The Mobility of an Ion in a Fermi Liquid

Clark, R. C.

doi:10.1088/0370-1328/82/5/315

Cited by 104 publications

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“…[1,2]). Especially, transport of an impurity in Bosonic [3] and Fermionic [4,5] quantum liquids has been studied since a few decades ago. Recent realizations of ultra-cold polarized two-component atomic Fermi gases [6][7][8][9][10][11][12], with their remarkable controllability over parameters such as interaction strength and individual populations, have made it possible to directly access this type of quantum many-body system.…”

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Superdiffusive nonequilibrium motion of an impurity in a Fermi sea

Kim

Huse²

2012

Phys. Rev. A

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We treat the nonequilibrium motion of a single impurity atom in a low-temperature single-species Fermi sea, interacting via a contact interaction. In the nonequilibrium regime, the impurity does a superdiffusive geometric random walk where the typical distance traveled grows with time as ∼ t d/(d+1) for the d-dimensional system with d ≥ 2. For nonzero temperature T , this crosses over to diffusive motion at long times with diffusivity D ∼ T −(d−1)/2 . These results apply also to a nonzero concentration of impurity atoms as long as they remain dilute and nondegenerate.PACS numbers: 03.75. Ss, 67.85.Lm, In condensed matter physics, the behavior of a single impurity immersed in a sea of majority particles has been one of the simplest many-body problems and attracted much attention (see, e.g. [1,2]). Especially, transport of an impurity in Bosonic [3] and Fermionic [4,5] quantum liquids has been studied since a few decades ago. Recent realizations of ultra-cold polarized two-component atomic Fermi gases [6][7][8][9][10][11][12], with their remarkable controllability over parameters such as interaction strength and individual populations, have made it possible to directly access this type of quantum many-body system. Meanwhile, there have been a number of theoretical works on the single impurity problem in an ultracold Fermi gas [13][14][15][16][17], investigating the equilibrium and nearequilibrium properties. Quite naturally, transport phenomena have also been studied [18]. More recently, transport experiments of an ultracold mass-balanced polarized Fermi gas [19] and an ultracold mass-imbalanced mixture with unequal populations [20] opened new opportunities to directly investigate nonequilibrium and dynamic properties of population-imbalanced Fermi systems.In this paper, we discuss nonequilibrium transport in the high polarization and low temperature regime, without restricting ourselves within small deviations from equilibrium. As a limiting case of high polarization and low temperature, we first consider a single minority atom moving in a zero-temperature Fermi sea of majority atoms. We find that the impurity does a superdiffusive geometric random walk, where the time between collisions grows in proportion to time, and the impurity loses a fraction of order one of its energy in each collision. InAs is conventional, we call the majority species "up" ↑ and the minority (impurity) species "down" ↓. Note that in the regimes we study in this paper, the statistics of the minority atoms do not enter, so they may equally well be bosons or fermions. Assume the minority atom is initially near the origin in real space, with some probability distribution of its momentum Q ↓ with Q ↓ k F ↑ , where k F ↑ is the Fermi momentum of the majority Fermi sea. The minority atom is "dressed" either as a polaron or as a molecule, with effective mass m * and thus energy E ↓ ≈ 2 Q 2 ↓ 2m * ; we choose the rest energy of the dressed minority atom as its zero of energy. We assume that E ↓ is low enough so that no internal excitations of th...

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Superdiffusive nonequilibrium motion of an impurity in a Fermi sea

Kim

Huse²

2012

Phys. Rev. A

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“…To discuss the relationship between the theories further, we remark that the previous results can be obtained as a special case of (1) by using an S V (K, v) derived using the effective-mass approximation. Furthermore, in these theories an assumption may be made 2 analogous to that used here in deriving (2) from (1), regarding the v dependence of the impurity-momentum distribution function; the mobility expression resulting is a special case of (2). Avoiding this assumption (as in Ref.…”

Section: Illmentioning

confidence: 99%

“…The important values of r contributing to (2) are those corresponding to 11\ ££. The effectivemass approximation is therefore inadequate whenever the average motion of the impurity through the surrounding fluid over an interval jS is significantly different from that of a free particle.…”

