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.

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Generate an image of the Wigner surmise (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.)

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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 ⓘ
Gaussian symplectic ensemble ⓘ
Gaussian unitary ensemble ⓘ
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 ⓘ
normalizationCondition ∫₀^∞ P(s) ds = 1 ⓘ
parameter Dyson index β ⓘ
level spacing s ⓘ
PoissonComparison Poisson distribution has P(s) = e^{-s} ⓘ
PoissonFeature no level repulsion ⓘ
predicts P(s) ∝ s^β e^{-a s^2} ⓘ
relatedConcept Wigner–Dyson statistics ⓘ
linked to: Wigner surmise

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 ⓘ

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Referenced by (7)

Full triples — surface form annotated when it differs from this entity's canonical label.

Eugene Wigner → knownFor → Wigner surmise ⓘ
Wigner surmise → relatedConcept → Wigner–Dyson statistics ⓘ
linked to: Wigner surmise
Wigner Jenő Pál → knownFor → Wigner surmise in random matrix theory ⓘ
linked to: Wigner surmise
Gaussian orthogonal ensemble → eigenvalueStatistics → Wigner–Dyson statistics ⓘ
linked to: Wigner surmise
Dyson index β → appearsIn → Wigner–Dyson statistics ⓘ
linked to: Wigner surmise
Poisson distribution with P(s) = e^{-s} → contrastedWith → Wigner–Dyson level spacing distributions ⓘ
linked to: Wigner surmise
quantum chaos → hasKeyConcept → Wigner–Dyson statistics ⓘ
linked to: Wigner surmise