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.
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 → |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.