We present an analytical treatment of a single ↓ atom within a Fermi sea of ↑ atoms, when the interaction is strong enough to produce a bound state, dressed by the Fermi sea. Our method makes use of a diagrammatic analysis, with the involved diagrams taking only into account at most two particle-hole pairs excitations. The agreement with existing Monte-Carlo results is excellent. In the BEC limit our equation reduces exactly to the Skorniakov and Ter-Martirosian equation. We present results when ↑ and ↓ atoms have different masses, which is of interest for experiments in progress.

Using a Fermi-liquid approach, we provide a comprehensive treatment of the current and current noise through a quantum dot whose low-energy behavior corresponds to an SU͑N͒ Kondo model, focusing on the case N = 4 relevant to carbon nanotube dots. We show that for general N, one needs to consider the effects of higher-order Fermi-liquid corrections even to describe low-voltage current and noise. We also show that the noise exhibits complex behavior due to the interplay between coherent shot noise, and noise arising from interaction-induced scattering events. We also treat various imperfections relevant to experiments, such as the effects of asymmetric dot-lead couplings.ductance and the shot noise as well as details on their derivation. In Sec. V, we summarize our main results for the conductance and shot noise of a SU͑N͒ Kondo quantum dot, and conclude. II. MODEL DESCRIPTION A. Kondo HamiltonianWe give here a compact synopsis of the quantum-dot model we study and how it gives rise to Kondo physics. The dot connected to the leads is described by the following Anderson Hamiltonian 29 . ͑1͒ c L/R,k is the annihilation operator for an electron of spin =1...N and energy k = បv F k ͑measured from the Fermi energy F ͒ confined on the left/right lead. d is the electron operator of the dot and n = d † d the corresponding density. U denotes the charging energy, d the single-particle energy on the dot and t L/R denotes the tunneling-matrix elements from the dot to the left/right lead. The general case of asymmetric leads contacts is parametrized by t L = t cos , t R = t sin with = ͓0, / 2͔. = / 4 recovers the symmetric case. The rotation in the basis of leads electrons

We present a field theoretic method for the calculation of the second and third virial coefficients b2 and b3 of 2-species fermions interacting via a contact interaction. The method is mostly analytic. We find a closed expression for b3 in terms of the 2 and 3-body T-matrices. We recover numerically, at unitarity, and also in the whole BEC-BCS crossover, previous numerical results for the third virial coefficient b3