Method to modify random matrix theory using short-time behavior in chaotic systems

2009 ◽  
Vol 80 (3) ◽  
Author(s):  
A. Matthew Smith ◽  
Lev Kaplan
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Chaotic Systems ◽  
Matrix Theory ◽  
Time Behavior ◽  
Short Time

scholarly journals Late time physics of holographic quantum chaos

2021 ◽  
Vol 11 (2) ◽  
Author(s):  
Alexander Altland ◽  
Julian Sonner
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Quantum Chaos ◽  
Bound States ◽  
Chaotic Systems ◽  
Matrix Theory ◽  
Effective Field ◽  
Late Time ◽  
Higher Dimensional ◽  
Goldstone Modes

Quantum chaotic systems are often defined via the assertion that their spectral statistics coincides with, or is well approximated by, random matrix theory. In this paper we explain how the universal content of random matrix theory emerges as the consequence of a simple symmetry-breaking principle and its associated Goldstone modes. This allows us to write down an effective-field theory (EFT) description of quantum chaotic systems, which is able to control the level statistics up to an accuracy {O} \left(e^{-S} \right)O(e−S) with SS the entropy. We explain how the EFT description emerges from explicit ensembles, using the example of a matrix model with arbitrary invariant potential, but also when and how it applies to individual quantum systems, without reference to an ensemble. Within AdS/CFT this gives a general framework to express correlations between ``different universes’’ and we explicitly demonstrate the bulk realization of the EFT in minimal string theory where the Goldstone modes are bound states of strings stretching between bulk spectral branes. We discuss the construction of the EFT of quantum chaos also in higher dimensional field theories, as applicable for example for higher-dimensional AdS/CFT dual pairs.

scholarly journals Quantum Chaotic Systems and Random Matrix Theory

2019 ◽  
pp. 12-1-12-18
Author(s):  
Akhilesh Pandey ◽  
Avanish Kumar ◽  
Sanjay Puri
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Chaotic Systems ◽  
Matrix Theory

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
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