scholarly journals Random matrix theory for transition strength densities in finite quantum systems: Results from embedded unitary ensembles

2015 ◽  
Vol 359 ◽  
pp. 252-289 ◽  
Author(s):  
V.K.B. Kota ◽  
Manan Vyas
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Quantum Systems ◽  
Transition Strength ◽  
Finite Quantum Systems

RANDOM MATRIX THEORY AND ITS APPLICATION TO THE DECAY OUT OF A SUPERDEFORMED BAND

2008 ◽  
Vol 17 (supp01) ◽  
pp. 292-303 ◽  
Author(s):  
JIANZHONG GU
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Rapid Development ◽  
Quantum Systems ◽  
Many Body ◽  
Superdeformed Band ◽  
Eigenvalues And Eigenfunctions ◽  
Physical Problems

Originally, random matrix theory (RMT) was designed by Wigner to deal with the statistics of eigenvalues and eigenfunctions of complex many-body quantum systems in 1950s. During the last two decades, the RMT underwent an unexpected and rapid development: The RMT has been successfully applied to an ever increasing variety of physical problems, and it has become an important tool to attack many-body problems. In this contribution I briefly outline the development of the RMT and introduce its basics. Its application to the decay out of a Superdeformed band and a comparison of the approach used in Ref. 34 with that proposed by Vigezzi et al are presented. Current theoretical activities on the decay out problem are reviewed, and the influence of the degree of chaoticity of the normally deformed states on the decay out intensity is examined systematically.

scholarly journals Superstatistics in Random Matrix Theory

2012 ◽  
Vol 17 (2) ◽  
pp. 157
Author(s):  
A.Y. Abul-Magd
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Chaotic Dynamics ◽  
Nearest Neighbor ◽  
Matrix Theory ◽  
Quantum Systems ◽  
Classical Counterpart ◽  
Successful Model ◽  
Modeling Systems ◽  
Base Invariance

Random matrix theory (RMT) provides a successful model for quantum systems, whose classical counterpart has chaotic dynamics. It is based on two assumptions: (1) matrix-element independence, and (2) base invariance. The last decade witnessed several attempts to extend RMT to describe quantum systems with mixed regular-chaotic dynamics. Most of the proposed generalizations keep the first assumption and violate the second. Recently, several authors have presented other versions of the theory that keep base invariance at the expense of allowing correlations between matrix elements. This is achieved by starting from non-extensive entropies rather than the standard Shannon entropy, or by following the basic prescription of the recently suggested concept of superstatistics. The latter concept was introduced as a generalization of equilibrium thermodynamics to describe non-equilibrium systems by allowing the temperature to fluctuate. We here review the superstatistical generalizations of RMT and illustrate their value by calculating the nearest-neighbor-spacing distributions and comparing the results of calculation with experiments on billiards modeling systems in transition from order to chaos. 

scholarly journals Higher-order spacing ratios in random matrix theory and complex quantum systems

2018 ◽  
Vol 98 (10) ◽  
Author(s):  
S. Harshini Tekur ◽  
Udaysinh T. Bhosale ◽  
M. S. Santhanam
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Quantum Systems ◽  
Higher Order

SSA, Random Matrix Theory, and Noise-Reduced Correlations

2016 ◽  
Author(s):  
Jan W Dash ◽  
Xipei Yang ◽  
Mario Bondioli ◽  
Harvey J. Stein
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory

History—an overview

2018 ◽  
Author(s):  
Oriol Bohigas ◽  
Hans A. Weidenmüller
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Rapid Development ◽  
The Past ◽  
History Of ◽  
And Mathematics

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 the first four decades of RMT. Later developments are partially covered. In the past 20 years RMT has experienced rapid development and has expanded into a number of areas of physics and mathematics.

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