Mathematical Sciences: The Quantum Behavior of Coupled Nonlinear Oscillators

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Under a previous NSF Grant (NO. 8702066), it was demonstrated that the discrete self-trapping (DST) equation is remarkably sinple to quantize, and this property has been used to characterize the quantum structure of local modes and of chaos. In this project Professor Scott will (i) use the DST equation to study the quantum behavior of a damped driven system, and (ii) use a slighlty modified DST equation to study the quantum structure of self-focusing ("blow-up"). This work has applications to optical spectroscopy and quantum chemistry.