This paper discusses how slow dynamics can occur in the vicinity of quantum phase transitions. In addition to critical slowing down, there are two additional sources of slow dynamics. Firstly, even for a pure system, there is a phase coherence time which diverges as the temperature tends to zero. This is hard to see from numerical studies in imaginary time and real time dynamics are needed. Secondly, in random systems, Griffiths-McCoy singularities occur at low temperature because of rare regions which are ``locally in the wrong phase'' due to of statistical fluctuations in the random interactions. These are particularly strong for systems with discrete, e.g. Ising, symmetry. The form of Griffiths-McCoy singularities in real time is not understood.
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