We review the Floquet theory of linear differential equations with periodic coefficients and discuss its applications to neutrino oscillations in matter of periodically varying density. In particular, we consider parametric resonance in neutrino oscillations which can occur in such media, and discuss implications for oscillations of neutrinos traversing the earth and passing through the earth's...

We study the parametric resonance of the neutrino oscillation through the matter whose density varies spatially. The Fourier analysis of the matter effect enables us to clarify the parametric resonance condition, which is summarized in a frequency matching between the neutrino oscillation and the spatial variation of the matter density. As a result, the n-th Fourier mode of a matter density pro...

We present an experimental investigation of parametric scattering processes and optical parametric oscillations in wire shaped, one-dimensional semiconductor microcavities. Far field emission patterns and corresponding band dispersion are studied by polarization resolved measurements and power dependence measurements under resonant and non-resonant excitation. The multiplicity of the photonic b...

We report quasi-phase-matched singly resonant optical parametric oscillation in electric-field-poled lithium niobate waveguides. Parametric gains as high as 250%/W, an oscillation threshold of 1.6 W (peak), idler output powers of 220 mW, and a tuning range of 1180-2080 nm for pump wavelengths of 756-772 nm have been observed. Pump depletion is limited to 40% because of the multiple launched tra...

We demonstrate that magnetic oscillations of a current-biased magnetic nanocontact can be parametrically excited by a microwave field applied at twice the resonant frequency of the oscillation. The threshold microwave amplitude for the onset of the oscillation decreases with increasing bias current, and vanishes at the transition to the auto-oscillation regime. Theoretical analysis shows that m...

Employing the quantum Hamiltonian describing the interaction of two-mode light (signalidler modes) generated by a nondegenerate parametric oscillator (NDPO) with two uncorrelated squeezed vacuum reservoirs (USVR), we derive the master equation. The corresponding Fokker-Planck equation for the Q-function is then solved employing a propagator method developed by K. Fesseha [J. Math. Phys. 33 2179...

We propose an approach to falsification of oscillation properties of parametric biological models, based on the recently developed techniques for testing continuous and hybrid systems. In this approach, an oscillation property can be specified using a hybrid automaton, which is then used to guide the exploration in the state and input spaces to search for the behaviors that do not satisfy the p...