Section: Illmentioning

confidence: 99%

Mobility of an Impurity in a Fermi Liquid

1969

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The mobility of ions in liquid He 3 is investigated by a method which avoids the assumption that ions recoil freely in collisions with Fermi quasiparticles. The temperature variation of the mobility is found to be much less than that previously predicted, and improved agreement with experiment is obtained.The damping force experienced by an impurity of atomic dimensions moving through a Fermi liquid (e.g., ions in He 3 under the influence of an electric field) is mainly due to collisions with quasiparticles if the temperature is sufficiently low. Previous theories of the mobility in this regime 1 " 3 involve a characteristic temperature T 0 = k F 2 /2Mk B (k F , M, and k B are the Fermi momentum of the liquid, the impurity effective mass, and Boltzmann's constant, respectively, and #=1), at which the mobility temperature dependence is predicted to change from T~2 at low temperatures to approximately T° at higher temperatures. This prediction is not supported by experiment. 4 With negative ions in He 3 the mobility at low temperatures (below |T 0 in the most favorable case) is only weakly temperature dependent, while with positive ions the low-temperature behavior (down to ~iT 0 ) resembles T~1 /3 rather than T~2. The above theories treat the recoil of the impurity during a collision by ascribing to it a definite effective mass. In the following, we describe a theory in which the recoil is treated in a more fundamental manner in terms of the Van Hove scattering function, and the discrepancy between theory and experiment referred to above is largely resolved.If the impurity were rigid and fixed in position, all scattering from it would be elastic and governed by a differential cross section cr(0). (The Fermi velocity is assumed to be large compared with all other relevant velocities, so that only the scattering angle 6 enters.) In fact the impurity is not fixed and the scattering is inelastic. We write the inelastic scattering cross section per unit solid angle as a(0)S^(K, co), where K and u) are the momentum and energy transfer, respectively, and v is the mean drift velocity of the impurity (under the influence of a fixed external force). S^(K, o>) is taken to be the usual scattering function 5 ' 6 which enters into the analogous problem of inelastic neutron scattering, 7 and gives the spectrum of the energy absorbed when the impurity is instantaneously given momentum K. With these assumptions, the rate at which momentum is transferred to the quasiparticles has the form

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“…The former case which corresponds to temperatures such that T«m€p/M was considered by Clark, 4 Abe and Aizu, 5 and Schappert 6 who found that 1/JUL ~(MT) 2 .…”

Section: Introductionmentioning

confidence: 99%

Low-Temperature Ion Mobility in Interacting Fermi Liquids

Gould

1969

Phys. Rev.

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Rev. 98, 1479Rev. 98, (1955. 5 L. Reatto and G. V. Chester, Phys. Rev. 155, 88 (1967). Quoted in what follows as (I). 6 In (I) the wave function contains \{r) in place ofx'(r). This has been done for simplicity and because it makes no difference for the considerations of that paper. In (I) \(r) is defined also with a cutoff on the E summation appearing in Eq. (7). In this paper we think that the contribution to \(r) due to the cutoff, which is a short-range function, is included in u(r).The temperature dependence of the mobility \x of a heavy ion in a neutral interacting Fermi liquid is found to be of the form 1/JU=JB-ST 2 lnl/T + 0(T 2 ) for low T where R and S are constants. The T 2 lnT term is a consequence of the Friedel density oscillations around the ion and would be absent for the noninteracting Fermi liquid investigated by other authors. The coefficients are calculated for the case of a large hard sphere. The pressure dependence of the coefficients and the predicted temperature dependence are in reasonable agreement with recent experimental data for negative ions in He 3 .

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The Mobility of an Ion in a Fermi Liquid

Cited by 104 publications

References 12 publications

Superdiffusive nonequilibrium motion of an impurity in a Fermi sea

Superdiffusive nonequilibrium motion of an impurity in a Fermi sea

Mobility of an Impurity in a Fermi Liquid

Low-Temperature Ion Mobility in Interacting Fermi Liquids

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