Non-equilibrium dynamics of ultracold atomic gases

The remarkable experimental progress in manipulating ultracold atomic gases during the last decade established these systems as versatile quantum simulators for basic problems in condensed-matter physics, where fundamental parameters such as the interaction strength between particles can be tuned by hand. Several basic many-body problems are now ex-perimentally accessible for the first time. One reason for this success is the fact that cold gases are clean systems that are very well decoupled from their environment. This feature is not always an advantage, however, because cold gases have a tendency not to equilibrate after a parameter change due to the missing coupling to dissipative degrees of freedom. The increasing complexity of the questions that are addressed with cold atoms nowadays thus makes a thorough theoretical understanding of the coherent non-equilibrium dynamics in such systems inevitable. In the first part of the research project I plan to study quantum mechanical many-body systems far from equilibrium, using analytical, field-theoretical methods. The focus will be on so called `quantum quench problems`, where the coherent time-evolution of a many-body system after a global parameter change is studied. Ultracold atoms offer the unique opportunity to investigate such questions experimentally, thus there will be a close connection between ongoing experiments and this theoretical work. Even though I will be mainly concerned with sudden quenches, where the parameters are changed instantly in time, I also want to study situations where the parameters are varied at a finite rate and establish connections to adiabatic dynamics of many-body systems. In particular, I want to study the influence of quantum critical points on the order-parameter dynamics following a quantum quench. The second part of the project deals with unconventional superfluidity and the consequences of scale invariance for the transport properties of ultracold atomic gases close to a Feshbach resonance. The equilibrium properties of these systems have been under extensive experimental and theoretical investigation during the last years. Of particular interest is the so called unitary point, where the interaction strength between the atoms diverges and the system is scale invariant. Right at this point, equilibrium as well as transport quantities are determined by universal, dimensionless numbers. The goal of this part of the project is to provide theoretical predictions for universal transport coefficients in strongly interacting Fermi gases. One particular example is the diffusion constant, which is currently being measured in experiments. Moreover, I`m going to study unconventional superfluid phases in equilibrium, such as p-wave instabilities in Fermi gases with a population imbalance.