupriya Govindan; L. Roberts Hunt
2005-01-01
Optical lattice filter structures including gains are introduced and analyzed. The photonic realization of the active, adaptive lattice filter is described. The algorithms which map between gains space and filter coefficients space are presented and studied. The sensitivities of filter parameters with respect to gains are derived and calculated. An example which is relevant to adaptive signal processing is also provided.
Flat Band Quastiperiodic Lattices
Bodyfelt, Joshua; Flach, Sergej; Danieli, Carlo
2014-03-01
Translationally invariant lattices with flat bands (FB) in their band structure possess irreducible compact localized flat band states, which can be understood through local rotation to a Fano structure. We present extension of these quasi-1D FB structures under incommensurate lattices, reporting on the FB effects to the Metal-Insulator Transition.
Courant, E.D.; Garren, A.A.
1985-10-01
A realistic, distributed interaction region (IR) lattice has been designed that includes new components discussed in the June 1985 lattice workshop. Unlike the test lattices, the lattice presented here includes utility straights and the mechanism for crossing the beams in the experimental straights. Moreover, both the phase trombones and the dispersion suppressors contain the same bending as the normal cells. Vertically separated beams and 6 Tesla, 1-in-1 magnets are assumed. Since the cells are 200 meters long, and have 60 degree phase advance, this lattice has been named RLD1, in analogy with the corresponding test lattice, TLD1. The quadrupole gradient is 136 tesla/meter in the cells, and has similar values in other quadrupoles except in those in the IR`s, where the maximum gradient is 245 tesla/meter. RLD1 has distributed IR`s; however, clustered realistic lattices can easily be assembled from the same components, as was recently done in a version that utilizes the same type of experimental and utility straights as those of RLD1.
Lattice gauge theory is now ten years old. Apart from the theoretical insight the lattice formulation gives, it is very well suited for computer simulations, as its inventor advocated already some five years ago at this school. Since three years this approach has extracted useful information out of lattice gauge theory and spurred many interesting questions. In the first lecture, I will assume there are no experts in the audience and explain some basic facts in quarkless quantumchromodynamics on a lattice (QCD). Then, in the second lecture, we shall review tests for the consistency of the numerical results so far obtained. The third lecture shall deal with a more esoteric subject: that of large N reduced models. The list of references is by no means meant to be exhaustive; for that the reader is referred to ref. 27
Lattice supersymmetric ward identities
SUSY Ward identities for the N=1 SU(2) SUSY Yang-Mills theory are studied on the lattice in a non-perturbative numerical approach. As a result a determination of the subtracted gluino mass is obtained
The architecture and capabilities of the computers currently in use for large-scale lattice QCD calculations are described and compared. Based on this present experience, possible future directions are discussed
Vector Lattice Vortex Solitons
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.
Full text: We sketch the general concepts of the lattice regularisation in quantum field theory, which enables Monte Carlo simulations and non-perturbative numerical measurements of observables in particle physics. We then address the status of lattice QCD with 2+1 flavours of dynamical quarks, where hadron masses can now be evaluated from the first principles of QCD close to the percent level. (author)
Bietenholz, Wolfgang [Universidad Nacional Autonoma de Mexico (UNAM) (Mexico)
2011-07-01
Full text: We sketch the general concepts of the lattice regularisation in quantum field theory, which enables Monte Carlo simulations and non-perturbative numerical measurements of observables in particle physics. We then address the status of lattice QCD with 2+1 flavours of dynamical quarks, where hadron masses can now be evaluated from the first principles of QCD close to the percent level. (author)
Automated Lattice Perturbation Theory
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.
Lattice Operators and Topologies
Eva Cogan
2009-01-01
Working within a complete (not necessarily atomic) Boolean algebra, we use a sublattice to define a topology on that algebra. Our operators generalize complement on a lattice which in turn abstracts the set theoretic operator. Less restricted than those of Banaschewski and Samuel, the operators exhibit some surprising behaviors. We consider properties of such lattices and their interrelations. Many of these properties are abstractions and generalizations of topological spaces. The approach is...
Bergner, Georg
2016-01-01
We discuss the motivations, difficulties and progress in the study of supersymmetric lattice gauge theories focusing in particular on ${\\cal N}=1$ and ${\\cal N}=4$ super Yang-Mills in four dimensions. Brief reviews of the corresponding lattice formalisms are given and current results are presented and discussed. We conclude with a summary of the main aspects of current work and prospects for the future.
Lattice supersymmetry and string phenomenology
Giedt, Joel
2003-01-01
I discuss the usefulness of lattice supersymmetry in relation to string phenomenology. I suggest how lattice results might be incorporated into string phenomenology. I outline difficulties and describe some constructions that contain an exact lattice version of supersymmetry, thereby reducing fine-tuning of the regulator. I mention some problems that occur for these lattices.
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...
Graphene antidot lattice waveguides
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...
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.
Optimality and uniqueness of the Leech lattice among lattices
Cohn, Henry; Kumar, Abhinav
2004-01-01
We prove that the Leech lattice is the unique densest lattice in R^24. The proof combines human reasoning with computer verification of the properties of certain explicit polynomials. We furthermore prove that no sphere packing in R^24 can exceed the Leech lattice's density by a factor of more than 1+1.65*10^(-30), and we give a new proof that E_8 is the unique densest lattice in R^8.
Singh, Kevin; Geiger, Zachary; Senaratne, Ruwan; Rajagopal, Shankari; Fujiwara, Kurt; Weld, David; Weld Group Team
2015-05-01
Quasiperiodicity is intimately involved in quantum phenomena from localization to the quantum Hall effect. Recent experimental investigation of quasiperiodic quantum effects in photonic and electronic systems have revealed intriguing connections to topological phenomena. However, such experiments have been limited by the absence of techniques for creating tunable quasiperiodic structures. We propose a new type of quasiperiodic optical lattice, constructed by intersecting a Gaussian beam with a 2D square lattice at an angle with an irrational tangent. The resulting potential, a generalization of the Fibonacci lattice, is a physical realization of the mathematical ``cut-and-project'' construction which underlies all quasiperiodic structures. Calculation of the energies and wavefunctions of atoms loaded into the proposed quasiperiodic lattice demonstrate a fractal energy spectrum and the existence of edge states. We acknowledge support from the ONR (award N00014-14-1-0805), the ARO and the PECASE program (award W911NF-14-1-0154), the AFOSR (award FA9550-12-1-0305), and the Alfred P. Sloan foundation (grant BR2013-110).
Bursa, Francis; Kroyter, Michael
2010-01-01
String field theory is a candidate for a full non-perturbative definition of string theory. We aim to define string field theory on a space-time lattice to investigate its behaviour at the quantum level. Specifically, we look at string field theory in a one dimensional linear dilaton background. We report the first results of our simulations.
Mickelsson, J
1996-01-01
A calculation of the chiral anomaly on a finite lattice without fermion doubling is presented . The lattice gauge field is defined in the spirit of noncommutative geometry. Standard formulas for the continuum anomaly are obtained as a limit.
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.
A set of eight test lattices for the SSC have been devised for such purposes as the investigation of the dependences of chromatic properties and dynamic aperture on the type, field, physical aperture and errors of the magnets, on the sextupole correction scheme, on the tunes and on the cell phase advances. They are distinguished from realistic lattices in that certain features of the latter are missing - most notably the crossing magnets that bring the two counter-rotating proton beams into collision at the interaction points, and the utility insertions, which are the sites for the injection, beam abort, and radiofrequency systems. Furthermore the placement of magnets in the cells is simplified. 7 refs., 9 figs., 2 tabs
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...
Hsu, Hsiao-Ping; Nadler, Walder; Grassberger, Peter
2005-07-01
The scaling behavior of randomly branched polymers in a good solvent is studied in two to nine dimensions, modeled by lattice animals on simple hypercubic lattices. For the simulations, we use a biased sequential sampling algorithm with re-sampling, similar to the pruned-enriched Rosenbluth method (PERM) used extensively for linear polymers. We obtain high statistics of animals with up to several thousand sites in all dimension 2⩽d⩽9. The partition sum (number of different animals) and gyration radii are estimated. In all dimensions we verify the Parisi-Sourlas prediction, and we verify all exactly known critical exponents in dimensions 2, 3, 4, and ⩾8. In addition, we present the hitherto most precise estimates for growth constants in d⩾3. For clusters with one site attached to an attractive surface, we verify the superuniversality of the cross-over exponent at the adsorption transition predicted by Janssen and Lyssy.
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.
This review concentrates on progress in lattice QCD during the last two years and, particularly, its impact on phenomenology. The two main technical developments have been successful implementations of lattice actions with exact chiral symmetry, and results from simulations with two light dynamical flavours which provide quantitative estimates of quenching effects for some quantities. Results are presented for the hadron spectrum, quark masses, heavy-quark decays and structure functions. Theoretical progress is encouraging renewed attempts to compute non-leptonic kaon decays. Although computing power continues to be a limitation, projects are underway to build multi-teraflops machines over the next three years, which will be around ten times more cost-effective than those of today. (author)
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
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.
The panel was attended by prominent physicists from most of the well-known laboratories in the field of light-water lattices, who exchanged the latest information on the status of work in their countries and discussed both the theoretical and the experimental aspects of the subjects. The supporting papers covered most problems, including criticality, resonance absorption, thermal utilization, spectrum calculations and the physics of plutonium bearing systems. Refs, figs and tabs
One of the major recent developments in particle theory has been the use of very high performance computers to obtain approximate numerical solutions of quantum field theories by formulating them on a finite space-time lattice. The great virtue of this new technique is that it avoids the straitjacket of perturbation theory and can thus attack new, but very fundamental problems, such as the calculation of hadron masses in quark-gluon field theory (quantum chromodynamics - QCD)
Digital lattice gauge theories
Zohar, Erez(Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748, Garching, Germany); Farace, Alessandro; 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 exp...
Lattice Vibrations in Chlorobenzenes:
Reynolds, P. A.; Kjems, Jørgen; White, J. W.
1974-01-01
Lattice vibrational dispersion curves for the ``intermolecular'' modes in the triclinic, one molecule per unit cell β phase of p‐C6D4Cl2 and p‐C6H4Cl2 have been obtained by inelastic neutron scattering. The deuterated sample was investigated at 295 and at 90°K and a linear extrapolation to 0°K was...
Homomorphisms on Lattices of Measures
Norris Sookoo
2009-01-01
Full Text Available Problem statement: Homomorphisms on lattices of measures defined on the quotient spaces of the integers were considered. These measures were defined in terms of Sharma-Kaushik partitions. The homomorphisms were studied in terms of their relationship with the underlying Sharma-Kaushik partitions. Approach: We defined certain mappings between lattices of Sharma-Kaushik partitions and showed that they are homomorphisms. These homomorphisms were mirrored in homorphisms between related lattices of measures. Results: We obtained the structure of certain homomorphisms of measures. Conclusion: Further information about homomorphisms between lattices of measures of the type considered here can be obtained by investigating the underlying lattices of Sharma-Kaushik partitions.
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...
Crystallographic Lattice Boltzmann Method
Namburi, Manjusha; Krithivasan, Siddharth; Ansumali, Santosh
2016-06-01
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.
We present a unified framework to describe lattice gauge theories by means of tensor networks: this framework is efficient as it exploits the high local symmetry content native to these systems by describing only the gauge invariant subspace. Compared to a standard tensor network description, the gauge invariant model allows one to increase real and imaginary time evolution up to a factor that is square of the dimension of the link variable. The gauge invariant tensor network description is based on the quantum link formulation, a compact and intuitive formulation for gauge theories on the lattice, which is alternative to and can be combined with the global symmetric tensor network description. We present some paradigmatic examples that show how this architecture might be used to describe the physics of condensed matter and high-energy physics systems. Finally, we present a cellular automata analysis which estimates the gauge invariant Hilbert space dimension as a function of the number of lattice sites that might guide the search for effective simplified models of complex theories. (paper)
Dielectric lattice gauge theory
Dielectric lattice gauge theory models are introduced. They involve variables PHI(b)epsilong that are attached to the links b = (x+esub(μ),x) of the lattice and take their values in the linear space g which consists of real linear combinations of matrices in the gauge group G. The polar decomposition PHI(b)=U(b)osub(μ)(x) specifies an ordinary lattice gauge field U(b) and a kind of dielectric field epsilonsub(ij)proportionalosub(i)osub(j)sup(*)deltasub(ij). A gauge invariant positive semidefinite kinetic term for the PHI-field is found, and it is shown how to incorporate Wilson fermions in a way which preserves Osterwalder Schrader positivity. Theories with G = SU(2) and without matter fields are studied in some detail. It is proved that confinement holds, in the sense that Wilson loop expectation values show an area law decay, if the Euclidean action has certain qualitative features which imply that PHI = 0 (i.e. dielectric field identical 0) is the unique maximum of the action. (orig.)
Toward lattice fractional vector calculus
Tarasov, Vasily E.
2014-09-01
An analog of fractional vector calculus for physical lattice models is suggested. We use an approach based on the models of three-dimensional lattices with long-range inter-particle interactions. The lattice analogs of fractional partial derivatives are represented by kernels of lattice long-range interactions, where the Fourier series transformations of these kernels have a power-law form with respect to wave vector components. In the continuum limit, these lattice partial derivatives give derivatives of non-integer order with respect to coordinates. In the three-dimensional description of the non-local continuum, the fractional differential operators have the form of fractional partial derivatives of the Riesz type. As examples of the applications of the suggested lattice fractional vector calculus, we give lattice models with long-range interactions for the fractional Maxwell equations of non-local continuous media and for the fractional generalization of the Mindlin and Aifantis continuum models of gradient elasticity.
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)
Collapsing lattice animals and lattice trees in two dimensions
Hsu, Hsiao-Ping; Grassberger, Peter
2005-01-01
We present high statistics simulations of weighted lattice bond animals and lattice trees on the square lattice, with fugacities for each non-bonded contact and for each bond between two neighbouring monomers. The simulations are performed using a newly developed sequential sampling method with resampling, very similar to the pruned-enriched Rosenbluth method (PERM) used for linear chain polymers. We determine with high precision the line of second order transitions from an extended to a coll...
Sortable elements and Cambrian lattices
Reading, Nathan
2005-01-01
We show that the Coxeter-sortable elements in a finite Coxeter group W are the minimal congruence-class representatives of a lattice congruence of the weak order on W. We identify this congruence as the Cambrian congruence on W, so that the Cambrian lattice is the weak order on Coxeter-sortable elements. These results exhibit W-Catalan combinatorics arising in the context of the lattice theory of the weak order on W.
Rasmussen, S. [Los Alamos National Lab., NM (United States)]|[Santa Fe Institute, NM (United States); Smith, J.R. [Santa Fe Institute, NM (United States)]|[Massachusetts Media Lab., Cambridge, MA (United States). Physics and Media Group
1995-05-01
We present a new style of molecular dynamics and self-assembly simulation, the Lattice Polymer Automaton (LPA). In the LPA all interactions, including electromagnetic forces, are decomposed and communicated via propagating particles, {open_quotes}photons.{close_quotes} The monomer-monomer bondforces, the molecular excluded volume forces, the longer range intermolecular forces, and the polymer-solvent interactions may all be modeled with propagating particles. The LPA approach differs significantly from both of the standard approaches, Monte Carlo lattice methods and Molecular Dynamics simulations. On the one hand, the LPA provides more realism than Monte Carlo methods, because it produces a time series of configurations of a single molecule, rather than a set of causally unrelated samples from a distribution of configurations. The LPA can therefore be used directly to study dynamical properties; one can in fact watch polymers move in real time. On the other hand, the LPA is fully discrete, and therefore much simpler than traditional Molecular Dynamics models, which are continuous and operate on much shorter time scales. Due to this simplicity it is possible to simulate longer real time periods, which should enable the study of molecular self-organization on workstations supercomputers are not needed.
