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Books on the topic 'Lattice formulation of QCD'

Author: Grafiati

Published: 4 June 2021

Last updated: 5 February 2022

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1

Lin, Huey-Wen, and Harvey B. Meyer, eds. Lattice QCD for Nuclear Physics. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-08022-2.

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2

Stokes, Finn M. Structure of Nucleon Excited States from Lattice QCD. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-25722-4.

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3

Can, Kadir Utku. Electromagnetic Form Factors of Charmed Baryons in Lattice QCD. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-10-8995-4.

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4

Xiang-Qian, Luo, and Gregory Eric B, eds. Non-perturbative methods and lattice QCD: Proceedings of the international workshop. Singapore: World Scientific, 2001.

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5

Ecole, d'été de physique théorique (Les Houches Haute-Savoie France) (93rd 2009). Modern perspectives in lattice QCD: Quantum field theory and high performance computing. Oxford: Oxford University Press, USA, 2011.

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6

Baral, Suman. Thomas-Fermi Model for Mesons and Noise Subtraction Techniques in Lattice QCD. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-30904-6.

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7

Doi, Takahiro. Lattice QCD Study for the Relation Between Confinement and Chiral Symmetry Breaking. Singapore: Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-6596-5.

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8

David, Blaschke, Karsch F, and Roberts Craig D, eds. Proceedings of the International Workshop on Understanding Deconfinement in QCD : Trento, Italy, 1-13 March 1999. Singapore: World Scientific, 2000.

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9

W, Schreiber A., Williams Anthony G, National Institute for Theoretical Physics (Australia), and Special Research Centre for the Subatomic Structure of Matter (Australia), eds. Proceedings of the Workshop on Lightcone QCD and Nonperturbative Hadron Physics: Adelaide, 13-22 December 1999. Singapore: World Scientific, 2000.

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10

Perspectives in Lattice Qcd. World Scientific Publishing Company, 2008.

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11

M, Green Anthony, ed. Hadronic physics from lattice QCD. New Jersey: World Scientific, 2004.

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12

Lin, Huey-Wen, and Harvey B. Meyer. Lattice QCD for Nuclear Physics. Springer, 2014.

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13

Green, Anthony M. Hadronic Physics from Lattice QCD. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/5637.

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14

(Editor), David Blaschke, Frithjof Karsch (Editor), and Craig D. Roberts (Editor), eds. Understanding Deconfinement in Qcd. World Scientific Publishing Company, 1999.

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15

Can, Kadir Utku. Electromagnetic Form Factors of Charmed Baryons in Lattice QCD. Springer, 2018.

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16

Can, Kadir Utku. Electromagnetic Form Factors of Charmed Baryons in Lattice QCD. Springer, 2019.

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17

Green, Anthony M. Hadronic Physics From Lattice QCD (International Review of Nuclear Physics). World Scientific Publishing Company, 2004.

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18

Doi, Takahiro. Lattice QCD Study for the Relation Between Confinement and Chiral Symmetry Breaking. Springer, 2017.

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19

Baral, Suman. Thomas-Fermi Model for Mesons and Noise Subtraction Techniques in Lattice QCD. Springer, 2020.

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20

Baral, Suman. Thomas-Fermi Model for Mesons and Noise Subtraction Techniques in Lattice QCD. Springer, 2019.

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21

Doi, Takahiro. Lattice QCD Study for the Relation Between Confinement and Chiral Symmetry Breaking. Springer, 2017.

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22

Perspectives in lattice QCD: Proceedings of the workshop : Nara International Seminar House, Nara, Japan, 31 October-11 November 2005. Hackensack, NJ: World Scientific, 2008.

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23

Perspectives in lattice QCD: Proceedings of the workshop : Nara International Seminar House, Nara, Japan, 31 October-11 November 2005. Hackensack, NJ: World Scientific, 2008.

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24

Succi, Sauro. Quantum Lattice Boltzmann (QLB). Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0032.

