In theoretical physics most problems can be solved only using certain approximations or numerical methods, and this motivated the study of the so-called integrable models where complete exact solutions can be found despite the models being truly interacting. Examples include statistical physical models, spin chains, and integrable quantum field theories. One model that has been investigated is the famous Heisenberg spin chain. A central topic in the last few years has been the nonequilibrium dynamics, in particular equlibration and thermalization in this model. Whereas a lot is known about the physical properties in equilibrium, there are very few results available about real time evolution. An interesting property is that in the long time limit the model does not equilibrate towards a Gibbs ensemble (as it would in the case of a generic quantum system), instead it forms steady states that are described by the so-called Generalized Gibbs Ensemble. In this respect the model is an exception to the general principles of statistical physics, and this raises many important questions. The research project aims to study a number of inter-connected open problems in relation with time evolution in the XXZ chain and related models. We intend to use the Bethe Ansatz and closely related methods, with a certain degree of numerical work involved. The research project can be considered pure mathematical physics, but the models describe real world experimental situations, and there is a possibility that the calculations will later be confirmed by experiments. The PhD student will work together with the advisor and other members of the BME Statistical Field Theory group.
The applicant is expected to have good problem solving skills in theoretical physics, and he/she should be interested in one dimensional integrable models.