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.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Wigner surmise canonical | 1 |
| Wigner surmise in random matrix theory | 1 |
| Wigner–Dyson statistics | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T818207 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Wigner surmise Context triple: [Eugene Wigner, knownFor, Wigner surmise]
-
A.
Wick’s theorem
Wick’s theorem is a fundamental result in quantum field theory that expresses time-ordered products of field operators as sums of normal-ordered products with all possible contractions, forming the basis for deriving Feynman rules and diagrammatic expansions.
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B.
Riemann–Siegel formula
The Riemann–Siegel formula is an asymptotic expression that efficiently approximates the Riemann zeta function on the critical line, playing a key role in the numerical study of its zeros.
-
C.
Born–Huang expansion
The Born–Huang expansion is a quantum mechanical method that systematically improves upon the Born–Oppenheimer approximation by including couplings between electronic and nuclear motions in molecular systems.
-
D.
Brillouin–Wigner perturbation theory
Brillouin–Wigner perturbation theory is a formulation of quantum mechanical perturbation theory that uses an energy-dependent effective Hamiltonian to obtain improved approximations to eigenvalues and eigenstates.
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E.
Kac ring model
The Kac ring model is a simplified mathematical model in statistical mechanics introduced by Mark Kac to illustrate how macroscopic irreversibility can emerge from time-reversible microscopic dynamics.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Wigner surmise Target entity description: 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.
-
A.
Wick’s theorem
Wick’s theorem is a fundamental result in quantum field theory that expresses time-ordered products of field operators as sums of normal-ordered products with all possible contractions, forming the basis for deriving Feynman rules and diagrammatic expansions.
-
B.
Riemann–Siegel formula
The Riemann–Siegel formula is an asymptotic expression that efficiently approximates the Riemann zeta function on the critical line, playing a key role in the numerical study of its zeros.
-
C.
Born–Huang expansion
The Born–Huang expansion is a quantum mechanical method that systematically improves upon the Born–Oppenheimer approximation by including couplings between electronic and nuclear motions in molecular systems.
-
D.
Brillouin–Wigner perturbation theory
Brillouin–Wigner perturbation theory is a formulation of quantum mechanical perturbation theory that uses an energy-dependent effective Hamiltonian to obtain improved approximations to eigenvalues and eigenstates.
-
E.
Kac ring model
The Kac ring model is a simplified mathematical model in statistical mechanics introduced by Mark Kac to illustrate how macroscopic irreversibility can emerge from time-reversible microscopic dynamics.
- F. None of above. chosen
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 surmise
self-linksurface differs
ⓘ
surface form:
Wigner–Dyson statistics
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 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Wigner surmise Description of subject: 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.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Wigner–Dyson statistics
this entity surface form:
Wigner surmise in random matrix theory