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We study the relation between energy and entanglement in an entanglement transfer problem. We first analyze the general setup of two entangled qubits ("a" and "b") exchanging this entanglement with two other independent qubits ("A" and "B"). Qubit "a" ("b") interacts with qubit "A" ("B") via a spin exchange-like unitary evolution. A physical realization of this scenario could be the problem of two-level atoms transferring entanglement to resonant cavities via independent JaynesCummings interactions. We study the dynamics of entanglement and energy for the second pair of qubits (tracing out the originally entangled ones) and show that these quantities are closely related. For example, the allowed quantum states occupy a restricted area in a phase diagram entanglement vs. energy. Moreover the curve which bounds this area is exactly the one followed if both interactions are equal and the entire four qubit system is isolated. We also consider the case when the target pair of qubits is subjected to losses and can spontaneously decay.

We show that the well known geometric phase, the Gouy phase in optics can be defined for matter waves in vacuum as well. In particular we show that the underlying physics for the "matter waves" Gouy phase is the generalized Schrödinger-Robertson uncertainty principle, more specifically, the off diagonal elements of the covariance matrix. Recent experiments involving the diffraction of fullerene molecules and the uncertainty principle are shown to be quantitatively consistent with the existence of a Gouy phase for matter waves.

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.

The Schrödinger equation for an atomic beam predicts that it must have a phase anomaly near the beam waist analogous to the Gouy phase of an electromagnetic beam. We propose here a feasible experiment which allows for the direct determination of this anomalous phase using Ramsey interferometry with Rydberg atoms. Possible experimental limitations are discussed and shown to be completely under control within the present day technology. We also discuss how this finding can open the possibility to use the spatial mode wavefunctions of atoms as q-dits, since the Gouy phase is an essential ingredient for making rotations in the quantum states.