Classical mechanics at T=0: Mobility of negative ions in ^{3}He

Chen, Yang; Prokof’ev, Nikolay

doi:10.1103/physrevlett.65.1761

Cited by 35 publications

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“…This diffusive motion means that it is meaningless to define an effective mass for the ion above T coh . The theory of ion mobility in normal 3 He has nevertheless been considerably refined since then [10][11][12].…”

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“…where R is the ion coordinate, H F the Hamiltonian of 3 He, and ρ(r) the 3 He density operator. We make use of the path integral technique and integrate out the Fermion degrees of freedom [11,12], and start by considering the case of normal 3 He. Using Feynman's path integral over R in imaginary time [14] the effective action in the partition function can be written…”

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“…For T ≪ T c we can neglect the contribution due to normal excitations and further simplify Eqs. (10,11) to…”

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Effective Masses of Ions in Superfluid3He-B

Prokof’ev

1995

Phys. Rev. Lett.

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We show that ion masses in superfluid 3 He ought to be enormously enhanced (by a factor of 10 2 ) as compared with the same ion masses in 4 He measured at low temperature. We calculate precisely the dependence of the effective mass on pressure in 3 He-B, and show that the coherent (ballistic) motion of ions in 3 He-B can be studied experimentally at T < (0.3 − 0.2) Tc.PACS numbers: 67., 66.20+dThe problem of ion motion in normal 3 He-liquid has been of long-standing interest, partly because of its connection with the "orthogonality catastrophe", but mostly because theorists have had a hard time explaining it. The ion motion is greatly overdamped at low temperature, by multiple scattering of 3 He quasiparticles, so theorists have concentrated on calculating the experimentally measurable ion mobility. Early perturbative calculations [1] predicted a mobility µ(T ) diverging as 1/T 2 below a temperature T 0 = p 2 F /M , where M is the bare ion effective mass ( M ∼ 100 − 260m 3 , depending on pressure, for the negative ion; here m 3 is the 3 He atomic mass). Experiments on both positive [2-4] and negative [2,[5][6][7][8] ions flatly contradicted this prediction; µ − is roughly constant through and below T 0 , all the way down to the superfluid transition T c .However this problem is a strong-coupling one. The dimensionless ion-3 He coupling is g = p 2 F σ tr /3π 2 , with σ tr the transport cross section, and g ≫ 1. The high-T scattering rate equals Γ = T 0 g ≫ T 0 , which is why the ion motion is overdamped already for T ≫ T 0 . Moreover, it was realised by Josephson and Lekner [9] that for T < Γ the ion recoil is not free, but Brownian diffusive, down to the unobservably low temperature T coh = T 0 ge −g . This diffusive motion means that it is meaningless to define an effective mass for the ion above T coh . The theory of ion mobility in normal 3 He has nevertheless been considerably refined since then [10][11][12].One obvious way for experimentalists to see coherent motion of an ion in 3 He is to go to the superfluid phases, where the gap cuts off the "orthogonality catastrophe". Remarkably, this possibility has not been explored, either in theory or experiment (although some mobility experiments have been done [8]-we return to these below). In this paper I give a detailed theory of ion dynamics, which is exact in the large-g limit. A very striking prediction emerges from this analysis -that the effective mass of ions in the superfluid phases will be very large (up to 2 · 10 4 m 3 , or some 100 times the bare ion mass). I calculate the effective mass M ef f (P ) as a function of pressure in the low-T limit in 3 He-B, and suggest how this prediction might be verified experimentally. This prediction (which is clearly out of the framework of the standard models [13]) should constitute a very stringent test of our ideas of particle dynamics in a Fermi liquid.The Hamiltonian is that of a spherical object in a Fermi liquid environment:where R is the ion coordinate, H F the Hamiltonian of 3 He, andρ(r) the 3 He density o...

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