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The Lattice Boltzmann concepts and applications described so far refer to classical, i.e., non-quantum physics. However, the LB formalism is not restricted to classical Newtonian mechanics and indeed an LB formulation of quantum mechanics, going by the name of quantum LB (QLB) has been in existence for more than two decades. Even though it would far-fetched to say that QLB represents a mainstream, in the recent years it has captured some revived interest, mostly on account of recent developments in quantum-computing research. This chapter provides an account of the QLB formulation: stay tuned, LBE goes quantum!

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25

Succi, Sauro. Lattice Relaxation Schemes. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0014.

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In Chapter 13, it was shown that the complexity of the LBE collision operator can be cut down dramatically by formulating discrete versions with prescribed local equilibria. In this chapter, the process is taken one step further by presenting a minimal formulation whereby the collision matrix is reduced to the identity, upfronted by a single relaxation parameter, fixing the viscosity of the lattice fluid. The idea is patterned after the celebrated Bhatnagar–Gross–Krook (BGK) model Boltzmann introduced in continuum kinetic theory as early as 1954. The second part of the chapter describes the comeback of the early LBE in optimized multi-relaxation form, as well as few recent variants hereof.

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26

Succi, Sauro. Lattice Gas-Cellular Automata. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0011.

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This chapter discusses the ancestor of the Lattice Boltzmann, the Boolean formulation of hydrodynamics known as lattice Gas Cellular Automata. In 1986, Uriel Frisch, Brosl Hasslacher and Yves Pomeau sent big waves across the fluid dynamics community: a simple cellular automaton obeying nothing but conservation laws at a microscopic level was able to reproduce the complexity of real fluid flows. This discovery spurred great excitement in the fluid dynamics community. The prospects were tantalizing: around free, intrinsically parallel computational paradigm for fluid flows. However, a few serious problems were quickly recognized and addressed with great intensity in the following years.

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27

(Editor), Artan Boriçi, Andreas Frommer (Editor), Bálint Joó (Editor), Anthony Kennedy (Editor), and Brian Pendleton (Editor), eds. QCD and Numerical Analysis III: Proceedings of the Third International Workshop on Numerical Analysis and Lattice QCD, Edinburgh, June-July 2003 (Lecture ... in Computational Science and Engineering). Springer, 2005.

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28

International Workshop on Lattice QCD on Parallel Computers ( 1997 : Tsukuba, Ibaraki, Japan)., ed. Lattice QCD on parallel computers: Proceedings of the International Workshop, Tsukuba, Ibaraki, Japan, 10-15 March, 1997. [Amsterdam, Netherland]: North-Holland, 1998.

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29

(Editor), G. Kilcup, and S. Sharpe (Editor), eds. Phenomenology and Lattice Qcd: Proceedings of the 1993 Vehling Summer School : University of Washington 21 June-21 July 1993. World Scientific Pub Co Inc, 1995.

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30

G, Kilcup, Sharpe Stephen Roger, Institute for Nuclear Theory (U.S.), and Uehling Summer School, eds. Phenomenology and lattice QCD: Proceedings of the 1993 Uehling Summer School : University of Washington, 21 June-2 July 1993. Singapore: World Scientific, 1995.

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31

Vigdor, Steven E. Water, Water, Here and There. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198814825.003.0004.

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Chapter 4 deals with the stability of the proton, hence of hydrogen, and how to reconcile that stability with the baryon number nonconservation (or baryon conservation) needed to establish a matter–antimatter imbalance in the infant universe. Sakharov’s three conditions for establishing a matter–antimatter imbalance are presented. Grand unified theories and experimental searches for proton decay are described. The concept of spontaneous symmetry breaking is introduced in describing the electroweak phase transition in the infant universe. That transition is treated as the potential site for introducing the imbalance between quarks and antiquarks, via either baryogenesis or leptogenesis models. The up–down quark mass difference is presented as essential for providing the stability of hydrogen and of the deuteron, which serves as a crucial stepping stone in stellar hydrogen-burning reactions that generate the energy and elements needed for life. Constraints on quark masses from lattice QCD calculations and violations of chiral symmetry are discussed.

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32

Horing, Norman J. Morgenstern. Graphene. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0012.

