Journal of Computational Electronics

, Volume 12, Issue 3, pp 388–396 | Cite as

Decoherence effects in the Wigner function formalism

  • Philipp Schwaha
  • Damien Querlioz
  • Philippe Dollfus
  • Jérôme Saint-Martin
  • Mihail NedjalkovEmail author
  • Siegfried Selberherr


We demonstrate the ability of the phase space formulation of quantum mechanics to provide convenient means and intuitive notions for exploring the process of transition from a quantum to a classical state known as decoherence. The Wigner equation, which is usually relevant for electron transport in nanostructures, augmented by the Boltzmann scattering operator is now applied to the time dependent transport problems which may be considered as benchmark examples for the decoherence role of phonons in semiconductor devices. Simulation results maintained by theoretical analysis show how scattering effectively destroys the interference effects. The initial coherence in the wave vector distribution is pushed towards the equilibrium distribution. In particular scattering by phonons hinders the natural spread of the density with time and advances it towards a classical localization. Furthermore, the decoherence effect due to phonons, is measured by the purity of the Wigner state, which decreases from its initial value of 1, with a rate depending on the lattice temperature, and by a functional comparing diagonal with off-diagonal elements of the density matrix.


Wigner function Quantum transport Phonons Decoherence 



This work has been supported by the Austrian Science Fund Project FWF-P21685.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Philipp Schwaha
    • 1
    • 3
  • Damien Querlioz
    • 2
  • Philippe Dollfus
    • 2
  • Jérôme Saint-Martin
    • 2
  • Mihail Nedjalkov
    • 1
    Email author
  • Siegfried Selberherr
    • 1
  1. 1.Institute for MicroelectronicsTU WienWienAustria
  2. 2.Institut d’Electronique FondamentaleUniversité Paris-Sud, CNRSOrsayFrance
  3. 3.AVL List GmbHGrazAustria

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