scholarly journals Effective gravitational action for 2D massive fermions

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Adel Bilal ◽  
Corinne de Lacroix ◽  
Harold Erbin
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Small Mass ◽  
Gravitational Action ◽  
Non Local ◽  
Liouville Action ◽  
Mass Expansion

Abstract We work out the effective gravitational action for 2D massive Euclidean fermions in a small mass expansion. Besides the leading Liouville action, the order m2 gravitational action contains a piece characteristic of the Mabuchi action, much as for 2D massive scalars, but also several non-local terms involving the Green’s functions and Green’s functions at coinciding points on the manifold.

Band gap Green's functions and localized oscillations

2007 ◽  
Vol 463 (2086) ◽  
pp. 2709-2727 ◽  
Author(s):  
Alexander B Movchan ◽  
Leonid I Slepyan
Keyword(s):  
Band Gap ◽  
Green's Functions ◽  
Green’S Functions ◽  
Discrete Models ◽  
Square Lattice ◽  
Asymptotic Expressions ◽  
Oscillation Modes ◽  
Non Local ◽  
Localized Mode ◽  
Made In

We consider some typical continuous and discrete models of structures possessing band gaps, and analyse the localized oscillation modes. General considerations show that such modes can exist at any frequency within the band gap provided an admissible local mass variation is made. In particular, we show that the upper bound of the sinusoidal wave frequency exists in a non-local interaction homogeneous waveguide, and we construct a localized mode existing there at high frequencies. The localized modes are introduced via the Green's functions for the corresponding uniform systems. We construct such functions and, in particular, present asymptotic expressions of the band gap anisotropic Green's function for the two-dimensional square lattice. The emphasis is made on the notion of the depth of band gap and evaluation of the rate of localization of the vibration modes. Detailed analysis of the extremal localization is conducted. In particular, this concerns an algorithm of a ‘neutral’ perturbation where the total mass of a complex central cell is not changed

scholarly journals The Green’s functions for peridynamic non-local diffusion

2016 ◽  
Vol 472 (2193) ◽  
pp. 20160185 ◽  
Author(s):  
L. J. Wang ◽  
J. F. Xu ◽  
J. X. Wang
Keyword(s):  
Diffusion Model ◽  
Classical Theory ◽  
Green's Functions ◽  
Green’S Functions ◽  
Point Sources ◽  
Spatial Gradient ◽  
Infinite Domains ◽  
Non Local ◽  
Local Solutions ◽  
Local Diffusion

In this work, we develop the Green’s function method for the solution of the peridynamic non-local diffusion model in which the spatial gradient of the generalized potential in the classical theory is replaced by an integral of a generalized response function in a horizon. We first show that the general solutions of the peridynamic non-local diffusion model can be expressed as functionals of the corresponding Green’s functions for point sources, along with volume constraints for non-local diffusion. Then, we obtain the Green’s functions by the Fourier transform method for unsteady and steady diffusions in infinite domains. We also demonstrate that the peridynamic non-local solutions converge to the classical differential solutions when the non-local length approaches zero. Finally, the peridynamic analytical solutions are applied to an infinite plate heated by a Gauss source, and the predicted variations of temperature are compared with the classical local solutions. The peridynamic non-local diffusion model predicts a lower rate of variation of the field quantities than that of the classical theory, which is consistent with experimental observations. The developed method is applicable to general diffusion-type problems.

Random Phase Approximation Plasma Phenomenology, Semiclassical and Hydrodynamic Models; Electrodynamics

2018 ◽  
Author(s):  
Norman J. Morgenstern Horing
Keyword(s):  
Quantum Well ◽  
Green's Functions ◽  
Green’S Functions ◽  
Random Phase ◽  
Electromagnetic Response ◽  
Quantum Plasma ◽  
Dielectric Tensor ◽  
Dielectric Screening ◽  
Non Local

Chapter 10 reviews both homogeneous and inhomogeneous quantum plasma dielectric response phenomenology starting with the RPA polarizability ring diagram in terms of thermal Green’s functions, also energy eigenfunctions. The homogeneous dynamic, non-local inverse dielectric screening functions (K) are exhibited for 3D, 2D, and 1D, encompassing the non-local plasmon spectra and static shielding (e.g. Friedel oscillations and Debye-Thomas-Fermi shielding). The role of a quantizing magnetic field in K is reviewed. Analytically simpler models are described: the semiclassical and classical limits and the hydrodynamic model, including surface plasmons. Exchange and correlation energies are discussed. The van der Waals interaction of two neutral polarizable systems (e.g. physisorption) is described by their individual two-particle Green’s functions: It devolves upon the role of the dynamic, non-local plasma image potential due to screening. The inverse dielectric screening function K also plays a central role in energy loss spectroscopy. Chapter 10 introduces electromagnetic dyadic Green’s functions and the inverse dielectric tensor; also the RPA dynamic, non-local conductivity tensor with application to a planar quantum well. Kramers–Krönig relations are discussed. Determination of electromagnetic response of a compound nanostructure system having several nanostructured parts is discussed, with applications to a quantum well in bulk plasma and also to a superlattice, resulting in coupled plasmon spectra and polaritons.

Green’s functions in non-local three-dimensional linear elasticity

2009 ◽  
Vol 465 (2111) ◽  
pp. 3463-3487 ◽  
Author(s):  
Olaf Weckner ◽  
Gerd Brunk ◽  
Michael A. Epton ◽  
Stewart A. Silling ◽  
Ebrahim Askari
Keyword(s):  
Green's Functions ◽  
Fourier Transforms ◽  
Green’S Functions ◽  
Three Dimensional ◽  
Point Load ◽  
Three Dimensions ◽  
Weak Formulation ◽  
Element Discretization ◽  
Linear Elastic Body ◽  
Non Local

In this paper, we compare small deformations in an infinite linear elastic body due to the presence of point loads within the classical, local formulation to the corresponding deformations in the peridynamic, non-local formulation. Owing to the linearity of the problem, the response to a point load can be used to obtain the response to general body force loading functions by superposition. Using Laplace and Fourier transforms, we thus obtain an integral representation for the three-dimensional peridynamic solution with the help of Green’s functions. We illustrate this new theoretical result by dynamic and static examples in one and three dimensions. In addition to this main result, we also derive the non-local three-dimensional jump conditions, as well as the weak formulation of peridynamics together with the associated finite element discretization.

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