Boundary Green’s function for spin-incoherent interacting electrons in one dimension

2007 ◽  
Vol 76 (8) ◽  
Author(s):  
Paata Kakashvili ◽  
Henrik Johannesson
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
One Dimension ◽  
Interacting Electrons

scholarly journals Exact Green's Function for the Finite Rectangular Potential Well in One Dimension

1985 ◽  
Vol 40 (4) ◽  
pp. 379-382 ◽  
Author(s):  
R. Baltin
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Free Particle ◽  
One Dimension ◽  
Potential Well ◽  
Complex Energy ◽  
One Dimensional ◽  
Special Cases ◽  
The One ◽  
Energy Plane

For the one-dimensional potential well with finite height V0( V0 > 0 or V0 < 0) the exact Green's function G is calculated by solving the differential equation. The poles of G in the complex energy plane are shown to coincide with the solutions to the Schrödinger eigenvalue equation for this potential. The well-known Green's functions for the special cases of the free particle and of the particle in an infinitely high potential box are recovered.

scholarly journals Pedagogical introduction to equilibrium Green's functions: condensed-matter examples with numerical implementations

2016 ◽  
Vol 39 (1) ◽  
Author(s):  
Mariana M. Odashima ◽  
Beatriz G. Prado ◽  
E. Vernek
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Function Method ◽  
Green's Functions ◽  
Green’S Functions ◽  
Relaxation Times ◽  
Scientific Language ◽  
Green’S Function Method ◽  
Discrete Lattices ◽  
Interacting Electrons

The Green's function method has applications in several fields in Physics, from classical differential equations to quantum many-body problems. In the quantum context, Green's functions are correlation functions, from which it is possible to extract information from the system under study, such as the density of states, relaxation times and response functions. Despite its power and versatility, it is known as a laborious and sometimes cumbersome method. Here we introduce the equilibrium Green's functions and the equation-of-motion technique, exemplifying the method in discrete lattices of non-interacting electrons. We start with simple models, such as the two-site molecule, the infinite and semi-infinite one-dimensional chains, and the two-dimensional ladder. Numerical implementations are developed via the recursive Green's function, implemented in Julia, an open-source, efficient and easy-to-learn scientific language. We also present a new variation of the surface recursive Green's function method, which can be of interest when simulating simultaneously the properties of surface and bulk.

Sign in / Sign up

Export Citation Format

Share Document