Impurity in a zero-temperature three-dimensional Fermi gas

Abstract

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.

6 pages, 1 figure

References in corpus (9)

• Observation of Fermi Polarons in a Tunable Fermi Liquid of Ultracold Atoms
• Bloch oscillations in one-dimensional spinor gas
• Collisional Properties of a Polarized Fermi Gas with Resonant Interactions
• The normal phase of an imbalanced Fermi gas
• Impurity Green's function of a one-dimensional Fermi-gas
• Perpetual motion and driven dynamics of a mobile impurity in a quantum fluid
• Finite-range effects in the unitary Fermi polaron
• Repulsive Fermi polarons with negative effective mass
• The self-energy of an impurity in an ideal Fermi gas to second order in the interaction strength