Introduction

Abstract

Linear response theory is a tool with which one can study systems that are driven out of equilibrium by external perturbations. The prototypical example is a first-principles justification of Ohm’s empirical law \(J = \sum _{j = 1}^d \sigma _j \, E_j\) (Ohm, Die galvanische Kette: mathematisch bearbeitet, 2010, [62]), which states that the current is linearly proportional to the applied external electric field: These ideas have been pioneered by Green (J. Chem. Phys. 22(3):398–413, 1954, [36]) and Kubo (J. Phys. Soc. Jap. 12(6):570–586 (1957), [51]) in the context of statistical mechanics, and later used by Strěda (J. Phys. C. 15(22):L717–L721, 1982, [79] to link the transverse conductivity in a 2d electron gas to the number of Landau levels below the Fermi energy.