Gross–Pitaevskii equation
E57416
equation in quantum many-body physics
mean-field theory
nonlinear Schrödinger equation
partial differential equation
The Gross–Pitaevskii equation is a nonlinear Schrödinger-type equation that describes the macroscopic wavefunction and dynamics of weakly interacting Bose gases at ultra-cold temperatures.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Gross–Pitaevskii equation canonical | 6 |
How this entity was disambiguated
This entity first appeared as the object of triple T461655 — 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: Gross–Pitaevskii equation Context triple: [Bose–Einstein condensate, hasTheoreticalBasis, Gross–Pitaevskii equation]
-
A.
Bose–Einstein condensate
A Bose–Einstein condensate is an exotic state of matter formed when a dilute gas of bosons is cooled to temperatures near absolute zero, causing a large fraction of the particles to occupy the same quantum state and behave as a single quantum entity.
-
B.
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.
-
C.
Smoluchowski coagulation equation
The Smoluchowski coagulation equation is a fundamental integro-differential equation in statistical physics that models how particles undergoing random collisions aggregate over time into larger clusters.
-
D.
Rayleigh–Schrödinger perturbation theory
Rayleigh–Schrödinger perturbation theory is a fundamental method in quantum mechanics for approximating the energies and states of a system by treating interactions as small corrections to an exactly solvable problem.
-
E.
Pippard nonlocal theory
Pippard nonlocal theory is a refinement of superconductivity theory that introduces spatially nonlocal relations between current and electromagnetic fields to account for finite coherence length effects beyond the London model.
- 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: Gross–Pitaevskii equation Target entity description: The Gross–Pitaevskii equation is a nonlinear Schrödinger-type equation that describes the macroscopic wavefunction and dynamics of weakly interacting Bose gases at ultra-cold temperatures.
-
A.
Bose–Einstein condensate
A Bose–Einstein condensate is an exotic state of matter formed when a dilute gas of bosons is cooled to temperatures near absolute zero, causing a large fraction of the particles to occupy the same quantum state and behave as a single quantum entity.
-
B.
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.
-
C.
Smoluchowski coagulation equation
The Smoluchowski coagulation equation is a fundamental integro-differential equation in statistical physics that models how particles undergoing random collisions aggregate over time into larger clusters.
-
D.
Rayleigh–Schrödinger perturbation theory
Rayleigh–Schrödinger perturbation theory is a fundamental method in quantum mechanics for approximating the energies and states of a system by treating interactions as small corrections to an exactly solvable problem.
-
E.
Pippard nonlocal theory
Pippard nonlocal theory is a refinement of superconductivity theory that introduces spatially nonlocal relations between current and electromagnetic fields to account for finite coherence length effects beyond the London model.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
equation in quantum many-body physics
ⓘ
mean-field theory ⓘ nonlinear Schrödinger equation ⓘ partial differential equation ⓘ |
| appliesTo |
dilute Bose–Einstein condensates
ⓘ
ultra-cold atomic gases ⓘ weakly interacting Bose gases ⓘ |
| approximationValidity |
dilute gas limit
ⓘ
low temperature limit ⓘ |
| assumes |
all bosons occupy the same single-particle state
ⓘ
contact interaction between particles ⓘ s-wave scattering dominance ⓘ |
| basedOn |
Hartree–Fock method
ⓘ
surface form:
Hartree approximation
mean-field approximation ⓘ |
| derivedFrom |
Schrödinger equation
ⓘ
surface form:
many-body Schrödinger equation
|
| describes |
dynamics of Bose–Einstein condensates
ⓘ
macroscopic wavefunction of a weakly interacting Bose gas ⓘ order parameter of a Bose–Einstein condensate ⓘ |
| field |
condensed matter physics
ⓘ
quantum optics ⓘ ultra-cold atom physics ⓘ |
| governs |
collective excitations in Bose–Einstein condensates
ⓘ
time evolution of condensate order parameter ⓘ |
| hasNonlinearityType | cubic nonlinearity ⓘ |
| hasParameter |
Planck constant
ⓘ
external potential ⓘ interaction strength ⓘ particle mass ⓘ s-wave scattering length ⓘ |
| hasSolutionType |
bright solitons
ⓘ
dark solitons ⓘ stationary states ⓘ time-dependent solutions ⓘ vortex lattice states ⓘ |
| includesTerm |
external trapping potential term
ⓘ
interaction energy term proportional to density ⓘ kinetic energy term ⓘ |
| mathematicalForm | nonlinear complex-valued partial differential equation ⓘ |
| namedAfter |
Eugene P. Gross
ⓘ
Lev Pitaevskii ⓘ |
| relatedTo |
Bogoliubov theory of weakly interacting Bose gases
ⓘ
nonlinear Schrödinger equation in nonlinear optics ⓘ |
| temperatureRegime | ultra-cold temperatures ⓘ |
| usedFor |
describing superfluid flow in dilute Bose systems
ⓘ
modeling vortices in Bose–Einstein condensates ⓘ simulating interference of Bose–Einstein condensates ⓘ studying collective modes of trapped condensates ⓘ studying ground-state properties of trapped condensates ⓘ studying solitons in Bose gases ⓘ |
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: Gross–Pitaevskii equation Description of subject: The Gross–Pitaevskii equation is a nonlinear Schrödinger-type equation that describes the macroscopic wavefunction and dynamics of weakly interacting Bose gases at ultra-cold temperatures.
Referenced by (6)
Full triples — surface form annotated when it differs from this entity's canonical label.