The semi-infinite q-boson system with boundary interaction
Duration: 30 mins 40 secs
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| Description: |
van Diejen, JF (Ponti cia Universidad Católica de Chile)
Thursday 11 July 2013, 11:30-12:00 |
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| Created: | 2013-07-16 09:02 |
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| Collection: | Discrete Integrable Systems |
| Publisher: | Isaac Newton Institute |
| Copyright: | van Diejen, JF |
| Language: | eng (English) |
| Abstract: | The q-boson system is a lattice discretization of the one-dimensional quantum nonlinear Schrödinger equation built of particle creation and annihilation operators representing the q-oscillator algebra. Its n-particle eigenfunctions are given by Hall-Littlewood functions. I will discuss a system of q-bosons on the semi-infinite lattice with boundary interactions arising from a quadratic deformation of the q-boson field algebra at the end point and show that the Bethe Ansatz eigenfunctions are given by Macdonald's three-parameter Hall-Littlewood functions with hyperoctahedral symmetry associated with the BC-type root system. From a stationary phase analysis, it then follows that the n-particle scattering matrix factorizes as a product of explicitly computed two-particle bulk and one-particle boundary scattering matrices. |
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