skip to main content

Title: Time series, correlation matrices and random matrix models

In this set of five lectures the authors have presented techniques to analyze open classical and quantum systems using correlation matrices. For diverse reasons we shall see that random matrices play an important role to describe a null hypothesis or a minimum information hypothesis for the description of a quantum system or subsystem. In the former case various forms of correlation matrices of time series associated with the classical observables of some system. The fact that such series are necessarily finite, inevitably introduces noise and this finite time influence lead to a random or stochastic component in these time series. By consequence random correlation matrices have a random component, and corresponding ensembles are used. In the latter we use random matrices to describe high temperature environment or uncontrolled perturbations, ensembles of differing chaotic systems etc. The common theme of the lectures is thus the importance of random matrix theory in a wide range of fields in and around physics.
Authors:
 [1] ;  [2]
  1. Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, C.P. 62210 Cuernavaca (Mexico)
  2. Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, C.P. 62210 Cuernavaca, México and Centro Internacional de Ciencias, C.P. 62210 Cuernavaca (Mexico)
Publication Date:
OSTI Identifier:
22264082
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1575; Journal Issue: 1; Conference: Latin-American school of physics Marcos Moshinsky Elaf: Nonlinear dynamics in Hamiltonian systems, Mexico City (Mexico), 22 Jul - 2 Aug 2013; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; CORRELATIONS; HYPOTHESIS; MATRICES; PERTURBATION THEORY; STOCHASTIC PROCESSES