Full counting statistics for boundary driven transport in presence of correlated gain and loss channels

Katha Ganguly; Bijay Kumar Agarwalla

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arXiv · 2511.12539

Full counting statistics for boundary driven transport in presence of correlated gain and loss channels

Katha Ganguly·Bijay Kumar Agarwalla

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Abstract

One of the major advances of quantum technology is the engineering of complex quantum channels in lattice systems that paves the way for a variety of novel non-equilibrium phenomena. For a boundary driven lattice with such engineered quantum channels, the analysis of the full counting statistics of current across boundaries has received limited attention. In this work, we consider a boundary driven free fermionic lattice with carefully engineered correlated gain and loss channels and obtain the cumulant generating function of the steady-state particle current. We also discuss the limit for simplifying the correlated gain-loss channel to a local gain-loss channel and obtain the average current and its fluctuation in such cases. Generally, in the presence of gain-loss, the current statistics are different at the two ends of the lattice. Hence, for both local and correlated gain-loss, we devise the conditions for which the statistics can coincide, giving rise to a $\mathcal{PT}$ symmetric balanced gain-loss scenario. A striking difference between the correlated gain-loss and their local counterpart is the emergence of nonreciprocity in the system and we observe that it has a dramatic impact in the current as well as fluctuations. Our work therefore provides interesting insights about the importance of engineered dissipators in boundary driven systems.

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Katha Ganguly, Bijay Kumar Agarwalla. 2025-11-16. Full counting statistics for boundary driven transport in presence of correlated gain and loss channels. https://arxiv.org/abs/2511.12539

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