Impurity in a zero-temperature three-dimensional Fermi gas
arxiv(2024)
摘要
We consider an impurity in a sea of zero-temperature fermions uniformly
distributed throughout the space. The impurity scatters on fermions. On
average, the momentum of impurity decreases with time as t^-1/(d+1) in d
dimensions, and the momentum distribution acquires a scaling form in the long
time limit. We solve the Lorentz-Boltzmann equation for the scaled momentum
distribution of the impurity in three dimensions. The solution is a combination
of confluent hypergeometric functions. In two spatial dimensions, the
Lorentz-Boltzmann equation is analytically intractable, so we merely extract a
few exact predictions about asymptotic behaviors when the scaled momentum of
the impurity is small or large.
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