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We study the properties of an impurity of mass $M$ moving through a spatially homogeneous three-dimensional fully polarized Fermi gas of particles of mass $m$. In the weakly attractive limit, where the effective coupling constant $gto0^-$ and perturbation theory can be used, both for a broad and a narrow Feshbach resonance, we obtain an explicit analytical expression for the complex energy $Delta E(KK)$ of the moving impurity up to order two included in $g$. This also gives access to its longitudinal and transverse effective masses $m_parallel^*(KK)$, $m_perp^*(KK)$, as functions of the impurity wave vector $KK$. Depending on the modulus of $KK$ and on the impurity-to-fermion mass ratio $M/m$ we identify four regions separated by singularities in derivatives with respect to $KK$ of the second-order term of $Delta E(KK)$, and we discuss the physical origin of these regions. Remarkably, the second-order term of $m_parallel^*(KK)$ presents points of non-differentiability, replaced by a logarithmic divergence for $M=m$, when $KK$ is on the Fermi surface of the fermions. We also discuss the third-order contribution and relevance for cold atom experiments.
The notion of a polaron, originally introduced in the context of electrons in ionic lattices, helps us to understand how a quantum impurity behaves when being immersed in and interacting with a many-body background. We discuss the impact of the impur
We present a variational calculation of the energy of an impurity immersed a double Fermi sea of non-interacting Fermions. We show that in the strong-coupling regime, the system undergoes a first order transition between polaronic and trimer states.
Recently, the topics of many-body localization (MBL) and one-dimensional strongly interacting few-body systems have received a lot of interest. These two topics have been largely developed separately. However, the generality of the latter as far as e
We simulate a balanced attractively interacting two-component Fermi gas in a one-dimensional lattice perturbed with a moving potential well or barrier. Using the time-evolving block decimation method, we study different velocities of the perturbation
We consider the highly spin-imbalanced limit of a two-component Fermi gas, where there is a small density of $downarrow$ impurities attractively interacting with a sea of $uparrow$ fermions. In the single-impurity limit at zero temperature, there exi