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Volumn 2, Issue 4, 2012, Pages

Time-dependent impurity in ultracold fermions: Orthogonality catastrophe and beyond

Author keywords

[No Author keywords available]

Indexed keywords

ENERGY DISTRIBUTION FUNCTIONS; EXPERIMENTAL REALIZATIONS; FERMI WAVE VECTORS; INTERACTION STRENGTH; NON-TRIVIAL DEPENDENCE; OPTICAL-LATTICE POTENTIAL; POWER-LAW CONTRIBUTION; POWER-LAW SINGULARITY;

EID: 84886241051     PISSN: None     EISSN: 21603308     Source Type: Journal    
DOI: 10.1103/PhysRevX.2.041020     Document Type: Article
Times cited : (274)

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    • It is important to point out that the scattering length a characterizing the scattering of the host fermions on the localized impurity is not the same as the scattering length of two free atoms [59,60]. In this paper, we take the energy difference between discrete levels of the impurity in a confining potential to be much larger than the Fermi energy of the host atoms so that we can neglect the scattering of the impurity atom into excited states; then the scattering amplitude has the canonical form, which is given in Eq. (3). In principle, when the Fermi energy becomes comparable to the energy splitting between discrete levels !c in the parabolic potential confining the impurity, there will be an additional dependence of f{eth}E{Thorn} on the E=!c, discussed in [59]; therefore, all response functions will also depend on EF=!c. Our discussion can be extended to find these dependencies
    • It is important to point out that the scattering length a characterizing the scattering of the host fermions on the localized impurity is not the same as the scattering length of two free atoms [59,60]. In this paper, we take the energy difference between discrete levels of the impurity in a confining potential to be much larger than the Fermi energy of the host atoms so that we can neglect the scattering of the impurity atom into excited states; then the scattering amplitude has the canonical form, which is given in Eq. (3). In principle, when the Fermi energy becomes comparable to the energy splitting between discrete levels !c in the parabolic potential confining the impurity, there will be an additional dependence of f{eth}E{Thorn} on the E=!c, discussed in [59]; therefore, all response functions will also depend on EF=!c. Our discussion can be extended to find these dependencies.
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