In this work we use the formalism of chord functions (emph{i.e.} characteristic functions) to analytically solve quadratic non-autonomous Hamiltonians coupled to a reservoir composed by an infinity set of oscillators, with Gaussian initial state. We
analytically obtain a solution for the characteristic function under dissipation, and therefore for the determinant of the covariance matrix and the von Neumann entropy, where the latter is the physical quantity of interest. We study in details two examples that are known to show dynamical squeezing and instability effects: the inverted harmonic oscillator and an oscillator with time dependent frequency. We show that it will appear in both cases a clear competition between instability and dissipation. If the dissipation is small when compared to the instability, the squeezing generation is dominant and one can see an increasing in the von Neumann entropy. When the dissipation is large enough, the dynamical squeezing generation in one of the quadratures is retained, thence the growth in the von Neumann entropy is contained.
We analytically exploit the two-mode Gaussian states nonunitary dynamics. We show that in the zero temperature limit, entanglement sudden death (ESD) will always occur for symmetric states (where initial single mode compression is $z_0$) provided the
two mode squeezing $r_0$ satisfies $0 < r_0 < 1/2 log (cosh (2 z_0)).$ We also give the analytical expressions for the time of ESD. Finally, we show the relation between the single modes initial impurities and the initial entanglement, where we exhibit that the later is suppressed by the former.
We investigate theoretically an open dynamics for two modes of electromagnetic field inside a microwave cavity. The dynamics is Markovian and determined by two types of reservoirs: the natural reservoirs due to dissipation and temperature of the cavi
ty, and an engineered one, provided by a stream of atoms passing trough the cavity, as devised in [Pielawa emph{et al.} emph{Phys. Rev. Lett.} textbf{98}, 240401 (2007)]. We found that, depending on the reservoir parameters, the system can have distinct phases for the asymptotic entanglement dynamics: it can disentangle at finite time or it can have persistent entanglement for large times, with the transition between them characterized by the possibility of asymptotical disentanglement. Incidentally, we also discuss the effects of dissipation on the scheme proposed in the above reference for generation of entangled states.
The dissipative dynamics of Gaussian squeezed states (GSS) and coherent superposition states (CSS) are analytically obtained and compared. Time scales for sustaining different quantum properties such as squeezing, negativity of the Wigner function or
photon number distribution are calculated. Some of these characteristic times also depend on initial conditions. For example, in the particular case of squeezing, we find that while the squeezing of CSS is only visible for small enough values of the field intensity, in GSS it is independent of this quantity, which may be experimentally advantageous. The asymptotic dynamics however is quite similar as revealed by the time evolution of the fidelity between states of the two classes.
We study and compare the information loss of a large class of Gaussian bipartite systems. It includes the usual Caldeira-Leggett type model as well as Anosov models (parametric oscillators, the inverted oscillator environment, etc), which exhibit ins
tability, one of the most important characteristics of chaotic systems. We establish a rigorous connection between the quantum Lyapunov exponents and coherence loss, and show that in the case of unstable environments coherence loss is completely determined by the upper quantum Lyapunov exponent, a behavior which is more universal than that of the Caldeira-Leggett type model.
