Transport through nanostructures: Finite time vs. finite size

Peter Schmitteckert (1, 2) , Sam T. Carr (1, 3) , Hubert Saleur (4, 5)

1 DFG - Deutsche Forschungsgemeinschaft - German Research Foundation
2 KIT - Karlsruhe Institute of Technology
3 University of Kent [Canterbury]
4 IPHT - Institut de Physique Théorique - UMR CNRS 3681
5 UCLA - University of California [Los Angeles]

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.

Domains: Other [cond-mat.other]

Peter Schmitteckert, Sam T. Carr, Hubert Saleur. Transport through nanostructures: Finite time vs. finite size. Physical Review B, 2014, 89 (08), pp.081401. ⟨10.1103/PhysRevB.89.081401⟩. ⟨cea-01065721⟩