Syer, D; Syer, D; Tremaine, S
1995-01-01
We describe a technique for solving the combined collisionless Boltzmann and Poisson equations in a discretised, or lattice, phase space. The time and the positions and velocities of `particles' take on integer values, and the forces are rounded to the nearest integer. The equations of motion are symplectic. In the limit of high resolution, the lattice equations become the usual integro-differential equations of stellar dynamics. The technique complements other tools for solving those equations approximately, such as N-body simulation, or techniques based on phase-space grids. Equilibria are found in a variety of shapes and sizes. They are true equilibria in the sense that they do not evolve with time, even slowly, unlike existing N-body approximations to stellar systems, which are subject to two-body relaxation. They can also be `tailor-made' in the sense that the mass distribution is constrained to be close to some pre-specified function. Their principal limitation is the amount of memory required to store ...
Sparse and composite coherent lattices
A method is described that yields a series of (D+1)-element wave-vector sets giving rise to (D=2 or 3)-dimensional coherent sparse lattices of any desired Bravais symmetry and primitive cell shape, but of increasing period relative to the excitation wavelength. By applying lattice symmetry operations to any of these sets, composite lattices of N>D+1 waves are constructed, having increased spatial frequency content but unchanged crystal group symmetry and periodicity. Optical lattices of widely spaced excitation maxima of diffraction-limited confinement and controllable polarization can thereby be created, possibly useful for quantum optics, lithography, or multifocal microscopy
Convection-diffusion lattice Boltzmann scheme for irregular lattices
Sman, van der R.G.M.; Ernst, M.H.
2000-01-01
In this paper, a lattice Boltzmann (LB) scheme for convection diffusion on irregular lattices is presented, which is free of any interpolation or coarse graining step. The scheme is derived using the axioma that the velocity moments of the equilibrium distribution equal those of the Maxwell-Boltzman
Elimination of spurious lattice fermion solutions and noncompact lattice QCD
Lee, T.D.
1997-09-22
It is well known that the Dirac equation on a discrete hyper-cubic lattice in D dimension has 2{sup D} degenerate solutions. The usual method of removing these spurious solutions encounters difficulties with chiral symmetry when the lattice spacing l {ne} 0, as exemplified by the persistent problem of the pion mass. On the other hand, we recall that in any crystal in nature, all the electrons do move in a lattice and satisfy the Dirac equation; yet there is not a single physical result that has ever been entangled with a spurious fermion solution. Therefore it should not be difficult to eliminate these unphysical elements. On a discrete lattice, particle hop from point to point, whereas in a real crystal the lattice structure in embedded in a continuum and electrons move continuously from lattice cell to lattice cell. In a discrete system, the lattice functions are defined only on individual points (or links as in the case of gauge fields). However, in a crystal the electron state vector is represented by the Bloch wave functions which are continuous functions in {rvec {gamma}}, and herein lies one of the essential differences.
Full text: Lattice-resolution scanning transmission electron microscopy (STEM) contrast, derived from coherent or incoherent scattering mechanisms, is finding application over a diverse range of problems on the atomic scale, particularly with the availability of coherent FEGs. Fundamental for the understanding of such contrast is the propagation within a crystal of a focused coherent probe formed by a collapsing spherical wave. Current Bloch wave descriptions construct the total wave function from a coherent superposition of Bloch states excited from a series of incident plane waves that span the full range of transverse momentum components in the focused probe. However this implementation of boundary conditions using phase-linked plane waves may be misleading in that the possibility of exciting antisymmetric states which provides the cross-talk between adjacent columns of atoms - appears at first sight to be excluded. We match the total probe wave function to a crystal wave function which incorporates all transverse momenta in the incident probe. This revised implementation of boundary conditions leads to a simple formula for excitation amplitude which enables the probe position dependent excitation of both symmetric and antisymmetric Bloch states to be predicted. Shortcomings of previous models for incoherent contrast are that interference between waves associated with mixed dynamic form factors for incoherent contrast is not addressed, and that an intensity contribution from dechannelled electrons is not taken into account. This simple revision of boundary conditions leads to a rigorous formulation for (i) coherent and (n) incoherent lattice resolution STEM contrast. The former (i) does not require principles of reciprocity to be invoked, and the latter (n) follows from a simple generalization of the theory of channelling contrast for ADF, BSE and ALCHEMI for an incident plane wave. Phase associated with products of transition amplitudes that occur in mixed
Lattice Boltzmann Model for Compressible Fluid on a Square Lattice
SUN Cheng-Hai
2000-01-01
A two-level four-direction lattice Boltzmann model is formulated on a square lattice to simulate compressible flows with a high Mach number. The particle velocities are adaptive to the mean velocity and internal energy. Therefore, the mean flow can have a high Mach number. Due to the simple form of the equilibrium distribution, the 4th order velocity tensors are not involved in the calculations. Unlike the standard lattice Boltzmann model, o special treatment is need for the homogeneity of 4th order velocity tensors on square lattices. The Navier-Stokes equations were derived by the Chapman-Enskog method from the BGK Boltzmann equation. The model can be easily extended to three-dimensional cubic lattices. Two-dimensional shock-wave propagation was simulated
Entangling gates in even Euclidean lattices such as Leech lattice
Planat, Michel
2010-01-01
We point out a organic relationship between real entangling n-qubit gates of quantum computation and the group of automorphisms of even Euclidean lattices of the corresponding dimension 2n. The type of entanglement that is found in the gates/generators of Aut() depends on the lattice. In particular, we investigate Zn lattices, Barnes-Wall lattices D4, E8, 16 (associated to n = 2, 3 and 4 qubits), and the Leech lattices h24 and 24 (associated to a 3-qubit/qutrit system). Balanced tripartite entanglement is found to be a basic feature of Aut(), a nding that bears out our recent work related to the Weyl group of E8 [1, 2].
We introduce a new framework for constructing black hole solutions that are holographically dual to strongly coupled field theories with explicitly broken translation invariance. Using a classical gravitational theory with a continuous global symmetry leads to constructions that involve solving ODEs instead of PDEs. We study in detail D=4 Einstein-Maxwell theory coupled to a complex scalar field with a simple mass term. We construct black holes dual to metallic phases which exhibit a Drude-type peak in the optical conductivity, but there is no evidence of an intermediate scaling that has been reported in other holographic lattice constructions. We also construct black holes dual to insulating phases which exhibit a suppression of spectral weight at low frequencies. We show that the model also admits a novel AdS3×ℝ solution
Excitonic surface lattice resonances
Humphrey, A. D.; Gentile, M. J.; Barnes, W. L.
2016-08-01
Electromagnetic resonances are important in controlling light at the nanoscale. The most studied such resonance is the surface plasmon resonance that is associated with metallic nanostructures. Here we explore an alternative resonance, the surface exciton-polariton resonance, one based on excitonic molecular materials. Our study is based on analytical and numerical modelling. We show that periodic arrays of suitable molecular nanoparticles may support surface lattice resonances that arise as a result of coherent interactions between the particles. Our results demonstrate that excitonic molecular materials are an interesting alternative to metals for nanophotonics; they offer the prospect of both fabrication based on supramolecular chemistry and optical functionality arising from the way the properties of such materials may be controlled with light.
A group theoretical analysis of modes of vibrations in hexagonal close-packed lattices has been made. The results have been used to classify the phonons at some special points in the Brillouin zone and factorized the secular determinant. Dispersion relations for phonons in magnesium along the two symmetry directions [0001] and [0110] have been measured (at room temperature) more accurately than reported earlier. The measurements have been made using a triple-axis spectrometer and a ''window filter'' spectrometer, both operated in the ''constant-Q'' mode. The results are compared with calculations based on three- and four-neighbour axially symmetric models. It is observed that the four-neighbour model gives a reasonably good description of the data. Even better agreement is obtained with a four-neighbour tensor force model. The force constants derived from the experiment have been used to compute the frequency distribution. (author)
Nuclear Physics and Lattice QCD
Savage, Martin J.
2005-01-01
Lattice QCD is progressing toward being able to impact our understanding of nuclei and nuclear processes. I discuss areas of nuclear physics that are becoming possible to explore with lattice QCD, the techniques that are currently available and the status of numerical explorations.
Lattice gauge theory: Present status
Lattice gauge theory is our primary tool for the study of non- perturbative phenomena in hadronic physics. In addition to giving quantitative information on confinement, the approach is yielding first principles calculations of hadronic spectra and matrix elements. After years of confusion, there has been significant recent progress in understanding issues of chiral symmetry on the lattice
An Introduction to Lattice QCD
Pène, O
1995-01-01
Lattice QCD is the only non-perturbative method based uniquely on the first principles of QCD. After a very simple introduction to the principles of lattice QCD, I discuss its present limitations and the type of processes it can deal with. Then I present some striking results in the light and heavy quarks sectors. Finally I try to guess the prospects.
Network coding with modular lattices
Kendziorra, Andreas
2010-01-01
In [1], K\\"otter and Kschischang presented a new model for error correcting codes in network coding. The alphabet in this model is the subspace lattice of a given vector space, a code is a subset of this lattice and the used metric on this alphabet is the map d: (U, V) \\longmapsto dim(U + V) - dim(U \\bigcap V). In this paper we generalize this model to arbitrary modular lattices, i.e. we consider codes, which are subsets of modular lattices. The used metric in this general case is the map d: (x, y) \\longmapsto h(x \\bigvee y) - h(x \\bigwedge y), where h is the height function of the lattice. We apply this model to submodule lattices. Moreover, we show a method to compute the size of spheres in certain modular lattices and present a sphere packing bound, a sphere covering bound, and a singleton bound for codes, which are subsets of modular lattices. [1] R. K\\"otter, F.R. Kschischang: Coding for errors and erasures in random network coding, IEEE Trans. Inf. Theory, Vol. 54, No. 8, 2008
Computing the writhe on lattices
Given a polygonal closed curve on a lattice or space group, we describe a method for computing the writhe of the curve as the average of weighted projected writhing numbers of the polygon in a few directions. These directions are determined by the lattice geometry, the weights are determined by areas of regions on the unit 2-sphere, and the regions are formed by the tangent indicatrix to the polygonal curve. We give a new formula for the writhe of polygons on the face centred cubic lattice and prove that the writhe of polygons on the body centred cubic lattice, the hexagonal simple lattice, and the diamond space group is always a rational number, and discuss applications to ring polymers
Lattice Induced Transparency in Metasurfaces
Manjappa, Manukumara; Singh, Ranjan
2016-01-01
Lattice modes are intrinsic to the periodic structures and their occurrence can be easily tuned and controlled by changing the lattice constant of the structural array. Previous studies have revealed excitation of sharp absorption resonances due to lattice mode coupling with the plasmonic resonances. Here, we report the first experimental observation of a lattice induced transparency (LIT) by coupling the first order lattice mode (FOLM) to the structural resonance of a metamaterial resonator at terahertz frequencies. The observed sharp transparency is a result of the destructive interference between the bright mode and the FOLM mediated dark mode. As the FOLM is swept across the metamaterial resonance, the transparency band undergoes large change in its bandwidth and resonance position. Besides controlling the transparency behaviour, LIT also shows a huge enhancement in the Q-factor and record high group delay of 28 ps, which could be pivotal in ultrasensitive sensing and slow light device applications.
Lattice design of FELI accelerator system
FELI is constructing an S-band linac accelerator system for generating wide range FEL (Free Electron Laser). The accelerator system has for lasing sections, almost isochronous offsetting lattices, and returning lattices. This paper describes the lattice design. (author)
The lattice dimension of a tree
Ovchinnikov, Sergei
2004-01-01
The lattice dimension of a graph G is the minimal dimension of a cubic lattice in which G can be isometrically embedded. We prove that the lattice dimension of a tree with n leaves is $\\lceil n/2 \\rceil$.
Lattice gas cellular automata and lattice Boltzmann models an introduction
Wolf-Gladrow, Dieter A
2000-01-01
Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new and promising methods for the numerical solution of nonlinear partial differential equations. The book provides an introduction for graduate students and researchers. Working knowledge of calculus is required and experience in PDEs and fluid dynamics is recommended. Some peculiarities of cellular automata are outlined in Chapter 2. The properties of various LGCA and special coding techniques are discussed in Chapter 3. Concepts from statistical mechanics (Chapter 4) provide the necessary theoretical background for LGCA and LBM. The properties of lattice Boltzmann models and a method for their construction are presented in Chapter 5.
$EE_8$-lattices and dihedral groups
Griess Jr., Robert L.; lam, Ching Hung
2008-01-01
We classify integral rootless lattices which are sums of pairs of $EE_8$-lattices (lattices isometric to $\\sqrt 2$ times the $E_8$-lattice) and which define dihedral groups of orders less than or equal to 12. Most of these may be seen in the Leech lattice. Our classification may help understand Miyamoto involutions on lattice type vertex operator algebras and give a context for the dihedral groups which occur in the Glauberman-Norton moonshine theory.
Kenneth Wilson and Lattice QCD
Ukawa, Akira
2015-09-01
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 better understanding of physics, better algorithms, and more powerful supercomputers have produced major breakthroughs in our understanding of the strong interactions. We review the salient results of this effort in understanding the hadron spectrum, the Cabibbo-Kobayashi-Maskawa matrix elements and CP violation, and quark-gluon plasma at high temperatures. We conclude with a brief summary and a future perspective.
Toward lattice fractional vector calculus
An analog of fractional vector calculus for physical lattice models is suggested. We use an approach based on the models of three-dimensional lattices with long-range inter-particle interactions. The lattice analogs of fractional partial derivatives are represented by kernels of lattice long-range interactions, where the Fourier series transformations of these kernels have a power-law form with respect to wave vector components. In the continuum limit, these lattice partial derivatives give derivatives of non-integer order with respect to coordinates. In the three-dimensional description of the non-local continuum, the fractional differential operators have the form of fractional partial derivatives of the Riesz type. As examples of the applications of the suggested lattice fractional vector calculus, we give lattice models with long-range interactions for the fractional Maxwell equations of non-local continuous media and for the fractional generalization of the Mindlin and Aifantis continuum models of gradient elasticity. (papers)
Introduction to lattice gauge theory
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 ≅ 1/α, where α is the lattice spacing. The continuum (physical) behavior is recovered in the limit α → 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. This will be the emphasis of the first lecture. In the second lecture, the author reviews the essential ingredients of formulating QCD on the lattice and discusses scaling and the continuum limit. In the last lecture the author summarizes the status of some of the main results. He also mentions the bottlenecks and possible directions for research. 88 refs
Pion structure from the lattice
In this thesis, we have discussed several aspects of the pion structure that are accessible with lattice QCD. In our introduction, we briefly mentioned QCD phenomenology for the pion that is obtained from experiments, namely the electromagnetic form factor connected to the charge radius, and the parton distribution functions (PDFs) which provide probabilities of finding a parton with a certain momentum fraction. These are embedded in the more general framework of generalised parton distributions (GPDs) which from the basis of this work. Special attention was paid to Mellin moments of GPDs that are parametrised in generalised form factors relevant for lattice calculations. The two subsequent Chapters were devoted to an introduction to lattice QCD and the lattice techniques we used. Here we started from the QCD Lagrangian and the path integral, to then explain our lattice gauge and fermion action, both going back to Wilson. For the latter we used the clover improved version for our dynamical two flavour simulations. We then gave details of the calculation of two- and three-point functions on the lattice, as well as the operators involved and how the matrix elements are extracted from the lattice data by building suitable ratios. The pion form factor was used for an exhaustive explanation of our methods to analyse the data. We investigated the momentum dependence of the form factor and its extrapolation to physical pion masses. We also payed attention to the lattice artifacts appearing in any lattice simulation. We also tried to estimate the size of finite volume corrections. We applied the established methods to the analysis of higher moments of the forward distributions and the second moment of the non-forward case. Finally, we gave an outlook on the densities of polarised quarks in the pion. (orig.)
