The linear response regime
http://www.yambo-code.org/andrea
Andrea Marini
The Linear Reponse Regime. A. Marini
People
The Linear Reponse Regime. A. Marini
The absorption spectrum
Absorption linearly related to the Imaginary part of the MACROSCOPIC
dielectric constant (frequency dependent)
The Linear Reponse Regime. A. Marini
Linear-response Regime
The Linear Reponse Regime. A. Marini
Kubo Formula
The Linear Reponse Regime. A. Marini
Response Functions
The Linear Reponse Regime. A. Marini
Macroscopic Perturbations ...
The Linear Reponse Regime. A. Marini
… microscopic observables
The Linear Reponse Regime. A. Marini
Macroscopic averages (I)
The Linear Reponse Regime. A. Marini
Macroscopic averages (II)
The Linear Reponse Regime. A. Marini
Macroscopic averages (III)
The Linear Reponse Regime. A. Marini
The dielectric function
Note that the dielectric function can be defined ONLY in terms of the
external slowly varying functions
The Linear Reponse Regime. A. Marini
Response function Dyson equations (I)
The Linear Reponse Regime. A. Marini
Response function Dyson equations (II)
Diagrammatically the
dyson equation for the
response function
defines the reducible
(  ) and irreducible
( P ) response functions
The Linear Reponse Regime. A. Marini
Independent particles (theory)
The Linear Reponse Regime. A. Marini
Independent particles (practice)
The Linear Reponse Regime. A. Marini
Independent (quasi)particles ?
The Linear Reponse Regime. A. Marini
IQP absorption
The Linear Reponse Regime. A. Marini
What is missing ?
The Linear Reponse Regime. A. Marini
Eelectron-hole pairs ...
LiF
Non
Interacting
Electron-hole
realm
E gap
The Linear Reponse Regime. A. Marini
… and plasmons
Drude
Plasmon
Silver
The plasmon condition is
The Linear Reponse Regime. A. Marini
Collective excitations
−1
W 0 ∼ε v
The accuracy of the GW approx is
connected to a precise description of the
poles of the screened interaction... the
PLASMONS
Although a plasmon is made up of electrons, it is
not an electron: it is a gang, or collection, of
electrons that get together under the urging of
the long-range Coulomb force and decide to act
in concert. Hence, for the purpose of discussing
their behavior, they may, like an orchestra or
choir, be considered as a single entity following
the same (Coulombic) conductor
The Linear Reponse Regime. A. Marini
The Lorentz oscillator
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The Drude Model
In a metal the electrons are free to move
and they react to an average electric field
ω0 =0
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A final look to real materials
Copper
Silver
Aluminium
The Linear Reponse Regime. A. Marini
References
G. Strinati, Rivista del Nuovo Cimento 11 (12)1 1988
M. Rohlfing and S. G. Louie, Phys. Rev. B 62, 4927 2000
G. Onida, L. Reining, and A. Rubio, Rev. Mod. Phys. 74, 601 2002.
Codes (GPL)
A. Marini et. al. www.yambo-code.org
L. Martin Samoa et. al. www.sax-project.org
L. Reining et. al. www.bethe-salpeter.org
C. Ambrosh-Draxl et. al. www.exciting-code.org
The Linear Reponse Regime. A. Marini