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Wigner-Dyson Distribution
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Summary
The
Wigner-Dyson Distribution
describes the
Statistical Properties
of the
Spacings between eigenvalues
of
Large random matrices
, often used in
Quantum Mechanics
and
Statistical Physics
to model
Complex Systems
. It highlights
Universality in
Spectral Statistics
, showing that these properties are largely independent of the specific details of the system's Hamiltonian, depending only on its
Symmetry class
.
Concepts
Random Matrix Theory
Eigenvalue Spacing
Quantum Chaos
Universality Class
Spectral Statistics
Orthogonal Ensemble
Unitary Ensemble
Symplectic Ensemble
Hamiltonian Systems
Level Repulsion
Eigenvalue Repulsion
GOE, GUE, GSE Ensembles
Level Spacing Distribution
Level Spacing Statistics
Relevant Degrees
Probability and Statistics 100%
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