Effective and Efficient Resonant Transitions in Periodically Modulated Quantum Systems

We analyze periodically modulated quantum systems with SU(2) and SU(1,1) symmetries. Transforming the Hamiltonian into the Floquet representation we apply the Lie transformation method, which allows us to classify all effective resonant transitions emerging in time-dependent systems. In the case of a single periodically perturbed system, we propose an explicit iterative procedure for the determination of the effective interaction constants corresponding to every resonance both for weak and strong modulation. For coupled quantum systems we determine the efficient resonant transitions appearing as a result of time modulation and intrinsic non-linearities.

Eigenmode Approach for a Periodic Composite Transducer Subject to Fluid Loading

A hybrid finite element eigenmode—Floquet mode representation is formulated and numerically implemented to study the performance of composite transducers subject to fluid loading. The periodic distribution of the piezoelectric elements in the form of rods in a dielectric host material permits consideration of only one unit cell of the distribution in the finite element solution. Again, due to periodicity, the acoustic field in the infinite fluid is represented as superposition of plane wave Floquet modes. The finite element method is used to solve the eigenmodes of vibration of the transducer and an eigenmode superposition with unknown weighting coefficients is interfaced with the Floquet representation. Continuity at the boundary is used to solve for both sets of unknown coefficients. The effect of rod cross section, concentration, material damping are studied as a function of frequency. Useful transducer parameters such as transmission efficiency and the conductance spectrum as well as reflection and transmission spectrum of the array are simulated numerically.