Caudrelier, V. & Crampe, N. (2007). Exact results for the onedimensional manybody problem with contact interaction: Including a tunable impurity. Reviews in Mathematical Physics (rmp), 19(4), pp. 349370. doi: 10.1142/S0129055X07002973

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Abstract
The onedimensional problem of N particles with contact interaction in the presence of a tunable transmitting and reflecting impurity is investigated along the lines of the coordinate Bethe ansatz. As a result, the system is shown to be exactly solvable by determining the eigenfunctions and the energy spectrum. The latter is given by the solutions of the Bethe ansatz equations which we establish for different boundary conditions in the presence of the impurity. These impurity Bethe equations contain as special cases wellknown Bethe equations for systems on the halfline. We briefly study them on their own through the toyexamples of one and two particles. It turns out that the impurity can be tuned to lift degeneracies in the energies and can create bound states when it is sufficiently attractive. The example of an impurity sitting at the center of a box and breaking parity invariance shows that such an impurity can be used to confine a stationary state asymmetrically. This could have interesting applications in condensed matter physics.
Item Type:  Article 

Additional Information:  Electronic version of an article published as V. CAUDRELIER and N. CRAMPÉ, Rev. Math. Phys. 19, 349 (2007). DOI: 10.1142/S0129055X07002973 © copyright World Scientific Publishing Company, Reviews in Mathematical Physics. 
Uncontrolled Keywords:  Coordinate Bethe ansatz, onedimensional bosons, delta interactions, impurity, Bethe equations 
Subjects:  Q Science > QA Mathematics Q Science > QC Physics 
Divisions:  School of Engineering & Mathematical Sciences > Department of Mathematical Science 
URI:  http://openaccess.city.ac.uk/id/eprint/163 
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