TL;DR
This paper reviews recent studies on quantum systems with time-dependent Hamiltonians that develop singularities, focusing on their evolution across space-time singularities in cosmological models.
Contribution
It provides an overview of the general properties of quantum evolution across singularities, highlighting recent progress in understanding these complex systems.
Findings
Quantum Hamiltonians can develop singularities over time.
Evolution across space-time singularities exhibits unique quantum behaviors.
Recent investigations reveal key properties of such quantum systems.
Abstract
In a number of model contexts, evolution across space-time singularities (reminiscent of the cosmological singularities) involves time-dependent quantum Hamiltonians developing a singularity as a function of time. In this contribution to the proceedings of the 3rd RTN workshop in Valencia, I review some recent investigations of the general properties of such systems.
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