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The Influence of the Symmetry of Identical Particles on Flight Times

Instituto de Física Fundamental, CSIC, Serrano 123, 28006 Madrid, Spain
Department of Chemistry and Chemical Biology, McMaster University, Hamilton, ON L8S 4M1, Canada
Chemical and Biological Physics Department, Weizmann Institute of Science, Rehovot 76100, Israel
Author to whom correspondence should be addressed.
Academic Editor: Vladimir Man’ko
Entropy 2021, 23(12), 1675;
Received: 5 November 2021 / Revised: 9 December 2021 / Accepted: 9 December 2021 / Published: 13 December 2021
(This article belongs to the Special Issue Quantum Mechanics and Its Foundations II)
In this work, our purpose is to show how the symmetry of identical particles can influence the time evolution of free particles in the nonrelativistic and relativistic domains as well as in the scattering by a potential δ-barrier. For this goal, we consider a system of either two distinguishable or indistinguishable (bosons and fermions) particles. Two sets of initial conditions have been studied: different initial locations with the same momenta, and the same locations with different momenta. The flight time distribution of particles arriving at a ‘screen’ is calculated in each case from the density and flux. Fermions display broader distributions as compared with either distinguishable particles or bosons, leading to earlier and later arrivals for all the cases analyzed here. The symmetry of the wave function seems to speed up or slow down the propagation of particles. Due to the cross terms, certain initial conditions lead to bimodality in the fermionic case. Within the nonrelativistic domain, and when the short-time survival probability is analyzed, if the cross term becomes important, one finds that the decay of the overlap of fermions is faster than for distinguishable particles which in turn is faster than for bosons. These results are of interest in the short time limit since they imply that the well-known quantum Zeno effect would be stronger for bosons than for fermions. Fermions also arrive earlier and later than bosons when they are scattered by a δ-barrier. Although the particle symmetry does affect the mean tunneling flight time, in the limit of narrow in momentum initial Gaussian wave functions, the mean times are not affected by symmetry but tend to the phase time for distinguishable particles. View Full-Text
Keywords: bosons; fermions; flight time distributions; tunneling times bosons; fermions; flight time distributions; tunneling times
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MDPI and ACS Style

Miret-Artés, S.; Dumont, R.S.; Rivlin, T.; Pollak, E. The Influence of the Symmetry of Identical Particles on Flight Times. Entropy 2021, 23, 1675.

AMA Style

Miret-Artés S, Dumont RS, Rivlin T, Pollak E. The Influence of the Symmetry of Identical Particles on Flight Times. Entropy. 2021; 23(12):1675.

Chicago/Turabian Style

Miret-Artés, Salvador, Randall S. Dumont, Tom Rivlin, and Eli Pollak. 2021. "The Influence of the Symmetry of Identical Particles on Flight Times" Entropy 23, no. 12: 1675.

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