© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:cond-mat/0010075 · Journal of Physics A Mathematical and General

Solitons in a one-dimensional interacting Bose-Einstein system

R. K. Bhaduri, Sankalpa Ghosh, M. V. N. Murthy, Diptiman Sen

Published Aug 17, 2001• 15 citations

Abstract

A modified Gross-Pitaevskii approximation was recently introduced for bosons in dimension d ⩽2 by Kolomeisky et al (Kolomeisky E B, Newman T J, Straley J P and Qi X 2000 Phys. Rev. Lett. 85 1146). We use the density-functional approach with a sixth-degree interaction energy term in the Bose field to reproduce the stationary-frame results of Kolomeisky et al for a one-dimensional Bose-Einstein system with a repulsive interaction. We also find a soliton solution for an attractive interaction, which may be boosted to a finite velocity by a Galilean transformation. The stability of such a soliton is discussed analytically. We provide a general treatment of stationary solutions in one dimension which includes the above solutions as special cases. This treatment leads to a variety of stationary wave solutions for both attractive and repulsive interactions.

DOI: 10.1088/0305-4470/34/34/302

Related papers

Many-body dark solitons in one-dimensional hard-core Bose gases

Manuele Tettamanti, Alberto Parola

The existence and stability of solitonic states in one-dimensional repulsive Bose-Einstein condensates is investigated within a fully many-body framework by considering the limit of infinite repulsion (Tonks-Girardeau gas). A class of stationary, shape-invariant states propagating at constant velocity are explicitly found and compared to the known solution of the Gross-Pitaevskii equation. The typical features attributed to nonlinearity are thus recovered in a purely linear theory, provided the full many-particle physics is correctly accounted for. However, the formation dynamics predicted by the Gross-Pitaevskii approximation considerably differs from the exact many-body evolution.

arXiv:2110.15140•Physical Review A•Oct 27, 2021•2 citations

Degenerate ground states and stability of spatial solitons in quasi-one-dimensional Bose-Einstein Condensates

Alain M. Dikandé

By examining the bound-state spectra of transverse fluctuations about one-dimensional, spatially localized dark and bright soliton wavetrains of the Gross-Pitaevskii equation, it is established that the low-temperature ground states of repulsive and attractive quasi-one-dimensional Bose-Einstein condensates are degenerate. In the one-soliton limit, both ground states are shown to possess two distinct transverse fluctuation modes which can couple to the spatial soliton: the first involves zero-energy exchange, costing only the soliton shape dressing via uniform translation of its centre of mass. The second mode contributes in a negative energy for the repulsive case, but positive energy in the attractive case. This unstability of the repulsive spatial soliton against localized transverse fluctuation modes invalidates the Gross-Pitaevskii equation for stationary solitonic processes in repulsive 1D Bose-Einstein-Condensate systems.

arXiv:cond-mat/0111418•Nov 21, 2001•1 citation

Lattice solitons in Bose-Einstein condensates

Nikolaos K. Efremidis, Demetrios N. Christodoulides

We systematically study the properties of lattice solitons in Bose-Einstein condensates with either attractive or repulsive atom interactions. This is done, by exactly solving the mean-field Gross-Pitaevskii equation in the presence of a periodic potential. We find new families of lattice soliton solutions that are characterized by the position of the energy eigenvalue within the associated band structure. These include lattice solitons in condensates with either attractive or repulsive atom interactions that exist in finite or semi-infinite gaps, as well as nonlinear modes that exhibit atomic population cutoffs.

Physical Review A•Jun 20, 2003•188 citations

Comment on “Low-Dimensional Bose Liquids: Beyond the Gross-Pitaevskii Approximation”

R. K. Bhaduri, Diptiman Sen

This is a comment on the work of Kolomeisky et al., Phys. Rev. Lett. 85, 1146 (2000). We point out that they are using the wrong form of the energy functional for one-dimensional fermions. We point out two possible forms of the energy functional, both of which can be derived from first principles but using different methods. One is obtained from the collective field theory method, while the other is derived from the extended Thomas-Fermi method. These two forms of the energy functional do not support the soliton solutions which are obtained by Kolomeisky et al.

arXiv:cond-mat/0105385•Physical Review Letters•May 14, 2001•5 citations

Dark and bright solitons in a quasi-one-dimensional Bose-Einstein condensate

Shun-Jin Wang, Chenglong Jia, Dun Zhao +2 more

The analytical dark and bright soliton solutions of the one-dimensional Gross-Pitaevskii equation with a confining potential are obtained. For the bright soliton, the recent experimental finding is studied, and the particle number of the soliton and the window of the particle numbers for the bright soliton to occur are estimated analytically and in good agreement with the experimental data. The existence of dark soliton for the attractive interaction and bright soliton for the repulsive interaction is predicted under proper conditions.

