Dynamical properties of one dimensional strongly correlated many-particle systems

At present two lines of work are envisaged. The first programme is concerned with non-equilibrium dynamics in open many-particle quantum systems. These can be conveniently described by so-called Lindblad equations. A general problem is that LE are difficult to analyse by either numerical or analytical means. It has been recently demonstrated that in particular examples Lindblad equations can be mapped onto non-hermitian integrable models. This opens up the possibility to bring integrable model techniques to bear on such problems and establish exactly solved paradigms of open interacting many-particle quantum systems. This project is squarely in the EPSRC grand challenge area "Emergence and Physics Far From Equilibrium". In the first part of the project exact results for the time evolution of two and four point functions will be obtained for the previously studied example imaginary-U Hubbard model. In the second part of the project other Lindblad equations will be analyzed with the objective of mapping them to non-herminitian integrable Hamiltonians, that have non-trivial steady states.
The second line of work is concerned with the theoretical modelling of inelastic neutron scattering experiments on the quasi-one dimensional quantum magnet SrCo2V2O8, which has been recently shown to exhibit confinement of topological excitations into meson-like bound states. An open problem are the effects of the weak three-dimensional couplings. Forthcoming experiments will measure the dispersion relations perpendicular to the chain direction, which will make it possible to determine the functional form of the interchain couplings. Once this has been achieved, the interchain coupling effects can be analyzed by combining existing results with a matrix random phase approximation. The result of such a theoretical analysis can then be compared to available inelastic neutron scattering data.