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Chapter 12 introduces Graphene, which is a two-dimensional “Dirac-like” material in the sense that its energy spectrum resembles that of a relativistic electron/positron (hole) described by the Dirac equation (having zero mass in this case). Its device-friendly properties of high electron mobility and excellent sensitivity as a sensor have attracted a huge world-wide research effort since its discovery about ten years ago. Here, the associated retarded Graphene Green’s function is treated and the dynamic, non-local dielectric function is discussed in the degenerate limit. The effects of a quantizing magnetic field on the Green’s function of a Graphene sheet and on its energy spectrum are derived in detail: Also the magnetic-field Green’s function and energy spectrum of a Graphene sheet with a quantum dot (modelled by a 2D Dirac delta-function potential) are thoroughly examined. Furthermore, Chapter 12 similarly addresses the problem of a Graphene anti-dot lattice in a magnetic field, discussing the Green’s function for propagation along the lattice axis, with a formulation of the associated eigen-energy dispersion relation. Finally, magnetic Landau quantization effects on the statistical thermodynamics of Graphene, including its Free Energy and magnetic moment, are also treated in Chapter 12 and are seen to exhibit magnetic oscillatory features.

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33

Succi, Sauro. LB for Flows with Suspended Objects: Fluid–Solid Interactions. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0031.

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In the recent years the theory of the fluctuating LB, as it was proposed and developed by A.J.C. Ladd in the early 90s, has undergone major developments, both at the level of theoretical foundations and practical implementation. This Chapter provides a cursory view of such developments, with special focus on the general formulation of fluid–solid interactions within the Lattice Boltzmann formalism. Clearly, the rheological behavior of these suspensions is highly accepted by the way the suspended particles interact with the fluid and among themselves. From the mathematical and computational standpoint, this configures a technically thick issue, namely the treatment of fluid-solid moving boundaries, in a more macroscopic-oriented context also known as fluid-structure interactions (FSI). In the sequel, a description of a number of methods which have been developed to include FSI within the LB formalism, is presented. In particular, the case of rigid and deformable bodies, both vital to many applications in science and engineering, shall be covered

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34

Horing, Norman J. Morgenstern. Interacting Electron–Hole–Phonon System. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0011.

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Chapter 11 employs variational differential techniques and the Schwinger Action Principle to derive coupled-field Green’s function equations for a multi-component system, modeled as an interacting electron-hole-phonon system. The coupled Fermion Green’s function equations involve five interactions (electron-electron, hole-hole, electron-hole, electron-phonon, and hole-phonon). Starting with quantum Hamilton equations of motion for the various electron/hole creation/annihilation operators and their nonequilibrium average/expectation values, variational differentiation with respect to particle sources leads to a chain of coupled Green’s function equations involving differing species of Green’s functions. For example, the 1-electron Green’s function equation is coupled to the 2-electron Green’s function (as earlier), also to the 1-electron/1-hole Green’s function, and to the Green’s function for 1-electron propagation influenced by a nontrivial phonon field. Similar remarks apply to the 1-hole Green’s function equation, and all others. Higher order Green’s function equations are derived by further variational differentiation with respect to sources, yielding additional couplings. Chapter 11 also introduces the 1-phonon Green’s function, emphasizing the role of electron coupling in phonon propagation, leading to dynamic, nonlocal electron screening of the phonon spectrum and hybridization of the ion and electron plasmons, a Bohm-Staver phonon mode, and the Kohn anomaly. Furthermore, the single-electron Green’s function with only phonon coupling can be rewritten, as usual, coupled to the 2-electron Green’s function with an effective time-dependent electron-electron interaction potential mediated by the 1-phonon Green’s function, leading to the polaron as an electron propagating jointly with its induced lattice polarization. An alternative formulation of the coupled Green’s function equations for the electron-hole-phonon model is applied in the development of a generalized shielded potential approximation, analysing its inverse dielectric screening response function and associated hybridized collective modes. A brief discussion of the (theoretical) origin of the exciton-plasmon interaction follows.

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