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Scattering of non-interacting, identical bosons or fermions by a one-dimensional Dirac delta function barrier potential underlines the importance of the role of statistics (that is, whether the particles obey Fermi–Dirac or Bose–Einstein statistics) in the scattering. We consider an initial wave function for the system that corresponds to one particle incident from the left and one from the right of the potential barrier. For bosons, both particles are scattered either to the left or to the right if the intensity reflection coefficient is 1/2, provided the left and right propagating wave packets fully overlap in the scattering region. For fermions, the particles “pass through” one another, provided the left and right propagating wave packets fully overlap in the scattering region, with zero probability that both particles are scattered to the left or right, consistent with the Pauli exclusion principle.
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Statistical Interaction Description of Pauli Crystals in 2D Systems of Harmonically Confined Fermions
Abstract It is conjectured that the Pauli exclusion principle alone may be responsible for a particular geometric arrangement of confined systems of identical fermions even when there is no interaction between them. These geometric structures, called Pauli crystals, are predicted for a two‐dimensional (2D) system of free fermions under harmonic confinement. In this work, the possibility of this outcome is pursued and a theoretical model is considered that may capture both qualitatively and quantitatively, the key features of the abovementioned setup. The results for and 6 particles show that the minimum energy configuration corresponds to and is in good quantitative agreement with the reported values of Pauli crystals seen in single‐shot imaging data obtained via the configuration density technique. Numerical results for larger systems of and 30 particles show that the crystalline configurations observed are not the same as the classical Wigner crystal structures that emerge should the confined charged particles interact with a Coulomb potential. An important question floated is whether such crystalline structures do really exist in a quantum system or whether they are artifacts of the methods used to analyze them.
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- Award ID(s):
- 1705084
- PAR ID:
- 10460766
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Annalen der Physik
- Volume:
- 531
- Issue:
- 10
- ISSN:
- 0003-3804
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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