Physical Review A•Jul 2, 2003•44 citations

Solitons in One-Dimensional Bose–Einstein Condensate with Higher-Order Interactions*

Ying Wang, Wei Wang, Shuyu Zhou

Abstract We model a one-dimensional Bose–Einstein condensate with the one-dimensional Gross–Pitaevskii equation (1D GPE) incorporating higher-order interaction effects. Based on the F-expansion method, we analytically solve the 1D GPE, identifying the typical soliton solution under certain experimental settings within the general wave-like solution set, and demonstrating the applicability of the theoretical treatment that is employed .

Communications in Theoretical Physics•Nov 1, 2017•13 citations

A modified Gross-Pitaevskii approximation was recently introduced for bosons in dimension d ⩽2 by Kolomeisky et al (Kolomeisky E B, Newman T J, Straley J P and Qi X 2000 Phys. Rev. Lett. 85 1146). We use the density-functional approach with a sixth-degree interaction energy term in the Bose field to reproduce the stationary-frame results of Kolomeisky et al for a one-dimensional Bose-Einstein system with a repulsive interaction. We also find a soliton solution for an attractive interaction, which may be boosted to a finite velocity by a Galilean transformation. The stability of such a soliton is discussed analytically. We provide a general treatment of stationary solutions in one dimension which includes the above solutions as special cases. This treatment leads to a variety of stationary wave solutions for both attractive and repulsive interactions.

The existence and stability of solitonic states in one-dimensional repulsive Bose-Einstein condensates is investigated within a fully many-body framework by considering the limit of infinite repulsion (Tonks-Girardeau gas). A class of stationary, shape-invariant states propagating at constant velocity are explicitly found and compared to the known solution of the Gross-Pitaevskii equation. The typical features attributed to nonlinearity are thus recovered in a purely linear theory, provided the full many-particle physics is correctly accounted for. However, the formation dynamics predicted by the Gross-Pitaevskii approximation considerably differs from the exact many-body evolution.

By examining the bound-state spectra of transverse fluctuations about one-dimensional, spatially localized dark and bright soliton wavetrains of the Gross-Pitaevskii equation, it is established that the low-temperature ground states of repulsive and attractive quasi-one-dimensional Bose-Einstein condensates are degenerate. In the one-soliton limit, both ground states are shown to possess two distinct transverse fluctuation modes which can couple to the spatial soliton: the first involves zero-energy exchange, costing only the soliton shape dressing via uniform translation of its centre of mass. The second mode contributes in a negative energy for the repulsive case, but positive energy in the attractive case. This unstability of the repulsive spatial soliton against localized transverse fluctuation modes invalidates the Gross-Pitaevskii equation for stationary solitonic processes in repulsive 1D Bose-Einstein-Condensate systems.

We systematically study the properties of lattice solitons in Bose-Einstein condensates with either attractive or repulsive atom interactions. This is done, by exactly solving the mean-field Gross-Pitaevskii equation in the presence of a periodic potential. We find new families of lattice soliton solutions that are characterized by the position of the energy eigenvalue within the associated band structure. These include lattice solitons in condensates with either attractive or repulsive atom interactions that exist in finite or semi-infinite gaps, as well as nonlinear modes that exhibit atomic population cutoffs.

This is a comment on the work of Kolomeisky et al., Phys. Rev. Lett. 85, 1146 (2000). We point out that they are using the wrong form of the energy functional for one-dimensional fermions. We point out two possible forms of the energy functional, both of which can be derived from first principles but using different methods. One is obtained from the collective field theory method, while the other is derived from the extended Thomas-Fermi method. These two forms of the energy functional do not support the soliton solutions which are obtained by Kolomeisky et al.

The analytical dark and bright soliton solutions of the one-dimensional Gross-Pitaevskii equation with a confining potential are obtained. For the bright soliton, the recent experimental finding is studied, and the particle number of the soliton and the window of the particle numbers for the bright soliton to occur are estimated analytically and in good agreement with the experimental data. The existence of dark soliton for the attractive interaction and bright soliton for the repulsive interaction is predicted under proper conditions.