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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 , Prof. Dr. A. Knorr