Scattering Hypervolume of Fermions in Two Dimensions
- URL: http://arxiv.org/abs/2205.02658v2
- Date: Sun, 31 Jul 2022 12:50:37 GMT
- Title: Scattering Hypervolume of Fermions in Two Dimensions
- Authors: Zipeng Wang and Shina Tan
- Abstract summary: We define the three-body scattering hypervolume $D_F$ for identical spin-polarized fermions in two dimensions.
We derive the expansions of such a wave function when three fermions are far apart or one pair and the third fermion are far apart.
We also calculate the shifts of energy and of pressure of spin-polarized two-dimensional Fermi gases due to a nonzero $D_F$ and the three-body recombination rate of spin-polarized ultracold atomic Fermi gases in two dimensions.
- Score: 8.35070936044077
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We define the three-body scattering hypervolume $D_F$ for identical
spin-polarized fermions in two dimensions, by considering the wave function of
three such fermions colliding at zero energy and zero orbital angular momentum.
We derive the asymptotic expansions of such a wave function when three fermions
are far apart or one pair and the third fermion are far apart, and $D_F$
appears in the coefficients of such expansions. For weak interaction
potentials, we derive an approximate formula of $D_F$ by using the Born
expansion. We then study the shift of energy of three such fermions in a large
periodic area due to $D_F$. This shift is proportional to $D_F$ times the
square of the area of the triangle formed by the momenta of the fermions. We
also calculate the shifts of energy and of pressure of spin-polarized
two-dimensional Fermi gases due to a nonzero $D_F$ and the three-body
recombination rate of spin-polarized ultracold atomic Fermi gases in two
dimensions.
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