Springer Tracts in Modern Physics

Semiclassical Approach to Mesoscopic Systems

Classical Trajectory Correlations and Wave Interference

Authors: Waltner, Daniel

  • Gives a modern approach
  • Features Ehrenfest-time effects in mesoscopic systems
  • Integrates basics and new results
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About this book

This volume describes mesoscopic systems with classically chaotic dynamics using semiclassical methods which combine elements of classical dynamics and quantum interference effects. Experiments and numerical studies show that Random Matrix Theory (RMT) explains physical properties of these systems well. This was conjectured more than 25 years ago by Bohigas, Giannoni and Schmit for the spectral properties. Since then, it has been a challenge to understand this connection analytically. 
The author offers his readers a clearly-written and up-to-date treatment of the topics covered. He extends previous semiclassical approaches that treated spectral and conductance properties. He shows that RMT results can in general only be obtained semiclassically when taking into account classical configurations not considered previously, for example those containing multiply traversed periodic orbits.

Furthermore, semiclassics is capable of describing effects beyond RMT. In this context he studies the effect of a non-zero Ehrenfest time, which is the minimal time needed for an initially spatially localized wave packet to show interference. He derives its signature on several quantities characterizing mesoscopic systems, e. g. dc and ac conductance, dc conductance variance, n-pair correlation functions of scattering matrices and the gap in the density of states of Andreev billiards.

About the authors

Daniel Waltner  (Dr. rer. nat. in a few days)
Universität Regensburg
Institut I - Theoretische Physik
93040 Regensburg
Germany
Daniel.Waltner@physik.uni-r.de

Reviews

From the reviews:

“Quantum chaos has been the subject of intensive theoretical and experimental investigations in the last forty years. … This is the subject of the present book, largely based upon the personal research activity of the author. … this book may be useful and interesting to the reader working on semi-classical approaches to quantum problems and chaotic phenomena in mesoscopic systems. Moreover, the beginner will also benefit from reading this book, thanks to the exhaustive bibliography given at the end of each chapter.” (Giorgio Cattapan, Mathematical Reviews, Issue 2012 m)


Table of contents (6 chapters)

  • Introduction

    Waltner, Daniel

    Pages 1-11

  • Semiclassical Techniques

    Waltner, Daniel

    Pages 13-39

  • Survival Probability and Fidelity Decay

    Waltner, Daniel

    Pages 41-87

  • Ehrenfest-Time Effects in Mesoscopic Systems

    Waltner, Daniel

    Pages 89-147

  • Semiclassical Analogues to Field-Theoretical Effects

    Waltner, Daniel

    Pages 149-166

Buy this book

eBook $149.00
price for USA (gross)
  • ISBN 978-3-642-24528-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $189.00
price for USA
  • ISBN 978-3-642-24527-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $189.00
price for USA
  • ISBN 978-3-642-44061-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Semiclassical Approach to Mesoscopic Systems
Book Subtitle
Classical Trajectory Correlations and Wave Interference
Authors
Series Title
Springer Tracts in Modern Physics
Series Volume
245
Copyright
2012
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag GmbH Berlin Heidelberg
eBook ISBN
978-3-642-24528-2
DOI
10.1007/978-3-642-24528-2
Hardcover ISBN
978-3-642-24527-5
Softcover ISBN
978-3-642-44061-8
Series ISSN
0081-3869
Edition Number
1
Number of Pages
X, 182
Topics