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### Project P4/2

#### Title

Emergence of Nonequilibrium Steady States in Periodically Driven Closed Composite Quantum Systems

#### Principal investigators

- Prof. Dr. Martin Holthaus (Universität Oldenburg)
- Prof. Dr. Andreas Engel (Universität Oldenburg)

#### Summary

Within the previous first funding period of FOR 2692 we have contributed to the area of "periodic thermodynamics", and have determined the probability distributions which govern the Floquet-state occupation probabilities for periodically driven open quantum systems of theoretical and experimental interest. In particular, we have demonstrated that the nonequilibrium magnetization of a periodically driven paramagnetic material is strongly affected by details concerning the spins' coupling to their environment, and have established the novel concept of "Floquet-state cooling", demonstrating that a Floquet state emerging from the ground state of a quantum system can carry even significantly higher population in the presence of a strong driving force than that ground state in thermal equilibrium. These results still rest on an approach which is equivalent to the usual Born-Markov approximation, disregarding potential complications due to the denseness of the quasienergy spectrum. In the second funding period we will therefore extend the above findings beyond the scope of that proposition, moving towards environments which actually "feel" the time-periodic driving force. To this end, we will study particular periodically driven quantum systems coupled to N bath oscillators which can be solved analytically for any N by means of a generalized Husimi transformation, and explore how the limit N -> infinity is approached. On the other hand, we will numerically investigate models of periodically driven bosonic Josephson junctions occupied by two particle species, one representing a periodically driven system, the other a bath. In this way, predictions implied by the Born-Markov-like formulation of periodic thermodynamics can be put to a hard test.

In addition, two strands of development arising out of the work accomplished in the first project period will be continued, namely, the task of selectively populating certain "resonant" Floquet states by means of suitably designed system-bath couplings and bath densities of states, and the variational computation of Floquet states of large systems which may not be amenable to the presently used standard numerical methods. As a long-term goal linking several of these subtopics we also consider the feasibility of Floquet condensates of weakly interacting atomic Bose gases in time-periodically modulated trapping potentials, which may exhibit some fairly unusual features.