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Linear Response Theory

Part of the SpringerBriefs in Mathematical Physics Book Series (volume 21)

DOI: 10.1007/978-3-319-56732-7

ISBN: 978-3-319-56731-0

Publisher: Springer International Publishing - Springer Journals

Jun 22, 2017

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Chapter 1Introduction

De Nittis, Giuseppe; Lein, Max

Pages: 1 –5

[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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym}...
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Chapter 2Setting, Hypotheses and Main Results

De Nittis, Giuseppe; Lein, Max

Pages: 7 –26

[The purpose of this chapter is to explain the setting of the analytic-algebraic approach to linear response theory presented in this book, enumerate the mathematical hypotheses and state the main results.]
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Chapter 3Mathematical Framework

De Nittis, Giuseppe; Lein, Max

Pages: 27 –52

[The purpose of this chapter is to introduce all the necessary mathematical notions, and make the remainder of the book self-contained. While none of mathematical objects covered here are new, our goal is to make this work accessible to as many people as possible.]
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Chapter 4A Unified Framework for Common Physical Systems

De Nittis, Giuseppe; Lein, Max

Pages: 53 –67

[It is explained how the setting detailed in Chaps. 2 and 3 directly applies to the most common examples treated in the physics literature. That includes quantum systems with and without magnetic fields, on the discrete and the continuum, periodic or random.]
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Chapter 5Studying the Dynamics

De Nittis, Giuseppe; Lein, Max

Pages: 69 –95

[Here, the unperturbed, perturbed and interaction dynamics are characterized and compared within the framework of Chap. 3. Among other things, cores and domains of the generators are identified, the existence of the propagators is proven, and their continuity in the perturbation parameter shown.]
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Chapter 6The Kubo Formula and Its Adiabatic Limit

De Nittis, Giuseppe; Lein, Max

Pages: 97 –119

[This chapter contains the proofs of our main results.]
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Chapter 7Applications

De Nittis, Giuseppe; Lein, Max

Pages: 121 –132

[The book closes by outlining a novel application, establishing linear response theory for periodic light conductors, and briefly explaining how previous treatments of the Quantum Hall Effect are subsumed by the analytic-algebraic approach to linear response theory developed here.]

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