For Hamiltonian families with known generators and hidden parameters, the exact query cost of implementing the inverse is determined by spectral sumset relations and representation-theoretic reduction, yielding polynomial or constant bounds for several many-body families.
Quantum chaos in the Dicke model and its variants
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abstract
Recently, the out-of-time-ordered correlator (OTOC) has gained much attention as an indicator of quantum chaos. In the semi-classical limit, its exponential growth rate resembles the classical Lyapunov exponent. The quantum-classical correspondence has been supported for the one-body chaotic systems as well as realistic systems with interactions, as in the Dicke model, a model of multi-two-level atoms and cavity field interactions. To this end, we calculate the OTOC for different variations of the Dicke model in an open quantum system setting. The connection between the superradiant phase transition of the Dicke model and the OTOC is studied. Further, we establish a relation between the OTOC and the second-order coherence function. This becomes important for the experimental studies of the OTOC and quantum chaos in the models of quantum optics.
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Algebraic Speedups for Exact Inversion of Hamiltonian Evolutions
For Hamiltonian families with known generators and hidden parameters, the exact query cost of implementing the inverse is determined by spectral sumset relations and representation-theoretic reduction, yielding polynomial or constant bounds for several many-body families.