  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 the nonintegrable model the
evidence is blurred due to chaotic behavior of the system in the region around
the critical energy.
