# Transport through nanostructures: Finite time vs. finite size

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.
Document type :
Journal articles

https://hal-cea.archives-ouvertes.fr/cea-01065721
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Submitted on : Thursday, September 18, 2014 - 2:23:24 PM
Last modification on : Wednesday, April 14, 2021 - 12:12:10 PM

### Identifiers

• HAL Id : cea-01065721, version 1
• ARXIV : 1307.7506

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### Citation

Peter Schmitteckert, Sam T. Carr, Hubert Saleur. Transport through nanostructures: Finite time vs. finite size. Physical Review B: Condensed Matter and Materials Physics (1998-2015), American Physical Society, 2014, 89 (08), pp.140. ⟨cea-01065721⟩

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