Legless locomotion in lattices
Schiebel, Perrin; Goldman, Daniel I.
2014-11-01
Little is known about interactions between an animal body and complex terrestrial terrain like sand and boulders during legless, undulatory travel (e.g. snake locomotion). We study the locomotor performance of Mojave shovel-nosed snakes (Chionactisoccipitalis , ~ 35 cm long) using a simplified model of heterogeneous terrain: symmetric lattices of obstacles. To quantify performance we measure mean forward speed and slip angle, βs, defined as the angle between the instantaneous velocity and tangent vectors at each point on the body. We find that below a critical peg density the presence of granular media results in high speed (~ 60 cm/s), low average slip (βs ~6°) snake performance as compared to movement in the same peg densities on hard ground (~ 25 cm/s and βs ~15°). Above this peg density, performance on granular and hard substrates converges. Speed on granular media decreases with increasing peg density to that of the speed on hard ground, while speed on hard ground remains constant. Conversely, βs on hard ground trends toward that on granular media as obstacle density increases.
Reliability analysis of interdependent lattices
Limiao, Zhang; Daqing, Li; Pengju, Qin; Bowen, Fu; Yinan, Jiang; Zio, Enrico; Rui, Kang
2016-06-01
Network reliability analysis has drawn much attention recently due to the risks of catastrophic damage in networked infrastructures. These infrastructures are dependent on each other as a result of various interactions. However, most of the reliability analyses of these interdependent networks do not consider spatial constraints, which are found important for robustness of infrastructures including power grid and transport systems. Here we study the reliability properties of interdependent lattices with different ranges of spatial constraints. Our study shows that interdependent lattices with strong spatial constraints are more resilient than interdependent Erdös-Rényi networks. There exists an intermediate range of spatial constraints, at which the interdependent lattices have minimal resilience.
Localized structures in Kagome lattices
Saxena, Avadh B [Los Alamos National Laboratory; Bishop, Alan R [Los Alamos National Laboratory; Law, K J H [UNIV OF MASSACHUSETTS; Kevrekidis, P G [UNIV OF MASSACHUSETTS
2009-01-01
We investigate the existence and stability of gap vortices and multi-pole gap solitons in a Kagome lattice with a defocusing nonlinearity both in a discrete case and in a continuum one with periodic external modulation. In particular, predictions are made based on expansion around a simple and analytically tractable anti-continuum (zero coupling) limit. These predictions are then confirmed for a continuum model of an optically-induced Kagome lattice in a photorefractive crystal obtained by a continuous transformation of a honeycomb lattice.
Borwein, J M; McPhedran, R C
2013-01-01
The study of lattice sums began when early investigators wanted to go from mechanical properties of crystals to the properties of the atoms and ions from which they were built (the literature of Madelung's constant). A parallel literature was built around the optical properties of regular lattices of atoms (initiated by Lord Rayleigh, Lorentz and Lorenz). For over a century many famous scientists and mathematicians have delved into the properties of lattices, sometimes unwittingly duplicating the work of their predecessors. Here, at last, is a comprehensive overview of the substantial body of
Perfect Matchings in Lattice Animals and Lattice Paths with Constraints
Došlić, Tomislav
2005-01-01
In the first part of this paper it is shown how to use ear decomposition techniques in proving existence and establishing lower bounds to the number of perfect matchings in lattice animals. A correspondence is then established between perfect matchings in certain classes of benzenoid graphs and paths in the rectangular lattice that satisfy certain diagonal constraints. This correspondence is used to give explicit formulas for the number of perfect matchings in hexagonal benzenoid graphs and t...
Hadron properties from lattice QCD
We discuss the status of current dyanmical lattice QCD simulations in connection to the emerging results on the low-lying baryon spectrum, excited states of the nucleon and the investigation of the structure of scalar mesons
De Soto, F; Carbonell, J; Leroy, J P; Pène, O; Roiesnel, C; Boucaud, Ph.
2007-01-01
We present the first results of a quantum field approach to nuclear models obtained by lattice techniques. Renormalization effects for fermion mass and coupling constant in case of scalar and pseudoscalar interaction lagrangian densities are discussed.
Integrating out lattice gauge fields
Vairinhos, Helvio
2014-01-01
The sign problem is a major obstacle to our understanding of the phase diagram of QCD at finite baryon density. Several numerical methods have been proposed to tackle this problem, but a full solution to the sign problem is still elusive. Motivated by this problem and by recent advances in diagrammatic Monte Carlo methods, we find a new exact representation of the partition function of pure lattice gauge theory that contains no link variables. This approach can be easily extended to include staggered fermions, and results in a diagrammatic representation of fermionic states as arrangements of monomers, dimers, and fermionic loops saturating the spacetime lattice. Our representations are exact for any value of the lattice coupling, and extend previous representations that are only valid in the strong coupling limit and at $O(\\beta)$. As a concrete example, we construct a monomer-dimer-loop representation of compact lattice QED.
Lattice tube model of proteins
Banavar, Jayanth R.; Cieplak, Marek; Maritan, Amos
2004-01-01
We present a new lattice model for proteins that incorporates a tube-like anisotropy by introducing a preference for mutually parallel alignments in the conformations. The model is demonstrated to capture many aspects of real proteins.
Lattice Tube Model of Proteins
Banavar, Jayanth R.; Cieplak, Marek; Maritan, Amos
2004-11-01
We present a new lattice model for proteins that incorporates a tubelike anisotropy by introducing a preference for mutually parallel alignments in the conformations. The model is demonstrated to capture many aspects of real proteins.
Hadronic Interactions with Lattice QCD
Savage, Martin J.
2008-01-01
I discuss recent results of the NPLQCD Collaboration regarding the calculation of hadronic interactions with lattice QCD. A particular emphasis will be spent on pi-pi scattering and other meson interactions.
Lubicz, Vittorio
2010-01-01
I review lattice calculations and results for hadronic parameters relevant for kaon physics, in particular the vector form factor f+(0) of semileptonic kaon decays, the ratio fK/fpi of leptonic decay constants and the kaon bag parameter BK. For each lattice calculation a colour code rating is assigned, by following a procedure which is being proposed by the Flavianet Lattice Averaging Group (FLAG), and the following final averages are obtained: f+(0)=0.962(3)(4), fK/fpi = 1.196(1)(10) and \\hat BK = 0.731(7)(35). In the last part of the talk, the present status of lattice studies of non-leptonic K--> pi pi decays is also briefly summarized.
The frequency/wave-vector dispersion relation for the normal modes of vibration in the major symmetry directions of body-centred cubic rubidium has been measured at 120° K. The large (∼ 75 cm3) single crystal was aligned with either a [110] or a [100] axis vertical, and constant incident frequencies between 3.8 and 5.5 x 1012 c,s were employed. The measurements were taken with the McMaster University triple-axis spectrometer at Chalk River in the constant-Q mode of operation. The dispersion curves are similar in shape to those of sodium and potassium. The ratio for a set of 104 values of q common to both sets of data, is 1.667 ± 0.005 with a standard deviation for an individual ratio from the mean of 0.05. The homology of the lattice vibrations for Na and Rb is poorer than for K and Rb. A Born-von Kármán analysis of the measurements has been made, and it is found that third nearest neighbour forces must be included to obtain reasonable agreement. More distant neighbour forces improve the fit relatively little. Axially symmetric constraints do not change the force constants significantly. As expected, the force constant 1XY is larger than 1XX, which suggests that the forces between nearest neighbours are repulsive. The initial slopes of the dispersion curves are considerably larger than the slopes deduced from ultrasonic measurements. The errors, mainly in the ultrasonic measurements, are barely sufficient to account for the differences. (author)
QCD thermodynamics from the lattice
We review the current methods and results of lattice simulations of quantum chromodynamics at nonzero temperatures and densities. The review is intended to introduce the subject to interested nonspecialists and beginners. It includes a brief overview of lattice gauge theory, a discussion of the determination of the crossover temperature, the QCD phase diagram at zero and nonzero densities, the equation of state, some in-medium properties of hadrons including charmonium, and some plasma transport coefficients. (orig.)
Interacting atoms in optical lattices
Mentink, Johan; Kokkelmans, Servaas
2008-01-01
We propose an easy to use model to solve for interacting atoms in an optical lattice. This model allows for the whole range of weakly to strongly interacting atoms, and it includes the coupling between relative and center-of-mass motion via anharmonic lattice terms. We apply this model to a high-precision spin dynamics experiment, and we discuss the corrections due to atomic interactions and the anharmonic coupling. Under suitable experimental conditions, energy can be transferred between the...
Local Rigidity Of Uniform Lattices
Gelander, Tsachik; Levit, Arie
2016-01-01
We establish local topological rigidity for uniform lattices in compactly generated groups, extending the result of Weil from the realm of Lie groups. We generalize the classical local rigidity theorem of Selberg, Calabi and Weil to irreducible uniform lattices in $\\text{Isom}(X)$ where $X$ is a proper $\\text{CAT}(0)$ space with no Euclidian factors, not isometric to the hyperbolic plane. We deduce an analog of Wang's finiteness theorem for certain non-positively curved metric spaces.
Boolean filters of distributive lattices
M. Sambasiva Rao
2013-07-01
Full Text Available In this paper we introduce the notion of Boolean filters in a pseudo-complemented distributive lattice and characterize the class of all Boolean filters. Further a set of equivalent conditions are derived for a proper filter to become a prime Boolean filter. Also a set of equivalent conditions is derived for a pseudo-complemented distributive lattice to become a Boolean algebra. Finally, a Boolean filter is characterized in terms of congruences.
Baryon spectroscopy in lattice QCD
Derek B. Leinweber; Wolodymyr Melnitchouk; David Richards; Anthony G. Williams; James Zanotti
2004-04-01
We review recent developments in the study of excited baryon spectroscopy in lattice QCD. After introducing the basic methods used to extract masses from correlation functions, we discuss various interpolating fields and lattice actions commonly used in the literature. We present a survey of results of recent calculations of excited baryons in quenched QCD, and outline possible future directions in the study of baryon spectra.
DeGrand, T. [Univ. of Colorado, Boulder, CO (United States). Dept. of Physics
1997-06-01
These lectures provide an introduction to lattice methods for nonperturbative studies of Quantum Chromodynamics. Lecture 1: Basic techniques for QCD and results for hadron spectroscopy using the simplest discretizations; lecture 2: Improved actions--what they are and how well they work; lecture 3: SLAC physics from the lattice-structure functions, the mass of the glueball, heavy quarks and {alpha}{sub s} (M{sub z}), and B-{anti B} mixing. 67 refs., 36 figs.
Transport in Sawtooth photonic lattices
Weimann, Steffen; Real, Bastián; Cantillano, Camilo; Szameit, Alexander; Vicencio, Rodrigo A
2016-01-01
We investigate, theoretically and experimentally, a photonic realization of a Sawtooth lattice. This special lattice exhibits two spectral bands, with one of them experiencing a complete collapse to a highly degenerate flat band for a special set of inter-site coupling constants. We report the ob- servation of different transport regimes, including strong transport inhibition due to the appearance of the non-diffractive flat band. Moreover, we excite localized Shockley surfaces states, residing in the gap between the two linear bands.
We discuss here lattice results for hadronic couplings and matrix elements relevant for weak transitions in heavy systems. Specifically, we present numerical computations of pseudoscalar and vector decay constants such as fD, fJ/Ψ, the B parameter for the charmed D-anti D system, as well as some preliminary results related to a lattice evaluation of the equivalent quantities for the bottom system. (orig./HSI)
Lattice Structures for Attractors I
Kalies, William D.; Mischaikow, Konstantin; Vandervorst, Robert C. A. M.
2013-01-01
We describe the basic lattice structures of attractors and repellers in dynamical systems. The structure of distributive lattices allows for an algebraic treatment of gradient-like dynamics in general dynamical systems, both invertible and noninvertible. We separate those properties which rely solely on algebraic structures from those that require some topological arguments, in order to lay a foundation for the development of algorithms to manipulate these structures computationally.
Multifractal behaviour of -simplex lattic
Sanjay Kumar; Debaprasad Giri; Sujata Krishna
2000-06-01
We study the asymptotic behaviour of resistance scaling and ﬂuctuation of resistance that give rise to ﬂicker noise in an -simplex lattice. We propose a simple method to calculate the resistance scaling and give a closed-form formula to calculate the exponent, , associated with resistance scaling, for any . Using current cumulant method we calculate the exact noise exponent for -simplex lattices.
Capacities on a finite lattice
Machida, Motoya
2011-01-01
In his influential work Choquet systematically studied capacities on Boolean algebras in a topological space, and gave a probabilistic interpretation for completely monotone (and completely alternating) capacities. Beyond complete monotonicity we can view a capacity as a marginal condition for probability distribution over the distributive lattice of dual order ideals. In this paper we discuss a combinatorial approach when capacities are defined over a finite lattice, and investigate Fr\\'{e}c...
Lattice splitting under intermittent flows
Schläpfer, Markus; Trantopoulos, Konstantinos
2010-01-01
We study the splitting of regular square lattices subject to stochastic intermittent flows. Various flow patterns are produced by different groupings of the nodes, based on their random alternation between two possible states. The resulting flows on the lattices decrease with the number of groups according to a power law. By Monte Carlo simulations we reveal how the time span until the occurrence of a splitting depends on the flow patterns. Increasing the flow fluctuation frequency shortens t...
These lectures provide an introduction to lattice methods for nonperturbative studies of Quantum Chromodynamics. Lecture 1: Basic techniques for QCD and results for hadron spectroscopy using the simplest discretizations; lecture 2: Improved actions--what they are and how well they work; lecture 3: SLAC physics from the lattice-structure functions, the mass of the glueball, heavy quarks and αs (Mz), and B-anti B mixing. 67 refs., 36 figs
Yamamoto, Arata
2016-01-01
We propose the lattice QCD calculation of the Berry phase which is defined by the ground state of a single fermion. We perform the ground-state projection of a single-fermion propagator, construct the Berry link variable on a momentum-space lattice, and calculate the Berry phase. As the first application, the first Chern number of the (2+1)-dimensional Wilson fermion is calculated by the Monte Carlo simulation.
Chiral symmetry and lattice fermions
Creutz, Michael
2013-01-01
Lattice gauge theory and chiral perturbation theory are among the primary tools for understanding non-perturbative aspects of QCD. I review several subtle and sometimes controversial issues that arise when combining these techniques. Among these are one failure of partially quenched chiral perturbation theory when the valence quarks become lighter than the average sea quark mass and a potential ambiguity in comparisons of perturbative and lattice properties of non-degenerate quarks.
Large intervals in the clone lattice
Goldstern, Martin; Shelah, Saharon
2002-01-01
We give three examples of large intervals in the lattice of (local) clones on an infinite set X, by exhibiting clones C_1, C_2, C_3 such that: (1) the interval [C_1, O] in the lattice of local clones is (as a lattice) isomorphic to {0,1,2, ...} under the divisibility relation, (2) the interval [C_2, O] in the lattice of local clones is isomorphic to the congruence lattice of an arbitrary semilattice, (3) the interval [C_3, O] in the lattice of all clones is isomorphic to the lattice of all fi...
