A model is proposed that describes the evolution of a mixed state of a quantum system for which gain and loss of energy or amplitude are present. Properties of the model are worked out in detail. In particular, invariant subspaces of the space of density matrices corresponding to the fixed points of the dynamics are identified, and the existence of a transition between the phase in which gain and loss are balanced and the phase in which this balance is lost is illustrated in terms of the time average of observables. The model is extended to include a noise term that results from a uniform random perturbation generated by white noise. Numerical studies of example systems show the emergence of equilibrium states that suppress the phase transition.
This research output has an Altmetric Attention Score of 2. This is our high-level measure of the quality and quantity of online attention that it has received. This Attention Score, as well as the ranking and number of research outputs shown below, was calculated when the research output was last mentioned on 05 December 2012.
All research outputs
#15,152,619
of 23,305,591 outputs
Outputs from Physical Review Letters
#24,663
of 36,085 outputs
Outputs of similar age
#176,533
of 280,805 outputs
Outputs of similar age from Physical Review Letters
#320
of 688 outputs
Altmetric has tracked 23,305,591 research outputs across all sources so far. This one is in the 32nd percentile – i.e., 32% of other outputs scored the same or lower than it.
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