We study the critical behavior of excited states and its relation to order and chaos in the Jaynes-Cummings and Dicke models of quantum optics. We show that both models exhibit a chain of excited-state quantum phase transitions demarcating the upper edge of the superradiant phase. For the Dicke model, the signatures of criticality in excited states are blurred by the onset of quantum chaos. We show that the emergence of quantum chaos is caused by the precursors of the excited-state quantum phase transition.

We analyze excited-state quantum phase transitions (ESQPTs) in three schematic (integrable and nonintegrable) models describing a single-mode bosonic field coupled to a collection of atoms. It is shown that the presence of the ESQPT in these models affects the quantum relaxation processes following an abrupt quench in the control parameter. Clear-cut evidence of the ESQPT effects is presented in integrable models, while in a nonintegrable model the evidence is blurred due to chaotic behavior of the system in the region around the critical energy.

The scattering of a weakly bound three-body system by a target is discussed. A transformed harmonic oscillator basis is used to provide an appropriate discrete and finite basis for treating the continuum part of the spectrum of the projectile. The continuum-discretized coupled-channels framework is used for the scattering calculations. The formalism is applied to different reactions, ${}^6\mathrm{He}$ $+$ ${}^{12}\mathrm{C}$ at 229.8 MeV, ${}^6\mathrm{He}$ $+$ ${}^{64}\mathrm{Zn}$ at 10 and 13.6 MeV, and ${}^6\mathrm{He}$ $+$ ${}^{208}\mathrm{Pb}$ at 22 MeV, induced by the Borromean nucleus ${}^6\mathrm{He}$. Both the Coulomb and nuclear interactions with a target are taken into account.

We analyze the decoherence induced on a single qubit by the interaction with a two-level boson system with critical internal dynamics. We explore how the decoherence process is affected by the presence of quantum phase transitions in the environment. We conclude that the dynamics of the qubit changes dramatically when the environment passes through a continuous excited state quantum phase transition. If the system-environment coupling energy equals the energy at which the environment has a critical behavior, the decoherence induced on the qubit is maximal and the fidelity tends to zero with finite size scaling obeying a power law.

The decoherence induced on a single qubit by its interaction with the environment is studied. The environment is modeled as a scalar two-level boson system that can go through either first-order or continuous-excited-state quantum phase transitions, depending on the values of the control parameters. A mean-field method based on the Tamm-Damkoff approximation is worked out in order to understand the observed behavior of the decoherence. Only the continuous-excited-state phase transition produces a noticeable effect in the decoherence of the qubit. This is maximal when the system-environment coupling brings the environment to the critical point for the continuous phase transition. In this situation, the decoherence factor (or the fidelity) goes to zero with a finite-size scaling power law.

The structure of the three-body Borromean nucleus ${}^6\mathrm{He}$ is approximated by a two-body di-neutron cluster model. The binding energy of the $2n\text{−}\alpha$ system is determined to obtain a correct description of the $2n\text{−}\alpha$ coordinate, as given by a realistic three-body model calculation. The model is applied to describe the breakup effects in elastic scattering of ${}^6\mathrm{He}$ on several targets, for which experimental data exist. We show that an adequate description of the di-neutron-core degree of freedom permits a fairly accurate description of the elastic scattering of ${}^6\mathrm{He}$ on different targets.