We 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.
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