Experiments using cold atoms with and without optical lattices as well as experiments on
trapped ions have recently given us access to the dynamics of quantum systems directly
in the time domain. Dynamical correlation functions in such systems can by now be
studied with single site addressability. This poses a serious challenge for theory to develop
novel methods to calculate time-dependent correlations both in equilibrium and following
a quantum quench.

This project consists of two parts:

(a) * Equilibrium dynamics*: Dynamical correlations at finite temperatures
in integrable one-dimensional quantum models will be calculated. We will combine a form
factor approach, the density-matrix renormalization group, and field theory calculations to
obtain the full time dependence. The results will be benchmarks, helpful in explaining experimental
data from neutron scattering and transport measurements, as well as providing
input for planned experiments on cold atomic gases.

(b) * Non-equilibrium dynamics*: Quantum quenches and steady
states after a quantum quench in integrable models will be investigated. The main focus
is on understanding what the correct ensemble is to describe the steady state. This will
require to construct all relevant conserved charges.