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arXiv · 2609.33724

Quantum Dynamics of Full Counting Statistics in Fermionic Lattices with Localized Gain

Bijay Kumar Agarwalla·Manas Kulkarni
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Abstract

We investigate the dynamics of full counting statistics (FCS) of the growth of the total number of fermions in a one-dimensional non-interacting lattice subjected to a localized particle gain (source) at one edge. The dynamics of the setup is modeled by the Gorini--Kossakowski--Sudarshan--Lindblad (GKSL) quantum master equation. We recast the counting problem that involves counting particle number at every lattice site to a problem where only the local injected site is involved. We employ the Schwinger-Keldysh path integral formalism within the GKSL framework and derive an analytical expression for the cumulant generating function at arbitrary times and obtain a Levitov-Lesovik type formula in the long-time limit, earlier derived for boundary driven setups in the steady-state. For clean lattices with either short- or long-range hopping, supporting single-particle delocalized eigenstates, we show that all cumulants grow linearly with time in the asymptotic regime. Our analytical results are in excellent agreement with direct numerical simulations. These findings establish a general framework for characterizing FCS and quantum fluctuations in driven open fermionic systems with localized particle injection.

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Bijay Kumar Agarwalla, Manas Kulkarni. 2026-09-27. Quantum Dynamics of Full Counting Statistics in Fermionic Lattices with Localized Gain. https://arxiv.org/abs/2609.33724

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