Isn't it the case that uncertainty predicts an above-zero temperature for empty space via quantum gyrations etc? I say that because I am not sure QM models apply at a theoretical absolute zero - its like wondering whether the frequency of light shifts at absolute zero - if there are photons present, perhaps that means the temperature is above absolute zero and it becomes difficult to interpret the question.
Nothing much. Plenty of experiments are done at a temperature so low that it is from a 'practical' point of view might as well be zero. The 'energy scale' is set by kb*T, and if all energy scales (e.g. gap energies etc) of your system are much higher than that you have essentially eliminated thermal fluctuations as a source of decoherence. All this means is that other sources of decoherence dominates.
Theoretically quantum phase transitions are defined as transitions which happen at T=0 by tuning some parameter. The phase transition is caused by quantum fluctuations, an example being the transverse Ising mode. In 1d it is a chain of spins with the interaction term for spin x and a field in the z direction. Since sigma^x and sigma^z don't commute, you can start in the ordered state with no field and at a certain coupling will have a phase transition to a disordered state.
Many quantum phase transitions, like the one above do not actually take place at nonzero temperature. However they critical point influences behavior at nonzero temperature. Getting back to your original question, one interesting scale in the system is the phase coherence time, or how long a system remembers its phase. At zero temperature this is infinite. In places where the temperature scale is lower than the distance from the critical point, the phase relaxation is finite but relatively long. However, right around the critical point at finite temperature, the phase relaxation becomes as short as possible and is on the same scale as the thermal relaxation time. This is called maximally incoherent. Thermal and quantum scales are on equal footing, and conventional methods used to study such systems break down.
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