Lattice dislocation in Si nanowires
Omar, M.S., E-mail: dr_m_s_omar@yahoo.co [Department of Physics, College of Science, University of Salahaddin, Arbil, Iraqi Kurdistan (Iraq); Taha, H.T. [Department of Physics, College of Science, University of Salahaddin, Arbil, Iraqi Kurdistan (Iraq)
2009-12-15
Modified formulas were used to calculate lattice thermal expansion, specific heat and Bulk modulus for Si nanowires with diameters of 115, 56, 37 and 22 nm. From these values and Gruneisen parameter taken from reference, mean lattice volumes were found to be as 20.03 A{sup 3} for the bulk and 23.63, 29.91, 34.69 and 40.46 A{sup 3} for Si nanowire diameters mentioned above, respectively. Their mean bonding length was calculated to be as 0.235 nm for the bulk and 0.248, 0.269, 0.282 and 0.297 nm for the nanowires diameter mentioned above, respectively. By dividing the nanowires diameter on the mean bonding length, number of layers per each nanowire size was found to be as 230, 104, 65 and 37 for the diameters mentioned above, respectively. Lattice dislocations in 22 nm diameter wire were found to be from 0.00324 nm for the 1st central lattice to 0.2579 nm for the last surface lattice. Such dislocation was smaller for larger wire diameters. Dislocation concentration found to change in Si nanowires according to the proportionalities of surface thickness to nanowire radius ratios.
Lattice magnetic analog of branched polymers, lattice animals and percolation
González, A E
1985-01-01
It is shown that the n = 0 limit of a magnetic system consisting of nq-component spins on a lattice, interacting with multibody forces and with an external magnetic field coupled to the first q components, gives us a correspondence with a system of branched polymers in a good solvent For certain specific values of the fugacities, a lattice animal point and a « quasi-percolation » point (in which only the exponents αP and νP can be extracted) are obtained.
Kaon fluctuations from lattice QCD
Noronha-Hostler, Jacquelyn; Gunther, Jana; Parotto, Paolo; Pasztor, Attila; Vazquez, Israel Portillo; Ratti, Claudia
2016-01-01
We show that it is possible to isolate a set of kaon fluctuations in lattice QCD. By means of the Hadron Resonance Gas (HRG) model, we calculate the actual kaon second-to-first fluctuation ratio, which receives contribution from primordial kaons and resonance decays, and show that it is very close to the one obtained for primordial kaons in the Boltzmann approximation. The latter only involves the strangeness and electric charge chemical potentials, which are functions of $T$ and $\\mu_B$ due to the experimental constraint on strangeness and electric charge, and can therefore be calculated on the lattice. This provides an unambiguous method to extract the kaon freeze-out temperature, by comparing the lattice results to the experimental values for the corresponding fluctuations.
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.
Phonons dispersions in auxetic lattices
Sparavigna, A [Dipartimento di Fisica, Politecnico di Torino, C.so Duca degli Abruzzi 24, Turin (Italy)
2007-12-15
The modes of vibrations in auxetic structures are studied, with models where the two-dimensional lattice is represented by a planar mesh with rod-like particles connected by strings. An auxetic membrane can be obtained modifying a honeycomb one, according to a model proposed by Evans et al. in 1991 and used to explain a negative elastic Poisson's ratio. This property means that auxetic materials have a lateral extension, instead to shrink, when they are stretched. The models here proposed with rod-like particles inserted in the structure have interesting behaviour of acoustic and rotational branches of phonon dispersions. Complete bandgaps of vibrations can be obtained for a proper choice of lattice coupling parameters and distribution of masses in the unit cell of the lattice.
Algebraic Lattices in QFT Renormalization
Borinsky, Michael
2016-04-01
The structure of overlapping subdivergences, which appear in the perturbative expansions of quantum field theory, is analyzed using algebraic lattice theory. It is shown that for specific QFTs the sets of subdivergences of Feynman diagrams form algebraic lattices. This class of QFTs includes the standard model. In kinematic renormalization schemes, in which tadpole diagrams vanish, these lattices are semimodular. This implies that the Hopf algebra of Feynman diagrams is graded by the coradical degree or equivalently that every maximal forest has the same length in the scope of BPHZ renormalization. As an application of this framework, a formula for the counter terms in zero-dimensional QFT is given together with some examples of the enumeration of primitive or skeleton diagrams.
Lattice QCD for nuclear physics
Meyer, Harvey
2015-01-01
With ever increasing computational resources and improvements in algorithms, new opportunities are emerging for lattice gauge theory to address key questions in strongly interacting systems, such as nuclear matter. Calculations today use dynamical gauge-field ensembles with degenerate light up/down quarks and the strange quark and it is possible now to consider including charm-quark degrees of freedom in the QCD vacuum. Pion masses and other sources of systematic error, such as finite-volume and discretization effects, are beginning to be quantified systematically. Altogether, an era of precision calculation has begun, and many new observables will be calculated at the new computational facilities. The aim of this set of lectures is to provide graduate students with a grounding in the application of lattice gauge theory methods to strongly interacting systems, and in particular to nuclear physics. A wide variety of topics are covered, including continuum field theory, lattice discretizations, hadron spect...
Nuclear Reactions from Lattice QCD
Briceño, Raúl A; Luu, Thomas C
2014-01-01
One of the overarching goals of nuclear physics is to rigorously compute properties of hadronic systems directly from the fundamental theory of strong interactions, Quantum Chromodynamics (QCD). In particular, the hope is to perform reliable calculations of nuclear reactions which will impact our understanding of environments that occur during big bang nucleosynthesis, the evolution of stars and supernovae, and within nuclear reactors and high energy/density facilities. Such calculations, being truly ab initio, would include all two-nucleon and three- nucleon (and higher) interactions in a consistent manner. Currently, lattice QCD provides the only reliable option for performing calculations of some of the low- energy hadronic observables. With the aim of bridging the gap between lattice QCD and nuclear many-body physics, the Institute for Nuclear Theory held a workshop on Nuclear Reactions from Lattice QCD on March 2013. In this review article, we report on the topics discussed in this workshop and the path ...
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...
Algebraic lattices in QFT renormalization
Borinsky, Michael
2015-01-01
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, the 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.
Nucleon structure from lattice QCD
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.
Nucleon structure from lattice QCD
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(a2) discretization effects.
Chiral symmetry on the lattice
The author reviews some of the difficulties associated with chiral symmetry in the context of a lattice regulator. The author discusses the structure of Wilson Fermions when the hopping parameter is in the vicinity of its critical value. Here one flavor contrasts sharply with the case of more, where a residual chiral symmetry survives anomalies. The author briefly discusses the surface mode approach, the use of mirror Fermions to cancel anomalies, and finally speculates on the problems with lattice versions of the standard model
Hadronic structure from the lattice
In recent years the investigation of hadron structure using lattice techniques has attracted growing attention. The computation of several important quantities has become feasible. Furthermore, theoretical developments as well as progress in algorithms and an increase in computing resources have contributed to a significantly improved control of systematic errors. In this article we give an overview on the work that has been carried out in the framework of the Hadron Physics I3 (I3HP) network ''Computational (lattice) hadron physics''. Here we not restrict ourselves to spin physics but focus on results for nucleon spectrum and structure from the QCDSF collaboration. (orig.)
Machines for lattice gauge theory
Mackenzie, P.B.
1989-05-01
The most promising approach to the solution of the theory of strong interactions is large scale numerical simulation using the techniques of lattice gauge theory. At the present time, computing requirements for convincing calculations of the properties of hadrons exceed the capabilities of even the most powerful commercial supercomputers. This has led to the development of massively parallel computers dedicated to lattice gauge theory. This talk will discuss the computing requirements behind these machines, and general features of the components and architectures of the half dozen major projects now in existence. 20 refs., 1 fig.
Machines for lattice gauge theory
The most promising approach to the solution of the theory of strong interactions is large scale numerical simulation using the techniques of lattice gauge theory. At the present time, computing requirements for convincing calculations of the properties of hadrons exceed the capabilities of even the most powerful commercial supercomputers. This has led to the development of massively parallel computers dedicated to lattice gauge theory. This talk will discuss the computing requirements behind these machines, and general features of the components and architectures of the half dozen major projects now in existence. 20 refs., 1 fig
Unconventional superconductivity in honeycomb lattice
P Sahebsara
2013-03-01
Full Text Available The possibility of symmetrical s-wave superconductivity in the honeycomb lattice is studied within a strongly correlated regime, using the Hubbard model. The superconducting order parameter is defined by introducing the Green function, which is obtained by calculating the density of the electrons . In this study showed that the superconducting order parameter appears in doping interval between 0 and 0.5, and x=0.25 is the optimum doping for the s-wave superconductivity in honeycomb lattice.
Chiral symmetry on the lattice
Creutz, M.
1994-11-01
The author reviews some of the difficulties associated with chiral symmetry in the context of a lattice regulator. The author discusses the structure of Wilson Fermions when the hopping parameter is in the vicinity of its critical value. Here one flavor contrasts sharply with the case of more, where a residual chiral symmetry survives anomalies. The author briefly discusses the surface mode approach, the use of mirror Fermions to cancel anomalies, and finally speculates on the problems with lattice versions of the standard model.
Graphene on graphene antidot lattices
Gregersen, Søren Schou; Pedersen, Jesper Goor; Power, Stephen;
2015-01-01
Graphene bilayer systems are known to exhibit a band gap when the layer symmetry is broken by applying a perpendicular electric field. The resulting band structure resembles that of a conventional semiconductor with a parabolic dispersion. Here, we introduce a bilayer graphene heterostructure......, where single-layer graphene is placed on top of another layer of graphene with a regular lattice of antidots. We dub this class of graphene systems GOAL: graphene on graphene antidot lattice. By varying the structure geometry, band-structure engineering can be performed to obtain linearly dispersing...
Nuclear Physics from Lattice QCD
William Detmold, Silas Beane, Konstantinos Orginos, Martin Savage
2011-01-01
We review recent progress toward establishing lattice Quantum Chromodynamics as a predictive calculational framework for nuclear physics. A survey of the current techniques that are used to extract low-energy hadronic scattering amplitudes and interactions is followed by a review of recent two-body and few-body calculations by the NPLQCD collaboration and others. An outline of the nuclear physics that is expected to be accomplished with Lattice QCD in the next decade, along with estimates of the required computational resources, is presented.
Hadron Interactions from lattice QCD
Aoki, Sinya
2016-01-01
We review our strategy to study hadron interactions from lattice QCD using newly proposed potential method. We first explain our strategy in the case of nuclear potentials and its application to nuclear physics. We then discuss the origin of the repulsive core, by adding strange quarks to the system. We also explore a possibility for H-dibaryon to exist in flavor SU(3) limit of lattice QCD. We conclude the paper with an application of our strategy to investigate the maximum mass of neutron stars.
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.
Modular equations and lattice sums
Rogers, Mathew; Yuttanan, Boonrod
2010-01-01
We highlight modular equations discovered by Somos and Ramanujan, and use them to prove new relations between lattice sums and hypergeometric functions. We also discuss progress towards solving Boyd's Mahler measure conjectures, and we conjecture a new formula for $L(E,2)$ of conductor 17 elliptic curves.
Method of manufacturing support lattice
The present invention concerns a method of manufacturing a support lattice for a reactor fuel assembly. A plurality of strip-like plates each having recesses formed at a predetermined longitudinal distance from the lateral end toward the lateral center intersect each other with the recesses being engaged to each other to assemble into a lattice-like configuration. Protrusions each extended from the lateral end faces are formed to the upper and the lower portions on the intersection for each of the strip-like plates and a window having a protrusion extended in the lateral direction is disposed in the central portion. Laser beams are condensed by a condenser lens so that the center line thereof agrees with the intersecting line of the strip-like plates. The condensed beams are irradiated vertically to the surface of the strip-like plates in the intermediate portion, to easily elevate temperature locally in the intermediate portion. Thus, a plurality of portions to be welded on the intersecting line of the support lattice can be welded all at once, to shorten the production step for the support lattices. (I.N.)
Confinement and lattice gauge theory
The motivation for formulating gauge theories on a lattice to study non-perturbative phenomena is reviewed, and recent progress supporting the compatibility of asymptotic freedom and quark confinement in the standard SU(3) Yang-Mills theory of the strong interaction is discussed
Nucleon structure using lattice QCD
Alexandrou, C.; Kallidonis, C. [Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; The Cyprus Institute, Nicosia (Cyprus). Computational-Based Science and technology Research Center; Constantinou, M.; Hatziyiannakou, K. [Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; Drach, V. [DESY Zeuthen (Germany). John von Neumann-Institut fuer Computing NIC; Jansen, K. [DESY Zeuthen (Germany). John von Neumann-Institut fuer Computing NIC; Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; Koutsou, G.; Vaquero, A. [The Cyprus Institute, Nicosia (Cyprus). Computational-Based Science and technology Research Center; Leontiou, T. [Frederick Univ, Nicosia (Cyprus). General Dept.
2013-03-15
A review of recent nucleon structure calculations within lattice QCD is presented. The nucleon excited states, the axial charge, the isovector momentum fraction and helicity distribution are discussed, assessing the methods applied for their study, including approaches to evaluate the disconnected contributions. Results on the spin carried by the quarks in the nucleon are also presented.
Differential geometry of group lattices
In a series of publications we developed ''differential geometry'' on discrete sets based on concepts of noncommutative geometry. In particular, it turned out that first-order differential calculi (over the algebra of functions) on a discrete set are in bijective correspondence with digraph structures where the vertices are given by the elements of the set. A particular class of digraphs are Cayley graphs, also known as group lattices. They are determined by a discrete group G and a finite subset S. There is a distinguished subclass of ''bicovariant'' Cayley graphs with the property ad(S)S subset of S. We explore the properties of differential calculi which arise from Cayley graphs via the above correspondence. The first-order calculi extend to higher orders and then allow us to introduce further differential geometric structures. Furthermore, we explore the properties of ''discrete'' vector fields which describe deterministic flows on group lattices. A Lie derivative with respect to a discrete vector field and an inner product with forms is defined. The Lie-Cartan identity then holds on all forms for a certain subclass of discrete vector fields. We develop elements of gauge theory and construct an analog of the lattice gauge theory (Yang-Mills) action on an arbitrary group lattice. Also linear connections are considered and a simple geometric interpretation of the torsion is established. By taking a quotient with respect to some subgroup of the discrete group, generalized differential calculi associated with so-called Schreier diagrams are obtained
Nuclear Lattice Simulations with EFT
This proceedings article is a summary of results from work done in collaboration with Bugra Borasoy and Thomas Schaefer. We study nuclear and neutron matter by combining chiral effective field theory with non-perturbative lattice methods. We present results for hot neutron matter at temperatures 20 to 40 MeV and densities below twice nuclear matter density
We review the formulation of field theory and statistical mechanics on a Poissonian random lattice. Topics discussed include random geometry, the construction of field equations for arbitrary spin, the free field spectrum and the question of localization illustrated in the one dimensional case
Orbital optical lattices with bosons
Kock, T.; Hippler, C.; Ewerbeck, A.; Hemmerich, A.
2016-02-01
This article provides a synopsis of our recent experimental work exploring Bose-Einstein condensation in metastable higher Bloch bands of optical lattices. Bipartite lattice geometries have allowed us to implement appropriate band structures, which meet three basic requirements: the existence of metastable excited states sufficiently protected from collisional band relaxation, a mechanism to excite the atoms initially prepared in the lowest band with moderate entropy increase, and the possibility of cross-dimensional tunneling dynamics, necessary to establish coherence along all lattice axes. A variety of bands can be selectively populated and a subsequent thermalization process leads to the formation of a condensate in the lowest energy state of the chosen band. As examples the 2nd, 4th and 7th bands in a bipartite square lattice are discussed. The geometry of the 2nd and 7th bands can be tuned such that two inequivalent energetically degenerate energy minima arise at the X ±-points at the edge of the 1st Brillouin zone. In this case even a small interaction energy is sufficient to lock the phase between the two condensation points such that a complex-valued chiral superfluid order parameter can emerge, which breaks time reversal symmetry. In the 4th band a condensate can be formed at the Γ-point in the center of the 1st Brillouin zone, which can be used to explore topologically protected band touching points. The new techniques to access orbital degrees of freedom in higher bands greatly extend the class of many-body scenarios that can be explored with bosons in optical lattices.
