Bethe-Salpeter Equation and Excitonic effects: a short introduction

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Bethe-Salpeter Equationand Excitonic effectsa
short introduction

• Valerio Olevano
• Laboratoire des Solides Irradiés
• École Polytechnique, Palaiseau

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Exciton and Bethe-Salpeter equation
RPA
GW
BSE
e-



P
O(2)
h
Polarisation
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Definitions
G Green Function
L 2-particles Correlation Function
2-particles Green Function
Polarization
Dielectric Function (observables)
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Bethe-Salpeter Equation
Bethe-Salpeter Equation
Interaction Kernel
S Self-Energy
W Screened Interaction
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Resolution of the BSEExcitonic Hamiltonian
Excitonic Eigenfunctions
Excitonic Eigenvalues
Excitonic Hamiltonian
Overlap Matrix
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Excitonic MacroscopicDielectric Function
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Excitonic HamiltonianResonant and Coupling terms
full diago of a Non-Hermitean matrix or ...
Hermitean
Symmetric
... diagonalization of an Hermitean matrix
(R) plus (eventually) Perturbation Theory