Nature of Lieb's "hole" excitations and two-phonon states of a Bose gas

Abstract

It is generally accepted that the ``hole'' and ``particle'' excitations are two independent types of excitations of a one-dimensional system of point bosons. We show for a weak coupling that the Lieb's ``hole'' with the momentum $p=j2\pi /L$ is $j$ identical interacting phonons with the momentum $2\pi /L$ (here, $L$ is the size of the system, and $\hslash =1$). We prove this assertion for $j=1,2$ by comparing solutions for a system of point bosons with solutions for a system of nonpoint bosons obtained in the limit of the point interaction. The additional arguments show that our conclusion should be true for any $j=1,2,\dots ,N$. Thus, at a weak coupling, the holes are not a physically independent type of quasiparticles. Moreover, we find the solution for two interacting phonons in a Bose system with an interatomic potential of the general form at a weak coupling and any dimension (1, 2, or 3). It is also shown for a weak coupling that the largest number of phonons in a Bose system is equal to the number of atoms $N$. Finally, we have studied the structure of wave functions for the Tonks--Girardeau gas and found that the properties of quasiparticles in this regime are quite strange.

26 one-column pages, 2 figures, v2: significant changes; an analysis for the Tonks-Girardeau gas is added

References in corpus (8)

• Many-Body Physics with Ultracold Gases
• Dynamical density-density correlations in the one-dimensional Bose gas
• Dynamical structure factor of one-dimensional Bose gases: experimental signatures of beyond-Luttinger liquid physics
• Observation of Dynamical Fermionization
• Exact exponents of edge singularities in dynamic correlation functions of 1D Bose gas
• Polarizability and dynamic structure factor of the one-dimensional Bose gas near the Tonks-Girardeau limit at finite temperatures
• Low-energy excitations of a one-dimensional Bose gas with weak contact repulsion
• The Lieb-Liniger Model as a Limit of Dilute Bosons in Three Dimensions

Cited by in corpus (4)

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• Exact crystalline solution for a one-dimensional few-boson system with point interaction
• Why a Bose-Einstein condensate cannot exist in a system of interacting bosons at ultrahigh temperatures
• Symmetry properties of the ground state of the system of interacting spinless bosons