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Quasi-periodically driven quantum parametric oscillators have been the subject of several recent investigations. Here we show that for such oscillators, the instability zones of the mean position and variance (alternatively the mean energy) for a time developing wave packet are identical for the strongest resonance in the three-dimensional parameter space of the quasi-periodic modulation as it is for the two-dimensional parameter space of the periodic modulations.
For a particle in a box, the operator $- i partial_x$ is not Hermitean. We provide an alternative construction of a momentum operator $p = p_R + i p_I$, which has a Hermitean component $p_R$ that can be extended to a self-adjoint operator, as well as
The quantum stochastic Schroedinger equation or Hudson-Parthasareathy (HP) equation is a powerful tool to construct unitary dilations of quantum dynamical semigroups and to develop the theory of measurements in continuous time via the construction of
A system of harmonic oscillators coupled via nonlinear interaction is a fundamental model in many branches of physics, from biophysics to electronics and condensed matter physics. In quantum optics, weak nonlinear interaction between light modes has
Some predictions of quantum mechanics are in contrast with the macroscopic realm of everyday experience, in particular those originated by the Heisenberg uncertainty principle, encoded in the non-commutativity of some measurable operators. Nonetheles
In this paper we review the basic results concerning the Wigner transform and then we completely solve the quantum forced harmonic/inverted oscillator in such a framework; eventually, the tunnel effect for the forced inverted oscillator is discussed.