On the Convergence of Monotone Lattice Matrices
Jing Jiang; Lan Shu; Xin’an Tian
2013-01-01
Since lattice matrices are useful tools in various domains like automata theory, design of switching circuits, logic of binary relations, medical diagnosis, markov chains, computer network, traffic control and so on, the study of the properties of lattice matrices is valuable. A lattice matrix A is called monotone if A is transitive or A is monotone increasing. In this paper, the convergence of monotone matrices is studied. The results obtained here develop the corresponding ones on lattice m...
Counting Lattice Animals in High Dimensions
Luther, Sebastian; Mertens, Stephan
2011-01-01
We present an implementation of Redelemeier's algorithm for the enumeration of lattice animals in high dimensional lattices. The implementation is lean and fast enough to allow us to extend the existing tables of animal counts, perimeter polynomials and series expansion coefficients in $d$-dimensional hypercubic lattices for $3 \\leq d\\leq 10$. From the data we compute formulas for perimeter polynomials for lattice animals of size $n\\leq 11$ in arbitrary dimension $d$. When amended by combinat...
Remarks on left-handed lattice fermions
Gattringer, Christof; Pak, Markus
2007-01-01
We study whether applying lattice projectors on a vector-like Ginsparg-Wilson Dirac operator is the only way to construct left-handed lattice fermions. Using RG transformations we derive an equation for the generating functional on the lattice, obtained by blocking from the continuum. We analyze how symmetries of the continuum theory manifest themselves in this lattice generating functional and how anomalies emerge. The formalism is applied to left-handed continuum fermions and we derive two ...
Feynman diagrams and their algebraic lattices
Borinsky, Michael
2015-01-01
We present the lattice structure of Feynman diagram renormalization in physical QFTs from the viewpoint of Dyson-Schwinger-Equations and the core Hopf algebra of Feynman diagrams. The lattice structure encapsules the nestedness of diagrams. This structure can be used to give explicit expressions for the counterterms in zero-dimensional QFTs using the lattice-Moebius function. Different applications for the tadpole-free quotient, in which all appearing elements correspond to semimodular lattices, are discussed.
Rootless pairs of $EE_8$-lattices
Griess, Jr., Robert L.; lam, Ching Hung
2008-01-01
We describe a classification of pairs $M, N$ of lattices isometric to $EE_8:=\\sqrt 2 E_8$ such that the lattice $M + N$ is integral and rootless and such that the dihedral group associated to them has order at most 12. It turns out that most of these pairs may be embedded in the Leech lattice. Complete proofs will appear in another article. This theory of integral lattices has connections to vertex operator algebra theory and moonshine.
Lattice QCD with dynamical chirally improved quarks
Full text: We simulate lattice QCD with two flavors of chirally improved dynamical (sea) quarks. The chirally improved lattice action allows to address some of the questions concerning chiral symmetry in lattice QCD.We discuss the status and prospects of our simulations as well as recent results. (author)
Trees, Animals, and Percolation on Hyperbolic Lattices
Madras, Neal; Wu, C.
2010-01-01
We study lattice trees, lattice animals, and percolation on non-Euclidean lattices that correspond to regular tessellations of two- and three-dimensional hyperbolic space. We prove that critical exponents of these models take on their mean field values. Our methods are mainly combinatorial and geometric.
Lattice QCD. A critical status report
The substantial progress that has been achieved in lattice QCD in the last years is pointed out. I compare the simulation cost and systematic effects of several lattice QCD formulations and discuss a number of topics such as lattice spacing scaling, applications of chiral perturbation theory, non-perturbative renormalization and finite volume effects. Additionally, the importance of demonstrating universality is emphasized. (orig.)
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.
Clar sextets in square graphene antidot lattices
Petersen, Rene; Pedersen, Thomas Garm; Jauho, Antti-Pekka
2011-01-01
A periodic array of holes transforms graphene from a semimetal into a semiconductor with a band gap tuneable by varying the parameters of the lattice. In earlier work only hexagonal lattices have been treated. Using atomistic models we here investigate the size of the band gap of a square lattice...
Spatiotemporal complexity in coupled map lattices
Some spatiotemporal patterns of couple map lattices are presented. The chaotic kink-like motions are shown for the phase motion of the coupled circle lattices. An extension of the couple map lattice approach to Hamiltonian dynamics is briefly reported. An attempt to characterize the high-dimensional attractor by the extension of the correlation dimension is discussed. (author)
The weighted lattice polynomials as aggregation functions
Marichal, Jean-Luc
2006-01-01
We define the concept of weighted lattice polynomials as lattice polynomials constructed from both variables and parameters. We provide equivalent forms of these functions in an arbitrary bounded distributive lattice. We also show that these functions include the class of discrete Sugeno integrals and that they are characterized by a remarkable median based decomposition formula.
Possible lattice organs in Cretaceous Thylacocephala
Lange, Sven; Schram, Frederick R.
2002-01-01
Structures, reminiscent of the lattice organs in thecostracan crustaceans, are described from the carapace cuticle of Cretaceous thylacocephalans. The new lattice organ like structures occur in pairs along the dorsal midline. While these have a similar outline to true lattice organs, they seem to la
Review of lattice studies of resonances
Mohler, Daniel
2012-01-01
I review recent progress in extracting resonance parameters using lattice field theory, with an emphasis on determining hadron resonances from lattice quantum chromodynamics. Until recently, the \\rho-meson channel was the only one considered, while, during the last year, several resonant channels have been investigated for the first time. Recent lattice results for scattering phase shifts in resonant channels are presented.
Lattice gaugefixing and other optics in lattice gauge theory
Yee, Ken
1992-06-01
We present results from four projects. In the first, quark and gluon propagators and effective masses and {Delta}I = 1/2 Rule operator matching coefficients are computed numerically in gaugefixed lattice QCD. In the second, the same quantities are evaluated analytically in the strong coupling, N {yields} {infinity} limit. In the third project, the Schwinger model is studied in covariant gauges, where we show that the effective electron mass varies with the gauge parameter and that longitudinal gaugefixing ambiguities affect operator product expansion coefficients (analogous to {Delta}I = 1/2 Rule matching coefficients) determined by matching gauge variant matrix elements. However, we find that matching coefficients even if shifted by the unphysical modes are {xi} invariant. In the fourth project, we show that the strong coupling parallelogram lattice Schwinger model as a different thermodynamic limit than the weak coupling continuum limit. As a function of lattice skewness angle these models span the {Delta} = {minus}1 critical line of 6-vertex models which, in turn, have been identified as c = 1 conformal field theories.
Lattice gaugefixing and other optics in lattice gauge theory
We present results from four projects. In the first, quark and gluon propagators and effective masses and ΔI = 1/2 Rule operator matching coefficients are computed numerically in gaugefixed lattice QCD. In the second, the same quantities are evaluated analytically in the strong coupling, N → ∞ limit. In the third project, the Schwinger model is studied in covariant gauges, where we show that the effective electron mass varies with the gauge parameter and that longitudinal gaugefixing ambiguities affect operator product expansion coefficients (analogous to ΔI = 1/2 Rule matching coefficients) determined by matching gauge variant matrix elements. However, we find that matching coefficients even if shifted by the unphysical modes are ξ invariant. In the fourth project, we show that the strong coupling parallelogram lattice Schwinger model as a different thermodynamic limit than the weak coupling continuum limit. As a function of lattice skewness angle these models span the Δ = -1 critical line of 6-vertex models which, in turn, have been identified as c = 1 conformal field theories
Lattice inputs to Flavor Physics
Della Morte, Michele
2015-01-01
We review recent lattice results for quark masses and low-energy hadronic parameters relevant for flavor physics. We do that by describing the FLAG initiative, with emphasis on its scope and rating criteria. The emerging picture is that while for light quantities a large number of computations using different approaches exist, and this increases the overall confidence on the final averages/estimates, in the heavy-light case the field is less advanced and, with the exception of decay constants, only a few computations are available. The precision reached for the light quantities is such that electromagnetic (EM) corrections, beyond the point-like approximation, are becoming relevant. We discuss recent computations of the spectrum based on direct simulations of QED+QCD. We also present theoretical developments for including EM effects in leptonic decays. We conclude describing recent results for the $K \\to \\pi \\pi$ transition amplitudes and prospects for tackling hadronic decays on the lattice.
Innovations in lattice QCD algorithms
Lattice QCD calculations demand a substantial amount of computing power in order to achieve the high precision results needed to better understand the nature of strong interactions, assist experiment to discover new physics, and predict the behavior of a diverse set of physical systems ranging from the proton itself to astrophysical objects such as neutron stars. However, computer power alone is clearly not enough to tackle the calculations we need to be doing today. A steady stream of recent algorithmic developments has made an important impact on the kinds of calculations we can currently perform. In this talk I am reviewing these algorithms and their impact on the nature of lattice QCD calculations performed today
Superconductivity in Anderson lattice model
We study the superconducting instabilities generated by the inclusion in the Anderson lattice model of a density-density attractive potential between correlated electrons on nearest-neighbouring sites. Using a description of the normal phase based on a perturbative expansion around the atomic limit, we treat the attractive potential in the broken symmetry Hartree-Fock scheme and analyze which of the possible symmetries of the superconducting order parameter leads to the highest possible transition temperature in the case of a two-dimensional square lattice. For values of the on-site f-repulsion large compared to the hopping amplitude, a suppression of any possible superconducting phase occurs, regardless of the of the symmetry of the order parameter. (author)
Innovations in Lattice QCD Algorithms
Lattice QCD calculations demand a substantial amount of computing power in order to achieve the high precision results needed to better understand the nature of strong interactions, assist experiment to discover new physics, and predict the behavior of a diverse set of physical systems ranging from the proton itself to astrophysical objects such as neutron stars. However, computer power alone is clearly not enough to tackle the calculations we need to be doing today. A steady stream of recent algorithmic developments has made an important impact on the kinds of calculations we can currently perform. In this talk I am reviewing these algorithms and their impact on the nature of lattice QCD calculations performed today
Fractional random walk lattice dynamics
Michelitsch, Thomas; Riascos, Alejandro Perez; Nowakowski, Andrzeij; Nicolleau, Franck
2016-01-01
We analyze time-discrete and continuous `fractional' random walks on undirected regular networks with special focus on cubic periodic lattices in $n=1,2,3,..$ dimensions.The fractional random walk dynamics is governed by a master equation involving {\\it fractional powers of Laplacian matrices $L^{\\frac{\\alpha}{2}}$}where $\\alpha=2$ recovers the normal walk.First we demonstrate thatthe interval $0\\textless{}\\alpha\\leq 2$ is admissible for the fractional random walk. We derive analytical expressions for fractional transition matrix and closely related the average return probabilities. We further obtain thefundamental matrix $Z^{(\\alpha)}$, and the mean relaxation time (Kemeny constant) for the fractional random walk.The representation for the fundamental matrix $Z^{(\\alpha)}$ relates fractional random walks with normal random walks.We show that the fractional transition matrix elements exihibit for large cubic $n$-dimensional lattices a power law decay of an $n$-dimensional infinite spaceRiesz fractional deriva...
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
Qcd Thermodynamics On A Lattice
Levkova, L A
2004-01-01
Numerical simulations of full QCD on anisotropic lattices provide a convenient way to study QCD thermodynamics with fixed physics scales and reduced lattice spacing errors. We report results from calculations with two flavors of dynamical staggered fermions, where all bare parameters and the renormalized anisotropy are kept constant and the temperature is changed in small steps by varying only the number of time slices. Including results from zero- temperature scale setting simulations, which determine the Karsch coefficients, allows for the calculation of the Equation of State at finite temperatures. We also report on studies of the chiral properties of dynamical domain-wall fermions combined with the DBW2 gauge action for different gauge couplings and fermion masses. For quenched theories, the DBW2 action gives a residual chiral symmetry breaking much smaller than what was found with more traditional choices for the gauge action. Our goal is to investigate the possibilities which this and further improvemen...
Lattice dynamics of strontium tungstate
Prabhatasree Goel; R Mittal; S L Chaplot; A K Tyagi
2008-11-01
We report here measurements of the phonon density of states and the lattice dynamics calculations of strontium tungstate (SrWO4). At ambient conditions this compound crystallizes to a body-centred tetragonal unit cell (space group I41/a) called scheelite structure. We have developed transferable interatomic potentials to study the lattice dynamics of this class of compounds. The model parameters have been fitted with respect to the experimentally available Raman and infra-red frequencies and the equilibrium unit cell parameters. Inelastic neutron scattering measurements have been carried out in the triple-axis spectrometer at Dhruva reactor. The measured phonon density of states is in good agreement with the theoretical calculations, thus validating the inter-atomic potential developed.
Entropy favours open colloidal lattices
Mao, Xiaoming; Chen, Qian; Granick, Steve
2013-03-01
Burgeoning experimental and simulation activity seeks to understand the existence of self-assembled colloidal structures that are not close-packed. Here we describe an analytical theory based on lattice dynamics and supported by experiments that reveals the fundamental role entropy can play in stabilizing open lattices. The entropy we consider is associated with the rotational and vibrational modes unique to colloids interacting through extended attractive patches. The theory makes predictions of the implied temperature, pressure and patch-size dependence of the phase diagram of open and close-packed structures. More generally, it provides guidance for the conditions at which targeted patchy colloidal assemblies in two and three dimensions are stable, thus overcoming the difficulty in exploring by experiment or simulation the full range of conceivable parameters.
Lattice dynamics of lithium oxide
Prabhatasree Goel; N Choudhury; S L Chaplot
2004-08-01
Li2O finds several important technological applications, as it is used in solid-state batteries, can be used as a blanket breeding material in nuclear fusion reactors, etc. Li2O exhibits a fast ion phase, characterized by a thermally induced dynamic disorder in the anionic sub-lattice of Li+, at elevated temperatures around 1200 K. We have carried out lattice-dynamical calculations of Li2O using a shell model in the quasi-harmonic approximation. The calculated phonon frequencies are in excellent agreement with the reported inelastic neutron scattering data. Thermal expansion, specific heat, elastic constants and equation of state have also been calculated which are in good agreement with the available experimental data.
Innovations in Lattice QCD Algorithms
Konstantinos Orginos
2006-06-25
Lattice QCD calculations demand a substantial amount of computing power in order to achieve the high precision results needed to better understand the nature of strong interactions, assist experiment to discover new physics, and predict the behavior of a diverse set of physical systems ranging from the proton itself to astrophysical objects such as neutron stars. However, computer power alone is clearly not enough to tackle the calculations we need to be doing today. A steady stream of recent algorithmic developments has made an important impact on the kinds of calculations we can currently perform. In this talk I am reviewing these algorithms and their impact on the nature of lattice QCD calculations performed today.
Symplectic maps for accelerator lattices
We describe a method for numerical construction of a symplectic map for particle propagation in a general accelerator lattice. The generating function of the map is obtained by integrating the Hamilton-Jacobi equation as an initial-value problem on a finite time interval. Given the generating function, the map is put in explicit form by means of a Fourier inversion technique. We give an example which suggests that the method has promise. 9 refs., 9 figs
Hadron Physics from Lattice QCD
Bietenholz, Wolfgang
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.
Lattice engineering technology and applications
Wang, Shumin
2012-01-01
This book contains comprehensive reviews of different technologies to harness lattice mismatch in semiconductor heterostructures and their applications in electronic and optoelectronic devices. While the book is a bit focused on metamorphic epitaxial growth, it also includes other methods like compliant substrate, selective area growth, wafer bonding and heterostructure nanowires etc. Basic knowledge on dislocations in semiconductors and innovative methods to eliminate threading dislocations are provided, and successful device applications are reviewed. It covers a variety of important semicon
Spin qubits in antidot lattices
Pedersen, Jesper Goor; Flindt, Christian; Mortensen, Niels Asger;
2008-01-01
We suggest and study designed defects in an otherwise periodic potential modulation of a two-dimensional electron gas as an alternative approach to electron spin based quantum information processing in the solid-state using conventional gate-defined quantum dots. We calculate the band structure and...... electron transport between distant defect states in the lattice, and for a tunnel coupling of neighboring defect states with corresponding electrostatically controllable exchange coupling between different electron spins....
