The Double-Slit Electron Diffraction Experiment with Aharonov-Bohm Phase Effect Revisited and the Divergence in its Asymptotic Form

  • D. AssafrãoEmail author
  • C. C. Favarato
  • S. V. B. Gonçalves
  • G. Simonelli
General and Applied Physics


In this work, we consider the experiment of diffraction and interference of electrons through a double slit added to the Aharonov-Bohm phase effect. We applied the asymptotic Fresnel functions to one term of the interference process obtaining an expression for the intensity with divergence for certain values of the flow parameter. This led us to an expression incapable of recovering the asymmetry effects of the diffraction pattern arising from the AB phase, as might be expected, since purely quantum effects cannot be classically reproduced.


Diffraction Aharonov-Bohm effect Path integrals Fresnel functions 



We wish to thank Alan Johnny Romanel Ambrozio for helpful communication during the preparation of this work. Simulations were performed in Mathematica Version 11.3, Wolfram Research, Champaign, IL.

Funding Information

This work has received partial financial supporting from CNPq (Brazil), CAPES (Brazil), and FAPES (Brazil).


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Copyright information

© Sociedade Brasileira de Física 2019

Authors and Affiliations

  1. 1.Department of PhysicsUniversidade Federal do Espírito SantoVitóriaBrazil
  2. 2.Department of Materials Science and TechnologyUniversidade Federal da Bahia, Escola PolitécnicaSalvadorBrazil

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