Here we show that the Gross-Pitaevskii equation (GPE) for Bose-Einstein condensates (BECs) admits hydrodynamic interpretation in a general Riemannian metric, and show that in this metric the momentum equation has a new term that is associated with local curvature and density distribution profile. In particular conditions of steady state a new Einstein's field equation is determined in presence of negative curvature. Since GPE governs BECs defects that are useful, analogue models in cosmology, a relativistic form of GPE is also considered to show connection with models of analogue gravity, thus providing further grounds for future investigations of black hole dynamics in cosmology.

Roitberg, A., Ricca, R. (2021). Hydrodynamic derivation of the Gross-Pitaevskii equation in general Riemannian metric. JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL, 54(31), 315201-315215 [10.1088/1751-8121/ac0aa0].

Hydrodynamic derivation of the Gross-Pitaevskii equation in general Riemannian metric

Roitberg A.
Primo
;
Ricca R. L.
2021

Abstract

Here we show that the Gross-Pitaevskii equation (GPE) for Bose-Einstein condensates (BECs) admits hydrodynamic interpretation in a general Riemannian metric, and show that in this metric the momentum equation has a new term that is associated with local curvature and density distribution profile. In particular conditions of steady state a new Einstein's field equation is determined in presence of negative curvature. Since GPE governs BECs defects that are useful, analogue models in cosmology, a relativistic form of GPE is also considered to show connection with models of analogue gravity, thus providing further grounds for future investigations of black hole dynamics in cosmology.
Articolo in rivista - Articolo scientifico
GPE hydrodynamics; Gross-Pitaevskii equation in Riemannian metric; Relativistic GPE;
English
1-lug-2021
2021
54
31
315201
315215
315201
reserved
Roitberg, A., Ricca, R. (2021). Hydrodynamic derivation of the Gross-Pitaevskii equation in general Riemannian metric. JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL, 54(31), 315201-315215 [10.1088/1751-8121/ac0aa0].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/324868
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