Random Matrices And The Statistical Theory Of Energy Levels D M L Mehta

Random Matrices and the Statistical Theory of Energy Levels D M.L. Mehta

Random Matrices and the Statistical Theory of Energy Levels

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.

Spectroscopy of Complex Oxide Interfaces

This book summarizes the most recent and compelling experimental results for complex oxide interfaces. The results of this book were obtained with the cutting-edge photoemission technique at highest energy resolution. Due to their fascinating properties for new-generation electronic devices and the challenge of investigating buried regions, the book chiefly focuses on complex oxide interfaces. The crucial feature of exploring buried interfaces is the use of soft X-ray angle-resolved photoemission spectroscopy (ARPES) operating on the energy range of a few hundred eV to increase the photoelectron mean free path, enabling the photons to penetrate through the top layers – in contrast to conventional ultraviolet (UV)-ARPES techniques. The results presented here, achieved by different research groups around the world, are summarized in a clearly structured way and discussed in comparison with other photoemission spectroscopy techniques and other oxide materials. They are complemented and supported by the most recent theoretical calculations as well as results of complementary experimental techniques including electron transport and inelastic resonant X-ray scattering.