On Brownian Motion in a Fermi Fluid

Publisher Website
Google Scholar
Abstract
Using the quantum‐mechanical Boltzmann equation we study the motion of a heavy ion (mass M) moving through a Fermi fluid of light particles [mass m, γ=(m/M)½≪1] under the influence of an electric field. We find, contrary to the classical case, that the condition γ≪1 is not sufficient to ensure that the ion undergoes Brownian motion (i.e., its motion is characterized by a Fokker—Planck equation). The condition γξ≪1 must hold, where ξ2 is the ratio of the Fermi energy to the temperature. When ξ is too large the ion will suffer large momentum changes upon colliding with the fermions and hence its motion will not be describable by a Fokker—Planck equation. In liquid 3He there is a temperature region (4°>T>1°K) in which a heavy ion experiences what we call quantum‐mechanical Brownian motion; the Fokker—Planck equation still holds but the friction coefficient contains quantum‐mechanical effects. Using our formula for mobility and the mobility data of Meyer we estimate the effective mass of an ion in liquid 3He to be about 20 times the mass of an 3He atom. This is in agreement with the recent measurements of Dahm and Sanders in liquid 4He. They have found the effective mass to be between 20 to 40 4He atoms. However, since only binary scattering events are accounted for in our mobility formula, its application to liquid 3He should be taken with reservation.