In this paper, we present a minimisation method for computing the ground stateof systems of coupled Gross–Pitaevskii equations. Our approach relies on a spectral decomposition of the solution into Hermite basis functions. Inserting the spectral representation into the energy functional yields a constrained nonlinear minimisation problem for the coefficients. For its numerical solution, we employ a Newton-like method with an approximate line-search strategy. We analyse this method and prove global convergence. Appropriate starting values for the minimisation process are determined by a standard continuation strategy. Numerical examples with two and three-component two-dimensional condensates are included. These experiments demonstrate the reliability of our method and nicely illustrate the effect of phase segregation.

A minimisation approach for computing the ground state of Gross–Pitaevskii systems

CALIARI, Marco;
2009-01-01

Abstract

In this paper, we present a minimisation method for computing the ground stateof systems of coupled Gross–Pitaevskii equations. Our approach relies on a spectral decomposition of the solution into Hermite basis functions. Inserting the spectral representation into the energy functional yields a constrained nonlinear minimisation problem for the coefficients. For its numerical solution, we employ a Newton-like method with an approximate line-search strategy. We analyse this method and prove global convergence. Appropriate starting values for the minimisation process are determined by a standard continuation strategy. Numerical examples with two and three-component two-dimensional condensates are included. These experiments demonstrate the reliability of our method and nicely illustrate the effect of phase segregation.
2009
minimisation; Gross-Pitaevskii; ground state
File in questo prodotto:
File Dimensione Formato  
preCORT09.pdf

accesso aperto

Tipologia: Documento in Post-print
Licenza: Dominio pubblico
Dimensione 565.26 kB
Formato Adobe PDF
565.26 kB Adobe PDF Visualizza/Apri
CORT09.pdf

non disponibili

Tipologia: Versione dell'editore
Licenza: Accesso ristretto
Dimensione 683.59 kB
Formato Adobe PDF
683.59 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/325478
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 33
  • ???jsp.display-item.citation.isi??? 32
social impact