Project A.2: Collective non-equilibrium dynamics in quantum systems near criticality

The key idea of this project is to apply statistical tools developed during the first funding period to transport versions of quantum phase transition models. We will derive Master equations for quantum critical systems, such as the quantum Ising chain in transverse magnetic field, and include counting fields that allow us to calculate the full counting statistics and time-dependent correlation functions such as the g⁽²⁾(τ)-function or the waiting time distribution w(τ). Our aim is to extract quantum critical behavior in, e.g., temporal correlation functions. Furthermore, we plan to investigate the role of the fluctuation theorem and its apparent violation when integrating out degrees of freedom near quantum criticality.
One of the challenges that requires expertise across the groups of the two PIs is to evaluate current cumulant generating functions beyond weak reservoir coupling, where non-Markovian effects become important. We also plan to use methods based on hierarchies of equations of motion that will possibly allow us to go beyond the Master equation (weak coupling) regime.

Project leaders: Prof. Dr. T. Brandes [1], Prof. Dr. A. Knorr [2]