  Linear response theory is a tool with which one can study systems that are
driven out of equilibrium by external perturbations. This monograph presents a
thoroughly modern framework to make linear response theory rigorous for a wide
array of systems, that is suitable for novel applications such as periodic and
random light conductors not yet covered in the literature. Our
analytic-algebraic approach, based on von Neumann algebras and associated
non-commutative $L^p$-spaces, can deal with discrete and continuous models
alike, and include effects of disorder. First, we explain the mathematical
setting, give a complete list of our hypotheses and state the main results,
which include Kubo and Kubo-Streda formulas. To make our book accessible to a
wide audience, we spend Chapters 3 and 4 explaining the mathematical
underpinnings such as non-commutative $L^p$- and Sobolev spaces, and
generalized commutators. Furthermore, we show how to construct a von Neumann
algebras from a topological dynamical system and a 2-cocycle, a procedure which
applies to discrete and continuous quantum systems. We dedicate Chapters 5 and
6 to the proofs of our main results. We close the book by sketching a novel
application, linear response theory for periodic and random light conductors.
This monograph is aimed at advanced students in mathematical physics and
researchers.
