scholarly journals Performance analysis of a physically constructed orthogonal representation of imaginary-time Green's function

2018 ◽  
Vol 98 (3) ◽  
Author(s):  
Naoya Chikano ◽  
Junya Otsuki ◽  
Hiroshi Shinaoka
Keyword(s):  
Performance Analysis ◽  
Green’S Function ◽  
Green's Function ◽  
Imaginary Time ◽  
Orthogonal Representation

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 SpM: Sparse modeling tool for analytic continuation of imaginary-time Green’s function

2019 ◽  
Vol 244 ◽  
pp. 319-323 ◽  
Author(s):  
Kazuyoshi Yoshimi ◽  
Junya Otsuki ◽  
Yuichi Motoyama ◽  
Masayuki Ohzeki ◽  
Hiroshi Shinaoka
Keyword(s):  
Green’S Function ◽  
Analytic Continuation ◽  
Green's Function ◽  
Imaginary Time ◽  
Sparse Modeling ◽  
Modeling Tool

GREEN'S FUNCTION MATCHING METHOD FOR REALISTIC CALCULATIONS OF INTERFACES

1985 ◽  
Vol 46 (C4) ◽  
pp. C4-321-C4-329 ◽  
Author(s):  
E. Molinari ◽  
G. B. Bachelet ◽  
M. Altarelli
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Matching Method
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