Gauge invariance and lattice monopoles
The number and the location of monopoles in Lattice configurations depend on the choice of the gauge, in contrast to the obvious requirement that monopoles, as physical objects, have a gauge-invariant status. It is proved, starting from non-abelian Bianchi identities, that monopoles are indeed gauge-invariant: the technique used to detect them has instead an efficiency which depends on the choice of the abelian projection, in a known and well understood way.
Screening in graphene antidot lattices
Schultz, Marco Haller; Jauho, A. P.; Pedersen, T. G.
2011-01-01
We compute the dynamical polarization function for a graphene antidot lattice in the random-phase approximation. The computed polarization functions display a much more complicated structure than what is found for pristine graphene (even when evaluated beyond the Dirac-cone approximation...... the plasmon dispersion law and find an approximate square-root dependence with a suppressed plasmon frequency as compared to doped graphene. The plasmon dispersion is nearly isotropic and the developed approximation schemes agree well with the full calculation....
Harmonic Lattice Dynamics of Germanium
The phonon dispersion relations of the Δ-, Λ-, and Σ-directions of germanium at 80 K are analysed in terms of current harmonic lattice dynamical models. On the basis of this experience, a new model is proposed which gives a unified account of the strong points of the previous models. The principal elements of the presented theory are quasiparticle bond charges combined with a valence force field
The principles of scale setting in lattice QCD as well as the advantages and disadvantages of various commonly used scales are discussed. After listing criteria for good scales, I concentrate on the main presently used ones with an emphasis on scales derived from the Yang-Mills gradient flow. For these I discuss discretisation errors, statistical precision and mass effects. A short review on numerical results also brings me to an unpleasant disagreement which remains to be explained.
Lattice defects in lithium tantalate
Lithium tantalate single crystals are used for piezoelectric devices. The lattice defects of this structure and their possible role on piezoelectric performances are investigated. Synthetic crystals are grown by a Czochralski process. To get homogeneous material it is necessary to start from a non-equimolar mixture of Li2O and Ta2O5 powders leading to a congruent melt. The resulting crystals are non-stoichiometric with an atomic ratio [Li]/[Li + Ta] ∼ 48%, and this induces a first kind of lattice defects: the point defects associated to this non-stoichiometry. When cooled down from high temperature, LiTaO3 suffers a second-order phase transition from a paraelectric phase R3-barc to a ferroelectric phase R3c which is the stable phase at room temperature. A second kind of lattice defects (ferroelectric domains) is generally nucleated at the transition. These defects constitute a poison for piezoelectric applications because the polarization vector c is reversed. One can in principle prevent their occurrence by a poling process (cooling under a static electric field). Dislocations and twins are other as-grown lattice defects; they can also be introduced by the usual machining processes (sawing, grinding ...). Furthermore because of the very high values of the piezoelectric constants, the stress field of the dislocations can induce ferroelectric domains around them, even at room temperature, and such domains cannot be removed by poling. The experimental techniques used are infrared spectroscopy and differential scanning calorimetry for the characterization of point defects and non-stoichiometry; chemical etching and transmission electron microscopy for the characterization of dislocations and twins. As-grown defects are studied and the ones introduced by machining; these latter ones are simulated by scratching and by plastic deformation under confining pressure. A few constant strain rate tests are also performed in the temperature range 20 to 700 0C. The subsequent
Sommer, Rainer [DESY, Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2014-02-15
The principles of scale setting in lattice QCD as well as the advantages and disadvantages of various commonly used scales are discussed. After listing criteria for good scales, I concentrate on the main presently used ones with an emphasis on scales derived from the Yang-Mills gradient flow. For these I discuss discretisation errors, statistical precision and mass effects. A short review on numerical results also brings me to an unpleasant disagreement which remains to be explained.
Anharmonic parametric excitation in optical lattices
Jauregui, R; Roati, G; Modugno, G
2001-01-01
We study both experimentally and theoretically the losses induced by parametric excitation in far-off-resonance optical lattices. The atoms confined in a 1D sinusoidal lattice present an excitation spectrum and dynamics substantially different from those expected for a harmonic potential. We develop a model based on the actual atomic Hamiltonian in the lattice and we introduce semiempirically a broadening of the width of lattice energy bands which can physically arise from inhomogeneities and fluctuations of the lattice, and also from atomic collisions. The position and strength of the parametric resonances and the evolution of the number of trapped atoms are satisfactorily described by our model.
Counting lattice animals in high dimensions
Luther, Sebastian; Mertens, Stephan
2011-09-01
We present an implementation of Redelemeier's algorithm for the enumeration of lattice animals in high-dimensional lattices. The implementation is lean and fast enough to allow us to extend the existing tables of animal counts, perimeter polynomials and series expansion coefficients in d-dimensional hypercubic lattices for 3 lattice animals of size n lattice animals of size n <= 14 and arbitrary d. We also use the enumeration data to compute numerical estimates for growth rates and exponents in high dimensions that agree very well with Monte Carlo simulations and recent predictions from field theory.
Present status of lattice gauge theories
The lattice formulation of the quark-gluon theory of strong interactions is outlined. No matter a version of the lattice gauge theory the ''string bit'' representation is used to solve the problem of the strong coupling expansion. A brief discussion is given of some major problems arising for: (1) large coupling and large lattice spacing, (2) the crossover from the gluon representation at small distances to the string representation at large ones, (3) constructing the strong coupling ground state at each lattice site independently, and (4) formulating the free quark theory on the lattice
A Lattice-Gas Model of Microemulsions
Boghosian, B M; Emerton, A N; Boghosian, Bruce M.; Coveney, Peter V.; Emerton, Andrew N.
1995-01-01
We develop a lattice gas model for the nonequilibrium dynamics of microemulsions. Our model is based on the immiscible lattice gas of Rothman and Keller, which we reformulate using a microscopic, particulate description so as to permit generalisation to more complicated interactions, and on the prescription of Chan and Liang for introducing such interparticle interactions into lattice gas dynamics. We present the results of simulations to demonstrate that our model exhibits the correct phenomenology, and we contrast it with both equilibrium lattice models of microemulsions, and to other lattice gas models.
Varieties of lattices with geometric descriptions
Santocanale, Luigi
2011-01-01
A lattice L is spatial if every element of L is a join of completely join-irreducible elements of L (points), and strongly spatial if it is spatial and the minimal coverings of completely join-irreducible elements are well-behaved. Herrmann, Pickering, and Roddy proved in 1994 that every modular lattice can be embedded, within its variety, into an algebraic and spatial lattice. We extend this result to n-distributive lattices, for fixed n. We deduce that the variety of all n-distributive lattices is generated by its finite members, thus it has a decidable word problem. We prove that every modular (resp., n-distributive) lattice embeds within its variety into some strongly spatial lattice. Every lattice which is either algebraic modular spatial or bi-algebraic is strongly spatial. We also construct a lattice that cannot be embedded, within its variety, into any algebraic and spatial lattice. This lattice has a least and a largest element, and it generates a locally finite variety. Furthermore, it is join-semid...
The Algebraic Properties of Concept Lattice
KaisheQu; JiyeLiang; JunhongWang; ZhongzhiShi
2004-01-01
Concept lattice is a powerful tool for data analysis. It has been applied widely to machine learning, knowledge discovery and software engineering and so on. Some aspects of concept lattice have been studied widely such as building lattice and rules extraction, as for its algebraic properties, there has not been discussed systematically. The paper suggests a binary operation between the elements for the set of all concepts in formal context. This turns the concept lattice in general significance into those with operators. We also proved that the concept lattice is a lattice in algebraic significance and studied its algebraic properties.These results provided theoretical foundation and a new method for further study of concept lattice.
Diagonal lattices and rootless $EE_8$ pairs
Griess, Robert L; Lam, Ching Hung
2011-01-01
Let E be an integral lattice. We first discuss some general properties of an SDC lattice, i.e., a sum of two diagonal copies of E in E \\bot E. In particular, we show that its group of isometries contains a wreath product. We then specialize this study to the case of E = E_8 and provide a new and fairly natural model for those rootless lattices which are sums of a pair of EE_8-lattices. This family of lattices was classified in [7]. We prove that this set of isometry types is in bijection with the set of conjugacy classes of rootless elements in the isometry group O(E_8), i.e., those h \\in O(E_8) such that the sublattice (h - 1)E_8 contains no roots. Finally, our model gives new embeddings of several of these lattices in the Leech lattice.
Properties of complements in the lattice of convergence structures
C. V. Riecke
1980-01-01
Relative complements and differences are investigated for several convergence structure lattices, especially the lattices of Kent convergence structures and the lattice of pretopologies. Convergence space properties preserved by relative complementation are studied. Mappings of some convergence structure lattices into related lattices of lattice homomorphisms are considered.
Attribute Extended Algorithm of Lattice-Valued Concept Lattice Based on Congener Formal Context
Li Yang
2014-01-01
Full Text Available This paper is the continuation of our research work about lattice-valued concept lattice based on lattice implication algebra. For a better application of lattice-valued concept lattice into data distributed storage and parallel processing, it is necessary to research attribute extended algorithm based on congener formal context. The definitions of attribute extended formal context and congener formal context are proposed. On condition that the extent set stays invariable when the new attribute is increased, the necessary and sufficient conditions of forming attribute values are researched. Based on these conditions, the algorithms of generating lattice-valued congener formal context and establishing concept lattice are given, by which we can provide a useful basis for union algorithm and constructing algorithm of lattice-valued concept lattices in distributed and parallel system.
Unbiased sampling of lattice Hamilton path ensembles
Mansfield, Marc L.
2006-10-01
Hamilton paths, or Hamiltonian paths, are walks on a lattice which visit each site exactly once. They have been proposed as models of globular proteins and of compact polymers. A previously published algorithm [Mansfield, Macromolecules 27, 5924 (1994)] for sampling Hamilton paths on simple square and simple cubic lattices is tested for bias and for efficiency. Because the algorithm is a Metropolis Monte Carlo technique obviously satisfying detailed balance, we need only demonstrate ergodicity to ensure unbiased sampling. Two different tests for ergodicity (exact enumeration on small lattices, nonexhaustive enumeration on larger lattices) demonstrate ergodicity unequivocally for small lattices and provide strong support for ergodicity on larger lattices. Two other sampling algorithms [Ramakrishnan et al., J. Chem. Phys. 103, 7592 (1995); Lua et al., Polymer 45, 717 (2004)] are both known to produce biases on both 2×2×2 and 3×3×3 lattices, but it is shown here that the current algorithm gives unbiased sampling on these same lattices. Successive Hamilton paths are strongly correlated, so that many iterations are required between statistically independent samples. Rules for estimating the number of iterations needed to dissipate these correlations are given. However, the iteration time is so fast that the efficiency is still very good except on extremely large lattices. For example, even on lattices of total size 10×10×10 we are able to generate tens of thousands of uncorrelated Hamilton paths per hour of CPU time.
Lattice dynamics and lattice thermal conductivity of thorium dicarbide
Liao, Zongmeng [Institute of Theoretical Physics and Department of Physics, East China Normal University, Shanghai 200241 (China); Huai, Ping, E-mail: huaiping@sinap.ac.cn [Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800 (China); Qiu, Wujie [Institute of Theoretical Physics and Department of Physics, East China Normal University, Shanghai 200241 (China); State Key Laboratory of High Performance Ceramics and Superfine Microstructure, Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai 200050 (China); Ke, Xuezhi, E-mail: xzke@phy.ecnu.edu.cn [Institute of Theoretical Physics and Department of Physics, East China Normal University, Shanghai 200241 (China); Zhang, Wenqing [State Key Laboratory of High Performance Ceramics and Superfine Microstructure, Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai 200050 (China); Zhu, Zhiyuan [Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800 (China)
2014-11-15
The elastic and thermodynamic properties of ThC{sub 2} with a monoclinic symmetry have been studied by means of density functional theory and direct force-constant method. The calculated properties including the thermal expansion, the heat capacity and the elastic constants are in a good agreement with experiment. Our results show that the vibrational property of the C{sub 2} dimer in ThC{sub 2} is similar to that of a free standing C{sub 2} dimer. This indicates that the C{sub 2} dimer in ThC{sub 2} is not strongly bonded to Th atoms. The lattice thermal conductivity for ThC{sub 2} was calculated by means of the Debye–Callaway model. As a comparison, the conductivity of ThC was also calculated. Our results show that the ThC and ThC{sub 2} contributions of the lattice thermal conductivity to the total conductivity are 29% and 17%, respectively.
Unconventional superconductivity in honeycomb lattice
P. Sahebsara; R Mohammadi
2013-01-01
The possibility of symmetrical s-wave superconductivity in the honeycomb lattice is studied within a strongly correlated regime, using the Hubbard model. The superconducting order parameter is defined by introducing the Green function, which is obtained by calculating the density of the electrons . In this study showed that the superconducting order parameter appears in doping interval between 0 and 0.5, and x=0.25 is the optimum doping for the s-wave superconductivity in honeycomb latt...
CANDU lattice uncertainties during burnup
Uncertainties associated with fundamental nuclear data accompany evaluated nuclear data libraries in the form of covariance matrices. As nuclear data are important parameters in reactor physics calculations, any associated uncertainty causes a loss of confidence in the calculation results. The quantification of output uncertainties is necessary to adequately establish safety margins of nuclear facilities. In this work, microscopic cross-section has been propagated through lattice burnup calculations applied to a generic CANDU® model. It was found that substantial uncertainty emerges during burnup even when fission yield fraction and decay rate uncertainties are neglected. (author)
Blocking transformations for lattice fermions
We introduce a class of chiral-symmetry breaking real space renormalization transformations, intended for renormalization group studies of lattice theories involving fermions. In massless free fermion theory (for a sensible choice of a certain parameter of the transformation) the scheme yields an acceptably local, Wilson-fermion-like fixed point action. We attempt to calculate a certain critical exponent in the two-flavour Schwinger model via a cumulant expansion based on our scheme. Possibilities for Monte Carlo renormalization group calculations are briefly mentioned. (orig.)
Solitary waves on tensegrity lattices
Fraternali, F.; Senatore, L.; Daraio, C.
2012-06-01
We study the dynamics of lattices formed by masses connected through tensegrity prisms. By employing analytic and numerical arguments, we show that such structures support two limit dynamic regimes controlled by the prisms' properties: (i) in the low-energy (sonic) regime the system supports the formation and propagation of solitary waves which exhibit sech2 shape and (ii) in the high-energy (ultrasonic) regime the system supports atomic-scale localization. Such peculiar features found in periodic arrays of tensegrity structures suggest their use for the creation of new composite materials (here called "tensegrity materials") of potential interest for applications in impact absorption, energy localization and in new acoustic devices.
Beautiful Baryons from Lattice QCD
Alexandrou, C.; Borrelli, A; Güsken, S.; Jegerlehner, F.; K. Schilling; Siegert, G.; Sommer, R
1994-01-01
We perform a lattice study of heavy baryons, containing one ($\\Lambda_b$) or two $b$-quarks ($\\Xi_b$). Using the quenched approximation we obtain for the mass of $\\Lambda_b$ $$ M_{\\Lambda_b}= 5.728 \\pm 0.144 \\pm 0.018 {\\rm GeV}.$$ The mass splitting between the $\\Lambda_b$ and the B-meson is found to increase by about 20\\% if the light quark mass is varied from the chiral limit to the strange quark mass.
