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Quantum Transport in Mesoscopic Systems: Complexity and Statistical Fluctuations. A Maximum Entropy Viewpoint

Pier A. Mello and Narendra Kumar

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198525820
eISBN:
9780191712234
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525820.001.0001
Subject:
Physics, Condensed Matter Physics / Materials

This book presents a statistical theory of complex wave scattering and quantum transport in a class of physical systems of current interest having chaotic classical dynamics (e.g., microwave cavities ... More


INTRODUCTION TO THE QUANTUM MECHANICAL TIME-INDEPENDENT SCATTERING THEORY I: ONE-DIMENSIONAL SCATTERING

Pier A. Mello and Narendra Kumar

in Quantum Transport in Mesoscopic Systems: Complexity and Statistical Fluctuations. A Maximum Entropy Viewpoint

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198525820
eISBN:
9780191712234
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525820.003.0002
Subject:
Physics, Condensed Matter Physics / Materials

This chapter is devoted to basic potential scattering theory, focusing on the case of a one-dimensional conductor and an open cavity with a one-channel lead connected to it. The contents of this ... More


Classic Food Web Theory

Kevin S. McCann

in Food Webs (MPB-50)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691134178
eISBN:
9781400840687
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691134178.003.0010
Subject:
Biology, Ecology

This chapter examines the basic assumptions of classic food web theory. It first considers the classic whole-community approach, which assumes that any specific matrix represents a sample from a ... More


The Hanle effect and the theory of resonance fluorescence experiments

Alan Corney

in Atomic and Laser Spectroscopy

Published in print:
2006
Published Online:
September 2007
ISBN:
9780199211456
eISBN:
9780191705915
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199211456.003.0015
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter provides an account of atomic resonance fluorescence and its depolarization by external magnetic fields, also known as the Hanle effect. Experiments in mercury vapour and their ... More


INTRODUCTION

Pier A. Mello and Narendra Kumar

in Quantum Transport in Mesoscopic Systems: Complexity and Statistical Fluctuations. A Maximum Entropy Viewpoint

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198525820
eISBN:
9780191712234
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525820.003.0001
Subject:
Physics, Condensed Matter Physics / Materials

This chapter introduces the notion of complex scattering of waves, emphasizes the generality of the ideas involved, and explains its relevance to the field of nuclear physics and microwave cavities. ... More


From the shell model to the compound nucleus

Helmut Hofmann

in The Physics of Warm Nuclei: with Analogies to Mesoscopic Systems

Published in print:
2008
Published Online:
September 2008
ISBN:
9780198504016
eISBN:
9780191708480
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198504016.003.0004
Subject:
Physics, Nuclear and Plasma Physics

This chapter examines nuclear properties that are related to the presence of interactions residual to the mean field. The elementary features of random matrix theory are explained, and the Wigner ... More


Average collective motion of small amplitude

Helmut Hofmann

in The Physics of Warm Nuclei: with Analogies to Mesoscopic Systems

Published in print:
2008
Published Online:
September 2008
ISBN:
9780198504016
eISBN:
9780191708480
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198504016.003.0006
Subject:
Physics, Nuclear and Plasma Physics

This chapter focuses on collective motion of isoscalar nature parameterized by shape variables. The equations of motion are derived from energy conservation as implied by self-consistency. A basic ... More


Random matrix approaches to open quantum systems

Henning Schomerus

in Stochastic Processes and Random Matrices: Lecture Notes of the Les Houches Summer School: Volume 104, July 2015

Published in print:
2017
Published Online:
January 2018
ISBN:
9780198797319
eISBN:
9780191838774
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198797319.003.0010
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Over the past decades, a great body of theoretical and mathematical work has been devoted to random-matrix descriptions of open quantum systems. This chapter reviews the physical origins and ... More


Bidiagonal Factorization

Shaun M. Fallat and Charles R. Johnson

in Totally Nonnegative Matrices

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691121574
eISBN:
9781400839018
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691121574.003.0003
Subject:
Mathematics, Applied Mathematics

