Classical and quantum integrable defects
Anastasia Doikou (Heriot-Watt University)
Tuesday 11th March, 2014 15:00-16:00 Maths 325
A systematic approach to classical integrable defects is proposed based on the underlying Poisson algebraic structure. Local integrals of motions are constructed as well as the time components of the corresponding Lax pairs for the sine-Gordon model. Continuity conditions imposed upon the time components of the Lax pair to all orders give rise to sewing conditions, which turn out to be compatible with the hierarchy of charges in involution. At the quantum level, using the Bethe ansatz methodology, we extract the transmission amplitudes for the XXZ model. These describe the interaction between the particle-like excitations displayed by the model and the spin impurity. In the attractive regime of the XXZ model, we also derive the breather's (bound states) transmission amplitude.