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Statistical Benchmarks for Quantum Transport in Complex Systems

From Characterisation to Design

  • Book
  • © 2018

Overview

Authors:
  1. Mattia Walschaers

    1. Laboratoire Kastler Brossel, Sorbonne University, CNRS, École Normale Supérieure, and Collège de France, Paris, France

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  • Nominated as an outstanding Ph.D thesis by the Albert Ludwig University, Freiburg, Germany
  • Provides an introduction to the algebraic formalism for many-particle systems, applied to modern problems such as boson sampling
  • Introduces a statistical approach to understand dynamical features of complex quantum systems
  • Presents extensive context, background, and mathematical formalism in an accessible way

Part of the book series: Springer Theses (Springer Theses)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xx
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  2. General Introduction

    1. Front Matter

      Pages 1-1
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    2. Perspectives and Outline

      • Mattia Walschaers
      Pages 3-19

    3. Essentials of Quantum Theory

      • Mattia Walschaers
      Pages 21-49

    4. Complex Quantum Systems and Random Matrix Theory

      • Mattia Walschaers
      Pages 51-74

  3. Single-Particle Quantum Transport

    1. Front Matter

      Pages 75-75
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    2. Efficient Transport in Closed Systems

      • Mattia Walschaers
      Pages 77-143

    3. Scattering Approach to Efficient Transport

      • Mattia Walschaers
      Pages 145-169

    4. Quantum Effects in Biological Systems

      • Mattia Walschaers
      Pages 171-195

  4. Many-Particle Quantum Transport

    1. Front Matter

      Pages 197-197
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    2. Describing Many-Particle Quantum Systems

      • Mattia Walschaers
      Pages 199-263

    3. Many-Particle Interference

      • Mattia Walschaers
      Pages 265-373

    4. Currents of Indistinguishable Particles

      • Mattia Walschaers
      Pages 375-419

  5. General Conclusions and Prospects

    1. Front Matter

      Pages 421-421
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    2. Conclusions and Outlook

      • Mattia Walschaers
      Pages 423-432

  6. Back Matter

    Pages 433-450
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Keywords

About this book

This book introduces a variety of statistical tools for characterising and designing the dynamical features of complex quantum systems. These tools are applied in the contexts of energy transfer in photosynthesis, and boson sampling. In dynamical quantum systems, complexity typically manifests itself via the interference of a rapidly growing number of paths that connect the initial and final states. The book presents the language of graphs and networks, providing a useful framework to discuss such scenarios and explore the rich phenomenology of transport phenomena. As the complexity increases, deterministic approaches rapidly become intractable, which leaves statistics as a viable alternative.

Authors and Affiliations

  • Laboratoire Kastler Brossel, Sorbonne University, CNRS, École Normale Supérieure, and Collège de France, Paris, France

    Mattia Walschaers

Bibliographic Information

  • Book Title: Statistical Benchmarks for Quantum Transport in Complex Systems

  • Book Subtitle: From Characterisation to Design

  • Authors: Mattia Walschaers

  • Series Title: Springer Theses

  • DOI: https://doi.org/10.1007/978-3-319-93151-7

  • Publisher: Springer Cham

  • eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)

  • Copyright Information: Springer Nature Switzerland AG 2018

  • Hardcover ISBN: 978-3-319-93150-0Published: 11 August 2018

  • Softcover ISBN: 978-3-030-06602-4Published: 26 December 2018

  • eBook ISBN: 978-3-319-93151-7Published: 31 July 2018

  • Series ISSN: 2190-5053

  • Series E-ISSN: 2190-5061

  • Edition Number: 1

  • Number of Pages: XX, 450

  • Number of Illustrations: 63 b/w illustrations, 17 illustrations in colour

  • Topics: Quantum Physics, Statistical Physics and Dynamical Systems, Complex Systems

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