Acta Physica Sinica

SOLITON EXITATION IN ONE-DIMENSIONAL QUANTUMb LATTICE GAS

CHEN CHUAN-YU, 广州师范学院物理系,广州,510400;中国高等科学技术中心(世界实验室)理论物理分中心

Published Jan 1, 1991• 0 citations

Abstract

In this paper, the non-linear properties of the nearest neighbor interaction between particles in one-dimensional quantum lattice gas are investigated, giving out the soliton theory of the model. The expressions of the solitons' energy and the effective soliton mass are also derived.

DOI: 10.7498/aps.40.1207

Related papers

Soliton in the Quantum Lattice Gas Model in One Dimension

Yuan Chen

The soliton solution in the quantum lattice gas model in one dimension is found. The width, the peak, the rest energy and the effective mass of the soliton are given. The condition of the soliton existing is pointed out. The dependence of the width, the peak and the energy of the soliton on the attraction energy between nearest neighbor particles are considered.

Acta Scientiarum Naturalium Universitatis SunyatseniJan 1, 19990 citations

Lattice gas with nearest-neighbor interaction in one dimension with arbitrary statistics

Cheng Kee Lai

We define a quantum lattice gas with arbitrary statistics. For a one-dimensional system with nearest-neighbor interaction, we show that the problem is exactly soluble by use of Bethe's hypothesis when the interaction Δ=±1. The ground state energy is then obtained for the fermions of spin 1/2. Two phases are found in the case Δ=-1.

Journal of Mathematical PhysicsOct 1, 1974286 citations

Rise and Fall of a Bright Soliton in an Optical Lattice

Piero Naldesi, Juan Polo, Boris A. Malomed +3 more

We study an ultracold atomic gas with attractive interactions in a one-dimensional optical lattice. We find that its excitation spectrum displays a quantum soliton band, corresponding to N-particle bound states, and a continuum band of other, mostly extended, states. For a system of a finite size, the two branches are degenerate in energy for weak interactions, while a gap opens above a threshold value of the interaction strength. We find that the interplay between degenerate extended and bound states has important consequences for both static and dynamical properties of the system. In particular, the solitonic states turn out to be protected from spatial perturbations and random disorder. We discuss how such dynamics implies that our system effectively provides an example of a quantum many-body system that, with the variation of the bosonic lattice filling, crosses over from integrable nonergodic to nonintegrable ergodic dynamics, through nonintegrable-nonergodic regimes.

arXiv:1804.10133Physical Review LettersFeb 6, 201926 citations

Beyond Gross-Pitaevskii equation for 1D gas: quasiparticles and solitons

Jakub Kopyciński, Maciej Łebek, Maciej Marciniak +3 more

Describing properties of a strongly interacting quantum many-body system poses a serious challenge both for theory and experiment. In this work, we study excitations of one-dimensional repulsive Bose gas for arbitrary interaction strength using a hydrodynamic approach. We use linearization to study particle (type-I) excitations and numerical minimization to study hole (type-II) excitations. We observe a good agreement between our approach and exact solutions of the Lieb-Liniger model for the particle modes and discrepancies for the hole modes. Therefore, the hydrodynamical equations find to be useful for long-wave structures like phonons and of a limited range of applicability for short-wave ones like narrow solitons. We discuss potential further applications of the method.

arXiv:2106.15289SciPost PhysicsJan 14, 20227 citations

Effect of interaction strength on gap solitons of Bose–Einstein condensates in optical lattices

Yang Ru-shu, Yang Jiang-he

We have developed a systematic analytical approach to the study on the dynamic properties of the linear and the nonlinear excitations for quasi-one-dimensional Bose–Einstein condensate trapped in optical lattices. A novel linear dispersion relation and an algebraic soliton solution of the condensate are derived analytically under consideration of Bose–Einstein condensate with a periodic potential. By analysing the soliton solution, we find that the interatomic interaction strength has an important effect on soliton dynamic properties of Bose–Einstein condensate.

Chinese Physics BApr 1, 20088 citations

Interaction forces among two-dimensional bright solitons and many-soliton molecules

Usama Al Khawaja

We consider two-dimensional bright matter-wave solitons in two-dimensional Bose-Einstein condensates. From the asymptotic form of their wave function, we derive an analytic expression for the force of interaction between solitons in the large separation limit, which turns out to decay with solitons separation Δ as F(Δ)∝exp(-Δ)/√Δ. Simulating the dynamics of two solitons using the relevant Gross-Pitaevskii equation, we obtain the force of the interaction for the full range of Δ, which turns out to be of molecular type. We show that many-soliton molecules can exist as a result of such a molecular-type of interaction. These include string-shaped, ring-shaped, or regular-lattice-shaped soliton molecules. By calculating their binding energy, we investigate the stability of these structures. Contrary to one-dimensional soliton molecules, which have no binding energy, two-dimensional molecules of a lattice of solitons with alternating phases are robust and have a negative binding energy. Lattices of size larger than 2 × 2 solitons have many discrete equilibrium values of the separation between two neighboring solitons.

Physical Review EMay 14, 20123 citations