Stochastic trajectories and excursions in a double quantum dot system

Abstract:We investigate the trajectory-level stochastic dynamics of a double quantum dot system using the formalism of stochastic excursions. An excursion is a sub-trajectory that begins when the system leaves a chosen reference state (or more generally, a set of states)---here, the empty double dot---and ends upon its first return to it. Filtering trajectories into excursions extends full counting statistics and gives access to the correlations between thermodynamic currents and excursion durations. The main objects of study are counting observables, defined as weighted sums of transition counts within a single excursion. For three main counting observables---charge current, dynamical activity, and entropy production---we compute averages and noise contributions and show how they provide insights into the operation of the double quantum dot system. At the trajectory level, we analyze outcome distributions for transport and connect the results with trade-offs between successful and unsuccessful events that shape the overall performance of the double quantum dot as a transport device. We then discuss the populations of the two dots, as well as their correlations. Finally, we illustrate how the framework provides insights into the thermodynamics of precision through the Fano factor and thermo-kinetic uncertainty relations, where different regimes are fundamentally constrained either by entropy production or by dynamical activity. Altogether, our work is a case study that highlights the utility of the excursion framework as a toolkit to analyze many quantities of interest and to uncover the structure of nonequilibrium fluctuations. Moreover, it also suggests new avenues for refining uncertainty relations and understanding transport in mesoscopic systems.

Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Statistical Mechanics (cond-mat.stat-mech)

arXiv:2605.20166 [quant-ph]

(or arXiv:2605.20166v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2605.20166 Focus to learn more arXiv-issued DOI via DataCite

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