scholarly journals Infra-Red Asymptotic Form of the One-Fermion Green's Function in Two-Dimensional Quantum Chromodynamics

1981 ◽  
Vol 65 (2) ◽  
pp. 783-786 ◽  
Author(s):  
K. Harada
Keyword(s):  
Green’S Function ◽  
Quantum Chromodynamics ◽  
Green's Function ◽  
Asymptotic Form ◽  
Two Dimensional ◽  
Infra Red ◽  
The One

scholarly journals DIFFERENTIAL EQUATION APPROACH FOR ONE- AND TWO-DIMENSIONAL LATTICE GREEN'S FUNCTION

2007 ◽  
Vol 21 (02n03) ◽  
pp. 139-154 ◽  
Author(s):  
J. H. ASAD
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Recurrence Relation ◽  
Green's Function ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The One ◽  
Lattice Green's Function ◽  
Lattice Green’S Function

A first-order differential equation of Green's function, at the origin G(0), for the one-dimensional lattice is derived by simple recurrence relation. Green's function at site (m) is then calculated in terms of G(0). A simple recurrence relation connecting the lattice Green's function at the site (m, n) and the first derivative of the lattice Green's function at the site (m ± 1, n) is presented for the two-dimensional lattice, a differential equation of second order in G(0, 0) is obtained. By making use of the latter recurrence relation, lattice Green's function at an arbitrary site is obtained in closed form. Finally, the phase shift and scattering cross-section are evaluated analytically and numerically for one- and two-impurities.

Thermodynamic Green’s Functions and Spectral Structure

2018 ◽  
Author(s):  
Norman J. Morgenstern Horing
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Spectral Weight ◽  
Statistical Thermodynamic ◽  
Spectral Structure ◽  
Imaginary Time ◽  
Translational Invariance ◽  
The One

Multiparticle thermodynamic Green’s functions, defined in terms of grand canonical ensemble averages of time-ordered products of creation and annihilation operators, are interpreted as tracing the amplitude for time-developing correlated interacting particle motions taking place in the background of a thermal ensemble. Under equilibrium conditions, time-translational invariance permits the one-particle thermal Green’s function to be represented in terms of a single frequency, leading to a Lehmann spectral representation whose frequency poles describe the energy spectrum. This Green’s function has finite values for both t>t′ and t<t′ (unlike retarded Green’s functions), and the two parts G1> and G1< (respectively) obey a simple proportionality relation that facilitates the introduction of a spectral weight function: It is also interpreted in terms of a periodicity/antiperiodicity property of a modified Green’s function in imaginary time capable of a Fourier series representation with imaginary (Matsubara) frequencies. The analytic continuation from imaginary time to real time is discussed, as are related commutator/anticommutator functions, also retarded/advanced Green’s functions, and the spectral weight sum rule is derived. Statistical thermodynamic information is shown to be embedded in physical features of the one- and two-particle thermodynamic Green’s functions.

scholarly journals Chemical Source Inversion Using Assimilated Constituent Observations in an Idealized Two-Dimensional System

2009 ◽  
Vol 137 (9) ◽  
pp. 3013-3025
Author(s):  
Andrew Tangborn ◽  
Robert Cooper ◽  
Steven Pawson ◽  
Zhibin Sun
Keyword(s):  
Kalman Filter ◽  
Green’S Function ◽  
Green's Function ◽  
Transport Model ◽  
Chemical Constituents ◽  
Gaussian Model ◽  
Satellite Observation ◽  
Dimensional System ◽  
Two Dimensional ◽  
Source Inversion

Abstract A source inversion technique for chemical constituents is presented that uses assimilated constituent observations rather than directly using the observations. The method is tested with a simple model problem, which is a two-dimensional Fourier–Galerkin transport model combined with a Kalman filter for data assimilation. Inversion is carried out using a Green’s function method and observations are simulated from a true state with added Gaussian noise. The forecast state uses the same spectral model but differs by an unbiased Gaussian model error and emissions models with constant errors. The numerical experiments employ both simulated in situ and satellite observation networks. Source inversion was carried out either by directly using synthetically generated observations with added noise or by first assimilating the observations and using the analyses to extract observations. Twenty identical twin experiments were conducted for each set of source and observation configurations, and it was found that in the limiting cases of a very few localized observations or an extremely large observation network there is little advantage to carrying out assimilation first. For intermediate observation densities, the source inversion error standard deviation is decreased by 50% to 90% when the observations are assimilated with the Kalman filter before carrying out the Green’s function inversion.

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