The lattice dynamics of imidazole
The lattice dynamics of imidazole have been investigated. To this end dispersion curves have been determined at 10 K by inelastic coherent neutron scattering. RAMAN measurements have been done to investigate identical gamma - point modes. The combination of extinction rules for RAMAN - and neutron scattering leads to the symmetry assignment of identical gamma - point modes. The experiment yields a force constant of the streching vibration of the hydrogen bond of 0.33 mdyn/A. A force model has been developed to describe the intermolecular atom - atom Interactions in imidazole. (orig./BHO)
Gluonic interactions from lattice QCD
Gluonic interactions are studied within lattice QCD. Hybrid mesons in which the gluonic field is excited into a higher energy state are evidenced from studying the static source potential and discovering that there is a spectrum of such potentials V/sub i/(R) unlike the unique potential obtained in electrodynamics. Results of the string tension K, namely (V(R+a)-V(R))/a, have been reanalyzed and using variational methods excellent consistency was achieved and is presented as a plot of V(R) versus R. Potentials corresponding to excited states of the gluonic field are obtained as main new results
Lattice Stern-Gerlach experiment
Luschevskaya, E V; Teryaev, O V
2016-01-01
We investigate the dependence of ground state energies of charged vector $\\rho$ and $K^{*}$ mesons on the value of magnetic field in the $SU(3)$ lattice gauge theory. It has been shown that the energy of a vector particle strongly depends on its spin projection on the field axis, and the magnetic dypole polarizability and hyperpolarizabilities give a large contribution to the meson energy at large fields. We calculate the g-factor of $\\rho^{\\pm}$ and $K^{*\\pm}$ mesons. Tensor of the dypole magnetic polarizability of the charged $\\rho$ meson at rest has been found.
Counting arithmetic lattices and surfaces
Belolipetsky, Mikhail; Gelander, Tsachik; Lubotzky, Alexander; Shalev, Aner
2010-01-01
We give estimates on the number $AL_H(x)$ of arithmetic lattices $\\Gamma$ of covolume at most $x$ in a simple Lie group $H$. In particular, we obtain a first concrete estimate on the number of arithmetic 3-manifolds of volume at most $x$. Our main result is for the classical case $H=PSL(2,R)$ where we compute the limit of $\\log AL_H(x) / x\\log x$ when $x\\to\\infty$. The proofs use several different techniques: geometric (bounding the number of generators of $\\Gamma$ as a function of its covolu...
Performance comparisons of low emittance lattices
The results of a performance analysis of four low emittance electron storage ring lattices provided to the authors by various members of the Lattice Working Group is presented. Altogether, four lattices were investigated. The beam energies of the four lattices are, respectively, 1.1, 2, 3, 4 GeV). A brief summary of the lattice parameters relevant to this study is given. The performance issues studied include an estimation of the longitudinal emittance expected for each lattice based on the effects of the longitudinal microwave instability, an estimation of the transverse emittance growth of the (required) dense bunches under the influence of intrabeam scattering (IBS), and an estimate of the Touschek lifetime. The analysis described here has been carried out with the LBL accelerator physics code ZAP
Working Group Report: Lattice Field Theory
Blum, T.; et al.,
2013-10-22
This is the report of the Computing Frontier working group on Lattice Field Theory prepared for the proceedings of the 2013 Community Summer Study ("Snowmass"). We present the future computing needs and plans of the U.S. lattice gauge theory community and argue that continued support of the U.S. (and worldwide) lattice-QCD effort is essential to fully capitalize on the enormous investment in the high-energy physics experimental program. We first summarize the dramatic progress of numerical lattice-QCD simulations in the past decade, with some emphasis on calculations carried out under the auspices of the U.S. Lattice-QCD Collaboration, and describe a broad program of lattice-QCD calculations that will be relevant for future experiments at the intensity and energy frontiers. We then present details of the computational hardware and software resources needed to undertake these calculations.
High frequency homogenisation for elastic lattices
Colquitt, D J; Makwana, M
2014-01-01
A complete methodology, based on a two-scale asymptotic approach, that enables the homogenisation of elastic lattices at non-zero frequencies is developed. Elastic lattices are distinguished from scalar lattices in that two or more types of coupled waves exist, even at low frequencies. Such a theory enables the determination of effective material properties at both low and high frequencies. The theoretical framework is developed for the propagation of waves through lattices of arbitrary geometry and dimension. The asymptotic approach provides a method through which the dispersive properties of lattices at frequencies near standing waves can be described; the theory accurately describes both the dispersion curves and the response of the lattice near the edges of the Brillouin zone. The leading order solution is expressed as a product between the standing wave solution and long-scale envelope functions that are eigensolutions of the homogenised partial differential equation. The general theory is supplemented b...
Unimodular Lattices for the Gaussian Wiretap Channel
Belfiore, Jean-Claude
2010-01-01
In a recent paper, the authors introduced a lattice invariant called "Secrecy Gain" which measures the confusion experienced by a passive eavesdropper on the Gaussian Wiretap Channel. We study, here, the behavior of this invariant for unimodular lattices by using tools from Modular Forms and show that, for some families of unimodular lattices, indexed by the dimension, the secrecy gain exponentially goes to infinity with the dimension.
Computing Shortest Lattice Vectors on Special Hardware
Schneider, Michael
2011-01-01
The shortest vector problem (SVP) in lattices is related to problems in combinatorial optimization, algorithmic number theory, communication theory, and cryptography. In 1996, Ajtai published his breakthrough idea how to create lattice-based one-way functions based on the worst-case hardness of an approximate version of SVP. Worst-case hardness is one of the outstanding properties of all modern lattice-based cryptographic schemes. Furthermore, there are no sub-exponential time algorithms know...
Simulations of lattice animals and trees
Hsu, Hsiao-Ping; Nadler, Walter; Grassberger, Peter
2004-01-01
The scaling behaviour of randomly branched polymers in a good solvent is studied in two to nine dimensions, using as microscopic models lattice animals and lattice trees on simple hypercubic lattices. As a stochastic sampling method we use a biased sequential sampling algorithm with re-sampling, similar to the pruned-enriched Rosenbluth method (PERM) used extensively for linear polymers. Essentially we start simulating percolation clusters (either site or bond), re-weigh them according to the...
A Viscosity Adaptive Lattice Boltzmann Method
Conrad, Daniel
2015-01-01
The present thesis describes the development and validation of a viscosity adaption method for the numerical simulation of non-Newtonian fluids on the basis of the Lattice Boltzmann Method (LBM), as well as the development and verification of the related software bundle SAM-Lattice. By now, Lattice Boltzmann Methods are established as an alternative approach to classical computational fluid dynamics methods. The LBM has been shown to be an accurate and efficient tool for the numerical...
Improved Lattice Actions with Chemical Potential
Bietenholz, W
1998-01-01
We give a prescription how to include a chemical potential \\mu into a general lattice action. This inclusion does not cause any lattice artifacts. Hence its application to an improved - or even perfect - action at \\mu =0 yields an improved resp. perfect action at arbitrary \\mu. For short-ranged improved actions, a good scaling behavior holds over a wide region, and the upper bound for the baryon density - which is known for the standard lattice actions - can be exceeded.
Topological Summation in Lattice Gauge Theory
Bietenholz, Wolfgang; Hip, Ivan
2012-01-01
In gauge theories the field configurations often occur in distinct topological sectors. In a lattice regularised system with chiral fermions, these sectors can be defined by referring to the Atiyah-Singer Index Theorem. However, if such a model is simulated with local updates of the lattice gauge configuration, the Monte Carlo history tends to get stuck in one sector for many steps, in particular on fine lattices. Then expectation values can be measured only within specific sectors. Here we p...
Soliton dynamics in deformable nonlinear lattices
Sukhorukov, Andrey A.
2005-01-01
We describe wave propagation and soliton localization in photonic lattices which are induced in a nonlinear medium by an optical interference pattern, taking into account the inherent lattice deformations at the soliton location. We obtain exact analytical solutions and identify the key factors defining soliton mobility, including the effects of gap merging and lattice imbalance, underlying the differences with discrete and gap solitons in conventional photonic structures.
Fajstrup, Lisbeth
The set of d-structures on a topological space form a lattice and in fact a locale. There is a Galois connection between the lattice of subsets of the space and the lattice of d-structures. Variation of the d-structures induces change in the spaces of directed paths. Hence variation of d-structur......-structures and variation of the “forbidden area” may be considered together via for instance (co)homology and homotopy sequences....
Collapsing lattice animals and lattice trees in two dimensions
Hsu, Hsiao-Ping; Grassberger, Peter
2005-06-01
We present high statistics simulations of weighted lattice bond animals and lattice trees on the square lattice, with fugacities for each non-bonded contact and for each bond between two neighbouring monomers. The simulations are performed using a newly developed sequential sampling method with resampling, very similar to the pruned-enriched Rosenbluth method (PERM) used for linear chain polymers. We determine with high precision the line of second-order transitions from an extended to a collapsed phase in the resulting two-dimensional phase diagram. This line includes critical bond percolation as a multicritical point, and we verify that this point divides the line into different universality classes. One of them corresponds to the collapse driven by contacts and includes the collapse of (weakly embeddable) trees. There is some evidence that the other is subdivided again into two parts with different universality classes. One of these (at the far side from collapsing trees) is bond driven and is represented by the Derrida-Herrmann model of animals having bonds only (no contacts). Between the critical percolation point and this bond-driven collapse seems to be an intermediate regime, whose other end point is a multicritical point P* where a transition line between two collapsed phases (one bond driven and the other contact driven) sparks off. This point P* seems to be attractive (in the renormalization group sense) from the side of the intermediate regime, so there are four universality classes on the transition line (collapsing trees, critical percolation, intermediate regime, and Derrida-Herrmann). We obtain very precise estimates for all critical exponents for collapsing trees. It is already harder to estimate the critical exponents for the intermediate regime. Finally, it is very difficult to obtain with our method good estimates of the critical parameters of the Derrida-Herrmann universality class. As regards the bond-driven to contact-driven transition in the
Trace maps of general Padovan lattices
Tong, Peiqing
2000-07-01
The two kinds of seven-dimensional trace maps of a new class of three-component quasiperiodic lattices, which are constructed based on the general Padovan sequences Sl+1 ={ Sl-1 m, Sl-2 n}, are derived for arbitrary integer value of m and n. It is shown that these lattices can be grouped into two distinct class. The lattices in class I correspond to n=1 and arbitrary m. They are shown to have volume-preserving second kind maps. The results are compared with those of other three-component quasiperiodic lattices.
Enumerations of lattice animals and trees
Jensen, Iwan
2000-01-01
We have developed an improved algorithm that allows us to enumerate the number of site animals on the square lattice up to size 46. We also calculate the number of lattice trees up to size 44 and the radius of gyration of both lattice animals and trees up to size 42. Analysis of the resulting series yields an improved estimate, $\\lambda = 4.062570(8)$, for the growth constant of lattice animals, and, $\\lambda_0 = 3.795254(8)$, for the growth constant of trees, and confirms to a very high degr...
Subwavelength lattice optics by evolutionary design.
Huntington, Mark D; Lauhon, Lincoln J; Odom, Teri W
2014-12-10
This paper describes a new class of structured optical materials--lattice opto-materials--that can manipulate the flow of visible light into a wide range of three-dimensional profiles using evolutionary design principles. Lattice opto-materials are based on the discretization of a surface into a two-dimensional (2D) subwavelength lattice whose individual lattice sites can be controlled to achieve a programmed optical response. To access a desired optical property, we designed a lattice evolutionary algorithm that includes and optimizes contributions from every element in the lattice. Lattice opto-materials can exhibit simple properties, such as on- and off-axis focusing, and can also concentrate light into multiple, discrete spots. We expanded the unit cell shapes of the lattice to achieve distinct, polarization-dependent optical responses from the same 2D patterned substrate. Finally, these lattice opto-materials can also be combined into architectures that resemble a new type of compound flat lens. PMID:25380062
Light propagation in optically induced Fibonacci lattices
Boguslawski, Martin; Timotijevic, Dejan V; Denz, Cornelia; Savic, Dragana M Jovic
2015-01-01
We report on the optical induction of Fibonacci lattices in photorefractive strontium barium niobate by use of Bessel beam waveguide-wise writing techniques. Fibonacci elements A and B are used as lattice periods. We further use the induced structures to execute probing experiments with variously focused Gaussian beams in order to observe light confinement owing to the quasiperiodic character of Fibonacci word sequences. Essentially, we show that Gaussian beam expansion is just slowed down in Fibonacci lattices, as compared with appropriate periodic lattices.
Midwest cousins of Barnes-Wall lattices
Griess Jr., Robert L.
2009-01-01
Given a rational lattice and suitable set of linear transformations, we construct a cousin lattice. Sufficient conditions are given for integrality, evenness and unimodularity. When the input is a Barnes-Wall lattice, we get multi-parameter series of cousins. There is a subseries consisting of unimodular lattices which have ranks $2^{d-1}\\pm 2^{d-k-1}$, for odd integers $d\\ge 3$ and integers $k=1,2, ..., \\frac {d-1}2$. Their minimum norms are moderately high: $2^{\\lfloor \\frac d2 \\rfloor -1}$.
Fuzzy Ideals and Fuzzy Distributive Lattices%Fuzzy Ideals and Fuzzy Distributive Lattices*
S.H.Dhanani; Y. S. Pawar
2011-01-01
Our main objective is to study properties of a fuzzy ideals (fuzzy dual ideals). A study of special types of fuzzy ideals (fuzzy dual ideals) is also furnished. Some properties of a fuzzy ideals (fuzzy dual ideals) are furnished. Properties of a fuzzy lattice homomorphism are discussed. Fuzzy ideal lattice of a fuzzy lattice is defined and discussed. Some results in fuzzy distributive lattice are proved.
Expansion in high dimension for the growth constants of lattice trees and lattice animals
Miranda, Yuri Mejia; Slade, Gordon
2012-01-01
We compute the first three terms of the 1/d expansions for the growth constants and one-point functions of nearest-neighbour lattice trees and lattice (bond) animals on the integer lattice Zd, with rigorous error estimates. The proof uses the lace expansion, together with a new expansion for the one-point functions based on inclusion-exclusion.
A Classification of Unimodular Lattice Wiretap Codes in Small Dimensions
Lin, Fuchun
2012-01-01
Lattice coding over a Gaussian wiretap channel, where an eavesdropper listens to transmissions between a transmitter and a legitimate receiver, is considered. A new lattice invariant called the secrecy gain is used as a code design criterion for wiretap lattice codes since it was shown to characterize the confusion that a chosen lattice can cause at the eavesdropper: the higher the secrecy gain of the lattice, the more confusion. In this paper, a formula for the secrecy gain of unimodular lattices is derived. Secrecy gains of extremal odd unimodular lattices as well as unimodular lattices in dimension n, 16 \\leq n \\leq 23 are computed, covering the 4 extremal odd unimodular lattices and all the 111 nonextremal unimodular lattices (both odd and even) providing thus a classification of the best wiretap lattice codes coming from unimodular lattices in dimension n, 8 < n \\leq 23. Finally, to permit lattice encoding via Construction A, the corresponding error correction codes are determined.
Gluonic Transversity from Lattice QCD
Detmold, W
2016-01-01
We present an exploratory study of the gluonic structure of the $\\phi$ meson using lattice QCD (LQCD). This includes the first investigation of gluonic transversity via the leading moment of the twist-two double-helicity-flip gluonic structure function $\\Delta(x,Q^2)$. This structure function only exists for targets of spin $J\\ge1$ and does not mix with quark distributions at leading twist, thereby providing a particularly clean probe of gluonic degrees of freedom. We also explore the gluonic analogue of the Soffer bound which relates the helicity flip and non-flip gluonic distributions, finding it to be saturated at the level of 80%. This work sets the stage for more complex LQCD studies of gluonic structure in the nucleon and in light nuclei where $\\Delta(x,Q^2)$ is an 'exotic glue' observable probing gluons in a nucleus not associated with individual nucleons.
