Quasimomentum of an elementary excitation for a system of point bosons under zero boundary conditions

Abstract

As is known, an elementary excitation of a many-particle system with boundaries is not characterized by a definite momentum. We obtain the formula for the quasimomentum of an elementary excitation for a one-dimensional system of $N$ spinless point bosons under zero boundary conditions (BCs). In this case, we use the Gaudin's solutions obtained with the help of the Bethe ansatz. We have also found the dispersion laws of the particle-like and hole-like excitations under zero BCs. They coincide with the known dispersion laws obtained for periodic BCs.

7 pages, 1 figure, v5: accepted version

References in corpus (4)

• Bosonizing one-dimensional cold atomic gases
• Ground-state energy and excitation spectrum of the Lieb-Liniger model : accurate analytical results and conjectures about the exact solution
• Uniqueness of the solution of the Gaudin's equations, which describe a one-dimensional system of point bosons with zero boundary conditions
• Low-lying energy levels of a one-dimensional weakly interacting Bose gas under zero boundary conditions

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• Nonuniform Bose-Einstein condensate. I. An improvement of the Gross-Pitaevskii method
• Exact crystalline solution for a one-dimensional few-boson system with point interaction
• Symmetry properties of the ground state of the system of interacting spinless bosons