Abstract
A countable set of asymptotic space-localized solutions is constructed by the complex germ method in the adiabatic approximation for the nonstationary Gross-Pitaevskii equation with nonlocal nonlinearity and a quadratic potential. The asymptotic parameter is 1/T, where T ≫ 1 is the adiabatic evolution time. A generalization of the Berry phase of the linear Schrödinger equation is formulated for the Gross-Pitaevskii equation. For the solutions constructed, the Berry phases are found in explicit form.
| Original language | English |
|---|---|
| Pages (from-to) | 1191-1206 |
| Number of pages | 16 |
| Journal | Journal of Physics A: Mathematical and General |
| Volume | 39 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - 3 Feb 2006 |
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ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
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Berry phases for the nonlocal Gross-Pitaevskii equation with a quadratic potential. / Litvinets, F. N.; Shapovalov, Aleksandr Vasilievich; Trifonov, A. Yu.
In: Journal of Physics A: Mathematical and General, Vol. 39, No. 5, 03.02.2006, p. 1191-1206.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Berry phases for the nonlocal Gross-Pitaevskii equation with a quadratic potential
AU - Litvinets, F. N.
AU - Shapovalov, Aleksandr Vasilievich
AU - Trifonov, A. Yu
PY - 2006/2/3
Y1 - 2006/2/3
N2 - A countable set of asymptotic space-localized solutions is constructed by the complex germ method in the adiabatic approximation for the nonstationary Gross-Pitaevskii equation with nonlocal nonlinearity and a quadratic potential. The asymptotic parameter is 1/T, where T ≫ 1 is the adiabatic evolution time. A generalization of the Berry phase of the linear Schrödinger equation is formulated for the Gross-Pitaevskii equation. For the solutions constructed, the Berry phases are found in explicit form.
AB - A countable set of asymptotic space-localized solutions is constructed by the complex germ method in the adiabatic approximation for the nonstationary Gross-Pitaevskii equation with nonlocal nonlinearity and a quadratic potential. The asymptotic parameter is 1/T, where T ≫ 1 is the adiabatic evolution time. A generalization of the Berry phase of the linear Schrödinger equation is formulated for the Gross-Pitaevskii equation. For the solutions constructed, the Berry phases are found in explicit form.
UR - http://www.scopus.com/inward/record.url?scp=31144445029&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=31144445029&partnerID=8YFLogxK
U2 - 10.1088/0305-4470/39/5/012
DO - 10.1088/0305-4470/39/5/012
M3 - Article
VL - 39
SP - 1191
EP - 1206
JO - Journal of Physics A: Mathematical and General
JF - Journal of Physics A: Mathematical and General
SN - 0305-4470
IS - 5
ER -