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Acta Scientiarum Naturalium Universitatis Sunyatseni

Soliton in the Quantum Lattice Gas Model in One Dimension

Yuan Chen

Published Jan 1, 1999• 0 citations
OpenAlex

Abstract

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.

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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.
Quantum lattice solitons in a system of two ultracold bosons near Feshbach resonance are investigated. It is shown that their binding energy, effective mass, and spatial width, can be manipulated varying the detuning from the Feshbach resonance. In the case of attractive atomic interactions, the molecule creation stabilizes the solitons. In the case of repulsive interactions, the molecule creation leads to the possibility of existence of bright solitons in some interval of detunings. Due to quantum fluctuations the soliton width is a random quantity. Its standard deviation is larger than the mean value for such a small number of particles.
The quantum-mechanical, fermion, attractive delta function gas in one dimension has many interesting, known physical properties, including some aspects of soliton behavior. Motivated by a desire to test the validity of the HF approximation to many-body systems, we have made a rigorous study of the HF theory of this gas. When the particle number is even we can show that although HF theory does not give energies accurately, it does correctly predict the known qualitative properties; in particular, only two-particle bound states exist.
We study the ground-state properties of a one-dimensional Bose gas with NNN-body attractive contact interactions. By using the explicit form of the bright soliton solution of a generalized nonlinear Schr\"odinger equation, we compute the chemical potential and the ground-state energy. For N=3N=3N=3, a localized soliton wave function exists only for a critical value of the interaction strength: in this case the ground state has an infinite degeneracy that can be parametrized by the chemical potential. The stabilization of the bright soliton solution by an external harmonic trap is also discussed, and a comparison with the effect of NNN-body attractive contact interactions in higher dimensions is presented.