Skip to main content

Decoherence effects in the Wigner function formalism

Journal of Computational Electronics volume 12, pages 388–396 (2013)Cite this article

Abstract

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.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

References

  1. Zurek, W.H.: Rev. Mod. Phys. 75(3), 715 (2003)

    MathSciNet  MATH  Article  Google Scholar 

  2. Vacchini, B., Hornberger, K.: Relaxation dynamics of a quantum Brownian particle in an ideal gas. Eur. Phys. J. Spec. Top. 151, 59–72 (2007)

    Article  Google Scholar 

  3. Halliwell, J.J.: Two derivations of the master equation of quantum Brownian motion. J. Phys. A, Math. Theor. 40, 3067–3080 (2007)

    MathSciNet  MATH  Article  Google Scholar 

  4. Hofheinz, M., Wang, H., Ansmann, M., Bialczak, R.C., Lucero, E., Neeley, M., O’Connell, A.D., Sank, D., Wenner, J., Martinis, J.M., Cleland, A.N.: Synthesizing arbitrary quantum states in a superconducting resonator. Nature 459, 546–549 (2009)

    Article  Google Scholar 

  5. Ferry, D.K., Akis, R., Bird, J.P.: Einselection in action: decoherence and pointer states in open quantum dots. Phys. Rev. Lett. 93, 026803 (2004)

    Article  Google Scholar 

  6. Knezevic, I.: Decoherence due to contacts in ballistic nanostructures. Phys. Rev. B 77, 125301 (2008)

    Article  Google Scholar 

  7. Joos, E., Zeh, H.D., Kiefer, C., Giulini, D.J.W., Kupsch, J., Stamatescu, I.O.: Decoherence and the Appearance of a Classical World in Quantum Theory. Springer, Berlin (2003)

    Book  Google Scholar 

  8. Pastawski, H.M., Foa Torres, L.E.F., Medina, E.: Electron-phonon interaction and electronic decoherence in molecular conductors. Chem. Phys. 281, 257–278 (2002)

    Article  Google Scholar 

  9. Buscemi, F., Cancellieri, E., Bordone, P., Bertoni, A., Jacoboni, C.: Electron decoherence in a semiconductor due to electron-phonon scattering. Physica Status Solidi (c) 5, 52–55 (2008)

    Article  Google Scholar 

  10. Querlioz, D., Dollfus, P.: The Wigner Monte Carlo Method for Nanoelectronic Devices—A Particle Description of Quantum Transport and Decoherence. ISTE-Wiley, New York (2010)

    MATH  Google Scholar 

  11. Nedjalkov, M., Selberherr, S., Ferry, D.K., Vasileska, D., Dollfus, P., Querlioz, D., Dimov, I., Schwaha, P.: Physical scales in the Wigner-Boltzmann equation. Ann. Phys. 328, 220–237 (2012)

    MathSciNet  Google Scholar 

  12. Jacoboni, C., Brunetti, R., Bordone, P., Bertoni, A.: Quantum transport and its simulation with the Wigner-function approach. Int. J. High Speed Electron. Syst. 11, 387–423 (2001)

    Google Scholar 

  13. Nedjalkov, M., Querlioz, D., Dollfus, P., Kosina, H.: Wigner function approach. In: Vasileska, D., Goodnick, S. (eds.) Nano-Electronic Devices: Semiclassical and Quantum Transport Modeling, pp. 289–358. Springer, New York (2011)

    Chapter  Google Scholar 

  14. Shifren, L., Ringhofer, C., Ferry, D.K.: A Wigner function-based quantum ensemble Monte Carlo study of a resonant tunneling diode. IEEE Trans. Electron Devices 50, 769–773 (2003)

    Article  Google Scholar 

  15. Querlioz, D., Saint-Martin, J., Nam Do, V., Bournel, A., Dollfus, P.: A study of quantum transport in end-of-roadmap DG-MOSFETs using a fully self-consistent Wigner Monte Carlo approach. IEEE Trans. Nanotechnol. 5, 737–744 (2006)

    Article  Google Scholar 

  16. Querlioz, D., Nha Nguyen, H., Saint-Martin, J., Bournel, A., Galdin- Retailleau, S., Dollfus, P.: Wigner-Boltzmann Monte Carlo approach to nanodevice simulation: from quantum to semiclassical transport. J. Comput. Electron. 8, 324–335 (2009)

    Article  Google Scholar 

  17. Nedjalkov, M., Kosina, H., Selberherr, S., Ringhofer, C., Ferry, D.K.: Unified particle approach to Wigner-Boltzmann transport in small semiconductor devices. Phys. Rev. B 70, 115319 (2004)

    Article  Google Scholar 

  18. Sverdlov, V., Grasser, T., Kosina, H., Selberherr, S.: Scattering and spacecharge effects in Wigner Monte Carlo simulations of single and double barrier devices. J. Comput. Electron. 5, 447–450 (2006)

    Article  Google Scholar 

  19. Manfredi, G., Feix, M.R.: Entropy and Wigner functions. Phys. Rev. E 62, 4665–4674 (2000)

    Article  Google Scholar 

Download references

Acknowledgements

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

Author information

Author notes

  1. Philipp Schwaha

    Present address: AVL List GmbH, Hans-List-Platz 1, 8020, Graz, Austria

Authors and Affiliations

  1. Institute for Microelectronics, TU Wien, 1040, Wien, Austria

    Philipp Schwaha, Mihail Nedjalkov & Siegfried Selberherr

  2. Institut d’Electronique Fondamentale, Université Paris-Sud, CNRS, 91405, Orsay, France

    Damien Querlioz, Philippe Dollfus & Jérôme Saint-Martin

Authors
  1. Philipp Schwaha
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Damien Querlioz
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Philippe Dollfus
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jérôme Saint-Martin
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Mihail Nedjalkov
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Siegfried Selberherr
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mihail Nedjalkov.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Schwaha, P., Querlioz, D., Dollfus, P. et al. Decoherence effects in the Wigner function formalism. J Comput Electron 12, 388–396 (2013). https://doi.org/10.1007/s10825-013-0480-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10825-013-0480-9

Keywords

  • Wigner function
  • Quantum transport
  • Phonons
  • Decoherence