Multiparametric quantum gl(2) algebras are presented according to a classification based on their corresponding Lie bialgebra structures. From them, the non-relativistic limit leading to quantum harmonic oscillator algebras is implemented in the form of generalized Lie bialgebra contractions.

He constructed a forcing term pðtÞ in L1ðRÞ such that (1) has at least one unbounded solution. This result may look non-intuitive if the equation is interpreted as the law of motion of a non-linear oscillator. In fact, the assumptions imply that the total force gðuÞ þ pðtÞ points inwards (for large juj) and a phenomenon of resonance, as in the harmonic oscillator, seems to be excluded by the su...

We show that nonlinear response of a quantum oscillator displays antiresonant dips as the field frequency passes adiabatically through multiphoton resonance. This coherent quantum effect has no analog in two-level systems. Its emergence is a consequence of special symmetry of a weakly nonlinear oscillator. We discuss the possibility to observe the antiresonance and the associated multiphoton Ra...