Two routes to the one-dimensional discrete nonpolynomial Schrodinger equation
Апстракт
The Bose-Einstein condensate (BEC), confined in a combination of the cigar-shaped trap and axial optical lattice, is studied in the framework of two models described by two versions of the one-dimensional (1D) discrete nonpolynomial Schrodinger equation (NPSE). Both models are derived from the three-dimensional Gross-Pitaevskii equation (3D GPE). To produce model 1 (which was derived in recent works), the 3D GPE is first reduced to the 1D continual NPSE, which is subsequently discretized. Model 2, which was not considered before, is derived by first discretizing the 3D GPE, which is followed by the reduction in the dimension. The two models seem very different; in particular, model 1 is represented by a single discrete equation for the 1D wave function, while model 2 includes an additional equation for the transverse width. Nevertheless, numerical analyses show similar behaviors of fundamental unstaggered solitons in both systems, as concerns their existence region and stability limits.... Both models admit the collapse of the localized modes, reproducing the fundamental property of the self-attractive BEC confined in tight traps. Thus, we conclude that the fundamental properties of discrete solitons predicted for the strongly trapped self-attracting BEC are reliable, as the two distinct models produce them in a nearly identical form. However, a difference between the models is found too, as strongly pinned (very narrow) discrete solitons, which were previously found in model 1, are not generated by model 2-in fact, in agreement with the continual 1D NPSE, which does not have such solutions either. In that respect, the newly derived model provides for a more accurate approximation for the trapped BEC.
Извор:
Chaos, 2009, 19, 4Финансирање / пројекти:
- Физика комплексних феномена у плазми, кондензованој материји и нелинеарној оптици (RS-MESTD-MPN2006-2010-141034)
- CARIPARO Foundation through Progetti di Eccellenza
- German-Israel Foundation [149/2006]
DOI: 10.1063/1.3248269
ISSN: 1054-1500
PubMed: 20059201
WoS: 000273221500006
Scopus: 2-s2.0-74349123035
Институција/група
VinčaTY - JOUR AU - Gligorić, Goran AU - Maluckov, Aleksandra AU - Salasnich, Luca AU - Malomed, Boris A. AU - Hadžievski, Ljupčo PY - 2009 UR - https://vinar.vin.bg.ac.rs/handle/123456789/3866 AB - The Bose-Einstein condensate (BEC), confined in a combination of the cigar-shaped trap and axial optical lattice, is studied in the framework of two models described by two versions of the one-dimensional (1D) discrete nonpolynomial Schrodinger equation (NPSE). Both models are derived from the three-dimensional Gross-Pitaevskii equation (3D GPE). To produce model 1 (which was derived in recent works), the 3D GPE is first reduced to the 1D continual NPSE, which is subsequently discretized. Model 2, which was not considered before, is derived by first discretizing the 3D GPE, which is followed by the reduction in the dimension. The two models seem very different; in particular, model 1 is represented by a single discrete equation for the 1D wave function, while model 2 includes an additional equation for the transverse width. Nevertheless, numerical analyses show similar behaviors of fundamental unstaggered solitons in both systems, as concerns their existence region and stability limits. Both models admit the collapse of the localized modes, reproducing the fundamental property of the self-attractive BEC confined in tight traps. Thus, we conclude that the fundamental properties of discrete solitons predicted for the strongly trapped self-attracting BEC are reliable, as the two distinct models produce them in a nearly identical form. However, a difference between the models is found too, as strongly pinned (very narrow) discrete solitons, which were previously found in model 1, are not generated by model 2-in fact, in agreement with the continual 1D NPSE, which does not have such solutions either. In that respect, the newly derived model provides for a more accurate approximation for the trapped BEC. T2 - Chaos T1 - Two routes to the one-dimensional discrete nonpolynomial Schrodinger equation VL - 19 IS - 4 DO - 10.1063/1.3248269 ER -
@article{ author = "Gligorić, Goran and Maluckov, Aleksandra and Salasnich, Luca and Malomed, Boris A. and Hadžievski, Ljupčo", year = "2009", abstract = "The Bose-Einstein condensate (BEC), confined in a combination of the cigar-shaped trap and axial optical lattice, is studied in the framework of two models described by two versions of the one-dimensional (1D) discrete nonpolynomial Schrodinger equation (NPSE). Both models are derived from the three-dimensional Gross-Pitaevskii equation (3D GPE). To produce model 1 (which was derived in recent works), the 3D GPE is first reduced to the 1D continual NPSE, which is subsequently discretized. Model 2, which was not considered before, is derived by first discretizing the 3D GPE, which is followed by the reduction in the dimension. The two models seem very different; in particular, model 1 is represented by a single discrete equation for the 1D wave function, while model 2 includes an additional equation for the transverse width. Nevertheless, numerical analyses show similar behaviors of fundamental unstaggered solitons in both systems, as concerns their existence region and stability limits. Both models admit the collapse of the localized modes, reproducing the fundamental property of the self-attractive BEC confined in tight traps. Thus, we conclude that the fundamental properties of discrete solitons predicted for the strongly trapped self-attracting BEC are reliable, as the two distinct models produce them in a nearly identical form. However, a difference between the models is found too, as strongly pinned (very narrow) discrete solitons, which were previously found in model 1, are not generated by model 2-in fact, in agreement with the continual 1D NPSE, which does not have such solutions either. In that respect, the newly derived model provides for a more accurate approximation for the trapped BEC.", journal = "Chaos", title = "Two routes to the one-dimensional discrete nonpolynomial Schrodinger equation", volume = "19", number = "4", doi = "10.1063/1.3248269" }
Gligorić, G., Maluckov, A., Salasnich, L., Malomed, B. A.,& Hadžievski, L.. (2009). Two routes to the one-dimensional discrete nonpolynomial Schrodinger equation. in Chaos, 19(4). https://doi.org/10.1063/1.3248269
Gligorić G, Maluckov A, Salasnich L, Malomed BA, Hadžievski L. Two routes to the one-dimensional discrete nonpolynomial Schrodinger equation. in Chaos. 2009;19(4). doi:10.1063/1.3248269 .
Gligorić, Goran, Maluckov, Aleksandra, Salasnich, Luca, Malomed, Boris A., Hadžievski, Ljupčo, "Two routes to the one-dimensional discrete nonpolynomial Schrodinger equation" in Chaos, 19, no. 4 (2009), https://doi.org/10.1063/1.3248269 . .