Linear Response Theory

An Analytic-Algebraic Approach

  • Giuseppe De Nittis
  • Max Lein

Part of the SpringerBriefs in Mathematical Physics book series (BRIEFSMAPHY, volume 21)

Table of contents

  1. Front Matter
    Pages i-x
  2. Giuseppe De Nittis, Max Lein
    Pages 1-5
  3. Giuseppe De Nittis, Max Lein
    Pages 7-26
  4. Giuseppe De Nittis, Max Lein
    Pages 27-52
  5. Giuseppe De Nittis, Max Lein
    Pages 53-67
  6. Giuseppe De Nittis, Max Lein
    Pages 69-95
  7. Giuseppe De Nittis, Max Lein
    Pages 97-119
  8. Giuseppe De Nittis, Max Lein
    Pages 121-132
  9. Back Matter
    Pages 133-138

About this book


This book presents a modern and systematic approach to Linear Response Theory (LRT) by combining analytic and algebraic ideas. LRT is a tool to study systems that are driven out of equilibrium by external perturbations. In particular the reader is provided with a new and robust tool to implement LRT for a wide array of systems. The proposed formalism in fact applies to periodic and random systems in the discrete and the continuum. After a short introduction describing the structure of the book, its aim and motivation, the basic elements of the theory are presented in chapter 2. The mathematical framework of the theory is outlined in chapters 3–5: the relevant von Neumann algebras, noncommutative $L^p$- and Sobolev spaces are introduced; their construction is then made explicit for common physical systems; the notion of isopectral perturbations and the associated dynamics are studied. Chapter 6 is dedicated to the main results, proofs of the Kubo and Kubo-Streda formulas. The book closes with a chapter about possible future developments and applications of the theory to periodic light conductors.
The book addresses a wide audience of mathematical physicists, focusing on the conceptual aspects rather than technical details and making algebraic methods accessible to analysts.


Sobolev spaces von Neumann algebras Maxwell operators Schroedinger-Landau operator Green-Kubo formula Kubo formula BdG superconductors Bogoliubov-de Gennes superconductors gauge-type perturbations photonic crystals thermal flux in superconductors

Authors and affiliations

  • Giuseppe De Nittis
    • 1
  • Max Lein
    • 2
  1. 1.Facultad de Matemáticas, Instituto de FísicaPontificia Universidad Católica de ChileSantiagoChile
  2. 2.Advanced Institute for Materials ResearchTohoku UniversitySendaiJapan

Bibliographic information

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