Wigner surmise
E98265
The Wigner surmise is an approximate formula in random matrix theory that describes the statistical distribution of spacings between neighboring energy levels in complex quantum systems.
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
approximate formula
→
probability distribution → result in random matrix theory → |
| appliesTo |
complex quantum systems
→
heavy nuclei → quantum chaotic systems → |
| approximates |
exact spacing distribution for large random matrices
→
|
| assumes |
level repulsion
→
|
| contrastsWith |
Poisson level spacing distribution
→
|
| describes |
distribution of spacings between neighboring energy levels
→
|
| DysonIndexValue |
β = 1 for GOE
→
β = 2 for GUE → β = 4 for GSE → |
| ensembleType |
Gaussian orthogonal ensemble
NERFINISHED
→
Gaussian symplectic ensemble NERFINISHED → Gaussian unitary ensemble NERFINISHED → |
| exactFor |
2×2 random matrices
→
|
| feature |
P(0) = 0
→
level repulsion exponent equals Dyson index β → |
| field |
mathematical physics
→
quantum chaos → random matrix theory → |
| gives |
nearest-neighbor level spacing distribution
→
|
| GOEFormula |
P(s) = (π/2) s exp(-π s^2 / 4)
→
|
| GSEFormula |
P(s) = (2^{18}/3^6 π^3) s^4 exp(-64 s^2 / 9π)
→
|
| GUEFormula |
P(s) = (32/π^2) s^2 exp(-4 s^2 / π)
→
|
| implies |
short-range correlations between eigenvalues
→
|
| meanSpacingCondition |
∫₀^∞ s P(s) ds = 1
→
|
| namedAfter |
Eugene Wigner
NERFINISHED
→
|
| normalizationCondition |
∫₀^∞ P(s) ds = 1
→
|
| parameter |
Dyson index β
NERFINISHED
→
level spacing s → |
| PoissonComparison |
Poisson distribution has P(s) = e^{-s}
NERFINISHED
→
|
| PoissonFeature |
no level repulsion
→
|
| predicts |
P(s) ∝ s^β e^{-a s^2}
→
|
| relatedConcept |
Wigner–Dyson statistics
NERFINISHED
→
spectral rigidity → unfolding of spectra → |
| status |
empirically accurate approximation for many physical systems
→
|
| usedFor |
modeling nuclear energy level statistics
→
testing quantum chaos in spectra → |
| usedIn |
analysis of complex atomic spectra
→
disordered systems → mesoscopic physics → quantum billiards → |
| yearProposed |
1950s
→
|
Referenced by (1)
| Subject (surface form when different) | Predicate |
|---|---|
|
Eugene Wigner
→
|
knownFor |