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

Abstract

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.

27 pages, 11 figures. Submission to SciPost

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Cited by in corpus (6)

• Ultrawide dark solitons and droplet-soliton coexistence in a dipolar Bose gas with strong contact interactions
• Formation and fragmentation of quantum droplets in a quasi-one dimensional dipolar Bose gas
• Quantum Monte Carlo-based density functional for one-dimensional Bose-Bose mixtures
• Solution of the v-representability problem on a one-dimensional torus
• Phase diagram and elementary excitations of strongly interacting droplets with non-local interactions
• Dynamics of quantum double dark-solitons and an exact finite-size scaling of Bose-Einstein condensation