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Comunicación presentada a: Meeting on Beauty in Physics - Theory and Experiment in Honor of Francesco Lachello on the Occasion of his 70th Birthday Location: México, may 14-18, 2012We study the similarities and differences between the phenomena of Quantum Decoherenceand Quantum Quench in presence of an Excited State Quantum Phase Transition (ESQPT).Weanalyze, on one hand, the decoherence induced on a single qubit by the interaction with a two-levelboson system with critical internal dynamics and, on the other, we treat the quantum relaxation processthat follows an abrupt quench in the control parameter of the system Hamiltonian. We explorehow the Quantum Decoherence and the quantum relaxation process are affected by the presence ofan ESQPT. We conclude that the dynamics of the qubit or the quantum relaxation process changedramatically when the system passes through a continuous ESQPT

Decoherence and quantum quench: Their relationship with excited state quantum phase transitions