This chapter introduces and methodically develops the important and useful topic of bidiagonal factorization. Factorization of matrices is one of the most important topics in matrix theory, and plays ... More


History—an overview

Oriol Bohigas and Hans A. Weidenmüller

in Stochastic Processes and Random Matrices: Lecture Notes of the Les Houches Summer School: Volume 104, July 2015

Published in print:
2017
Published Online:
January 2018
ISBN:
9780198797319
eISBN:
9780191838774
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198797319.003.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

An overview of the history of random matrix theory (RMT) is provided in this chapter. Starting from its inception, the authors sketch the history of RMT until about 1990, focusing their attention on ... More


Random matrices and number theory: some recent themes

Jon P. Keating

in Stochastic Processes and Random Matrices: Lecture Notes of the Les Houches Summer School: Volume 104, July 2015

Published in print:
2017
Published Online:
January 2018
ISBN:
9780198797319
eISBN:
9780191838774
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198797319.003.0008
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The aim of this chapter is to motivate and describe some recent developments concerning the applications of random matrix theory to problems in number theory. The first section provides a brief and ... More


Random matrix theory and quantum chromodynamics

Gernot Akemann

in Stochastic Processes and Random Matrices: Lecture Notes of the Les Houches Summer School: Volume 104, July 2015

Published in print:
2017
Published Online:
January 2018
ISBN:
9780198797319
eISBN:
9780191838774
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198797319.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter was originally presented to a mixed audience of physicists and mathematicians with some basic working knowledge of random matrix theory. The first part is devoted to the solution of the ... More


Modern telecommunications: a playground for physicists?

Aris L. Moustakas

in Stochastic Processes and Random Matrices: Lecture Notes of the Les Houches Summer School: Volume 104, July 2015

Published in print:
2017
Published Online:
January 2018
ISBN:
9780198797319
eISBN:
9780191838774
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198797319.003.0009
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Data traffic in wireless networks has been increasing exponentially for a long time and is expected to continue this trend. The emerging data-hungry applications, such as video-on-demand and cloud ... More


Preliminary Results and Discussion

Shaun M. Fallat and Charles R. Johnson

in Totally Nonnegative Matrices

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691121574
eISBN:
9781400839018
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691121574.003.0002
Subject:
Mathematics, Applied Mathematics

This chapter lays out a number of basic and fundamental properties of TN matrices along with a compilation of facts and results from core matrix theory that are useful for further development of this ... More


Random matrix theory and (big) data analysis

Jean-Philippe Bouchaud

in Stochastic Processes and Random Matrices: Lecture Notes of the Les Houches Summer School: Volume 104, July 2015

Published in print:
2017
Published Online:
January 2018
ISBN:
9780198797319
eISBN:
9780191838774
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198797319.003.0006
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter reviews methods from random matrix theory to extract information about a large signal matrix C (for example, a correlation matrix arising in big data problems), from its noisy ... More


Stochastic Processes and Random Matrices: Lecture Notes of the Les Houches Summer School: Volume 104, July 2015

Grégory Schehr, Alexander Altland, Yan V. Fyodorov, Neil O'Connell, and Leticia F. Cugliandolo (eds)

Published in print:
2017
Published Online:
January 2018
ISBN:
9780198797319
eISBN:
9780191838774
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198797319.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The field of stochastic processes and random matrix theory (RMT) has been a rapidly evolving subject during the past fifteen years where the continuous development and discovery of new tools, ... More


Random matrices and loop equations

Bertrand Eynard

in Stochastic Processes and Random Matrices: Lecture Notes of the Les Houches Summer School: Volume 104, July 2015

Published in print:
2017
Published Online:
January 2018
ISBN:
9780198797319
eISBN:
9780191838774
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198797319.003.0007
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter is an introduction to algebraic methods in random matrix theory (RMT). In the first section, the random matrix ensembles are introduced and it is shown that going beyond the usual Wigner ... More


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