Yang–Yang equation
E265150
The Yang–Yang equation is a fundamental integral equation in statistical mechanics that describes the thermodynamic properties of one-dimensional interacting Bose gases within the Bethe ansatz framework.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Yang–Yang equation canonical | 1 |
| Yang–Yang equations | 1 |
| Yang–Yang thermodynamics | 1 |
| thermodynamic Bethe ansatz | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2422939 — 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: Yang–Yang equation Context triple: [C. N. Yang, knownFor, Yang–Yang equation]
-
A.
Tomonaga–Schwinger equation
The Tomonaga–Schwinger equation is a relativistic generalization of the Schrödinger equation that formulates quantum field evolution on arbitrary spacelike hypersurfaces, forming a key part of covariant quantum field theory.
-
B.
Schwinger–Dyson equations
The Schwinger–Dyson equations are a set of integral equations in quantum field theory that relate correlation functions and encode the full dynamics of a quantum field.
-
C.
Bethe–Salpeter equation
The Bethe–Salpeter equation is a relativistic quantum field theory equation that describes bound states of two interacting particles, such as electron–hole pairs in quantum electrodynamics.
-
D.
Fokker–Planck equation
The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
-
E.
Esaki–Tsu relation
The Esaki–Tsu relation is a fundamental formula in semiconductor physics that describes the nonlinear current–voltage characteristics and negative differential conductivity of electrons in superlattices under high electric fields.
- 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: Yang–Yang equation Target entity description: The Yang–Yang equation is a fundamental integral equation in statistical mechanics that describes the thermodynamic properties of one-dimensional interacting Bose gases within the Bethe ansatz framework.
-
A.
Tomonaga–Schwinger equation
The Tomonaga–Schwinger equation is a relativistic generalization of the Schrödinger equation that formulates quantum field evolution on arbitrary spacelike hypersurfaces, forming a key part of covariant quantum field theory.
-
B.
Schwinger–Dyson equations
The Schwinger–Dyson equations are a set of integral equations in quantum field theory that relate correlation functions and encode the full dynamics of a quantum field.
-
C.
Bethe–Salpeter equation
The Bethe–Salpeter equation is a relativistic quantum field theory equation that describes bound states of two interacting particles, such as electron–hole pairs in quantum electrodynamics.
-
D.
Fokker–Planck equation
The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
-
E.
Esaki–Tsu relation
The Esaki–Tsu relation is a fundamental formula in semiconductor physics that describes the nonlinear current–voltage characteristics and negative differential conductivity of electrons in superlattices under high electric fields.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
integral equation
ⓘ
thermodynamic Bethe ansatz equation ⓘ |
| appliesTo |
Lieb–Liniger model
ⓘ
delta-function interacting Bose gas ⓘ interacting Bose gas ⓘ one-dimensional Bose gas ⓘ |
| assumes |
integrability of the model
ⓘ
thermodynamic limit ⓘ |
| basedOn |
Bethe ansatz quantization conditions
ⓘ
linked to:
Bethe ansatz
string hypothesis for rapidities ⓘ |
| captures | effects of interactions on thermodynamic quantities ⓘ |
| characteristic | nonlinear integral equation ⓘ |
| describes |
equilibrium thermodynamics of integrable quantum systems
ⓘ
thermodynamic properties of one-dimensional interacting Bose gases ⓘ |
| developedBy |
C. P. Yang
ⓘ
linked to:
C. N. Yang
Chen Ning Yang ⓘ
linked to:
C. N. Yang
|
| domain |
finite temperature
ⓘ
grand canonical ensemble ⓘ |
| field |
quantum many-body physics
ⓘ
statistical mechanics ⓘ |
| framework | Bethe ansatz ⓘ |
| influenced | thermodynamic Bethe ansatz for other integrable models ⓘ |
| involves |
kernel determined by two-body scattering phase shift
ⓘ
logarithmic term from Bose statistics ⓘ |
| publishedIn |
Journal of Mathematical Physics
ⓘ
Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction ⓘ
linked to:
Lieb–Liniger model
|
| relatedTo |
Bethe equations
ⓘ
linked to:
Bethe ansatz
Lieb–Liniger equations ⓘ
linked to:
Lieb–Liniger model
dressed energy formalism ⓘ |
| relates |
chemical potential
ⓘ
dressed energy ⓘ interaction strength ⓘ quasi-momentum distribution ⓘ temperature ⓘ |
| solutionMethod |
nonlinear integral equation techniques
ⓘ
numerical iteration ⓘ |
| usedFor |
calculation of entropy density
ⓘ
calculation of excitation spectrum at finite temperature ⓘ calculation of free energy density ⓘ calculation of particle density ⓘ calculation of pressure ⓘ calculation of specific heat ⓘ |
| usedIn |
analysis of quantum integrable models at finite temperature
ⓘ
study of cold atomic gases in one dimension ⓘ |
| validFor | repulsive interactions in one-dimensional Bose gas ⓘ |
| yearProposed | 1969 ⓘ |
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: Yang–Yang equation Description of subject: The Yang–Yang equation is a fundamental integral equation in statistical mechanics that describes the thermodynamic properties of one-dimensional interacting Bose gases within the Bethe ansatz framework.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Yang–Yang equation
linked to: Yang–Yang equation
linked to: Yang–Yang equation