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Abstract
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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