Nonequilibrium phenomena in many-body quantum systems

This thesis contributes to the field of nonequilibrium phenomena in
many-body quantum systems. The properties of systems driven out of
equilibrium are studied from three different perspectives:
dynamics, thermodynamics, and dynamical phase transitions. The
real-time dynamics of quenched quantum systems is studied on the
basis of explicit examples of strongly-correlated many-body systems
such as the Kondo model, the Luttinger liquid, and the anisotropic
Heisenberg chain. The thermodynamic point of view is addressed in
terms of the nonequilibrium work fluctuation theorems. In
particular, it is shown that work distribution functions and thus
also the Crooks relation can be measured in optical spectra of the
x-ray edge type. The central aspect of this thesis is the
definition of a dynamical phase transition for closed quantum
many-body systems that is then analyzed in detail for the
one-dimensional transverse field Ising model. In the end the
properties of periodically driven quantum systems is discussed for
different models such as the Kondo model, resonant level model, and
the Luttinger liquid.