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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*

- 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*

- 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*

- 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*

- 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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