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arXiv · 1307.7506

Transport through nanostructures: Finite time vs. finite size

Peter Schmitteckert·Sam T. Carr·Hubert Saleur
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Abstract

Numerical simulations and experiments on nanostructures out of equilibrium usually exhibit strong finite size and finite measuring time $t_m$ effects. We discuss how these affect the determination of the full counting statistics for a general quantum impurity problem. We find that, while there are many methods available to improve upon finite-size effects, any real-time simulation or experiment will still be subject to finite time effects: in short size matters, but time is limiting. We show that the leading correction to the cumulant generating function (CGF) at zero temperature for single-channel quantum impurity problems goes as $\ln t_m$ and is universally related to the steady state CGF itself for non-interacting systems. We then give detailed numerical evidence for the case of the self-dual interacting resonant level model that this relation survives the addition of interactions. This allows the extrapolation of finite measuring time in our numerics to the long-time limit, to excellent agreement with Bethe-ansatz results.

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Peter Schmitteckert, Sam T. Carr, Hubert Saleur. 2013-08-26. Transport through nanostructures: Finite time vs. finite size. https://doi.org/10.1103/physrevb.89.081401

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