Reduced dynamics of full counting statistics

Felix A. Pollock, Emanuel Gull, Kavan Modi*, Guy Cohen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number027
JournalSciPost Physics
Issue number2
StatePublished - Aug 2022


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