Monday, July 15, 2013

1307.3387 (Hironobu Fujishima et al.)

Perturbative Analysis of Potential Scattering Problems in the
Lieb-Liniger Model

Hironobu Fujishima, Tetsu Yajima
The Lieb-Liniger model which has a weak external potential term under the periodic boundary condition is investigated. By exploiting the Bethe states as bases, we perform a perturbation analysis up to the first order to obtain the shifts of eigenenergies and corresponding eigenstates which have been brought about by the external potential. If we take a sufficiently large system, the eigenstates can be "the Schr\"odinger's cat states". Expectation values of the density operator taken between two Bethe states can be calculated with the aid of the Slavnov's formula and we evaluate the influence of the many-body interaction to the system under the external potential. The system is insensitive to the external potential because of the many-body interaction.
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