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Transport through nanostructures: Finite time versus finite size

Peter Schmitteckert, Sam T. Carr, and Hubert Saleur
Phys. Rev. B 89, 081401(R) – Published 5 February 2014
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Abstract

Numerical simulations and experiments on nanostructures out of equilibrium usually exhibit strong finite size and finite measuring time tm 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 is proportional to lntm, where the constant of proportionality is universally related to the steady state CGF itself for non-interacting systems; universal in this context means independent of details of the quench procedure, i.e., independent of the switching on of both voltage and counting field. We 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, in excellent agreement with Bethe-ansatz results.

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  • Received 26 August 2013
  • Revised 13 November 2013

DOI:https://doi.org/10.1103/PhysRevB.89.081401

©2014 American Physical Society

Authors & Affiliations

Peter Schmitteckert1,2, Sam T. Carr1,3, and Hubert Saleur4,5

  • 1DFG Center for Functional Nanostructures, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany
  • 2Institute of Nanotechnology, Karlsruhe Institute of Technology, 76344 Eggenstein-Leopoldshafen, Germany
  • 3School of Physical Sciences, University of Kent, Canterbury CT2 7NH, United Kingdom
  • 4Institut de Physique Théorique, CEA, IPhT and CNRS, URA2306, F-91191 Gif Sur Yvette, France
  • 5Department of Physics, University of Southern California, Los Angeles, California 90089-0484, USA

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Issue

Vol. 89, Iss. 8 — 15 February 2014

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