Semiclassical corrections to the large- N limit of Dicke's model.

We use a semiclassical expansion as an alternative derivation of the well-known, rigorous result obtained by Hepp and Lieb for the classical limit of the spin-boson model. We also explicitly derive correction terms to the classical limit previously obtained in the context of Heisenberg equations of motion. We analyze the size and shape of the N (number of atoms) vs t (time) domain whithin which the corrections so obtained are useful.

Entanglement and classical instabilities: fingerprints of electron-hole-to-exciton phase transition in a simple model.

We propose a schematic model to study the formation of excitons in bilayer electron systems. The phase transition is signalized both in the quantum and classical versions of the model. In the present contribution we show that not only the quantum ground state but also higher energy states, up to the energy of the corresponding classical separatrix orbit, "sense" the transition. We also show two types of one-to-one correspondences in this system: On the one hand, between the changes in the degree of entanglement for these low-lying quantum states and the changes in the density of energy levels; on the other hand, between the variation in the expected number of excitons for a given quantum state and the behavior of the corresponding classical orbit.

Quantum-classical transition of the open quartic oscillator: The role of the environment.

We investigate the classical and quantum dynamics of the open quartic oscillator model. Typically quantum behavior such as collapses and revivals (also squeezing) are induced by the nonlinearity of the model. We show that purely diffusive environments, as expected, attenuate such phenomena. We obtain analytical results in both regimes classical and quantum and discuss the effect of a diffusive reservoir in the two cases. We show that "separation times" as usually defined in the literature are strongly observable (and initial condition) dependent, rendering a solid definition of a unique classical limit rather difficult. In particular, the separation time for the variance can be smaller than that for the expectation value of the position of the centroid of the wave packet. We find a hierarchy of time scales which depends on the observable and the reservoir.