| Summary: | We present a theory of modified reduced dynamics in the presence of counting
fields. Reduced dynamics techniques are useful for describing open quantum
systems at long emergent timescales when the memory timescales are short.
However, they can be difficult to formulate for observables spanning the system
and its environment, such as those characterizing transport properties. A large
variety of mixed system--environment observables, as well as their statistical
properties, can be evaluated by considering counting fields. Given a numerical
method able to simulate the field-modified dynamics over the memory timescale,
we show that the long-lived full counting statistics can be efficiently
obtained from the reduced dynamics. We demonstrate the utility of the technique
by computing the long-time current in the nonequilibrium Anderson impurity
model from short-time Monte Carlo simulations.
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