Random Matrices and the Statistical Theory of Energy Levels
eBook - PDF

Random Matrices and the Statistical Theory of Energy Levels

  1. 270 pages
  2. English
  3. PDF
  4. Only available on web
eBook - PDF

Random Matrices and the Statistical Theory of Energy Levels

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Table of contents
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About This Book

Random Matrices and the Statistical Theory of Energy Levels focuses on the processes, methodologies, calculations, and approaches involved in random matrices and the statistical theory of energy levels, including ensembles and density and correlation functions. The publication first elaborates on the joint probability density function for the matrix elements and eigenvalues, including the Gaussian unitary, symplectic, and orthogonal ensembles and time-reversal invariance. The text then examines the Gaussian ensembles, as well as the asymptotic formula for the level density and partition function. The manuscript elaborates on the Brownian motion model, circuit ensembles, correlation functions, thermodynamics, and spacing distribution of circular ensembles. Topics include continuum model for the spacing distribution, thermodynamic quantities, joint probability density function for the eigenvalues, stationary and nonstationary ensembles, and ensemble averages. The publication then examines the joint probability density functions for two nearby spacings and invariance hypothesis and matrix element correlations. The text is a valuable source of data for researchers interested in random matrices and the statistical theory of energy levels.

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Information

Publisher
Academic Press
Year
2014
ISBN
9781483258560
Topic
Mathematik
Subtopic
Lineare Algebra

Table of contents

  1. Front Cover
  2. Random Matrices and the Statistical Theory of Energy Levels
  3. Copyright Page
  4. Table of Contents
  5. Preface
  6. Chapter 1. Introduction
  7. Chapter 2. Gaussian Ensembles. The Joint Probability Density Function of the Matrix Elements
  8. Chapter 3. Gaussian Ensembles. The Joint Probability Density Function of the Eigenvalues
  9. Chapter 4. Gaussian Ensembles
  10. Chapter 5. The Gaussian Orthogonal Ensemble
  11. Chpater 6. The Gaussian Unitary and Symplectic Ensembles
  12. Chapter 7. Brownian Motion Model
  13. Chapter 8. Circular Ensembles
  14. Chapter 9. Circular Ensembles. Correlation Functions, Spacing Distribution, etc
  15. Chapter 10. Circular Ensembles. Thermodynamics
  16. Chapter 11. The Orthogonal Circular Ensemble. Wigner's Method
  17. Chapter 12. Matrices with Gaussian Element Densities But with No Unitary or Hermitian Condition Imposed
  18. Chapter 13. Gaussian Ensembles. Level Density in the Tail of the Semicircle
  19. Chapter 14. Bordered Matrices
  20. Chapter 15. Invariance Hypothesis and Matrix Element Correlations
  21. Chapter 16. The Joint Probability Density Functions for Two Nearby Spacings
  22. Chapter 17. Restricted Trace Ensembles. Ensembles Related to the Classical Orthogonal Polynomials
  23. Appendices
  24. References
  25. Index