Linear response - Kubo formula Linear response - Kubo formula - - PowerPoint PPT Presentation

Linear response - Kubo formula Linear response - Kubo formula

system with small external perturbation

unperturbed system

perturbation coupling to field operators adiabatic switching on

measure: density matrix

linear response

Heisenberg representation

Kubo formula

Linear response - Kubo formula Linear response - Kubo formula

determine density matrix

equation of motion:

time-dependent perturbation theory

with unperturbed (equilibrium) interaction representation with

Linear response - Kubo formula Linear response - Kubo formula

formal solution:

assumption

Kubo formula

Linear response - Kubo formula examples Linear response - Kubo formula examples

magnetic susceptibility

perturbation measure magnetization

magnetic field

dielectric susceptibility

perturbation spin

charge density scalar potential

measure charge density