Entropy of unimodular Lattice Triangulations
Knauf, Johannes F; Mecke, Klaus
2014-01-01
Triangulations are important objects of study in combinatorics, finite element simulations and quantum gravity, where its entropy is crucial for many physical properties. Due to their inherent complex topological structure even the number of possible triangulations is unknown for large systems. We present a novel algorithm for an approximate enumeration which is based on calculations of the density of states using the Wang-Landau flat histogram sampling. For triangulations on two-dimensional integer lattices we achive excellent agreement with known exact numbers of small triangulations as well as an improvement of analytical calculated asymptotics. The entropy density is $C=2.196(3)$ consistent with rigorous upper and lower bounds. The presented numerical scheme can easily be applied to other counting and optimization problems.
Pion structure from lattice QCD
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.
Lattice mechanics of origami tessellations.
Evans, Arthur A; Silverberg, Jesse L; Santangelo, Christian D
2015-07-01
Origami-based design holds promise for developing materials whose mechanical properties are tuned by crease patterns introduced to thin sheets. Although there have been heuristic developments in constructing patterns with desirable qualities, the bridge between origami and physics has yet to be fully developed. To truly consider origami structures as a class of materials, methods akin to solid mechanics need to be developed to understand their long-wavelength behavior. We introduce here a lattice theory for examining the mechanics of origami tessellations in terms of the topology of their crease pattern and the relationship between the folds at each vertex. This formulation provides a general method for associating mechanical properties with periodic folded structures and allows for a concrete connection between more conventional materials and the mechanical metamaterials constructed using origami-based design. PMID:26274299
Defect solitons in photonic lattices.
Yang, Jianke; Chen, Zhigang
2006-02-01
Nonlinear defect modes (defect solitons) and their stability in one-dimensional photonic lattices with focusing saturable nonlinearity are investigated. It is shown that defect solitons bifurcate out from every infinitesimal linear defect mode. Low-power defect solitons are linearly stable in lower bandgaps but unstable in higher bandgaps. At higher powers, defect solitons become unstable in attractive defects, but can remain stable in repulsive defects. Furthermore, for high-power solitons in attractive defects, we found a type of Vakhitov-Kolokolov (VK) instability which is different from the usual VK instability based on the sign of the slope in the power curve. Lastly, we demonstrate that in each bandgap, in addition to defect solitons which bifurcate from linear defect modes, there is also an infinite family of other defect solitons which can be stable in certain parameter regimes. PMID:16605473
Mesons on a transverse lattice
Dalley, S
2001-01-01
The meson eigenstates of the light-cone Hamiltonian in a coarse transverse lattice gauge theory are investigated. Building upon previous work in pure gauge theory, the Hamiltonian and its Fock space are expanded in powers of dynamical fields. In the leading approximation, the couplings appearing in the Hamiltonian are renormalised by demanding restoration of space-time symmetries broken by the cut-off. Additional requirements from chiral symmetry are discussed and difficulties in imposing them from first principles in the leading approximation are noted. A phenomenological calculation is then performed, in which chiral symmetry in spontaneously broken form is modelled by imposing the physical pion-rho mass splitting as a constraint. The light-cone wavefunctions of the resulting Hamiltonian are used to compute decay constants, form factors and quark momentum and spin distributions for the pion and rho mesons. Extensions beyond leading order, and the implications for first principles calculations, are briefly d...
Lattice quantum gravity - an update
Ambjorn, J; Loll, R
2010-01-01
We advocate lattice methods as the tool of choice to constructively define a background-independent theory of Lorentzian quantum gravity and explore its physical properties in the Planckian regime. The formulation that arguably has most furthered our understanding of quantum gravity (and of various pitfalls present in the nonperturbative sector) uses dynamical triangulations to regularize the nonperturbative path integral over geometries. Its Lorentzian version in terms of Causal Dynamical Triangulations (CDT) - in addition to having a definite quantum signature on short scales - has been shown to reproduce important features of the classical theory on large scales. This article recaps the most important developments in CDT of the last few years for the physically relevant case of four spacetime dimensions, and describes its status quo at present.
Fermion determinants in lattice QCD
Johnson, C A
2001-01-01
The main topic of this thesis concerns efficient algorithms for the calculation of determinants of the kind of matrix typically encountered in lattice QCD. In particular an efficient method for calculating the fermion determinant is described. Such a calculation is useful to illustrate the effects of light dynamical (virtual) quarks. The methods employed in this thesis are stochastic methods, based on the Lanczos algorithm, which is used for the solution of large, sparse matrix problems via a partial tridiagonalisation of the matrix. Here an implementation is explored which requires less exhaustive treatment of the matrix than previous Lanczos methods. This technique exploits the analogy between the Lanczos tridiagonalisation algorithm and Gaussian quadrature in order to calculate the fermion determinant. A technique for determining a number of the eigenvalues of the matrix is also presented. A demonstration is then given of how one can improve upon this estimate considerably using variance reduction techniqu...
Monte Carlo lattice program KIM
The Monte Carlo program KIM solves the steady-state linear neutron transport equation for a fixed-source problem or, by successive fixed-source runs, for the eigenvalue problem, in a two-dimensional thermal reactor lattice. Fluxes and reaction rates are the main quantities computed by the program, from which power distribution and few-group averaged cross sections are derived. The simulation ranges from 10 MeV to zero and includes anisotropic and inelastic scattering in the fast energy region, the epithermal Doppler broadening of the resonances of some nuclides, and the thermalization phenomenon by taking into account the thermal velocity distribution of some molecules. Besides the well known combinatorial geometry, the program allows complex configurations to be represented by a discrete set of points, an approach greatly improving calculation speed
Stassis, C.; Zaretsky, J.; Misemer, D. K.;;
1983-01-01
A large single crystal of FCC Ca was grown and was used to study the lattice dynamics of this divalent metal by coherent inelastic neutron scattering. The phonon dispersion curves were measured, at room temperature, along the [ξ00], [ξξ0], [ξξξ], and [0ξ1] symmetry directions. The dispersion curves...... to the propagation of elastic waves. The frequencies of the T1[ξξ0] branch for ξ between approximately 0.5 and 0.8 are slightly above the velocity-of-sound line determined from the low-frequency measurements. Since a similar effect has been observed in FCC Yb, it is natural to assume that the anomalous dispersion...
Lattice image studies of ordered alloys
Lattice imaging in electron microscopy was successfully applied to the study of ordering in alloys. The approach included computer simulation (Mg3Cd), study of atomic arrangements near ordered lattice defects (Ni4Mo), fringe changes during phase transformation, and identification of fringe periodicities in alloys quenched from above the critical ordering temperature. (U.S.)
Compact lattice QED with Wilson fermions
We study the phase structure and the chiral limit of 4d compact lattice QED with Wilson fermions (both dynamical and quenched). We use the standard Wilson gauge action and also a modified one suppressing lattice artifacts. Different techniques and observables to locate the chiral limit are discussed. (orig.)
Two-color surface lattice solitons
Xu, Zhiyong; Kivshar, Yuri S.
2008-01-01
We study the properties of surface solitons generated at the edge of a semi-infinite photonic lattice in nonlinear quadratic media, namely two-color surface lattice solitons. We analyze the impact of phase mismatch on existence and stability of surface modes, and find novel classes of two-color twisted surface solitons which are stable in a large domain of their existence.
Quantum theory and the lattice join
An informal explanation is presented of Birkhoff's and von Neumann's proposal according to which it is necessary, due to quantum theory, to replace the well-known lattice of properties, which is a heritage from George Boole, by a new quantum lattice of properties mirroring the structure of the Hilbert space. (Z.S.). 4 figs., 12 refs
Lattice dynamics of ferromagnetic superconductor UGe2
Satyam Shinde; Prafulla K Jha
2008-11-01
This paper reports the lattice dynamical study of the UGe2 using a lattice dynamical model theory based on pairwise interactions under the framework of the shell model. The calculated phonon dispersion curves and phonon density of states are in good agreement with the measured data.
Secrecy Gain: a Wiretap Lattice Code Design
Belfiore, Jean-Claude
2010-01-01
We propose the notion of secrecy gain as a code design criterion for wiretap lattice codes to be used over an additive white Gaussian noise channel. Our analysis relies on the error probabilites of both the legitimate user and the eavesdropper. We focus on geometrical properties of lattices, described by their theta series, to characterize good wiretap codes.
Strongly correlated electrons on frustrated lattices
P. Fulde
2008-06-01
Full Text Available We give an overview of recent work on charge degrees of freedom of strongly correlated electrons on geometrically frustrated lattices. Special attention is paid to the checkerboard lattice, i.e., the two-dimensional version of a pyrochlore lattice and to the kagomé lattice. For the checkerboard lattice it is shown that at half filling when spin degrees of freedom are neglected and at quarter filling when they are included excitations with fractional charges ±e/2 may exist. The same holds true for the three-dimensional pyrochlore lattice. In the former case the fractional charges are confined. The origin of the weak, constant confining force is discussed and some similarities to quarks and to string theory are pointed out. For the checkerboard lattice a formulation in terms of a compact U(1 gauge theory is described. Furthermore a new kinetic mechanism for ferromagnetism at special fillings of a kagomé lattice is discussed.
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.
Minimal Varieties of Representable Commutative Residuated Lattices
Horčík, Rostislav
2012-01-01
Roč. 100, č. 6 (2012), s. 1063-1078. ISSN 0039-3215 R&D Projects: GA ČR GAP202/10/1826 Institutional research plan: CEZ:AV0Z10300504 Keywords : commutative residuated lattice * subvariety lattice * minimal variety * substructural logic * maximally consistent logic Subject RIV: BA - General Mathematics Impact factor: 0.342, year: 2012
Soliton control in fading optical lattices
Kartashov, Yaroslav V.; Vysloukh, Victor A.; Torner, Lluis
2006-01-01
We predict new phenomena, such as soliton steering and soliton fission, in optical lattices that fade away exponentially along the propagation direction. Such lattices, featuring tunable decay rates, arise in photorefractive crystals in the wavelength range 360-400 nm. We show that the predicted phenomena offer different opportunities for soliton control.
Beautiful mass predictions from scalar lattice QCD
Samuel, S.; Moriarty, K.J.M.
1986-07-31
Scalar lattice QCD methods are used to accurately predict the masses of hadrons with beauty, that is, states which contain a b quark. These states have not yet been seen in the laboratory. The accuracy of the predictions (approx.=25 MeV) make the calculation a good test of lattice methods as well as providing useful guidance for experimentalists.
The contact polytope of the Leech lattice
Dutour Sikiric, M.; Schuermann, A.; Vallentin, Frank
2010-01-01
The contact polytope of a lattice is the convex hull of its shortest vectors. In this paper we classify the facets of the contact polytope of the Leech lattice up to symmetry. There are 1, 197, 362, 269, 604, 214, 277, 200 many facets in 232 orbits.
Ultracold quantum gases in triangular optical lattices
Over recent years, exciting developments in the field of ultracold atoms confined in optical lattices have led to numerous theoretical proposals devoted to the quantum simulation of problems e.g. known from condensed matter physics. Many of those ideas demand experimental environments with non-cubic lattice geometries. In this paper, we report on the implementation of a versatile three-beam lattice allowing for the generation of triangular as well as hexagonal optical lattices. As an important step, the superfluid-Mott insulator (SF-MI) quantum phase transition has been observed and investigated in detail in this lattice geometry for the first time. In addition to this, we study the physics of spinor Bose-Einstein condensates (BEC) in the presence of the triangular optical lattice potential, especially spin changing dynamics across the SF-MI transition. Our results suggest that, below the SF-MI phase transition, a well-established mean-field model describes the observed data when renormalizing the spin-dependent interaction. Interestingly, this opens up new perspectives for a lattice-driven tuning of a spin dynamics resonance occurring through the interplay of the quadratic Zeeman effect and spin-dependent interaction. Finally, we discuss further lattice configurations that can be realized with our setup.
Ultracold quantum gases in triangular optical lattices
Becker, C; Soltan-Panahi, P; Doerscher, S; Sengstock, K [Institut fuer Laserphysik, Universitaet Hamburg, Hamburg D-22761 (Germany); Kronjaeger, J; Bongs, K, E-mail: cbecker@physnet.uni-hamburg.d [MUARC, School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT (United Kingdom)
2010-06-15
Over recent years, exciting developments in the field of ultracold atoms confined in optical lattices have led to numerous theoretical proposals devoted to the quantum simulation of problems e.g. known from condensed matter physics. Many of those ideas demand experimental environments with non-cubic lattice geometries. In this paper, we report on the implementation of a versatile three-beam lattice allowing for the generation of triangular as well as hexagonal optical lattices. As an important step, the superfluid-Mott insulator (SF-MI) quantum phase transition has been observed and investigated in detail in this lattice geometry for the first time. In addition to this, we study the physics of spinor Bose-Einstein condensates (BEC) in the presence of the triangular optical lattice potential, especially spin changing dynamics across the SF-MI transition. Our results suggest that, below the SF-MI phase transition, a well-established mean-field model describes the observed data when renormalizing the spin-dependent interaction. Interestingly, this opens up new perspectives for a lattice-driven tuning of a spin dynamics resonance occurring through the interplay of the quadratic Zeeman effect and spin-dependent interaction. Finally, we discuss further lattice configurations that can be realized with our setup.
Parrondo games as lattice gas automata
Meyer, David A.; Blumer, Heather
2001-01-01
Parrondo games are coin flipping games with the surprising property that alternating plays of two losing games can produce a winning game. We show that this phenomenon can be modelled by probabilistic lattice gas automata. Furthermore, motivated by the recent introduction of quantum coin flipping games, we show that quantum lattice gas automata provide an interesting definition for quantum Parrondo games.
Lattice Platonic Solids and their Ehrhart polynomial
E. J. Ionascu
2013-01-01
Full Text Available First, we calculate the Ehrhart polynomial associated to an arbitrary cube with integer coordinates for its vertices. Then, we use this result to derive relationships between the Ehrhart polynomials for regular lattice tetrahedra and those for regular lattice octahedra. These relations allow one to reduce the calculation of these polynomials to only one coefficient.
The Pfaff lattice on symplectic matrices
Kodama, Yuji [Department of Mathematics, Ohio State University, Columbus, OH 43210 (United States); Pierce, Virgil U, E-mail: kodama@math.ohio-state.ed, E-mail: piercevu@utpa.ed [Department of Mathematics, University of Texas-Pan American, Edinburg, TX 78539 (United States)
2010-02-05
The Pfaff lattice is an integrable system arising from the SR-group factorization in an analogous way to how the Toda lattice arises from the QR-group factorization. In our earlier paper (Kodama and Pierce 2007 Int. Math. Res. Not. (arXiv:0705.0510)), we studied the Pfaff lattice hierarchy for the case where the Lax matrix is defined to be a lower Hessenberg matrix. In this paper we deal with the case of a symplectic lower Hessenberg Lax matrix, this forces the Lax matrix to take a 2 x 2 block tridiagonal shape. We then show that the odd members of the Pfaff lattice hierarchy are trivial, while the even members are equivalent to the indefinite Toda lattice hierarchy defined in Kodama and Ye (1996 Physica D 91 321-39). This is analogous to the case of the Toda lattice hierarchy in relation to the Kac-van Moerbeke system. In the case with the initial matrix having only real or imaginary eigenvalues, the fixed points of the even flows are given by 2 x 2 block diagonal matrices with zero diagonals. We also consider a family of skew-orthogonal polynomials with a symplectic recursion relation related to the Pfaff lattice and find that they are succinctly expressed in terms of orthogonal polynomials appearing in the indefinite Toda lattice.
Producing Bose condensates using optical lattices
Olshanii, Maxim; Weiss, David
2002-01-01
We relate the entropies of ensembles of atoms in optical lattices to atoms in simple traps. We then determine which ensembles of lattice-bound atoms will adiabatically transform into a Bose condensate. This shows a feasible approach to Bose condensation without evaporative cooling.