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Physics
Random Matrix Theory and Applications (Web)
Syllabus
Co-ordinated by :
IIT Kharagpur
Available from :
2014-12-23
Lec :
1
Modules / Lectures
General Considerations
Complexity in physical systems: various forms
Statistical behavior of physical properties
Need of random matrix models
Maximum entropy approach to complex systems : an information theoretic viewpoint
Probability and information entropy
Natural probability measure: the role of symmetries
The maximum entropy criterion in the context of statistical inferences
Random matrix ensembles : General
Nature of ensemble: Role of symmetry, interactions and other system conditions: Part I
Nature of ensemble: Role of symmetry, interactions and other system conditions: Part II
Nature of ensemble: Role of symmetry, interactions and other system conditions: Part III
Basis invariance vs Basis dependence of the ensemble: part I
Basis invariance vs Basis dependence of the ensemble: part II
Invariant Gaussian ensembles of Hermitian matrices: Wigner-Dyson ensembles (general)
Invariant Gaussian ensembles of Hermitian matrices: eigenvalues-distribution of 2 2 Wigner-Dyson ensembles
Invariant Gaussian ensembles of Hermitian matrices: eigenvalues/ eigenfunctions distributions of N X N Wigner-Dyson ensembles
Invariant Gaussian ensembles of Hermitian matrices: Chiral ensembles
Invariant Gaussian ensembles of Hermitian matrices: particle-hole ensembles
Time-periodic systems and circular ensembles of unitary matrices
Non-Hermitian, Laguerre ensembles, Multi-cut ensembles etc.
Correlations and fluctuation measures
Level Density
Fluctuation measures of eigenvalues: basics
2nd order level correlations
Higher order fluctuation measures
Fluctuation measures of eigenfunctions
Fluctuation measures of eigenfunctions (Contd.)
Multifractality, Universality etc.
System dependent random matrix ensemble
Varying system conditions and transition between stationary ensembles
Common mathematical formulation of eigenvalue statistics
Common mathematical formulation of uctuation measures: Examples
Connection to one dimensional Calogero-Sutherland Hamiltonian
Correlated random matrix ensembles: common mathematical formulation of eigenvalues statistics
Critical ensembles and role of complexity parameter
Applications to quantum systems
Random matrix theory of quantum transport
Quantum Chaos and Random matrix theory
Disordered Systems and Random matrix theory
Many body physics, eld theories and Random matrix theory
Application to classical systems
Financial and Atmospheric uctuations
Complex Networks
Biological Systems
Application to classical and quantum optics
Waves in solid, liquids and number-theory
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