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.

5 pages + 3 pages supplementary material

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Cited by in corpus (8)

• Energy transport between two integrable spin chains
• Numerically exact full counting statistics of the nonequilibrium Anderson impurity model
• Revealing strong correlations in higher order transport statistics: a noncrossing approximation approach
• Full counting statistics in the not-so-long-time limit
• Exact equilibrium results in the Interacting Resonant Level Model
• Gibbs phenomenon and the emergence of the steady-state in quantum transport
• Realizing the interacting resonant level model using a quantum dot detector
• Local density of states of the interacting resonant level model at zero temperature